TSTP Solution File: BOO008-4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO008-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 : Thu Jul 14 23:44:32 EDT 2022
% Result : Unsatisfiable 1.07s 1.24s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 108
% Number of leaves : 168
% Syntax : Number of clauses : 774 ( 397 unt; 0 nHn; 366 RR)
% Number of literals : 1315 (1314 equ; 544 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 1583 ( 72 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X) ).
cnf(commutativity_of_multiply,axiom,
multiply(X,Y) = multiply(Y,X) ).
cnf(distributivity1,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ).
cnf(distributivity2,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity ).
cnf(prove_associativity,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_4,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_3]) ).
cnf(refute_0_5,plain,
add(add(a,b),c) = add(c,add(a,b)),
inference(subst,[],[refute_0_4:[bind(X,$fot(c)),bind(Y,$fot(add(a,b)))]]) ).
cnf(refute_0_6,plain,
( add(add(a,b),c) != add(c,add(a,b))
| add(a,add(b,c)) != add(c,add(a,b))
| add(a,add(b,c)) = add(add(a,b),c) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(a,add(b,c)),add(add(a,b),c)) ),[1],$fot(add(c,add(a,b)))]]) ).
cnf(refute_0_7,plain,
( add(a,add(b,c)) != add(c,add(a,b))
| add(a,add(b,c)) = add(add(a,b),c) ),
inference(resolve,[$cnf( $equal(add(add(a,b),c),add(c,add(a,b))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
add(a,add(b,c)) != add(c,add(a,b)),
inference(resolve,[$cnf( $equal(add(a,add(b,c)),add(add(a,b),c)) )],[refute_0_7,prove_associativity]) ).
cnf(refute_0_9,plain,
add(X_10,multiply(X_11,X_12)) = multiply(add(X_10,X_11),add(X_10,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_10,plain,
add(X_11,X_10) = add(X_10,X_11),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_11,plain,
( add(X_11,X_10) != add(X_10,X_11)
| add(X_10,X_11) = add(X_11,X_10) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_11,X_10))),bind(Y0,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_12,plain,
add(X_10,X_11) = add(X_11,X_10),
inference(resolve,[$cnf( $equal(add(X_11,X_10),add(X_10,X_11)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( add(X_10,X_11) != add(X_11,X_10)
| add(X_10,multiply(X_11,X_12)) != multiply(add(X_10,X_11),add(X_10,X_12))
| add(X_10,multiply(X_11,X_12)) = multiply(add(X_11,X_10),add(X_10,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,X_12)),multiply(add(X_10,X_11),add(X_10,X_12))) ),[1,0],$fot(add(X_11,X_10))]]) ).
cnf(refute_0_14,plain,
( add(X_10,multiply(X_11,X_12)) != multiply(add(X_10,X_11),add(X_10,X_12))
| add(X_10,multiply(X_11,X_12)) = multiply(add(X_11,X_10),add(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(add(X_10,X_11),add(X_11,X_10)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
add(X_10,multiply(X_11,X_12)) = multiply(add(X_11,X_10),add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,X_12)),multiply(add(X_10,X_11),add(X_10,X_12))) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
add(add(X_11,X_70),multiply(X_11,X_12)) = multiply(add(X_11,add(X_11,X_70)),add(add(X_11,X_70),X_12)),
inference(subst,[],[refute_0_15:[bind(X_10,$fot(add(X_11,X_70)))]]) ).
cnf(refute_0_17,plain,
add(X_10,multiply(inverse(X_10),X_12)) = multiply(add(X_10,inverse(X_10)),add(X_10,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(inverse(X_10))),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_18,plain,
add(X_10,inverse(X_10)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_19,plain,
( add(X_10,multiply(inverse(X_10),X_12)) != multiply(add(X_10,inverse(X_10)),add(X_10,X_12))
| add(X_10,inverse(X_10)) != multiplicative_identity
| add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(add(X_10,inverse(X_10)),add(X_10,X_12))) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_20,plain,
( add(X_10,multiply(inverse(X_10),X_12)) != multiply(add(X_10,inverse(X_10)),add(X_10,X_12))
| add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(add(X_10,inverse(X_10)),add(X_10,X_12))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X,multiplicative_identity) = multiply(multiplicative_identity,X),
inference(subst,[],[commutativity_of_multiply:[bind(Y,$fot(multiplicative_identity))]]) ).
cnf(refute_0_23,plain,
( multiply(X,multiplicative_identity) != X
| multiply(X,multiplicative_identity) != multiply(multiplicative_identity,X)
| multiply(multiplicative_identity,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiplicative_identity),X) ),[0],$fot(multiply(multiplicative_identity,X))]]) ).
cnf(refute_0_24,plain,
( multiply(X,multiplicative_identity) != X
| multiply(multiplicative_identity,X) = X ),
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),multiply(multiplicative_identity,X)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(multiplicative_identity,X) = X,
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),X) )],[multiplicative_id1,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(multiplicative_identity,add(X_10,X_12)) = add(X_10,X_12),
inference(subst,[],[refute_0_25:[bind(X,$fot(add(X_10,X_12)))]]) ).
cnf(refute_0_27,plain,
( multiply(multiplicative_identity,add(X_10,X_12)) != add(X_10,X_12)
| add(X_10,multiply(inverse(X_10),X_12)) != multiply(multiplicative_identity,add(X_10,X_12))
| add(X_10,multiply(inverse(X_10),X_12)) = add(X_10,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(multiplicative_identity,add(X_10,X_12))) ),[1],$fot(add(X_10,X_12))]]) ).
cnf(refute_0_28,plain,
( add(X_10,multiply(inverse(X_10),X_12)) != multiply(multiplicative_identity,add(X_10,X_12))
| add(X_10,multiply(inverse(X_10),X_12)) = add(X_10,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(X_10,X_12)),add(X_10,X_12)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
add(X_10,multiply(inverse(X_10),X_12)) = add(X_10,X_12),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(multiplicative_identity,add(X_10,X_12))) )],[refute_0_21,refute_0_28]) ).
cnf(refute_0_30,plain,
add(X_10,multiply(inverse(X_10),add(inverse(inverse(X_10)),X_46))) = add(X_10,add(inverse(inverse(X_10)),X_46)),
inference(subst,[],[refute_0_29:[bind(X_12,$fot(add(inverse(inverse(X_10)),X_46)))]]) ).
cnf(refute_0_31,plain,
multiply(X_37,add(inverse(X_37),X_39)) = add(multiply(X_37,inverse(X_37)),multiply(X_37,X_39)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_37)),bind(Y,$fot(inverse(X_37))),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_32,plain,
multiply(X_37,inverse(X_37)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_33,plain,
( multiply(X_37,add(inverse(X_37),X_39)) != add(multiply(X_37,inverse(X_37)),multiply(X_37,X_39))
| multiply(X_37,inverse(X_37)) != additive_identity
| multiply(X_37,add(inverse(X_37),X_39)) = add(additive_identity,multiply(X_37,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,add(inverse(X_37),X_39)),add(multiply(X_37,inverse(X_37)),multiply(X_37,X_39))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_34,plain,
( multiply(X_37,add(inverse(X_37),X_39)) != add(multiply(X_37,inverse(X_37)),multiply(X_37,X_39))
| multiply(X_37,add(inverse(X_37),X_39)) = add(additive_identity,multiply(X_37,X_39)) ),
inference(resolve,[$cnf( $equal(multiply(X_37,inverse(X_37)),additive_identity) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(X_37,add(inverse(X_37),X_39)) = add(additive_identity,multiply(X_37,X_39)),
inference(resolve,[$cnf( $equal(multiply(X_37,add(inverse(X_37),X_39)),add(multiply(X_37,inverse(X_37)),multiply(X_37,X_39))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
add(X,additive_identity) = add(additive_identity,X),
inference(subst,[],[commutativity_of_add:[bind(Y,$fot(additive_identity))]]) ).
cnf(refute_0_37,plain,
( add(X,additive_identity) != X
| add(X,additive_identity) != add(additive_identity,X)
| add(additive_identity,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(add(X,additive_identity),X) ),[0],$fot(add(additive_identity,X))]]) ).
cnf(refute_0_38,plain,
( add(X,additive_identity) != X
| add(additive_identity,X) = X ),
inference(resolve,[$cnf( $equal(add(X,additive_identity),add(additive_identity,X)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
add(additive_identity,X) = X,
inference(resolve,[$cnf( $equal(add(X,additive_identity),X) )],[additive_id1,refute_0_38]) ).
cnf(refute_0_40,plain,
add(additive_identity,multiply(X_37,X_39)) = multiply(X_37,X_39),
inference(subst,[],[refute_0_39:[bind(X,$fot(multiply(X_37,X_39)))]]) ).
cnf(refute_0_41,plain,
( multiply(X_37,add(inverse(X_37),X_39)) != add(additive_identity,multiply(X_37,X_39))
| add(additive_identity,multiply(X_37,X_39)) != multiply(X_37,X_39)
| multiply(X_37,add(inverse(X_37),X_39)) = multiply(X_37,X_39) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_37,add(inverse(X_37),X_39)),multiply(X_37,X_39)) ),[0],$fot(add(additive_identity,multiply(X_37,X_39)))]]) ).
cnf(refute_0_42,plain,
( multiply(X_37,add(inverse(X_37),X_39)) != add(additive_identity,multiply(X_37,X_39))
| multiply(X_37,add(inverse(X_37),X_39)) = multiply(X_37,X_39) ),
inference(resolve,[$cnf( $equal(add(additive_identity,multiply(X_37,X_39)),multiply(X_37,X_39)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(X_37,add(inverse(X_37),X_39)) = multiply(X_37,X_39),
inference(resolve,[$cnf( $equal(multiply(X_37,add(inverse(X_37),X_39)),add(additive_identity,multiply(X_37,X_39))) )],[refute_0_35,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(inverse(X_10),add(inverse(inverse(X_10)),X_46)) = multiply(inverse(X_10),X_46),
inference(subst,[],[refute_0_43:[bind(X_37,$fot(inverse(X_10))),bind(X_39,$fot(X_46))]]) ).
cnf(refute_0_45,plain,
( multiply(inverse(X_10),add(inverse(inverse(X_10)),X_46)) != multiply(inverse(X_10),X_46)
| add(X_10,multiply(inverse(X_10),add(inverse(inverse(X_10)),X_46))) != add(X_10,add(inverse(inverse(X_10)),X_46))
| add(X_10,multiply(inverse(X_10),X_46)) = add(X_10,add(inverse(inverse(X_10)),X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),add(inverse(inverse(X_10)),X_46))),add(X_10,add(inverse(inverse(X_10)),X_46))) ),[0,1],$fot(multiply(inverse(X_10),X_46))]]) ).
cnf(refute_0_46,plain,
( add(X_10,multiply(inverse(X_10),add(inverse(inverse(X_10)),X_46))) != add(X_10,add(inverse(inverse(X_10)),X_46))
| add(X_10,multiply(inverse(X_10),X_46)) = add(X_10,add(inverse(inverse(X_10)),X_46)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_10),add(inverse(inverse(X_10)),X_46)),multiply(inverse(X_10),X_46)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
add(X_10,multiply(inverse(X_10),X_46)) = add(X_10,add(inverse(inverse(X_10)),X_46)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),add(inverse(inverse(X_10)),X_46))),add(X_10,add(inverse(inverse(X_10)),X_46))) )],[refute_0_30,refute_0_46]) ).
cnf(refute_0_48,plain,
add(X_10,multiply(inverse(X_10),X_46)) = add(X_10,X_46),
inference(subst,[],[refute_0_29:[bind(X_12,$fot(X_46))]]) ).
cnf(refute_0_49,plain,
( add(X_10,multiply(inverse(X_10),X_46)) != add(X_10,X_46)
| add(X_10,multiply(inverse(X_10),X_46)) != add(X_10,add(inverse(inverse(X_10)),X_46))
| add(X_10,X_46) = add(X_10,add(inverse(inverse(X_10)),X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_46)),add(X_10,add(inverse(inverse(X_10)),X_46))) ),[0],$fot(add(X_10,X_46))]]) ).
cnf(refute_0_50,plain,
( add(X_10,multiply(inverse(X_10),X_46)) != add(X_10,add(inverse(inverse(X_10)),X_46))
| add(X_10,X_46) = add(X_10,add(inverse(inverse(X_10)),X_46)) ),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_46)),add(X_10,X_46)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
add(X_10,X_46) = add(X_10,add(inverse(inverse(X_10)),X_46)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_46)),add(X_10,add(inverse(inverse(X_10)),X_46))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(X_45,add(inverse(X_45),inverse(inverse(X_45)))) = multiply(X_45,inverse(inverse(X_45))),
inference(subst,[],[refute_0_43:[bind(X_37,$fot(X_45)),bind(X_39,$fot(inverse(inverse(X_45))))]]) ).
cnf(refute_0_53,plain,
add(inverse(X_45),inverse(inverse(X_45))) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(inverse(X_45)))]]) ).
cnf(refute_0_54,plain,
( multiply(X_45,add(inverse(X_45),inverse(inverse(X_45)))) != multiply(X_45,inverse(inverse(X_45)))
| add(inverse(X_45),inverse(inverse(X_45))) != multiplicative_identity
| multiply(X_45,multiplicative_identity) = multiply(X_45,inverse(inverse(X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_45,add(inverse(X_45),inverse(inverse(X_45)))),multiply(X_45,inverse(inverse(X_45)))) ),[0,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_55,plain,
( multiply(X_45,add(inverse(X_45),inverse(inverse(X_45)))) != multiply(X_45,inverse(inverse(X_45)))
| multiply(X_45,multiplicative_identity) = multiply(X_45,inverse(inverse(X_45))) ),
inference(resolve,[$cnf( $equal(add(inverse(X_45),inverse(inverse(X_45))),multiplicative_identity) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(X_45,multiplicative_identity) = multiply(X_45,inverse(inverse(X_45))),
inference(resolve,[$cnf( $equal(multiply(X_45,add(inverse(X_45),inverse(inverse(X_45)))),multiply(X_45,inverse(inverse(X_45)))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(X_45,multiplicative_identity) = X_45,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(X_45))]]) ).
cnf(refute_0_58,plain,
( multiply(X_45,multiplicative_identity) != X_45
| multiply(X_45,multiplicative_identity) != multiply(X_45,inverse(inverse(X_45)))
| X_45 = multiply(X_45,inverse(inverse(X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_45,multiplicative_identity),multiply(X_45,inverse(inverse(X_45)))) ),[0],$fot(X_45)]]) ).
cnf(refute_0_59,plain,
( multiply(X_45,multiplicative_identity) != multiply(X_45,inverse(inverse(X_45)))
| X_45 = multiply(X_45,inverse(inverse(X_45))) ),
inference(resolve,[$cnf( $equal(multiply(X_45,multiplicative_identity),X_45) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),add(X_10,additive_identity)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_61,plain,
add(X_10,additive_identity) = X_10,
inference(subst,[],[additive_id1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_62,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),add(X_10,additive_identity))
| add(X_10,additive_identity) != X_10
| add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),add(X_10,additive_identity))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_63,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),add(X_10,additive_identity))
| add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10) ),
inference(resolve,[$cnf( $equal(add(X_10,additive_identity),X_10) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),add(X_10,additive_identity))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( multiply(X,Y) != multiply(Y,X)
| multiply(Y,X) = multiply(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_66,plain,
multiply(Y,X) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(Y,X)) )],[commutativity_of_multiply,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(add(X_10,X_11),X_10) = multiply(X_10,add(X_10,X_11)),
inference(subst,[],[refute_0_66:[bind(X,$fot(X_10)),bind(Y,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_68,plain,
( multiply(add(X_10,X_11),X_10) != multiply(X_10,add(X_10,X_11))
| add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),X_10)
| add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),X_10)) ),[1],$fot(multiply(X_10,add(X_10,X_11)))]]) ).
cnf(refute_0_69,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),X_10)
| add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),X_10),multiply(X_10,add(X_10,X_11))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),X_10)) )],[refute_0_64,refute_0_69]) ).
cnf(refute_0_71,plain,
add(X_18,multiply(X_19,additive_identity)) = multiply(X_18,add(X_18,X_19)),
inference(subst,[],[refute_0_70:[bind(X_10,$fot(X_18)),bind(X_11,$fot(X_19))]]) ).
cnf(refute_0_72,plain,
add(X_19,X_18) = add(X_18,X_19),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_19)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_73,plain,
( add(X_19,X_18) != add(X_18,X_19)
| add(X_18,X_19) = add(X_19,X_18) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_19,X_18))),bind(Y0,$fot(add(X_18,X_19)))]]) ).
cnf(refute_0_74,plain,
add(X_18,X_19) = add(X_19,X_18),
inference(resolve,[$cnf( $equal(add(X_19,X_18),add(X_18,X_19)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( add(X_18,X_19) != add(X_19,X_18)
| add(X_18,multiply(X_19,additive_identity)) != multiply(X_18,add(X_18,X_19))
| add(X_18,multiply(X_19,additive_identity)) = multiply(X_18,add(X_19,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_18,multiply(X_19,additive_identity)),multiply(X_18,add(X_18,X_19))) ),[1,1],$fot(add(X_19,X_18))]]) ).
cnf(refute_0_76,plain,
( add(X_18,multiply(X_19,additive_identity)) != multiply(X_18,add(X_18,X_19))
| add(X_18,multiply(X_19,additive_identity)) = multiply(X_18,add(X_19,X_18)) ),
inference(resolve,[$cnf( $equal(add(X_18,X_19),add(X_19,X_18)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
add(X_18,multiply(X_19,additive_identity)) = multiply(X_18,add(X_19,X_18)),
inference(resolve,[$cnf( $equal(add(X_18,multiply(X_19,additive_identity)),multiply(X_18,add(X_18,X_19))) )],[refute_0_71,refute_0_76]) ).
cnf(refute_0_78,plain,
add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = multiply(inverse(inverse(X_32)),add(X_32,inverse(inverse(X_32)))),
inference(subst,[],[refute_0_77:[bind(X_18,$fot(inverse(inverse(X_32)))),bind(X_19,$fot(X_32))]]) ).
cnf(refute_0_79,plain,
add(X_13,multiply(inverse(X_13),inverse(inverse(X_13)))) = add(X_13,inverse(inverse(X_13))),
inference(subst,[],[refute_0_29:[bind(X_10,$fot(X_13)),bind(X_12,$fot(inverse(inverse(X_13))))]]) ).
cnf(refute_0_80,plain,
multiply(inverse(X_13),inverse(inverse(X_13))) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(inverse(X_13)))]]) ).
cnf(refute_0_81,plain,
( multiply(inverse(X_13),inverse(inverse(X_13))) != additive_identity
| add(X_13,multiply(inverse(X_13),inverse(inverse(X_13)))) != add(X_13,inverse(inverse(X_13)))
| add(X_13,additive_identity) = add(X_13,inverse(inverse(X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,multiply(inverse(X_13),inverse(inverse(X_13)))),add(X_13,inverse(inverse(X_13)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_82,plain,
( add(X_13,multiply(inverse(X_13),inverse(inverse(X_13)))) != add(X_13,inverse(inverse(X_13)))
| add(X_13,additive_identity) = add(X_13,inverse(inverse(X_13))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_13),inverse(inverse(X_13))),additive_identity) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
add(X_13,additive_identity) = add(X_13,inverse(inverse(X_13))),
inference(resolve,[$cnf( $equal(add(X_13,multiply(inverse(X_13),inverse(inverse(X_13)))),add(X_13,inverse(inverse(X_13)))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
add(X_13,additive_identity) = X_13,
inference(subst,[],[additive_id1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_85,plain,
( add(X_13,additive_identity) != X_13
| add(X_13,additive_identity) != add(X_13,inverse(inverse(X_13)))
| X_13 = add(X_13,inverse(inverse(X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,additive_identity),add(X_13,inverse(inverse(X_13)))) ),[0],$fot(X_13)]]) ).
cnf(refute_0_86,plain,
( add(X_13,additive_identity) != add(X_13,inverse(inverse(X_13)))
| X_13 = add(X_13,inverse(inverse(X_13))) ),
inference(resolve,[$cnf( $equal(add(X_13,additive_identity),X_13) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
X_13 = add(X_13,inverse(inverse(X_13))),
inference(resolve,[$cnf( $equal(add(X_13,additive_identity),add(X_13,inverse(inverse(X_13)))) )],[refute_0_83,refute_0_86]) ).
cnf(refute_0_88,plain,
X_32 = add(X_32,inverse(inverse(X_32))),
inference(subst,[],[refute_0_87:[bind(X_13,$fot(X_32))]]) ).
cnf(refute_0_89,plain,
( X_32 != add(X_32,inverse(inverse(X_32)))
| add(X_32,inverse(inverse(X_32))) = X_32 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_32)),bind(Y0,$fot(add(X_32,inverse(inverse(X_32)))))]]) ).
cnf(refute_0_90,plain,
add(X_32,inverse(inverse(X_32))) = X_32,
inference(resolve,[$cnf( $equal(X_32,add(X_32,inverse(inverse(X_32)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( add(X_32,inverse(inverse(X_32))) != X_32
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) != multiply(inverse(inverse(X_32)),add(X_32,inverse(inverse(X_32))))
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = multiply(inverse(inverse(X_32)),X_32) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),multiply(inverse(inverse(X_32)),add(X_32,inverse(inverse(X_32))))) ),[1,1],$fot(X_32)]]) ).
cnf(refute_0_92,plain,
( add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) != multiply(inverse(inverse(X_32)),add(X_32,inverse(inverse(X_32))))
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = multiply(inverse(inverse(X_32)),X_32) ),
inference(resolve,[$cnf( $equal(add(X_32,inverse(inverse(X_32))),X_32) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = multiply(inverse(inverse(X_32)),X_32),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),multiply(inverse(inverse(X_32)),add(X_32,inverse(inverse(X_32))))) )],[refute_0_78,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(inverse(inverse(X_32)),X_32) = multiply(X_32,inverse(inverse(X_32))),
inference(subst,[],[refute_0_66:[bind(X,$fot(X_32)),bind(Y,$fot(inverse(inverse(X_32))))]]) ).
cnf(refute_0_95,plain,
( multiply(inverse(inverse(X_32)),X_32) != multiply(X_32,inverse(inverse(X_32)))
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) != multiply(inverse(inverse(X_32)),X_32)
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = multiply(X_32,inverse(inverse(X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),multiply(inverse(inverse(X_32)),X_32)) ),[1],$fot(multiply(X_32,inverse(inverse(X_32))))]]) ).
cnf(refute_0_96,plain,
( add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) != multiply(inverse(inverse(X_32)),X_32)
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = multiply(X_32,inverse(inverse(X_32))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_32)),X_32),multiply(X_32,inverse(inverse(X_32)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = multiply(X_32,inverse(inverse(X_32))),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),multiply(inverse(inverse(X_32)),X_32)) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
add(inverse(inverse(X_32)),additive_identity) = inverse(inverse(X_32)),
inference(subst,[],[additive_id1:[bind(X,$fot(inverse(inverse(X_32))))]]) ).
cnf(refute_0_99,plain,
add(multiply(additive_identity,X_21),Y) = add(Y,multiply(additive_identity,X_21)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,X_21)))]]) ).
cnf(refute_0_100,plain,
add(X_10,multiply(additive_identity,X_12)) = multiply(add(X_10,additive_identity),add(X_10,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_101,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
| add(X_10,additive_identity) != X_10
| add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_102,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
| add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(add(X_10,additive_identity),X_10) )],[refute_0_61,refute_0_101]) ).
cnf(refute_0_103,plain,
add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) )],[refute_0_100,refute_0_102]) ).
cnf(refute_0_104,plain,
add(Y,multiply(additive_identity,X_21)) = multiply(Y,add(Y,X_21)),
inference(subst,[],[refute_0_103:[bind(X_10,$fot(Y)),bind(X_12,$fot(X_21))]]) ).
cnf(refute_0_105,plain,
( add(Y,multiply(additive_identity,X_21)) != multiply(Y,add(Y,X_21))
| add(multiply(additive_identity,X_21),Y) != add(Y,multiply(additive_identity,X_21))
| add(multiply(additive_identity,X_21),Y) = multiply(Y,add(Y,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_21),Y),add(Y,multiply(additive_identity,X_21))) ),[1],$fot(multiply(Y,add(Y,X_21)))]]) ).
cnf(refute_0_106,plain,
( add(multiply(additive_identity,X_21),Y) != add(Y,multiply(additive_identity,X_21))
| add(multiply(additive_identity,X_21),Y) = multiply(Y,add(Y,X_21)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,X_21)),multiply(Y,add(Y,X_21))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
add(multiply(additive_identity,X_21),Y) = multiply(Y,add(Y,X_21)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_21),Y),add(Y,multiply(additive_identity,X_21))) )],[refute_0_99,refute_0_106]) ).
cnf(refute_0_108,plain,
add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) = multiply(multiply(X_19,additive_identity),add(multiply(X_19,additive_identity),X_34)),
inference(subst,[],[refute_0_107:[bind(Y,$fot(multiply(X_19,additive_identity))),bind(X_21,$fot(X_34))]]) ).
cnf(refute_0_109,plain,
add(multiply(X_19,additive_identity),Y) = add(Y,multiply(X_19,additive_identity)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(X_19,additive_identity)))]]) ).
cnf(refute_0_110,plain,
add(Y,multiply(X_19,additive_identity)) = multiply(Y,add(Y,X_19)),
inference(subst,[],[refute_0_70:[bind(X_10,$fot(Y)),bind(X_11,$fot(X_19))]]) ).
cnf(refute_0_111,plain,
( add(Y,multiply(X_19,additive_identity)) != multiply(Y,add(Y,X_19))
| add(multiply(X_19,additive_identity),Y) != add(Y,multiply(X_19,additive_identity))
| add(multiply(X_19,additive_identity),Y) = multiply(Y,add(Y,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_19,additive_identity),Y),add(Y,multiply(X_19,additive_identity))) ),[1],$fot(multiply(Y,add(Y,X_19)))]]) ).
cnf(refute_0_112,plain,
( add(multiply(X_19,additive_identity),Y) != add(Y,multiply(X_19,additive_identity))
| add(multiply(X_19,additive_identity),Y) = multiply(Y,add(Y,X_19)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(X_19,additive_identity)),multiply(Y,add(Y,X_19))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
add(multiply(X_19,additive_identity),Y) = multiply(Y,add(Y,X_19)),
inference(resolve,[$cnf( $equal(add(multiply(X_19,additive_identity),Y),add(Y,multiply(X_19,additive_identity))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
add(multiply(X_19,additive_identity),X_34) = multiply(X_34,add(X_34,X_19)),
inference(subst,[],[refute_0_113:[bind(Y,$fot(X_34))]]) ).
cnf(refute_0_115,plain,
( add(multiply(X_19,additive_identity),X_34) != multiply(X_34,add(X_34,X_19))
| add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) != multiply(multiply(X_19,additive_identity),add(multiply(X_19,additive_identity),X_34))
| add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) = multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)),multiply(multiply(X_19,additive_identity),add(multiply(X_19,additive_identity),X_34))) ),[1,1],$fot(multiply(X_34,add(X_34,X_19)))]]) ).
cnf(refute_0_116,plain,
( add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) != multiply(multiply(X_19,additive_identity),add(multiply(X_19,additive_identity),X_34))
| add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) = multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_19,additive_identity),X_34),multiply(X_34,add(X_34,X_19))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) = multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)),multiply(multiply(X_19,additive_identity),add(multiply(X_19,additive_identity),X_34))) )],[refute_0_108,refute_0_116]) ).
cnf(refute_0_118,plain,
add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) = multiply(multiply(additive_identity,X_34),add(multiply(additive_identity,X_34),X_21)),
inference(subst,[],[refute_0_107:[bind(Y,$fot(multiply(additive_identity,X_34)))]]) ).
cnf(refute_0_119,plain,
add(multiply(additive_identity,X_34),X_21) = multiply(X_21,add(X_21,X_34)),
inference(subst,[],[refute_0_107:[bind(Y,$fot(X_21)),bind(X_21,$fot(X_34))]]) ).
cnf(refute_0_120,plain,
( add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) != multiply(multiply(additive_identity,X_34),add(multiply(additive_identity,X_34),X_21))
| add(multiply(additive_identity,X_34),X_21) != multiply(X_21,add(X_21,X_34))
| add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) = multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)),multiply(multiply(additive_identity,X_34),add(multiply(additive_identity,X_34),X_21))) ),[1,1],$fot(multiply(X_21,add(X_21,X_34)))]]) ).
cnf(refute_0_121,plain,
( add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) != multiply(multiply(additive_identity,X_34),add(multiply(additive_identity,X_34),X_21))
| add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) = multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_34),X_21),multiply(X_21,add(X_21,X_34))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) = multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)),multiply(multiply(additive_identity,X_34),add(multiply(additive_identity,X_34),X_21))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
( multiply(X,add(Y,Z)) != add(multiply(X,Y),multiply(X,Z))
| add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_124,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[distributivity2,refute_0_123]) ).
cnf(refute_0_125,plain,
add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) = multiply(additive_identity,add(X_21,X_34)),
inference(subst,[],[refute_0_124:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_21)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_126,plain,
( add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) != multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34)))
| add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) != multiply(additive_identity,add(X_21,X_34))
| multiply(additive_identity,add(X_21,X_34)) = multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)),multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34)))) ),[0],$fot(multiply(additive_identity,add(X_21,X_34)))]]) ).
cnf(refute_0_127,plain,
( add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) != multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34)))
| multiply(additive_identity,add(X_21,X_34)) = multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)),multiply(additive_identity,add(X_21,X_34))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)) = multiply(multiply(additive_identity,X_12),add(X_32,multiply(additive_identity,X_12))),
inference(subst,[],[refute_0_77:[bind(X_18,$fot(multiply(additive_identity,X_12))),bind(X_19,$fot(X_32))]]) ).
cnf(refute_0_129,plain,
add(X_32,multiply(additive_identity,X_12)) = multiply(X_32,add(X_32,X_12)),
inference(subst,[],[refute_0_103:[bind(X_10,$fot(X_32))]]) ).
cnf(refute_0_130,plain,
( add(X_32,multiply(additive_identity,X_12)) != multiply(X_32,add(X_32,X_12))
| add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)) != multiply(multiply(additive_identity,X_12),add(X_32,multiply(additive_identity,X_12)))
| add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)) = multiply(multiply(additive_identity,X_12),multiply(X_32,add(X_32,X_12))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)),multiply(multiply(additive_identity,X_12),add(X_32,multiply(additive_identity,X_12)))) ),[1,1],$fot(multiply(X_32,add(X_32,X_12)))]]) ).
cnf(refute_0_131,plain,
( add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)) != multiply(multiply(additive_identity,X_12),add(X_32,multiply(additive_identity,X_12)))
| add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)) = multiply(multiply(additive_identity,X_12),multiply(X_32,add(X_32,X_12))) ),
inference(resolve,[$cnf( $equal(add(X_32,multiply(additive_identity,X_12)),multiply(X_32,add(X_32,X_12))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)) = multiply(multiply(additive_identity,X_12),multiply(X_32,add(X_32,X_12))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)),multiply(multiply(additive_identity,X_12),add(X_32,multiply(additive_identity,X_12)))) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
( add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)) != multiply(multiply(additive_identity,X_12),multiply(X_32,add(X_32,X_12)))
| multiply(multiply(additive_identity,X_12),multiply(X_32,add(X_32,X_12))) = add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)))),bind(Y0,$fot(multiply(multiply(additive_identity,X_12),multiply(X_32,add(X_32,X_12)))))]]) ).
cnf(refute_0_134,plain,
multiply(multiply(additive_identity,X_12),multiply(X_32,add(X_32,X_12))) = add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_12),multiply(X_32,additive_identity)),multiply(multiply(additive_identity,X_12),multiply(X_32,add(X_32,X_12)))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34))) = add(multiply(additive_identity,X_34),multiply(X_21,additive_identity)),
inference(subst,[],[refute_0_134:[bind(X_12,$fot(X_34)),bind(X_32,$fot(X_21))]]) ).
cnf(refute_0_136,plain,
( multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34))) != add(multiply(additive_identity,X_34),multiply(X_21,additive_identity))
| multiply(additive_identity,add(X_21,X_34)) != multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34)))
| multiply(additive_identity,add(X_21,X_34)) = add(multiply(additive_identity,X_34),multiply(X_21,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_21,X_34)),multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34)))) ),[1],$fot(add(multiply(additive_identity,X_34),multiply(X_21,additive_identity)))]]) ).
cnf(refute_0_137,plain,
( multiply(additive_identity,add(X_21,X_34)) != multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34)))
| multiply(additive_identity,add(X_21,X_34)) = add(multiply(additive_identity,X_34),multiply(X_21,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34))),add(multiply(additive_identity,X_34),multiply(X_21,additive_identity))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)) != multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34)))
| multiply(additive_identity,add(X_21,X_34)) = add(multiply(additive_identity,X_34),multiply(X_21,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_21,X_34)),multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34)))) )],[refute_0_127,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(additive_identity,add(X_21,X_34)) = add(multiply(additive_identity,X_34),multiply(X_21,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_21),multiply(additive_identity,X_34)),multiply(multiply(additive_identity,X_34),multiply(X_21,add(X_21,X_34)))) )],[refute_0_122,refute_0_138]) ).
cnf(refute_0_140,plain,
( multiply(additive_identity,add(X_21,X_34)) != add(multiply(additive_identity,X_34),multiply(X_21,additive_identity))
| add(multiply(additive_identity,X_34),multiply(X_21,additive_identity)) = multiply(additive_identity,add(X_21,X_34)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(additive_identity,add(X_21,X_34)))),bind(Y0,$fot(add(multiply(additive_identity,X_34),multiply(X_21,additive_identity))))]]) ).
cnf(refute_0_141,plain,
add(multiply(additive_identity,X_34),multiply(X_21,additive_identity)) = multiply(additive_identity,add(X_21,X_34)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_21,X_34)),add(multiply(additive_identity,X_34),multiply(X_21,additive_identity))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) = multiply(additive_identity,add(X_19,X_34)),
inference(subst,[],[refute_0_141:[bind(X_21,$fot(X_19))]]) ).
cnf(refute_0_143,plain,
( add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) != multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19)))
| add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) != multiply(additive_identity,add(X_19,X_34))
| multiply(additive_identity,add(X_19,X_34)) = multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)),multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19)))) ),[0],$fot(multiply(additive_identity,add(X_19,X_34)))]]) ).
cnf(refute_0_144,plain,
( add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) != multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19)))
| multiply(additive_identity,add(X_19,X_34)) = multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)),multiply(additive_identity,add(X_19,X_34))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)) = multiply(multiply(X_28,additive_identity),add(multiply(X_28,additive_identity),X_19)),
inference(subst,[],[refute_0_113:[bind(Y,$fot(multiply(X_28,additive_identity)))]]) ).
cnf(refute_0_146,plain,
add(multiply(X_28,additive_identity),X_19) = multiply(X_19,add(X_19,X_28)),
inference(subst,[],[refute_0_113:[bind(Y,$fot(X_19)),bind(X_19,$fot(X_28))]]) ).
cnf(refute_0_147,plain,
( add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)) != multiply(multiply(X_28,additive_identity),add(multiply(X_28,additive_identity),X_19))
| add(multiply(X_28,additive_identity),X_19) != multiply(X_19,add(X_19,X_28))
| add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)) = multiply(multiply(X_28,additive_identity),multiply(X_19,add(X_19,X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)),multiply(multiply(X_28,additive_identity),add(multiply(X_28,additive_identity),X_19))) ),[1,1],$fot(multiply(X_19,add(X_19,X_28)))]]) ).
cnf(refute_0_148,plain,
( add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)) != multiply(multiply(X_28,additive_identity),add(multiply(X_28,additive_identity),X_19))
| add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)) = multiply(multiply(X_28,additive_identity),multiply(X_19,add(X_19,X_28))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),X_19),multiply(X_19,add(X_19,X_28))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)) = multiply(multiply(X_28,additive_identity),multiply(X_19,add(X_19,X_28))),
inference(resolve,[$cnf( $equal(add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)),multiply(multiply(X_28,additive_identity),add(multiply(X_28,additive_identity),X_19))) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
( add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)) != multiply(multiply(X_28,additive_identity),multiply(X_19,add(X_19,X_28)))
| multiply(multiply(X_28,additive_identity),multiply(X_19,add(X_19,X_28))) = add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)))),bind(Y0,$fot(multiply(multiply(X_28,additive_identity),multiply(X_19,add(X_19,X_28)))))]]) ).
cnf(refute_0_151,plain,
multiply(multiply(X_28,additive_identity),multiply(X_19,add(X_19,X_28))) = add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(X_19,additive_identity),multiply(X_28,additive_identity)),multiply(multiply(X_28,additive_identity),multiply(X_19,add(X_19,X_28)))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19))) = add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)),
inference(subst,[],[refute_0_151:[bind(X_19,$fot(X_34)),bind(X_28,$fot(X_19))]]) ).
cnf(refute_0_153,plain,
( multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19))) != add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))
| multiply(additive_identity,add(X_19,X_34)) != multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19)))
| multiply(additive_identity,add(X_19,X_34)) = add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_19,X_34)),multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19)))) ),[1],$fot(add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)))]]) ).
cnf(refute_0_154,plain,
( multiply(additive_identity,add(X_19,X_34)) != multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19)))
| multiply(additive_identity,add(X_19,X_34)) = add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19))),add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
( add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)) != multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19)))
| multiply(additive_identity,add(X_19,X_34)) = add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_19,X_34)),multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19)))) )],[refute_0_144,refute_0_154]) ).
cnf(refute_0_156,plain,
multiply(additive_identity,add(X_19,X_34)) = add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_34),multiply(X_19,additive_identity)),multiply(multiply(X_19,additive_identity),multiply(X_34,add(X_34,X_19)))) )],[refute_0_117,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(additive_identity,add(additive_identity,X_39)) = add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39)),
inference(subst,[],[distributivity2:[bind(X,$fot(additive_identity)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_158,plain,
add(multiply(additive_identity,additive_identity),Y) = add(Y,multiply(additive_identity,additive_identity)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_159,plain,
add(X_18,multiply(additive_identity,additive_identity)) = multiply(X_18,add(X_18,additive_identity)),
inference(subst,[],[refute_0_70:[bind(X_10,$fot(X_18)),bind(X_11,$fot(additive_identity))]]) ).
cnf(refute_0_160,plain,
add(X_18,additive_identity) = X_18,
inference(subst,[],[additive_id1:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_161,plain,
( add(X_18,multiply(additive_identity,additive_identity)) != multiply(X_18,add(X_18,additive_identity))
| add(X_18,additive_identity) != X_18
| add(X_18,multiply(additive_identity,additive_identity)) = multiply(X_18,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_18,multiply(additive_identity,additive_identity)),multiply(X_18,add(X_18,additive_identity))) ),[1,1],$fot(X_18)]]) ).
cnf(refute_0_162,plain,
( add(X_18,multiply(additive_identity,additive_identity)) != multiply(X_18,add(X_18,additive_identity))
| add(X_18,multiply(additive_identity,additive_identity)) = multiply(X_18,X_18) ),
inference(resolve,[$cnf( $equal(add(X_18,additive_identity),X_18) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
add(X_18,multiply(additive_identity,additive_identity)) = multiply(X_18,X_18),
inference(resolve,[$cnf( $equal(add(X_18,multiply(additive_identity,additive_identity)),multiply(X_18,add(X_18,additive_identity))) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y),
inference(subst,[],[refute_0_163:[bind(X_18,$fot(Y))]]) ).
cnf(refute_0_165,plain,
( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,Y)
| add(multiply(additive_identity,additive_identity),Y) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) ),[1],$fot(multiply(Y,Y))]]) ).
cnf(refute_0_166,plain,
( add(multiply(additive_identity,additive_identity),Y) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,Y)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_158,refute_0_166]) ).
cnf(refute_0_168,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39)) = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)),
inference(subst,[],[refute_0_167:[bind(Y,$fot(multiply(additive_identity,X_39)))]]) ).
cnf(refute_0_169,plain,
( multiply(additive_identity,add(additive_identity,X_39)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39)) != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| multiply(additive_identity,add(additive_identity,X_39)) = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(additive_identity,add(additive_identity,X_39)),multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) ),[0],$fot(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39)))]]) ).
cnf(refute_0_170,plain,
( multiply(additive_identity,add(additive_identity,X_39)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39))
| multiply(additive_identity,add(additive_identity,X_39)) = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39)),multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
multiply(additive_identity,add(additive_identity,X_39)) = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_39)),add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39))) )],[refute_0_157,refute_0_170]) ).
cnf(refute_0_172,plain,
multiply(X_37,add(X_38,multiplicative_identity)) = add(multiply(X_37,X_38),multiply(X_37,multiplicative_identity)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(Z,$fot(multiplicative_identity))]]) ).
cnf(refute_0_173,plain,
multiply(X_37,multiplicative_identity) = X_37,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_174,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != add(multiply(X_37,X_38),multiply(X_37,multiplicative_identity))
| multiply(X_37,multiplicative_identity) != X_37
| multiply(X_37,add(X_38,multiplicative_identity)) = add(multiply(X_37,X_38),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),add(multiply(X_37,X_38),multiply(X_37,multiplicative_identity))) ),[1,1],$fot(X_37)]]) ).
cnf(refute_0_175,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != add(multiply(X_37,X_38),multiply(X_37,multiplicative_identity))
| multiply(X_37,add(X_38,multiplicative_identity)) = add(multiply(X_37,X_38),X_37) ),
inference(resolve,[$cnf( $equal(multiply(X_37,multiplicative_identity),X_37) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(X_37,add(X_38,multiplicative_identity)) = add(multiply(X_37,X_38),X_37),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),add(multiply(X_37,X_38),multiply(X_37,multiplicative_identity))) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
add(X_13,multiply(inverse(X_13),multiplicative_identity)) = add(X_13,multiplicative_identity),
inference(subst,[],[refute_0_29:[bind(X_10,$fot(X_13)),bind(X_12,$fot(multiplicative_identity))]]) ).
cnf(refute_0_178,plain,
multiply(inverse(X_13),multiplicative_identity) = inverse(X_13),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(inverse(X_13)))]]) ).
cnf(refute_0_179,plain,
( multiply(inverse(X_13),multiplicative_identity) != inverse(X_13)
| add(X_13,multiply(inverse(X_13),multiplicative_identity)) != add(X_13,multiplicative_identity)
| add(X_13,inverse(X_13)) = add(X_13,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,multiply(inverse(X_13),multiplicative_identity)),add(X_13,multiplicative_identity)) ),[0,1],$fot(inverse(X_13))]]) ).
cnf(refute_0_180,plain,
( add(X_13,multiply(inverse(X_13),multiplicative_identity)) != add(X_13,multiplicative_identity)
| add(X_13,inverse(X_13)) = add(X_13,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_13),multiplicative_identity),inverse(X_13)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
add(X_13,inverse(X_13)) = add(X_13,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_13,multiply(inverse(X_13),multiplicative_identity)),add(X_13,multiplicative_identity)) )],[refute_0_177,refute_0_180]) ).
cnf(refute_0_182,plain,
add(X_13,inverse(X_13)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_183,plain,
( add(X_13,inverse(X_13)) != add(X_13,multiplicative_identity)
| add(X_13,inverse(X_13)) != multiplicative_identity
| multiplicative_identity = add(X_13,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,inverse(X_13)),add(X_13,multiplicative_identity)) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_184,plain,
( add(X_13,inverse(X_13)) != add(X_13,multiplicative_identity)
| multiplicative_identity = add(X_13,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_13,inverse(X_13)),multiplicative_identity) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
multiplicative_identity = add(X_13,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_13,inverse(X_13)),add(X_13,multiplicative_identity)) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
( multiplicative_identity != add(X_13,multiplicative_identity)
| add(X_13,multiplicative_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_13,multiplicative_identity)))]]) ).
cnf(refute_0_187,plain,
add(X_13,multiplicative_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_13,multiplicative_identity)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
add(X_38,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[refute_0_187:[bind(X_13,$fot(X_38))]]) ).
cnf(refute_0_189,plain,
multiply(X_37,add(X_38,multiplicative_identity)) = multiply(X_37,add(X_38,multiplicative_identity)),
introduced(tautology,[refl,[$fot(multiply(X_37,add(X_38,multiplicative_identity)))]]) ).
cnf(refute_0_190,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != multiply(X_37,add(X_38,multiplicative_identity))
| add(X_38,multiplicative_identity) != multiplicative_identity
| multiply(X_37,add(X_38,multiplicative_identity)) = multiply(X_37,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),multiply(X_37,add(X_38,multiplicative_identity))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_191,plain,
( add(X_38,multiplicative_identity) != multiplicative_identity
| multiply(X_37,add(X_38,multiplicative_identity)) = multiply(X_37,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),multiply(X_37,add(X_38,multiplicative_identity))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
multiply(X_37,add(X_38,multiplicative_identity)) = multiply(X_37,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_38,multiplicative_identity),multiplicative_identity) )],[refute_0_188,refute_0_191]) ).
cnf(refute_0_193,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_194,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_193]) ).
cnf(refute_0_195,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != multiply(X_37,multiplicative_identity)
| multiply(X_37,multiplicative_identity) != X_37
| multiply(X_37,add(X_38,multiplicative_identity)) = X_37 ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(multiply(X_37,add(X_38,multiplicative_identity)))),bind(Y0,$fot(multiply(X_37,multiplicative_identity))),bind(Z0,$fot(X_37))]]) ).
cnf(refute_0_196,plain,
( multiply(X_37,multiplicative_identity) != X_37
| multiply(X_37,add(X_38,multiplicative_identity)) = X_37 ),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),multiply(X_37,multiplicative_identity)) )],[refute_0_192,refute_0_195]) ).
cnf(refute_0_197,plain,
multiply(X_37,add(X_38,multiplicative_identity)) = X_37,
inference(resolve,[$cnf( $equal(multiply(X_37,multiplicative_identity),X_37) )],[refute_0_173,refute_0_196]) ).
cnf(refute_0_198,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != X_37
| multiply(X_37,add(X_38,multiplicative_identity)) != add(multiply(X_37,X_38),X_37)
| X_37 = add(multiply(X_37,X_38),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),add(multiply(X_37,X_38),X_37)) ),[0],$fot(X_37)]]) ).
cnf(refute_0_199,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != add(multiply(X_37,X_38),X_37)
| X_37 = add(multiply(X_37,X_38),X_37) ),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),X_37) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
add(Y,multiply(Y,Z)) = multiply(add(Y,Y),add(Y,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_201,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),add(X_10,inverse(X_10))),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(inverse(X_10)))]]) ).
cnf(refute_0_202,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),add(X_10,inverse(X_10)))
| add(X_10,inverse(X_10)) != multiplicative_identity
| add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_203,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),add(X_10,inverse(X_10)))
| add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_18,refute_0_202]) ).
cnf(refute_0_204,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) )],[refute_0_201,refute_0_203]) ).
cnf(refute_0_205,plain,
multiply(add(X_10,X_11),multiplicative_identity) = add(X_10,X_11),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_206,plain,
( multiply(add(X_10,X_11),multiplicative_identity) != add(X_10,X_11)
| add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),multiplicative_identity)
| add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) ),[1],$fot(add(X_10,X_11))]]) ).
cnf(refute_0_207,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),multiplicative_identity)
| add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),multiplicative_identity),add(X_10,X_11)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
add(X_24,multiply(X_24,inverse(X_24))) = add(X_24,X_24),
inference(subst,[],[refute_0_208:[bind(X_10,$fot(X_24)),bind(X_11,$fot(X_24))]]) ).
cnf(refute_0_210,plain,
multiply(X_24,inverse(X_24)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_211,plain,
( multiply(X_24,inverse(X_24)) != additive_identity
| add(X_24,multiply(X_24,inverse(X_24))) != add(X_24,X_24)
| add(X_24,additive_identity) = add(X_24,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_24,multiply(X_24,inverse(X_24))),add(X_24,X_24)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_212,plain,
( add(X_24,multiply(X_24,inverse(X_24))) != add(X_24,X_24)
| add(X_24,additive_identity) = add(X_24,X_24) ),
inference(resolve,[$cnf( $equal(multiply(X_24,inverse(X_24)),additive_identity) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
add(X_24,additive_identity) = add(X_24,X_24),
inference(resolve,[$cnf( $equal(add(X_24,multiply(X_24,inverse(X_24))),add(X_24,X_24)) )],[refute_0_209,refute_0_212]) ).
cnf(refute_0_214,plain,
add(X_24,additive_identity) = X_24,
inference(subst,[],[additive_id1:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_215,plain,
( add(X_24,additive_identity) != X_24
| add(X_24,additive_identity) != add(X_24,X_24)
| X_24 = add(X_24,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_24,additive_identity),add(X_24,X_24)) ),[0],$fot(X_24)]]) ).
cnf(refute_0_216,plain,
( add(X_24,additive_identity) != add(X_24,X_24)
| X_24 = add(X_24,X_24) ),
inference(resolve,[$cnf( $equal(add(X_24,additive_identity),X_24) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
X_24 = add(X_24,X_24),
inference(resolve,[$cnf( $equal(add(X_24,additive_identity),add(X_24,X_24)) )],[refute_0_213,refute_0_216]) ).
cnf(refute_0_218,plain,
Y = add(Y,Y),
inference(subst,[],[refute_0_217:[bind(X_24,$fot(Y))]]) ).
cnf(refute_0_219,plain,
( Y != add(Y,Y)
| add(Y,Y) = Y ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(Y)),bind(Y0,$fot(add(Y,Y)))]]) ).
cnf(refute_0_220,plain,
add(Y,Y) = Y,
inference(resolve,[$cnf( $equal(Y,add(Y,Y)) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
( add(Y,Y) != Y
| add(Y,multiply(Y,Z)) != multiply(add(Y,Y),add(Y,Z))
| add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_222,plain,
( add(Y,multiply(Y,Z)) != multiply(add(Y,Y),add(Y,Z))
| add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)) ),
inference(resolve,[$cnf( $equal(add(Y,Y),Y) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) )],[refute_0_200,refute_0_222]) ).
cnf(refute_0_224,plain,
add(X_37,multiply(X_37,X_38)) = multiply(X_37,add(X_37,X_38)),
inference(subst,[],[refute_0_223:[bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_225,plain,
add(multiply(X_37,X_38),X_37) = add(X_37,multiply(X_37,X_38)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_37)),bind(Y,$fot(multiply(X_37,X_38)))]]) ).
cnf(refute_0_226,plain,
( add(X_37,multiply(X_37,X_38)) != multiply(X_37,add(X_37,X_38))
| add(multiply(X_37,X_38),X_37) != add(X_37,multiply(X_37,X_38))
| add(multiply(X_37,X_38),X_37) = multiply(X_37,add(X_37,X_38)) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(multiply(X_37,X_38),X_37))),bind(Y0,$fot(add(X_37,multiply(X_37,X_38)))),bind(Z0,$fot(multiply(X_37,add(X_37,X_38))))]]) ).
cnf(refute_0_227,plain,
( add(X_37,multiply(X_37,X_38)) != multiply(X_37,add(X_37,X_38))
| add(multiply(X_37,X_38),X_37) = multiply(X_37,add(X_37,X_38)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_37,X_38),X_37),add(X_37,multiply(X_37,X_38))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
add(multiply(X_37,X_38),X_37) = multiply(X_37,add(X_37,X_38)),
inference(resolve,[$cnf( $equal(add(X_37,multiply(X_37,X_38)),multiply(X_37,add(X_37,X_38))) )],[refute_0_224,refute_0_227]) ).
cnf(refute_0_229,plain,
( X_37 != add(multiply(X_37,X_38),X_37)
| add(multiply(X_37,X_38),X_37) != multiply(X_37,add(X_37,X_38))
| X_37 = multiply(X_37,add(X_37,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_37,multiply(X_37,add(X_37,X_38))) ),[0],$fot(add(multiply(X_37,X_38),X_37))]]) ).
cnf(refute_0_230,plain,
( X_37 != add(multiply(X_37,X_38),X_37)
| X_37 = multiply(X_37,add(X_37,X_38)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_37,X_38),X_37),multiply(X_37,add(X_37,X_38))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != add(multiply(X_37,X_38),X_37)
| X_37 = multiply(X_37,add(X_37,X_38)) ),
inference(resolve,[$cnf( $equal(X_37,add(multiply(X_37,X_38),X_37)) )],[refute_0_199,refute_0_230]) ).
cnf(refute_0_232,plain,
X_37 = multiply(X_37,add(X_37,X_38)),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),add(multiply(X_37,X_38),X_37)) )],[refute_0_176,refute_0_231]) ).
cnf(refute_0_233,plain,
( X_37 != multiply(X_37,add(X_37,X_38))
| multiply(X_37,add(X_37,X_38)) = X_37 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_37)),bind(Y0,$fot(multiply(X_37,add(X_37,X_38))))]]) ).
cnf(refute_0_234,plain,
multiply(X_37,add(X_37,X_38)) = X_37,
inference(resolve,[$cnf( $equal(X_37,multiply(X_37,add(X_37,X_38))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
multiply(additive_identity,add(additive_identity,X_39)) = additive_identity,
inference(subst,[],[refute_0_234:[bind(X_37,$fot(additive_identity)),bind(X_38,$fot(X_39))]]) ).
cnf(refute_0_236,plain,
( multiply(additive_identity,add(additive_identity,X_39)) != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| multiply(additive_identity,add(additive_identity,X_39)) != additive_identity
| additive_identity = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_39)),multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_237,plain,
( multiply(additive_identity,add(additive_identity,X_39)) != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| additive_identity = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_39)),additive_identity) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),
inference(subst,[],[refute_0_103:[bind(X_10,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_239,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),
inference(subst,[],[refute_0_167:[bind(Y,$fot(multiply(additive_identity,X_12)))]]) ).
cnf(refute_0_240,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) ),[0],$fot(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)))]]) ).
cnf(refute_0_241,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_238,refute_0_241]) ).
cnf(refute_0_243,plain,
add(X_12,additive_identity) = X_12,
inference(subst,[],[additive_id1:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_244,plain,
multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,add(X_12,additive_identity)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(X_12,additive_identity)))]]) ).
cnf(refute_0_245,plain,
( multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| add(X_12,additive_identity) != X_12
| multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) ),[1,1],$fot(X_12)]]) ).
cnf(refute_0_246,plain,
( add(X_12,additive_identity) != X_12
| multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(add(X_12,additive_identity),X_12) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) = multiply(additive_identity,add(X_12,additive_identity)),
inference(subst,[],[refute_0_124:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_12)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_249,plain,
( add(multiply(additive_identity,X_21),Y) != multiply(Y,add(Y,X_21))
| multiply(Y,add(Y,X_21)) = add(multiply(additive_identity,X_21),Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(multiply(additive_identity,X_21),Y))),bind(Y0,$fot(multiply(Y,add(Y,X_21))))]]) ).
cnf(refute_0_250,plain,
multiply(Y,add(Y,X_21)) = add(multiply(additive_identity,X_21),Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_21),Y),multiply(Y,add(Y,X_21))) )],[refute_0_107,refute_0_249]) ).
cnf(refute_0_251,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)),
inference(subst,[],[refute_0_250:[bind(Y,$fot(multiply(additive_identity,additive_identity))),bind(X_21,$fot(X_12))]]) ).
cnf(refute_0_252,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)))),bind(Y0,$fot(add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)))),bind(Z0,$fot(multiply(additive_identity,add(X_12,additive_identity))))]]) ).
cnf(refute_0_253,plain,
( add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_248,refute_0_253]) ).
cnf(refute_0_255,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)))),bind(Y0,$fot(multiply(additive_identity,add(X_12,additive_identity)))),bind(Z0,$fot(multiply(additive_identity,X_12)))]]) ).
cnf(refute_0_256,plain,
( multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,X_12)) )],[refute_0_247,refute_0_256]) ).
cnf(refute_0_258,plain,
( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),multiply(additive_identity,X_12)) ),[0],$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)))]]) ).
cnf(refute_0_259,plain,
( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),multiply(additive_identity,X_12)) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_242,refute_0_259]) ).
cnf(refute_0_261,plain,
multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) = multiply(additive_identity,X_39),
inference(subst,[],[refute_0_260:[bind(X_12,$fot(X_39))]]) ).
cnf(refute_0_262,plain,
( multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) != multiply(additive_identity,X_39)
| additive_identity != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| additive_identity = multiply(additive_identity,X_39) ),
introduced(tautology,[equality,[$cnf( $equal(additive_identity,multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) ),[1],$fot(multiply(additive_identity,X_39))]]) ).
cnf(refute_0_263,plain,
( additive_identity != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| additive_identity = multiply(additive_identity,X_39) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)),multiply(additive_identity,X_39)) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
( multiply(additive_identity,add(additive_identity,X_39)) != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| additive_identity = multiply(additive_identity,X_39) ),
inference(resolve,[$cnf( $equal(additive_identity,multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) )],[refute_0_237,refute_0_263]) ).
cnf(refute_0_265,plain,
additive_identity = multiply(additive_identity,X_39),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_39)),multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) )],[refute_0_171,refute_0_264]) ).
cnf(refute_0_266,plain,
( additive_identity != multiply(additive_identity,X_39)
| multiply(additive_identity,X_39) = additive_identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(additive_identity,X_39)))]]) ).
cnf(refute_0_267,plain,
multiply(additive_identity,X_39) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(additive_identity,X_39)) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
multiply(additive_identity,add(X_19,X_34)) = additive_identity,
inference(subst,[],[refute_0_267:[bind(X_39,$fot(add(X_19,X_34)))]]) ).
cnf(refute_0_269,plain,
( multiply(additive_identity,add(X_19,X_34)) != add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))
| multiply(additive_identity,add(X_19,X_34)) != additive_identity
| additive_identity = add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_19,X_34)),add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_270,plain,
( multiply(additive_identity,add(X_19,X_34)) != add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))
| additive_identity = add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_19,X_34)),additive_identity) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = multiply(add(multiply(X_30,additive_identity),Y),add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))),
inference(subst,[],[distributivity1:[bind(X,$fot(multiply(X_30,additive_identity))),bind(Z,$fot(inverse(multiply(additive_identity,X_30))))]]) ).
cnf(refute_0_272,plain,
add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))) = add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity))),
inference(subst,[],[refute_0_208:[bind(X_10,$fot(multiply(additive_identity,X_29))),bind(X_11,$fot(inverse(multiply(X_29,additive_identity))))]]) ).
cnf(refute_0_273,plain,
add(multiply(X_28,additive_identity),inverse(multiply(X_28,additive_identity))) = multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28)),
inference(subst,[],[refute_0_113:[bind(Y,$fot(inverse(multiply(X_28,additive_identity)))),bind(X_19,$fot(X_28))]]) ).
cnf(refute_0_274,plain,
add(multiply(X_28,additive_identity),inverse(multiply(X_28,additive_identity))) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(multiply(X_28,additive_identity)))]]) ).
cnf(refute_0_275,plain,
( add(multiply(X_28,additive_identity),inverse(multiply(X_28,additive_identity))) != multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28))
| add(multiply(X_28,additive_identity),inverse(multiply(X_28,additive_identity))) != multiplicative_identity
| multiplicative_identity = multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_28,additive_identity),inverse(multiply(X_28,additive_identity))),multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28))) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_276,plain,
( add(multiply(X_28,additive_identity),inverse(multiply(X_28,additive_identity))) != multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28))
| multiplicative_identity = multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),inverse(multiply(X_28,additive_identity))),multiplicative_identity) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
multiplicative_identity = multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28)),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),inverse(multiply(X_28,additive_identity))),multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28))) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
add(multiply(X_28,additive_identity),X_27) = multiply(X_27,add(X_27,X_28)),
inference(subst,[],[refute_0_113:[bind(Y,$fot(X_27)),bind(X_19,$fot(X_28))]]) ).
cnf(refute_0_279,plain,
multiply(additive_identity,X_28) = multiply(X_28,additive_identity),
inference(subst,[],[commutativity_of_multiply:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_28))]]) ).
cnf(refute_0_280,plain,
( multiply(additive_identity,X_28) != multiply(X_28,additive_identity)
| multiply(X_28,additive_identity) = multiply(additive_identity,X_28) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(additive_identity,X_28))),bind(Y0,$fot(multiply(X_28,additive_identity)))]]) ).
cnf(refute_0_281,plain,
multiply(X_28,additive_identity) = multiply(additive_identity,X_28),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_28),multiply(X_28,additive_identity)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
( multiply(X_28,additive_identity) != multiply(additive_identity,X_28)
| add(multiply(X_28,additive_identity),X_27) != multiply(X_27,add(X_27,X_28))
| add(multiply(additive_identity,X_28),X_27) = multiply(X_27,add(X_27,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_28,additive_identity),X_27),multiply(X_27,add(X_27,X_28))) ),[0,0],$fot(multiply(additive_identity,X_28))]]) ).
cnf(refute_0_283,plain,
( add(multiply(X_28,additive_identity),X_27) != multiply(X_27,add(X_27,X_28))
| add(multiply(additive_identity,X_28),X_27) = multiply(X_27,add(X_27,X_28)) ),
inference(resolve,[$cnf( $equal(multiply(X_28,additive_identity),multiply(additive_identity,X_28)) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
add(multiply(additive_identity,X_28),X_27) = multiply(X_27,add(X_27,X_28)),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),X_27),multiply(X_27,add(X_27,X_28))) )],[refute_0_278,refute_0_283]) ).
cnf(refute_0_285,plain,
( add(multiply(additive_identity,X_28),X_27) != multiply(X_27,add(X_27,X_28))
| multiply(X_27,add(X_27,X_28)) = add(multiply(additive_identity,X_28),X_27) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(multiply(additive_identity,X_28),X_27))),bind(Y0,$fot(multiply(X_27,add(X_27,X_28))))]]) ).
cnf(refute_0_286,plain,
multiply(X_27,add(X_27,X_28)) = add(multiply(additive_identity,X_28),X_27),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_28),X_27),multiply(X_27,add(X_27,X_28))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28)) = add(multiply(additive_identity,X_28),inverse(multiply(X_28,additive_identity))),
inference(subst,[],[refute_0_286:[bind(X_27,$fot(inverse(multiply(X_28,additive_identity))))]]) ).
cnf(refute_0_288,plain,
( multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28)) != add(multiply(additive_identity,X_28),inverse(multiply(X_28,additive_identity)))
| multiplicative_identity != multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28))
| multiplicative_identity = add(multiply(additive_identity,X_28),inverse(multiply(X_28,additive_identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplicative_identity,multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28))) ),[1],$fot(add(multiply(additive_identity,X_28),inverse(multiply(X_28,additive_identity))))]]) ).
cnf(refute_0_289,plain,
( multiplicative_identity != multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28))
| multiplicative_identity = add(multiply(additive_identity,X_28),inverse(multiply(X_28,additive_identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28)),add(multiply(additive_identity,X_28),inverse(multiply(X_28,additive_identity)))) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
multiplicative_identity = add(multiply(additive_identity,X_28),inverse(multiply(X_28,additive_identity))),
inference(resolve,[$cnf( $equal(multiplicative_identity,multiply(inverse(multiply(X_28,additive_identity)),add(inverse(multiply(X_28,additive_identity)),X_28))) )],[refute_0_277,refute_0_289]) ).
cnf(refute_0_291,plain,
multiplicative_identity = add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity))),
inference(subst,[],[refute_0_290:[bind(X_28,$fot(X_29))]]) ).
cnf(refute_0_292,plain,
( multiplicative_identity != add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity)))
| add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity))) = multiplicative_identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity)))))]]) ).
cnf(refute_0_293,plain,
add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity))) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity)))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
( add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))) != add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity)))
| add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity))) != multiplicative_identity
| add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))) = multiplicative_identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))),multiplicative_identity) ),[0],$fot(add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity))))]]) ).
cnf(refute_0_295,plain,
( add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))) != add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity)))
| add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity))),multiplicative_identity) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))) = multiplicative_identity,
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))),add(multiply(additive_identity,X_29),inverse(multiply(X_29,additive_identity)))) )],[refute_0_272,refute_0_295]) ).
cnf(refute_0_297,plain,
add(multiply(X_28,additive_identity),multiply(inverse(multiply(X_28,additive_identity)),X_12)) = multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28)),
inference(subst,[],[refute_0_113:[bind(Y,$fot(multiply(inverse(multiply(X_28,additive_identity)),X_12))),bind(X_19,$fot(X_28))]]) ).
cnf(refute_0_298,plain,
add(multiply(X_28,additive_identity),multiply(inverse(multiply(X_28,additive_identity)),X_12)) = add(multiply(X_28,additive_identity),X_12),
inference(subst,[],[refute_0_29:[bind(X_10,$fot(multiply(X_28,additive_identity)))]]) ).
cnf(refute_0_299,plain,
( add(multiply(X_28,additive_identity),multiply(inverse(multiply(X_28,additive_identity)),X_12)) != multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28))
| add(multiply(X_28,additive_identity),multiply(inverse(multiply(X_28,additive_identity)),X_12)) != add(multiply(X_28,additive_identity),X_12)
| add(multiply(X_28,additive_identity),X_12) = multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_28,additive_identity),multiply(inverse(multiply(X_28,additive_identity)),X_12)),multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28))) ),[0],$fot(add(multiply(X_28,additive_identity),X_12))]]) ).
cnf(refute_0_300,plain,
( add(multiply(X_28,additive_identity),multiply(inverse(multiply(X_28,additive_identity)),X_12)) != multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28))
| add(multiply(X_28,additive_identity),X_12) = multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),multiply(inverse(multiply(X_28,additive_identity)),X_12)),add(multiply(X_28,additive_identity),X_12)) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
add(multiply(X_28,additive_identity),X_12) = multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28)),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),multiply(inverse(multiply(X_28,additive_identity)),X_12)),multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28))) )],[refute_0_297,refute_0_300]) ).
cnf(refute_0_302,plain,
multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28)) = add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12)),
inference(subst,[],[refute_0_286:[bind(X_27,$fot(multiply(inverse(multiply(X_28,additive_identity)),X_12)))]]) ).
cnf(refute_0_303,plain,
( multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28)) != add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12))
| add(multiply(X_28,additive_identity),X_12) != multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28))
| add(multiply(X_28,additive_identity),X_12) = add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_28,additive_identity),X_12),multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28))) ),[1],$fot(add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12)))]]) ).
cnf(refute_0_304,plain,
( add(multiply(X_28,additive_identity),X_12) != multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28))
| add(multiply(X_28,additive_identity),X_12) = add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28)),add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
add(multiply(X_28,additive_identity),X_12) = add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12)),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),X_12),multiply(multiply(inverse(multiply(X_28,additive_identity)),X_12),add(multiply(inverse(multiply(X_28,additive_identity)),X_12),X_28))) )],[refute_0_301,refute_0_304]) ).
cnf(refute_0_306,plain,
( add(multiply(X_28,additive_identity),X_12) != add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12))
| add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12)) = add(multiply(X_28,additive_identity),X_12) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(multiply(X_28,additive_identity),X_12))),bind(Y0,$fot(add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12))))]]) ).
cnf(refute_0_307,plain,
add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12)) = add(multiply(X_28,additive_identity),X_12),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),X_12),add(multiply(additive_identity,X_28),multiply(inverse(multiply(X_28,additive_identity)),X_12))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))) = add(multiply(X_29,additive_identity),inverse(multiply(additive_identity,X_29))),
inference(subst,[],[refute_0_307:[bind(X_12,$fot(inverse(multiply(additive_identity,X_29)))),bind(X_28,$fot(X_29))]]) ).
cnf(refute_0_309,plain,
( add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))) != add(multiply(X_29,additive_identity),inverse(multiply(additive_identity,X_29)))
| add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))) != multiplicative_identity
| add(multiply(X_29,additive_identity),inverse(multiply(additive_identity,X_29))) = multiplicative_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))),multiplicative_identity) ),[0],$fot(add(multiply(X_29,additive_identity),inverse(multiply(additive_identity,X_29))))]]) ).
cnf(refute_0_310,plain,
( add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))) != multiplicative_identity
| add(multiply(X_29,additive_identity),inverse(multiply(additive_identity,X_29))) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))),add(multiply(X_29,additive_identity),inverse(multiply(additive_identity,X_29)))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
add(multiply(X_29,additive_identity),inverse(multiply(additive_identity,X_29))) = multiplicative_identity,
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_29),multiply(inverse(multiply(X_29,additive_identity)),inverse(multiply(additive_identity,X_29)))),multiplicative_identity) )],[refute_0_296,refute_0_310]) ).
cnf(refute_0_312,plain,
add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))) = multiplicative_identity,
inference(subst,[],[refute_0_311:[bind(X_29,$fot(X_30))]]) ).
cnf(refute_0_313,plain,
( add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) != multiply(add(multiply(X_30,additive_identity),Y),add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))))
| add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))) != multiplicative_identity
| add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = multiply(add(multiply(X_30,additive_identity),Y),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))),multiply(add(multiply(X_30,additive_identity),Y),add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_314,plain,
( add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) != multiply(add(multiply(X_30,additive_identity),Y),add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))))
| add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = multiply(add(multiply(X_30,additive_identity),Y),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))),multiplicative_identity) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = multiply(add(multiply(X_30,additive_identity),Y),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))),multiply(add(multiply(X_30,additive_identity),Y),add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))))) )],[refute_0_271,refute_0_314]) ).
cnf(refute_0_316,plain,
multiply(add(multiply(X_30,additive_identity),Y),multiplicative_identity) = add(multiply(X_30,additive_identity),Y),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(multiply(X_30,additive_identity),Y)))]]) ).
cnf(refute_0_317,plain,
( multiply(add(multiply(X_30,additive_identity),Y),multiplicative_identity) != add(multiply(X_30,additive_identity),Y)
| add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) != multiply(add(multiply(X_30,additive_identity),Y),multiplicative_identity)
| add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = add(multiply(X_30,additive_identity),Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))),multiply(add(multiply(X_30,additive_identity),Y),multiplicative_identity)) ),[1],$fot(add(multiply(X_30,additive_identity),Y))]]) ).
cnf(refute_0_318,plain,
( add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) != multiply(add(multiply(X_30,additive_identity),Y),multiplicative_identity)
| add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = add(multiply(X_30,additive_identity),Y) ),
inference(resolve,[$cnf( $equal(multiply(add(multiply(X_30,additive_identity),Y),multiplicative_identity),add(multiply(X_30,additive_identity),Y)) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = add(multiply(X_30,additive_identity),Y),
inference(resolve,[$cnf( $equal(add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))),multiply(add(multiply(X_30,additive_identity),Y),multiplicative_identity)) )],[refute_0_315,refute_0_318]) ).
cnf(refute_0_320,plain,
multiply(Y,multiplicative_identity) = Y,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_321,plain,
multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) = multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))),
introduced(tautology,[refl,[$fot(multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))))]]) ).
cnf(refute_0_322,plain,
( multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) != multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))))
| add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))) != multiplicative_identity
| multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) = multiply(Y,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))),multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_323,plain,
( add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))) != multiplicative_identity
| multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) = multiply(Y,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))),multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) = multiply(Y,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))),multiplicative_identity) )],[refute_0_312,refute_0_323]) ).
cnf(refute_0_325,plain,
( multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) != multiply(Y,multiplicative_identity)
| multiply(Y,multiplicative_identity) != Y
| multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) = Y ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))))),bind(Y0,$fot(multiply(Y,multiplicative_identity))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_326,plain,
( multiply(Y,multiplicative_identity) != Y
| multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) = Y ),
inference(resolve,[$cnf( $equal(multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))),multiply(Y,multiplicative_identity)) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) = Y,
inference(resolve,[$cnf( $equal(multiply(Y,multiplicative_identity),Y) )],[refute_0_320,refute_0_326]) ).
cnf(refute_0_328,plain,
add(multiply(X_28,additive_identity),multiply(Y,Z)) = multiply(add(multiply(X_28,additive_identity),Y),add(multiply(X_28,additive_identity),Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(multiply(X_28,additive_identity)))]]) ).
cnf(refute_0_329,plain,
add(multiply(X_28,additive_identity),Y) = multiply(Y,add(Y,X_28)),
inference(subst,[],[refute_0_113:[bind(X_19,$fot(X_28))]]) ).
cnf(refute_0_330,plain,
( add(multiply(X_28,additive_identity),Y) != multiply(Y,add(Y,X_28))
| add(multiply(X_28,additive_identity),multiply(Y,Z)) != multiply(add(multiply(X_28,additive_identity),Y),add(multiply(X_28,additive_identity),Z))
| add(multiply(X_28,additive_identity),multiply(Y,Z)) = multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_28,additive_identity),multiply(Y,Z)),multiply(add(multiply(X_28,additive_identity),Y),add(multiply(X_28,additive_identity),Z))) ),[1,0],$fot(multiply(Y,add(Y,X_28)))]]) ).
cnf(refute_0_331,plain,
( add(multiply(X_28,additive_identity),multiply(Y,Z)) != multiply(add(multiply(X_28,additive_identity),Y),add(multiply(X_28,additive_identity),Z))
| add(multiply(X_28,additive_identity),multiply(Y,Z)) = multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),Y),multiply(Y,add(Y,X_28))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
add(multiply(X_28,additive_identity),multiply(Y,Z)) = multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),multiply(Y,Z)),multiply(add(multiply(X_28,additive_identity),Y),add(multiply(X_28,additive_identity),Z))) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
multiply(Y,add(Y,X_28)) = Y,
inference(subst,[],[refute_0_234:[bind(X_37,$fot(Y)),bind(X_38,$fot(X_28))]]) ).
cnf(refute_0_334,plain,
multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)) = multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)),
introduced(tautology,[refl,[$fot(multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)))]]) ).
cnf(refute_0_335,plain,
( multiply(Y,add(Y,X_28)) != Y
| multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)) != multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z))
| multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)) = multiply(Y,add(multiply(X_28,additive_identity),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)),multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z))) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_336,plain,
( multiply(Y,add(Y,X_28)) != Y
| multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)) = multiply(Y,add(multiply(X_28,additive_identity),Z)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)),multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)) = multiply(Y,add(multiply(X_28,additive_identity),Z)),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,X_28)),Y) )],[refute_0_333,refute_0_336]) ).
cnf(refute_0_338,plain,
( multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)) != multiply(Y,add(multiply(X_28,additive_identity),Z))
| add(multiply(X_28,additive_identity),multiply(Y,Z)) != multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z))
| add(multiply(X_28,additive_identity),multiply(Y,Z)) = multiply(Y,add(multiply(X_28,additive_identity),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_28,additive_identity),multiply(Y,Z)),multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z))) ),[1],$fot(multiply(Y,add(multiply(X_28,additive_identity),Z)))]]) ).
cnf(refute_0_339,plain,
( add(multiply(X_28,additive_identity),multiply(Y,Z)) != multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z))
| add(multiply(X_28,additive_identity),multiply(Y,Z)) = multiply(Y,add(multiply(X_28,additive_identity),Z)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z)),multiply(Y,add(multiply(X_28,additive_identity),Z))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
add(multiply(X_28,additive_identity),multiply(Y,Z)) = multiply(Y,add(multiply(X_28,additive_identity),Z)),
inference(resolve,[$cnf( $equal(add(multiply(X_28,additive_identity),multiply(Y,Z)),multiply(multiply(Y,add(Y,X_28)),add(multiply(X_28,additive_identity),Z))) )],[refute_0_332,refute_0_339]) ).
cnf(refute_0_341,plain,
add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))),
inference(subst,[],[refute_0_340:[bind(Z,$fot(inverse(multiply(additive_identity,X_30)))),bind(X_28,$fot(X_30))]]) ).
cnf(refute_0_342,plain,
( multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) != Y
| add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) != multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))))
| add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = Y ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))))),bind(Y0,$fot(multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_343,plain,
( multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))) != Y
| add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = Y ),
inference(resolve,[$cnf( $equal(add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))),multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30))))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) = Y,
inference(resolve,[$cnf( $equal(multiply(Y,add(multiply(X_30,additive_identity),inverse(multiply(additive_identity,X_30)))),Y) )],[refute_0_327,refute_0_343]) ).
cnf(refute_0_345,plain,
( add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) != Y
| add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) != add(multiply(X_30,additive_identity),Y)
| Y = add(multiply(X_30,additive_identity),Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))),add(multiply(X_30,additive_identity),Y)) ),[0],$fot(Y)]]) ).
cnf(refute_0_346,plain,
( add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))) != add(multiply(X_30,additive_identity),Y)
| Y = add(multiply(X_30,additive_identity),Y) ),
inference(resolve,[$cnf( $equal(add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))),Y) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
Y = add(multiply(X_30,additive_identity),Y),
inference(resolve,[$cnf( $equal(add(multiply(X_30,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_30)))),add(multiply(X_30,additive_identity),Y)) )],[refute_0_319,refute_0_346]) ).
cnf(refute_0_348,plain,
( Y != add(multiply(X_30,additive_identity),Y)
| add(multiply(X_30,additive_identity),Y) = Y ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(Y)),bind(Y0,$fot(add(multiply(X_30,additive_identity),Y)))]]) ).
cnf(refute_0_349,plain,
add(multiply(X_30,additive_identity),Y) = Y,
inference(resolve,[$cnf( $equal(Y,add(multiply(X_30,additive_identity),Y)) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)) = multiply(X_19,additive_identity),
inference(subst,[],[refute_0_349:[bind(Y,$fot(multiply(X_19,additive_identity))),bind(X_30,$fot(X_34))]]) ).
cnf(refute_0_351,plain,
( add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)) != multiply(X_19,additive_identity)
| additive_identity != add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))
| additive_identity = multiply(X_19,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(additive_identity,add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))) ),[1],$fot(multiply(X_19,additive_identity))]]) ).
cnf(refute_0_352,plain,
( additive_identity != add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))
| additive_identity = multiply(X_19,additive_identity) ),
inference(resolve,[$cnf( $equal(add(multiply(X_34,additive_identity),multiply(X_19,additive_identity)),multiply(X_19,additive_identity)) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
( multiply(additive_identity,add(X_19,X_34)) != add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))
| additive_identity = multiply(X_19,additive_identity) ),
inference(resolve,[$cnf( $equal(additive_identity,add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))) )],[refute_0_270,refute_0_352]) ).
cnf(refute_0_354,plain,
additive_identity = multiply(X_19,additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_19,X_34)),add(multiply(X_34,additive_identity),multiply(X_19,additive_identity))) )],[refute_0_156,refute_0_353]) ).
cnf(refute_0_355,plain,
( additive_identity != multiply(X_19,additive_identity)
| multiply(X_19,additive_identity) = additive_identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(X_19,additive_identity)))]]) ).
cnf(refute_0_356,plain,
multiply(X_19,additive_identity) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(X_19,additive_identity)) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
multiply(X_32,additive_identity) = additive_identity,
inference(subst,[],[refute_0_356:[bind(X_19,$fot(X_32))]]) ).
cnf(refute_0_358,plain,
add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),
introduced(tautology,[refl,[$fot(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)))]]) ).
cnf(refute_0_359,plain,
( multiply(X_32,additive_identity) != additive_identity
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) != add(inverse(inverse(X_32)),multiply(X_32,additive_identity))
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = add(inverse(inverse(X_32)),additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),add(inverse(inverse(X_32)),multiply(X_32,additive_identity))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_360,plain,
( multiply(X_32,additive_identity) != additive_identity
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = add(inverse(inverse(X_32)),additive_identity) ),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),add(inverse(inverse(X_32)),multiply(X_32,additive_identity))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = add(inverse(inverse(X_32)),additive_identity),
inference(resolve,[$cnf( $equal(multiply(X_32,additive_identity),additive_identity) )],[refute_0_357,refute_0_360]) ).
cnf(refute_0_362,plain,
( add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) != add(inverse(inverse(X_32)),additive_identity)
| add(inverse(inverse(X_32)),additive_identity) != inverse(inverse(X_32))
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = inverse(inverse(X_32)) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)))),bind(Y0,$fot(add(inverse(inverse(X_32)),additive_identity))),bind(Z0,$fot(inverse(inverse(X_32))))]]) ).
cnf(refute_0_363,plain,
( add(inverse(inverse(X_32)),additive_identity) != inverse(inverse(X_32))
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = inverse(inverse(X_32)) ),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),add(inverse(inverse(X_32)),additive_identity)) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) = inverse(inverse(X_32)),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_32)),additive_identity),inverse(inverse(X_32))) )],[refute_0_98,refute_0_363]) ).
cnf(refute_0_365,plain,
( add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) != multiply(X_32,inverse(inverse(X_32)))
| add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) != inverse(inverse(X_32))
| inverse(inverse(X_32)) = multiply(X_32,inverse(inverse(X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),multiply(X_32,inverse(inverse(X_32)))) ),[0],$fot(inverse(inverse(X_32)))]]) ).
cnf(refute_0_366,plain,
( add(inverse(inverse(X_32)),multiply(X_32,additive_identity)) != multiply(X_32,inverse(inverse(X_32)))
| inverse(inverse(X_32)) = multiply(X_32,inverse(inverse(X_32))) ),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),inverse(inverse(X_32))) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
inverse(inverse(X_32)) = multiply(X_32,inverse(inverse(X_32))),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_32)),multiply(X_32,additive_identity)),multiply(X_32,inverse(inverse(X_32)))) )],[refute_0_97,refute_0_366]) ).
cnf(refute_0_368,plain,
( inverse(inverse(X_32)) != multiply(X_32,inverse(inverse(X_32)))
| multiply(X_32,inverse(inverse(X_32))) = inverse(inverse(X_32)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(inverse(X_32)))),bind(Y0,$fot(multiply(X_32,inverse(inverse(X_32)))))]]) ).
cnf(refute_0_369,plain,
multiply(X_32,inverse(inverse(X_32))) = inverse(inverse(X_32)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_32)),multiply(X_32,inverse(inverse(X_32)))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
multiply(X_45,inverse(inverse(X_45))) = inverse(inverse(X_45)),
inference(subst,[],[refute_0_369:[bind(X_32,$fot(X_45))]]) ).
cnf(refute_0_371,plain,
( X_45 != multiply(X_45,inverse(inverse(X_45)))
| multiply(X_45,inverse(inverse(X_45))) != inverse(inverse(X_45))
| X_45 = inverse(inverse(X_45)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_45,inverse(inverse(X_45))) ),[0],$fot(multiply(X_45,inverse(inverse(X_45))))]]) ).
cnf(refute_0_372,plain,
( X_45 != multiply(X_45,inverse(inverse(X_45)))
| X_45 = inverse(inverse(X_45)) ),
inference(resolve,[$cnf( $equal(multiply(X_45,inverse(inverse(X_45))),inverse(inverse(X_45))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
( multiply(X_45,multiplicative_identity) != multiply(X_45,inverse(inverse(X_45)))
| X_45 = inverse(inverse(X_45)) ),
inference(resolve,[$cnf( $equal(X_45,multiply(X_45,inverse(inverse(X_45)))) )],[refute_0_59,refute_0_372]) ).
cnf(refute_0_374,plain,
X_45 = inverse(inverse(X_45)),
inference(resolve,[$cnf( $equal(multiply(X_45,multiplicative_identity),multiply(X_45,inverse(inverse(X_45)))) )],[refute_0_56,refute_0_373]) ).
cnf(refute_0_375,plain,
( X_45 != inverse(inverse(X_45))
| inverse(inverse(X_45)) = X_45 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_45)),bind(Y0,$fot(inverse(inverse(X_45))))]]) ).
cnf(refute_0_376,plain,
inverse(inverse(X_45)) = X_45,
inference(resolve,[$cnf( $equal(X_45,inverse(inverse(X_45))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
inverse(inverse(X_10)) = X_10,
inference(subst,[],[refute_0_376:[bind(X_45,$fot(X_10))]]) ).
cnf(refute_0_378,plain,
add(inverse(inverse(X_10)),X_46) = add(inverse(inverse(X_10)),X_46),
introduced(tautology,[refl,[$fot(add(inverse(inverse(X_10)),X_46))]]) ).
cnf(refute_0_379,plain,
( add(inverse(inverse(X_10)),X_46) != add(inverse(inverse(X_10)),X_46)
| inverse(inverse(X_10)) != X_10
| add(inverse(inverse(X_10)),X_46) = add(X_10,X_46) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_10)),X_46),add(inverse(inverse(X_10)),X_46)) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_380,plain,
( inverse(inverse(X_10)) != X_10
| add(inverse(inverse(X_10)),X_46) = add(X_10,X_46) ),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_10)),X_46),add(inverse(inverse(X_10)),X_46)) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
add(inverse(inverse(X_10)),X_46) = add(X_10,X_46),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),X_10) )],[refute_0_377,refute_0_380]) ).
cnf(refute_0_382,plain,
add(X_10,add(inverse(inverse(X_10)),X_46)) = add(X_10,add(inverse(inverse(X_10)),X_46)),
introduced(tautology,[refl,[$fot(add(X_10,add(inverse(inverse(X_10)),X_46)))]]) ).
cnf(refute_0_383,plain,
( add(X_10,add(inverse(inverse(X_10)),X_46)) != add(X_10,add(inverse(inverse(X_10)),X_46))
| add(inverse(inverse(X_10)),X_46) != add(X_10,X_46)
| add(X_10,add(inverse(inverse(X_10)),X_46)) = add(X_10,add(X_10,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,add(inverse(inverse(X_10)),X_46)),add(X_10,add(inverse(inverse(X_10)),X_46))) ),[1,1],$fot(add(X_10,X_46))]]) ).
cnf(refute_0_384,plain,
( add(inverse(inverse(X_10)),X_46) != add(X_10,X_46)
| add(X_10,add(inverse(inverse(X_10)),X_46)) = add(X_10,add(X_10,X_46)) ),
inference(resolve,[$cnf( $equal(add(X_10,add(inverse(inverse(X_10)),X_46)),add(X_10,add(inverse(inverse(X_10)),X_46))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
add(X_10,add(inverse(inverse(X_10)),X_46)) = add(X_10,add(X_10,X_46)),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_10)),X_46),add(X_10,X_46)) )],[refute_0_381,refute_0_384]) ).
cnf(refute_0_386,plain,
( add(X_10,X_46) != add(X_10,add(inverse(inverse(X_10)),X_46))
| add(X_10,add(inverse(inverse(X_10)),X_46)) != add(X_10,add(X_10,X_46))
| add(X_10,X_46) = add(X_10,add(X_10,X_46)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_10,X_46),add(X_10,add(X_10,X_46))) ),[0],$fot(add(X_10,add(inverse(inverse(X_10)),X_46)))]]) ).
cnf(refute_0_387,plain,
( add(X_10,X_46) != add(X_10,add(inverse(inverse(X_10)),X_46))
| add(X_10,X_46) = add(X_10,add(X_10,X_46)) ),
inference(resolve,[$cnf( $equal(add(X_10,add(inverse(inverse(X_10)),X_46)),add(X_10,add(X_10,X_46))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
add(X_10,X_46) = add(X_10,add(X_10,X_46)),
inference(resolve,[$cnf( $equal(add(X_10,X_46),add(X_10,add(inverse(inverse(X_10)),X_46))) )],[refute_0_51,refute_0_387]) ).
cnf(refute_0_389,plain,
add(X_11,X_70) = add(X_11,add(X_11,X_70)),
inference(subst,[],[refute_0_388:[bind(X_10,$fot(X_11)),bind(X_46,$fot(X_70))]]) ).
cnf(refute_0_390,plain,
( add(X_11,X_70) != add(X_11,add(X_11,X_70))
| add(X_11,add(X_11,X_70)) = add(X_11,X_70) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_11,X_70))),bind(Y0,$fot(add(X_11,add(X_11,X_70))))]]) ).
cnf(refute_0_391,plain,
add(X_11,add(X_11,X_70)) = add(X_11,X_70),
inference(resolve,[$cnf( $equal(add(X_11,X_70),add(X_11,add(X_11,X_70))) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
( add(X_11,add(X_11,X_70)) != add(X_11,X_70)
| add(add(X_11,X_70),multiply(X_11,X_12)) != multiply(add(X_11,add(X_11,X_70)),add(add(X_11,X_70),X_12))
| add(add(X_11,X_70),multiply(X_11,X_12)) = multiply(add(X_11,X_70),add(add(X_11,X_70),X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_11,X_70),multiply(X_11,X_12)),multiply(add(X_11,add(X_11,X_70)),add(add(X_11,X_70),X_12))) ),[1,0],$fot(add(X_11,X_70))]]) ).
cnf(refute_0_393,plain,
( add(add(X_11,X_70),multiply(X_11,X_12)) != multiply(add(X_11,add(X_11,X_70)),add(add(X_11,X_70),X_12))
| add(add(X_11,X_70),multiply(X_11,X_12)) = multiply(add(X_11,X_70),add(add(X_11,X_70),X_12)) ),
inference(resolve,[$cnf( $equal(add(X_11,add(X_11,X_70)),add(X_11,X_70)) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
add(add(X_11,X_70),multiply(X_11,X_12)) = multiply(add(X_11,X_70),add(add(X_11,X_70),X_12)),
inference(resolve,[$cnf( $equal(add(add(X_11,X_70),multiply(X_11,X_12)),multiply(add(X_11,add(X_11,X_70)),add(add(X_11,X_70),X_12))) )],[refute_0_16,refute_0_393]) ).
cnf(refute_0_395,plain,
multiply(add(X_11,X_70),add(add(X_11,X_70),X_12)) = add(X_11,X_70),
inference(subst,[],[refute_0_234:[bind(X_37,$fot(add(X_11,X_70))),bind(X_38,$fot(X_12))]]) ).
cnf(refute_0_396,plain,
( multiply(add(X_11,X_70),add(add(X_11,X_70),X_12)) != add(X_11,X_70)
| add(add(X_11,X_70),multiply(X_11,X_12)) != multiply(add(X_11,X_70),add(add(X_11,X_70),X_12))
| add(add(X_11,X_70),multiply(X_11,X_12)) = add(X_11,X_70) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_11,X_70),multiply(X_11,X_12)),multiply(add(X_11,X_70),add(add(X_11,X_70),X_12))) ),[1],$fot(add(X_11,X_70))]]) ).
cnf(refute_0_397,plain,
( add(add(X_11,X_70),multiply(X_11,X_12)) != multiply(add(X_11,X_70),add(add(X_11,X_70),X_12))
| add(add(X_11,X_70),multiply(X_11,X_12)) = add(X_11,X_70) ),
inference(resolve,[$cnf( $equal(multiply(add(X_11,X_70),add(add(X_11,X_70),X_12)),add(X_11,X_70)) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
add(add(X_11,X_70),multiply(X_11,X_12)) = add(X_11,X_70),
inference(resolve,[$cnf( $equal(add(add(X_11,X_70),multiply(X_11,X_12)),multiply(add(X_11,X_70),add(add(X_11,X_70),X_12))) )],[refute_0_394,refute_0_397]) ).
cnf(refute_0_399,plain,
add(add(add(X_10,X_11),X_121),multiply(add(X_10,X_11),add(X_12,X_10))) = add(add(X_10,X_11),X_121),
inference(subst,[],[refute_0_398:[bind(X_11,$fot(add(X_10,X_11))),bind(X_12,$fot(add(X_12,X_10))),bind(X_70,$fot(X_121))]]) ).
cnf(refute_0_400,plain,
add(X_12,X_10) = add(X_10,X_12),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_12)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_401,plain,
( add(X_12,X_10) != add(X_10,X_12)
| add(X_10,X_12) = add(X_12,X_10) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_12,X_10))),bind(Y0,$fot(add(X_10,X_12)))]]) ).
cnf(refute_0_402,plain,
add(X_10,X_12) = add(X_12,X_10),
inference(resolve,[$cnf( $equal(add(X_12,X_10),add(X_10,X_12)) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
( add(X_10,X_12) != add(X_12,X_10)
| add(X_10,multiply(X_11,X_12)) != multiply(add(X_10,X_11),add(X_10,X_12))
| add(X_10,multiply(X_11,X_12)) = multiply(add(X_10,X_11),add(X_12,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,X_12)),multiply(add(X_10,X_11),add(X_10,X_12))) ),[1,1],$fot(add(X_12,X_10))]]) ).
cnf(refute_0_404,plain,
( add(X_10,multiply(X_11,X_12)) != multiply(add(X_10,X_11),add(X_10,X_12))
| add(X_10,multiply(X_11,X_12)) = multiply(add(X_10,X_11),add(X_12,X_10)) ),
inference(resolve,[$cnf( $equal(add(X_10,X_12),add(X_12,X_10)) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
add(X_10,multiply(X_11,X_12)) = multiply(add(X_10,X_11),add(X_12,X_10)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,X_12)),multiply(add(X_10,X_11),add(X_10,X_12))) )],[refute_0_9,refute_0_404]) ).
cnf(refute_0_406,plain,
( add(X_10,multiply(X_11,X_12)) != multiply(add(X_10,X_11),add(X_12,X_10))
| multiply(add(X_10,X_11),add(X_12,X_10)) = add(X_10,multiply(X_11,X_12)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_10,multiply(X_11,X_12)))),bind(Y0,$fot(multiply(add(X_10,X_11),add(X_12,X_10))))]]) ).
cnf(refute_0_407,plain,
multiply(add(X_10,X_11),add(X_12,X_10)) = add(X_10,multiply(X_11,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,X_12)),multiply(add(X_10,X_11),add(X_12,X_10))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
( multiply(add(X_10,X_11),add(X_12,X_10)) != add(X_10,multiply(X_11,X_12))
| add(add(add(X_10,X_11),X_121),multiply(add(X_10,X_11),add(X_12,X_10))) != add(add(X_10,X_11),X_121)
| add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) = add(add(X_10,X_11),X_121) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(add(X_10,X_11),X_121),multiply(add(X_10,X_11),add(X_12,X_10))),add(add(X_10,X_11),X_121)) ),[0,1],$fot(add(X_10,multiply(X_11,X_12)))]]) ).
cnf(refute_0_409,plain,
( add(add(add(X_10,X_11),X_121),multiply(add(X_10,X_11),add(X_12,X_10))) != add(add(X_10,X_11),X_121)
| add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) = add(add(X_10,X_11),X_121) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),add(X_12,X_10)),add(X_10,multiply(X_11,X_12))) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) = add(add(X_10,X_11),X_121),
inference(resolve,[$cnf( $equal(add(add(add(X_10,X_11),X_121),multiply(add(X_10,X_11),add(X_12,X_10))),add(add(X_10,X_11),X_121)) )],[refute_0_399,refute_0_409]) ).
cnf(refute_0_411,plain,
( X_24 != add(X_24,X_24)
| add(X_24,X_24) = X_24 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_24)),bind(Y0,$fot(add(X_24,X_24)))]]) ).
cnf(refute_0_412,plain,
add(X_24,X_24) = X_24,
inference(resolve,[$cnf( $equal(X_24,add(X_24,X_24)) )],[refute_0_217,refute_0_411]) ).
cnf(refute_0_413,plain,
add(X_10,X_10) = X_10,
inference(subst,[],[refute_0_412:[bind(X_24,$fot(X_10))]]) ).
cnf(refute_0_414,plain,
add(X_11,add(X_10,X_10)) = add(X_11,add(X_10,X_10)),
introduced(tautology,[refl,[$fot(add(X_11,add(X_10,X_10)))]]) ).
cnf(refute_0_415,plain,
( add(X_10,X_10) != X_10
| add(X_11,add(X_10,X_10)) != add(X_11,add(X_10,X_10))
| add(X_11,add(X_10,X_10)) = add(X_11,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_11,add(X_10,X_10)),add(X_11,add(X_10,X_10))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_416,plain,
( add(X_10,X_10) != X_10
| add(X_11,add(X_10,X_10)) = add(X_11,X_10) ),
inference(resolve,[$cnf( $equal(add(X_11,add(X_10,X_10)),add(X_11,add(X_10,X_10))) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
add(X_11,add(X_10,X_10)) = add(X_11,X_10),
inference(resolve,[$cnf( $equal(add(X_10,X_10),X_10) )],[refute_0_413,refute_0_416]) ).
cnf(refute_0_418,plain,
multiply(Y,add(Y,Z)) = Y,
inference(subst,[],[refute_0_234:[bind(X_37,$fot(Y)),bind(X_38,$fot(Z))]]) ).
cnf(refute_0_419,plain,
( multiply(Y,add(Y,Z)) != Y
| add(Y,multiply(Y,Z)) != multiply(Y,add(Y,Z))
| add(Y,multiply(Y,Z)) = Y ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(Y,add(Y,Z))) ),[1],$fot(Y)]]) ).
cnf(refute_0_420,plain,
( add(Y,multiply(Y,Z)) != multiply(Y,add(Y,Z))
| add(Y,multiply(Y,Z)) = Y ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,Z)),Y) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
add(Y,multiply(Y,Z)) = Y,
inference(resolve,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(Y,add(Y,Z))) )],[refute_0_223,refute_0_420]) ).
cnf(refute_0_422,plain,
add(add(X_60,X_59),multiply(add(X_60,X_59),add(X_59,X_61))) = add(X_60,X_59),
inference(subst,[],[refute_0_421:[bind(Y,$fot(add(X_60,X_59))),bind(Z,$fot(add(X_59,X_61)))]]) ).
cnf(refute_0_423,plain,
add(X_59,multiply(X_60,X_61)) = multiply(add(X_60,X_59),add(X_59,X_61)),
inference(subst,[],[refute_0_15:[bind(X_10,$fot(X_59)),bind(X_11,$fot(X_60)),bind(X_12,$fot(X_61))]]) ).
cnf(refute_0_424,plain,
( add(X_59,multiply(X_60,X_61)) != multiply(add(X_60,X_59),add(X_59,X_61))
| multiply(add(X_60,X_59),add(X_59,X_61)) = add(X_59,multiply(X_60,X_61)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_59,multiply(X_60,X_61)))),bind(Y0,$fot(multiply(add(X_60,X_59),add(X_59,X_61))))]]) ).
cnf(refute_0_425,plain,
multiply(add(X_60,X_59),add(X_59,X_61)) = add(X_59,multiply(X_60,X_61)),
inference(resolve,[$cnf( $equal(add(X_59,multiply(X_60,X_61)),multiply(add(X_60,X_59),add(X_59,X_61))) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
( multiply(add(X_60,X_59),add(X_59,X_61)) != add(X_59,multiply(X_60,X_61))
| add(add(X_60,X_59),multiply(add(X_60,X_59),add(X_59,X_61))) != add(X_60,X_59)
| add(add(X_60,X_59),add(X_59,multiply(X_60,X_61))) = add(X_60,X_59) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_60,X_59),multiply(add(X_60,X_59),add(X_59,X_61))),add(X_60,X_59)) ),[0,1],$fot(add(X_59,multiply(X_60,X_61)))]]) ).
cnf(refute_0_427,plain,
( add(add(X_60,X_59),multiply(add(X_60,X_59),add(X_59,X_61))) != add(X_60,X_59)
| add(add(X_60,X_59),add(X_59,multiply(X_60,X_61))) = add(X_60,X_59) ),
inference(resolve,[$cnf( $equal(multiply(add(X_60,X_59),add(X_59,X_61)),add(X_59,multiply(X_60,X_61))) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
add(add(X_60,X_59),add(X_59,multiply(X_60,X_61))) = add(X_60,X_59),
inference(resolve,[$cnf( $equal(add(add(X_60,X_59),multiply(add(X_60,X_59),add(X_59,X_61))),add(X_60,X_59)) )],[refute_0_422,refute_0_427]) ).
cnf(refute_0_429,plain,
add(add(add(X_10,X_11),X_116),add(X_116,multiply(add(X_10,X_11),add(X_12,X_10)))) = add(add(X_10,X_11),X_116),
inference(subst,[],[refute_0_428:[bind(X_59,$fot(X_116)),bind(X_60,$fot(add(X_10,X_11))),bind(X_61,$fot(add(X_12,X_10)))]]) ).
cnf(refute_0_430,plain,
( multiply(add(X_10,X_11),add(X_12,X_10)) != add(X_10,multiply(X_11,X_12))
| add(add(add(X_10,X_11),X_116),add(X_116,multiply(add(X_10,X_11),add(X_12,X_10)))) != add(add(X_10,X_11),X_116)
| add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(add(X_10,X_11),X_116) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(add(X_10,X_11),X_116),add(X_116,multiply(add(X_10,X_11),add(X_12,X_10)))),add(add(X_10,X_11),X_116)) ),[0,1,1],$fot(add(X_10,multiply(X_11,X_12)))]]) ).
cnf(refute_0_431,plain,
( add(add(add(X_10,X_11),X_116),add(X_116,multiply(add(X_10,X_11),add(X_12,X_10)))) != add(add(X_10,X_11),X_116)
| add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(add(X_10,X_11),X_116) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),add(X_12,X_10)),add(X_10,multiply(X_11,X_12))) )],[refute_0_407,refute_0_430]) ).
cnf(refute_0_432,plain,
add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(add(X_10,X_11),X_116),
inference(resolve,[$cnf( $equal(add(add(add(X_10,X_11),X_116),add(X_116,multiply(add(X_10,X_11),add(X_12,X_10)))),add(add(X_10,X_11),X_116)) )],[refute_0_429,refute_0_431]) ).
cnf(refute_0_433,plain,
add(Z,multiply(Y,Z)) = multiply(add(Z,Y),add(Z,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Z))]]) ).
cnf(refute_0_434,plain,
Z = add(Z,Z),
inference(subst,[],[refute_0_217:[bind(X_24,$fot(Z))]]) ).
cnf(refute_0_435,plain,
( Z != add(Z,Z)
| add(Z,Z) = Z ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(Z)),bind(Y0,$fot(add(Z,Z)))]]) ).
cnf(refute_0_436,plain,
add(Z,Z) = Z,
inference(resolve,[$cnf( $equal(Z,add(Z,Z)) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
( add(Z,Z) != Z
| add(Z,multiply(Y,Z)) != multiply(add(Z,Y),add(Z,Z))
| add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),add(Z,Z))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_438,plain,
( add(Z,multiply(Y,Z)) != multiply(add(Z,Y),add(Z,Z))
| add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z) ),
inference(resolve,[$cnf( $equal(add(Z,Z),Z) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z),
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),add(Z,Z))) )],[refute_0_433,refute_0_438]) ).
cnf(refute_0_440,plain,
multiply(add(Z,Y),Z) = multiply(Z,add(Z,Y)),
inference(subst,[],[refute_0_66:[bind(X,$fot(Z)),bind(Y,$fot(add(Z,Y)))]]) ).
cnf(refute_0_441,plain,
( multiply(add(Z,Y),Z) != multiply(Z,add(Z,Y))
| add(Z,multiply(Y,Z)) != multiply(add(Z,Y),Z)
| add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),Z)) ),[1],$fot(multiply(Z,add(Z,Y)))]]) ).
cnf(refute_0_442,plain,
( add(Z,multiply(Y,Z)) != multiply(add(Z,Y),Z)
| add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(add(Z,Y),Z),multiply(Z,add(Z,Y))) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)),
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),Z)) )],[refute_0_439,refute_0_442]) ).
cnf(refute_0_444,plain,
multiply(Z,add(Z,Y)) = Z,
inference(subst,[],[refute_0_234:[bind(X_37,$fot(Z)),bind(X_38,$fot(Y))]]) ).
cnf(refute_0_445,plain,
( multiply(Z,add(Z,Y)) != Z
| add(Z,multiply(Y,Z)) != multiply(Z,add(Z,Y))
| add(Z,multiply(Y,Z)) = Z ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(Z,add(Z,Y))) ),[1],$fot(Z)]]) ).
cnf(refute_0_446,plain,
( add(Z,multiply(Y,Z)) != multiply(Z,add(Z,Y))
| add(Z,multiply(Y,Z)) = Z ),
inference(resolve,[$cnf( $equal(multiply(Z,add(Z,Y)),Z) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
add(Z,multiply(Y,Z)) = Z,
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(Z,add(Z,Y))) )],[refute_0_443,refute_0_446]) ).
cnf(refute_0_448,plain,
add(add(add(Y,X_113),X_115),multiply(Y,add(add(Y,X_113),X_115))) = add(add(Y,X_113),X_115),
inference(subst,[],[refute_0_447:[bind(Z,$fot(add(add(Y,X_113),X_115)))]]) ).
cnf(refute_0_449,plain,
multiply(X_37,add(add(X_37,X_21),X_39)) = add(multiply(X_37,add(X_37,X_21)),multiply(X_37,X_39)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_37)),bind(Y,$fot(add(X_37,X_21))),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_450,plain,
add(multiply(additive_identity,X_21),X_37) = multiply(X_37,add(X_37,X_21)),
inference(subst,[],[refute_0_107:[bind(Y,$fot(X_37))]]) ).
cnf(refute_0_451,plain,
( add(multiply(additive_identity,X_21),X_37) != multiply(X_37,add(X_37,X_21))
| multiply(X_37,add(X_37,X_21)) = add(multiply(additive_identity,X_21),X_37) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(multiply(additive_identity,X_21),X_37))),bind(Y0,$fot(multiply(X_37,add(X_37,X_21))))]]) ).
cnf(refute_0_452,plain,
multiply(X_37,add(X_37,X_21)) = add(multiply(additive_identity,X_21),X_37),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_21),X_37),multiply(X_37,add(X_37,X_21))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
( multiply(X_37,add(X_37,X_21)) != add(multiply(additive_identity,X_21),X_37)
| multiply(X_37,add(add(X_37,X_21),X_39)) != add(multiply(X_37,add(X_37,X_21)),multiply(X_37,X_39))
| multiply(X_37,add(add(X_37,X_21),X_39)) = add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,add(add(X_37,X_21),X_39)),add(multiply(X_37,add(X_37,X_21)),multiply(X_37,X_39))) ),[1,0],$fot(add(multiply(additive_identity,X_21),X_37))]]) ).
cnf(refute_0_454,plain,
( multiply(X_37,add(add(X_37,X_21),X_39)) != add(multiply(X_37,add(X_37,X_21)),multiply(X_37,X_39))
| multiply(X_37,add(add(X_37,X_21),X_39)) = add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) ),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_37,X_21)),add(multiply(additive_identity,X_21),X_37)) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
multiply(X_37,add(add(X_37,X_21),X_39)) = add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)),
inference(resolve,[$cnf( $equal(multiply(X_37,add(add(X_37,X_21),X_39)),add(multiply(X_37,add(X_37,X_21)),multiply(X_37,X_39))) )],[refute_0_449,refute_0_454]) ).
cnf(refute_0_456,plain,
add(X_37,multiply(X_37,X_39)) = X_37,
inference(subst,[],[refute_0_421:[bind(Y,$fot(X_37)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_457,plain,
add(additive_identity,X_37) = X_37,
inference(subst,[],[refute_0_39:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_458,plain,
multiply(additive_identity,X_21) = additive_identity,
inference(subst,[],[refute_0_267:[bind(X_39,$fot(X_21))]]) ).
cnf(refute_0_459,plain,
add(multiply(additive_identity,X_21),X_37) = add(multiply(additive_identity,X_21),X_37),
introduced(tautology,[refl,[$fot(add(multiply(additive_identity,X_21),X_37))]]) ).
cnf(refute_0_460,plain,
( multiply(additive_identity,X_21) != additive_identity
| add(multiply(additive_identity,X_21),X_37) != add(multiply(additive_identity,X_21),X_37)
| add(multiply(additive_identity,X_21),X_37) = add(additive_identity,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_21),X_37),add(multiply(additive_identity,X_21),X_37)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_461,plain,
( multiply(additive_identity,X_21) != additive_identity
| add(multiply(additive_identity,X_21),X_37) = add(additive_identity,X_37) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_21),X_37),add(multiply(additive_identity,X_21),X_37)) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
add(multiply(additive_identity,X_21),X_37) = add(additive_identity,X_37),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_21),additive_identity) )],[refute_0_458,refute_0_461]) ).
cnf(refute_0_463,plain,
( add(multiply(additive_identity,X_21),X_37) != add(additive_identity,X_37)
| add(additive_identity,X_37) != X_37
| add(multiply(additive_identity,X_21),X_37) = X_37 ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(multiply(additive_identity,X_21),X_37))),bind(Y0,$fot(add(additive_identity,X_37))),bind(Z0,$fot(X_37))]]) ).
cnf(refute_0_464,plain,
( add(additive_identity,X_37) != X_37
| add(multiply(additive_identity,X_21),X_37) = X_37 ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_21),X_37),add(additive_identity,X_37)) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
add(multiply(additive_identity,X_21),X_37) = X_37,
inference(resolve,[$cnf( $equal(add(additive_identity,X_37),X_37) )],[refute_0_457,refute_0_464]) ).
cnf(refute_0_466,plain,
add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) = add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)),
introduced(tautology,[refl,[$fot(add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)))]]) ).
cnf(refute_0_467,plain,
( add(multiply(additive_identity,X_21),X_37) != X_37
| add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) != add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39))
| add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) = add(X_37,multiply(X_37,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)),add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39))) ),[1,0],$fot(X_37)]]) ).
cnf(refute_0_468,plain,
( add(multiply(additive_identity,X_21),X_37) != X_37
| add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) = add(X_37,multiply(X_37,X_39)) ),
inference(resolve,[$cnf( $equal(add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)),add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39))) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) = add(X_37,multiply(X_37,X_39)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_21),X_37),X_37) )],[refute_0_465,refute_0_468]) ).
cnf(refute_0_470,plain,
( add(X_37,multiply(X_37,X_39)) != X_37
| add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) != add(X_37,multiply(X_37,X_39))
| add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) = X_37 ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)))),bind(Y0,$fot(add(X_37,multiply(X_37,X_39)))),bind(Z0,$fot(X_37))]]) ).
cnf(refute_0_471,plain,
( add(X_37,multiply(X_37,X_39)) != X_37
| add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) = X_37 ),
inference(resolve,[$cnf( $equal(add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)),add(X_37,multiply(X_37,X_39))) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) = X_37,
inference(resolve,[$cnf( $equal(add(X_37,multiply(X_37,X_39)),X_37) )],[refute_0_456,refute_0_471]) ).
cnf(refute_0_473,plain,
( multiply(X_37,add(add(X_37,X_21),X_39)) != add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39))
| add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)) != X_37
| multiply(X_37,add(add(X_37,X_21),X_39)) = X_37 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_37,add(add(X_37,X_21),X_39)),X_37) ),[0],$fot(add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)))]]) ).
cnf(refute_0_474,plain,
( multiply(X_37,add(add(X_37,X_21),X_39)) != add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39))
| multiply(X_37,add(add(X_37,X_21),X_39)) = X_37 ),
inference(resolve,[$cnf( $equal(add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39)),X_37) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
multiply(X_37,add(add(X_37,X_21),X_39)) = X_37,
inference(resolve,[$cnf( $equal(multiply(X_37,add(add(X_37,X_21),X_39)),add(add(multiply(additive_identity,X_21),X_37),multiply(X_37,X_39))) )],[refute_0_455,refute_0_474]) ).
cnf(refute_0_476,plain,
multiply(Y,add(add(Y,X_113),X_115)) = Y,
inference(subst,[],[refute_0_475:[bind(X_21,$fot(X_113)),bind(X_37,$fot(Y)),bind(X_39,$fot(X_115))]]) ).
cnf(refute_0_477,plain,
( multiply(Y,add(add(Y,X_113),X_115)) != Y
| add(add(add(Y,X_113),X_115),multiply(Y,add(add(Y,X_113),X_115))) != add(add(Y,X_113),X_115)
| add(add(add(Y,X_113),X_115),Y) = add(add(Y,X_113),X_115) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(add(Y,X_113),X_115),multiply(Y,add(add(Y,X_113),X_115))),add(add(Y,X_113),X_115)) ),[0,1],$fot(Y)]]) ).
cnf(refute_0_478,plain,
( add(add(add(Y,X_113),X_115),multiply(Y,add(add(Y,X_113),X_115))) != add(add(Y,X_113),X_115)
| add(add(add(Y,X_113),X_115),Y) = add(add(Y,X_113),X_115) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(add(Y,X_113),X_115)),Y) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
add(add(add(Y,X_113),X_115),Y) = add(add(Y,X_113),X_115),
inference(resolve,[$cnf( $equal(add(add(add(Y,X_113),X_115),multiply(Y,add(add(Y,X_113),X_115))),add(add(Y,X_113),X_115)) )],[refute_0_448,refute_0_478]) ).
cnf(refute_0_480,plain,
add(X_10,multiply(inverse(X_10),add(X_44,inverse(inverse(X_10))))) = add(X_10,add(X_44,inverse(inverse(X_10)))),
inference(subst,[],[refute_0_29:[bind(X_12,$fot(add(X_44,inverse(inverse(X_10)))))]]) ).
cnf(refute_0_481,plain,
multiply(X_37,add(X_38,inverse(X_37))) = add(multiply(X_37,X_38),multiply(X_37,inverse(X_37))),
inference(subst,[],[distributivity2:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(Z,$fot(inverse(X_37)))]]) ).
cnf(refute_0_482,plain,
( multiply(X_37,add(X_38,inverse(X_37))) != add(multiply(X_37,X_38),multiply(X_37,inverse(X_37)))
| multiply(X_37,inverse(X_37)) != additive_identity
| multiply(X_37,add(X_38,inverse(X_37))) = add(multiply(X_37,X_38),additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,add(X_38,inverse(X_37))),add(multiply(X_37,X_38),multiply(X_37,inverse(X_37)))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_483,plain,
( multiply(X_37,add(X_38,inverse(X_37))) != add(multiply(X_37,X_38),multiply(X_37,inverse(X_37)))
| multiply(X_37,add(X_38,inverse(X_37))) = add(multiply(X_37,X_38),additive_identity) ),
inference(resolve,[$cnf( $equal(multiply(X_37,inverse(X_37)),additive_identity) )],[refute_0_32,refute_0_482]) ).
cnf(refute_0_484,plain,
multiply(X_37,add(X_38,inverse(X_37))) = add(multiply(X_37,X_38),additive_identity),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,inverse(X_37))),add(multiply(X_37,X_38),multiply(X_37,inverse(X_37)))) )],[refute_0_481,refute_0_483]) ).
cnf(refute_0_485,plain,
add(multiply(X_37,X_38),additive_identity) = multiply(X_37,X_38),
inference(subst,[],[additive_id1:[bind(X,$fot(multiply(X_37,X_38)))]]) ).
cnf(refute_0_486,plain,
( multiply(X_37,add(X_38,inverse(X_37))) != add(multiply(X_37,X_38),additive_identity)
| add(multiply(X_37,X_38),additive_identity) != multiply(X_37,X_38)
| multiply(X_37,add(X_38,inverse(X_37))) = multiply(X_37,X_38) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_37,add(X_38,inverse(X_37))),multiply(X_37,X_38)) ),[0],$fot(add(multiply(X_37,X_38),additive_identity))]]) ).
cnf(refute_0_487,plain,
( multiply(X_37,add(X_38,inverse(X_37))) != add(multiply(X_37,X_38),additive_identity)
| multiply(X_37,add(X_38,inverse(X_37))) = multiply(X_37,X_38) ),
inference(resolve,[$cnf( $equal(add(multiply(X_37,X_38),additive_identity),multiply(X_37,X_38)) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
multiply(X_37,add(X_38,inverse(X_37))) = multiply(X_37,X_38),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,inverse(X_37))),add(multiply(X_37,X_38),additive_identity)) )],[refute_0_484,refute_0_487]) ).
cnf(refute_0_489,plain,
multiply(inverse(X_10),add(X_44,inverse(inverse(X_10)))) = multiply(inverse(X_10),X_44),
inference(subst,[],[refute_0_488:[bind(X_37,$fot(inverse(X_10))),bind(X_38,$fot(X_44))]]) ).
cnf(refute_0_490,plain,
( multiply(inverse(X_10),add(X_44,inverse(inverse(X_10)))) != multiply(inverse(X_10),X_44)
| add(X_10,multiply(inverse(X_10),add(X_44,inverse(inverse(X_10))))) != add(X_10,add(X_44,inverse(inverse(X_10))))
| add(X_10,multiply(inverse(X_10),X_44)) = add(X_10,add(X_44,inverse(inverse(X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),add(X_44,inverse(inverse(X_10))))),add(X_10,add(X_44,inverse(inverse(X_10))))) ),[0,1],$fot(multiply(inverse(X_10),X_44))]]) ).
cnf(refute_0_491,plain,
( add(X_10,multiply(inverse(X_10),add(X_44,inverse(inverse(X_10))))) != add(X_10,add(X_44,inverse(inverse(X_10))))
| add(X_10,multiply(inverse(X_10),X_44)) = add(X_10,add(X_44,inverse(inverse(X_10)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_10),add(X_44,inverse(inverse(X_10)))),multiply(inverse(X_10),X_44)) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
add(X_10,multiply(inverse(X_10),X_44)) = add(X_10,add(X_44,inverse(inverse(X_10)))),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),add(X_44,inverse(inverse(X_10))))),add(X_10,add(X_44,inverse(inverse(X_10))))) )],[refute_0_480,refute_0_491]) ).
cnf(refute_0_493,plain,
add(X_10,multiply(inverse(X_10),X_44)) = add(X_10,X_44),
inference(subst,[],[refute_0_29:[bind(X_12,$fot(X_44))]]) ).
cnf(refute_0_494,plain,
( add(X_10,multiply(inverse(X_10),X_44)) != add(X_10,X_44)
| add(X_10,multiply(inverse(X_10),X_44)) != add(X_10,add(X_44,inverse(inverse(X_10))))
| add(X_10,X_44) = add(X_10,add(X_44,inverse(inverse(X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_44)),add(X_10,add(X_44,inverse(inverse(X_10))))) ),[0],$fot(add(X_10,X_44))]]) ).
cnf(refute_0_495,plain,
( add(X_10,multiply(inverse(X_10),X_44)) != add(X_10,add(X_44,inverse(inverse(X_10))))
| add(X_10,X_44) = add(X_10,add(X_44,inverse(inverse(X_10)))) ),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_44)),add(X_10,X_44)) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
add(X_10,X_44) = add(X_10,add(X_44,inverse(inverse(X_10)))),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_44)),add(X_10,add(X_44,inverse(inverse(X_10))))) )],[refute_0_492,refute_0_495]) ).
cnf(refute_0_497,plain,
add(X_44,inverse(inverse(X_10))) = add(X_44,inverse(inverse(X_10))),
introduced(tautology,[refl,[$fot(add(X_44,inverse(inverse(X_10))))]]) ).
cnf(refute_0_498,plain,
( add(X_44,inverse(inverse(X_10))) != add(X_44,inverse(inverse(X_10)))
| inverse(inverse(X_10)) != X_10
| add(X_44,inverse(inverse(X_10))) = add(X_44,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_44,inverse(inverse(X_10))),add(X_44,inverse(inverse(X_10)))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_499,plain,
( inverse(inverse(X_10)) != X_10
| add(X_44,inverse(inverse(X_10))) = add(X_44,X_10) ),
inference(resolve,[$cnf( $equal(add(X_44,inverse(inverse(X_10))),add(X_44,inverse(inverse(X_10)))) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
add(X_44,inverse(inverse(X_10))) = add(X_44,X_10),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),X_10) )],[refute_0_377,refute_0_499]) ).
cnf(refute_0_501,plain,
add(X_10,add(X_44,inverse(inverse(X_10)))) = add(X_10,add(X_44,inverse(inverse(X_10)))),
introduced(tautology,[refl,[$fot(add(X_10,add(X_44,inverse(inverse(X_10)))))]]) ).
cnf(refute_0_502,plain,
( add(X_10,add(X_44,inverse(inverse(X_10)))) != add(X_10,add(X_44,inverse(inverse(X_10))))
| add(X_44,inverse(inverse(X_10))) != add(X_44,X_10)
| add(X_10,add(X_44,inverse(inverse(X_10)))) = add(X_10,add(X_44,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,add(X_44,inverse(inverse(X_10)))),add(X_10,add(X_44,inverse(inverse(X_10))))) ),[1,1],$fot(add(X_44,X_10))]]) ).
cnf(refute_0_503,plain,
( add(X_44,inverse(inverse(X_10))) != add(X_44,X_10)
| add(X_10,add(X_44,inverse(inverse(X_10)))) = add(X_10,add(X_44,X_10)) ),
inference(resolve,[$cnf( $equal(add(X_10,add(X_44,inverse(inverse(X_10)))),add(X_10,add(X_44,inverse(inverse(X_10))))) )],[refute_0_501,refute_0_502]) ).
cnf(refute_0_504,plain,
add(X_10,add(X_44,inverse(inverse(X_10)))) = add(X_10,add(X_44,X_10)),
inference(resolve,[$cnf( $equal(add(X_44,inverse(inverse(X_10))),add(X_44,X_10)) )],[refute_0_500,refute_0_503]) ).
cnf(refute_0_505,plain,
( add(X_10,X_44) != add(X_10,add(X_44,inverse(inverse(X_10))))
| add(X_10,add(X_44,inverse(inverse(X_10)))) != add(X_10,add(X_44,X_10))
| add(X_10,X_44) = add(X_10,add(X_44,X_10)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_10,X_44),add(X_10,add(X_44,X_10))) ),[0],$fot(add(X_10,add(X_44,inverse(inverse(X_10)))))]]) ).
cnf(refute_0_506,plain,
( add(X_10,X_44) != add(X_10,add(X_44,inverse(inverse(X_10))))
| add(X_10,X_44) = add(X_10,add(X_44,X_10)) ),
inference(resolve,[$cnf( $equal(add(X_10,add(X_44,inverse(inverse(X_10)))),add(X_10,add(X_44,X_10))) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
add(X_10,X_44) = add(X_10,add(X_44,X_10)),
inference(resolve,[$cnf( $equal(add(X_10,X_44),add(X_10,add(X_44,inverse(inverse(X_10))))) )],[refute_0_496,refute_0_506]) ).
cnf(refute_0_508,plain,
add(multiply(X_11,inverse(X_55)),X_55) = add(multiply(X_11,inverse(X_55)),add(X_55,multiply(X_11,inverse(X_55)))),
inference(subst,[],[refute_0_507:[bind(X_10,$fot(multiply(X_11,inverse(X_55)))),bind(X_44,$fot(X_55))]]) ).
cnf(refute_0_509,plain,
add(X_55,multiply(X_11,inverse(X_55))) = add(X_55,X_11),
inference(subst,[],[refute_0_208:[bind(X_10,$fot(X_55))]]) ).
cnf(refute_0_510,plain,
( add(X_55,multiply(X_11,inverse(X_55))) != add(X_55,X_11)
| add(multiply(X_11,inverse(X_55)),X_55) != add(multiply(X_11,inverse(X_55)),add(X_55,multiply(X_11,inverse(X_55))))
| add(multiply(X_11,inverse(X_55)),X_55) = add(multiply(X_11,inverse(X_55)),add(X_55,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_11,inverse(X_55)),X_55),add(multiply(X_11,inverse(X_55)),add(X_55,multiply(X_11,inverse(X_55))))) ),[1,1],$fot(add(X_55,X_11))]]) ).
cnf(refute_0_511,plain,
( add(multiply(X_11,inverse(X_55)),X_55) != add(multiply(X_11,inverse(X_55)),add(X_55,multiply(X_11,inverse(X_55))))
| add(multiply(X_11,inverse(X_55)),X_55) = add(multiply(X_11,inverse(X_55)),add(X_55,X_11)) ),
inference(resolve,[$cnf( $equal(add(X_55,multiply(X_11,inverse(X_55))),add(X_55,X_11)) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
add(multiply(X_11,inverse(X_55)),X_55) = add(multiply(X_11,inverse(X_55)),add(X_55,X_11)),
inference(resolve,[$cnf( $equal(add(multiply(X_11,inverse(X_55)),X_55),add(multiply(X_11,inverse(X_55)),add(X_55,multiply(X_11,inverse(X_55))))) )],[refute_0_508,refute_0_511]) ).
cnf(refute_0_513,plain,
add(multiply(X_11,inverse(X_55)),X_55) = add(X_55,multiply(X_11,inverse(X_55))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_55)),bind(Y,$fot(multiply(X_11,inverse(X_55))))]]) ).
cnf(refute_0_514,plain,
( add(X_55,multiply(X_11,inverse(X_55))) != add(X_55,X_11)
| add(multiply(X_11,inverse(X_55)),X_55) != add(X_55,multiply(X_11,inverse(X_55)))
| add(multiply(X_11,inverse(X_55)),X_55) = add(X_55,X_11) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(multiply(X_11,inverse(X_55)),X_55))),bind(Y0,$fot(add(X_55,multiply(X_11,inverse(X_55))))),bind(Z0,$fot(add(X_55,X_11)))]]) ).
cnf(refute_0_515,plain,
( add(X_55,multiply(X_11,inverse(X_55))) != add(X_55,X_11)
| add(multiply(X_11,inverse(X_55)),X_55) = add(X_55,X_11) ),
inference(resolve,[$cnf( $equal(add(multiply(X_11,inverse(X_55)),X_55),add(X_55,multiply(X_11,inverse(X_55)))) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
add(multiply(X_11,inverse(X_55)),X_55) = add(X_55,X_11),
inference(resolve,[$cnf( $equal(add(X_55,multiply(X_11,inverse(X_55))),add(X_55,X_11)) )],[refute_0_509,refute_0_515]) ).
cnf(refute_0_517,plain,
( add(multiply(X_11,inverse(X_55)),X_55) != add(X_55,X_11)
| add(multiply(X_11,inverse(X_55)),X_55) != add(multiply(X_11,inverse(X_55)),add(X_55,X_11))
| add(X_55,X_11) = add(multiply(X_11,inverse(X_55)),add(X_55,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_11,inverse(X_55)),X_55),add(multiply(X_11,inverse(X_55)),add(X_55,X_11))) ),[0],$fot(add(X_55,X_11))]]) ).
cnf(refute_0_518,plain,
( add(multiply(X_11,inverse(X_55)),X_55) != add(multiply(X_11,inverse(X_55)),add(X_55,X_11))
| add(X_55,X_11) = add(multiply(X_11,inverse(X_55)),add(X_55,X_11)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_11,inverse(X_55)),X_55),add(X_55,X_11)) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
add(multiply(X_11,inverse(X_55)),add(X_55,X_11)) = add(add(X_55,X_11),multiply(X_11,inverse(X_55))),
inference(subst,[],[refute_0_4:[bind(X,$fot(add(X_55,X_11))),bind(Y,$fot(multiply(X_11,inverse(X_55))))]]) ).
cnf(refute_0_520,plain,
( add(X_55,X_11) != add(multiply(X_11,inverse(X_55)),add(X_55,X_11))
| add(multiply(X_11,inverse(X_55)),add(X_55,X_11)) != add(add(X_55,X_11),multiply(X_11,inverse(X_55)))
| add(X_55,X_11) = add(add(X_55,X_11),multiply(X_11,inverse(X_55))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_55,X_11),add(add(X_55,X_11),multiply(X_11,inverse(X_55)))) ),[0],$fot(add(multiply(X_11,inverse(X_55)),add(X_55,X_11)))]]) ).
cnf(refute_0_521,plain,
( add(X_55,X_11) != add(multiply(X_11,inverse(X_55)),add(X_55,X_11))
| add(X_55,X_11) = add(add(X_55,X_11),multiply(X_11,inverse(X_55))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_11,inverse(X_55)),add(X_55,X_11)),add(add(X_55,X_11),multiply(X_11,inverse(X_55)))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
( add(multiply(X_11,inverse(X_55)),X_55) != add(multiply(X_11,inverse(X_55)),add(X_55,X_11))
| add(X_55,X_11) = add(add(X_55,X_11),multiply(X_11,inverse(X_55))) ),
inference(resolve,[$cnf( $equal(add(X_55,X_11),add(multiply(X_11,inverse(X_55)),add(X_55,X_11))) )],[refute_0_518,refute_0_521]) ).
cnf(refute_0_523,plain,
add(X_55,X_11) = add(add(X_55,X_11),multiply(X_11,inverse(X_55))),
inference(resolve,[$cnf( $equal(add(multiply(X_11,inverse(X_55)),X_55),add(multiply(X_11,inverse(X_55)),add(X_55,X_11))) )],[refute_0_512,refute_0_522]) ).
cnf(refute_0_524,plain,
( add(X_10,X_44) != add(X_10,add(X_44,X_10))
| add(X_10,add(X_44,X_10)) = add(X_10,X_44) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_10,X_44))),bind(Y0,$fot(add(X_10,add(X_44,X_10))))]]) ).
cnf(refute_0_525,plain,
add(X_10,add(X_44,X_10)) = add(X_10,X_44),
inference(resolve,[$cnf( $equal(add(X_10,X_44),add(X_10,add(X_44,X_10))) )],[refute_0_507,refute_0_524]) ).
cnf(refute_0_526,plain,
add(X_11,add(X_55,X_11)) = add(X_11,X_55),
inference(subst,[],[refute_0_525:[bind(X_10,$fot(X_11)),bind(X_44,$fot(X_55))]]) ).
cnf(refute_0_527,plain,
add(multiply(inverse(X_55),X_12),X_55) = add(multiply(inverse(X_55),X_12),add(X_55,multiply(inverse(X_55),X_12))),
inference(subst,[],[refute_0_507:[bind(X_10,$fot(multiply(inverse(X_55),X_12))),bind(X_44,$fot(X_55))]]) ).
cnf(refute_0_528,plain,
add(X_55,multiply(inverse(X_55),X_12)) = add(X_55,X_12),
inference(subst,[],[refute_0_29:[bind(X_10,$fot(X_55))]]) ).
cnf(refute_0_529,plain,
( add(X_55,multiply(inverse(X_55),X_12)) != add(X_55,X_12)
| add(multiply(inverse(X_55),X_12),X_55) != add(multiply(inverse(X_55),X_12),add(X_55,multiply(inverse(X_55),X_12)))
| add(multiply(inverse(X_55),X_12),X_55) = add(multiply(inverse(X_55),X_12),add(X_55,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(inverse(X_55),X_12),X_55),add(multiply(inverse(X_55),X_12),add(X_55,multiply(inverse(X_55),X_12)))) ),[1,1],$fot(add(X_55,X_12))]]) ).
cnf(refute_0_530,plain,
( add(multiply(inverse(X_55),X_12),X_55) != add(multiply(inverse(X_55),X_12),add(X_55,multiply(inverse(X_55),X_12)))
| add(multiply(inverse(X_55),X_12),X_55) = add(multiply(inverse(X_55),X_12),add(X_55,X_12)) ),
inference(resolve,[$cnf( $equal(add(X_55,multiply(inverse(X_55),X_12)),add(X_55,X_12)) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
add(multiply(inverse(X_55),X_12),X_55) = add(multiply(inverse(X_55),X_12),add(X_55,X_12)),
inference(resolve,[$cnf( $equal(add(multiply(inverse(X_55),X_12),X_55),add(multiply(inverse(X_55),X_12),add(X_55,multiply(inverse(X_55),X_12)))) )],[refute_0_527,refute_0_530]) ).
cnf(refute_0_532,plain,
add(multiply(inverse(X_55),X_12),X_55) = add(X_55,multiply(inverse(X_55),X_12)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_55)),bind(Y,$fot(multiply(inverse(X_55),X_12)))]]) ).
cnf(refute_0_533,plain,
( add(X_55,multiply(inverse(X_55),X_12)) != add(X_55,X_12)
| add(multiply(inverse(X_55),X_12),X_55) != add(X_55,multiply(inverse(X_55),X_12))
| add(multiply(inverse(X_55),X_12),X_55) = add(X_55,X_12) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(multiply(inverse(X_55),X_12),X_55))),bind(Y0,$fot(add(X_55,multiply(inverse(X_55),X_12)))),bind(Z0,$fot(add(X_55,X_12)))]]) ).
cnf(refute_0_534,plain,
( add(X_55,multiply(inverse(X_55),X_12)) != add(X_55,X_12)
| add(multiply(inverse(X_55),X_12),X_55) = add(X_55,X_12) ),
inference(resolve,[$cnf( $equal(add(multiply(inverse(X_55),X_12),X_55),add(X_55,multiply(inverse(X_55),X_12))) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
add(multiply(inverse(X_55),X_12),X_55) = add(X_55,X_12),
inference(resolve,[$cnf( $equal(add(X_55,multiply(inverse(X_55),X_12)),add(X_55,X_12)) )],[refute_0_528,refute_0_534]) ).
cnf(refute_0_536,plain,
( add(multiply(inverse(X_55),X_12),X_55) != add(X_55,X_12)
| add(multiply(inverse(X_55),X_12),X_55) != add(multiply(inverse(X_55),X_12),add(X_55,X_12))
| add(X_55,X_12) = add(multiply(inverse(X_55),X_12),add(X_55,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(inverse(X_55),X_12),X_55),add(multiply(inverse(X_55),X_12),add(X_55,X_12))) ),[0],$fot(add(X_55,X_12))]]) ).
cnf(refute_0_537,plain,
( add(multiply(inverse(X_55),X_12),X_55) != add(multiply(inverse(X_55),X_12),add(X_55,X_12))
| add(X_55,X_12) = add(multiply(inverse(X_55),X_12),add(X_55,X_12)) ),
inference(resolve,[$cnf( $equal(add(multiply(inverse(X_55),X_12),X_55),add(X_55,X_12)) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
add(multiply(inverse(X_55),X_12),add(X_55,X_12)) = add(add(X_55,X_12),multiply(inverse(X_55),X_12)),
inference(subst,[],[refute_0_4:[bind(X,$fot(add(X_55,X_12))),bind(Y,$fot(multiply(inverse(X_55),X_12)))]]) ).
cnf(refute_0_539,plain,
( add(X_55,X_12) != add(multiply(inverse(X_55),X_12),add(X_55,X_12))
| add(multiply(inverse(X_55),X_12),add(X_55,X_12)) != add(add(X_55,X_12),multiply(inverse(X_55),X_12))
| add(X_55,X_12) = add(add(X_55,X_12),multiply(inverse(X_55),X_12)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_55,X_12),add(add(X_55,X_12),multiply(inverse(X_55),X_12))) ),[0],$fot(add(multiply(inverse(X_55),X_12),add(X_55,X_12)))]]) ).
cnf(refute_0_540,plain,
( add(X_55,X_12) != add(multiply(inverse(X_55),X_12),add(X_55,X_12))
| add(X_55,X_12) = add(add(X_55,X_12),multiply(inverse(X_55),X_12)) ),
inference(resolve,[$cnf( $equal(add(multiply(inverse(X_55),X_12),add(X_55,X_12)),add(add(X_55,X_12),multiply(inverse(X_55),X_12))) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
( add(multiply(inverse(X_55),X_12),X_55) != add(multiply(inverse(X_55),X_12),add(X_55,X_12))
| add(X_55,X_12) = add(add(X_55,X_12),multiply(inverse(X_55),X_12)) ),
inference(resolve,[$cnf( $equal(add(X_55,X_12),add(multiply(inverse(X_55),X_12),add(X_55,X_12))) )],[refute_0_537,refute_0_540]) ).
cnf(refute_0_542,plain,
add(X_55,X_12) = add(add(X_55,X_12),multiply(inverse(X_55),X_12)),
inference(resolve,[$cnf( $equal(add(multiply(inverse(X_55),X_12),X_55),add(multiply(inverse(X_55),X_12),add(X_55,X_12))) )],[refute_0_531,refute_0_541]) ).
cnf(refute_0_543,plain,
add(X_12,add(X_55,X_12)) = add(X_12,X_55),
inference(subst,[],[refute_0_525:[bind(X_10,$fot(X_12)),bind(X_44,$fot(X_55))]]) ).
cnf(refute_0_544,plain,
add(add(X_55,X_12),X_12) = add(X_12,add(X_55,X_12)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_12)),bind(Y,$fot(add(X_55,X_12)))]]) ).
cnf(refute_0_545,plain,
( add(X_12,add(X_55,X_12)) != add(X_12,X_55)
| add(add(X_55,X_12),X_12) != add(X_12,add(X_55,X_12))
| add(add(X_55,X_12),X_12) = add(X_12,X_55) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(X_55,X_12),X_12))),bind(Y0,$fot(add(X_12,add(X_55,X_12)))),bind(Z0,$fot(add(X_12,X_55)))]]) ).
cnf(refute_0_546,plain,
( add(X_12,add(X_55,X_12)) != add(X_12,X_55)
| add(add(X_55,X_12),X_12) = add(X_12,X_55) ),
inference(resolve,[$cnf( $equal(add(add(X_55,X_12),X_12),add(X_12,add(X_55,X_12))) )],[refute_0_544,refute_0_545]) ).
cnf(refute_0_547,plain,
add(add(X_55,X_12),X_12) = add(X_12,X_55),
inference(resolve,[$cnf( $equal(add(X_12,add(X_55,X_12)),add(X_12,X_55)) )],[refute_0_543,refute_0_546]) ).
cnf(refute_0_548,plain,
add(add(X_68,X_67),multiply(inverse(X_68),X_12)) = multiply(add(inverse(X_68),add(X_68,X_67)),add(add(X_68,X_67),X_12)),
inference(subst,[],[refute_0_15:[bind(X_10,$fot(add(X_68,X_67))),bind(X_11,$fot(inverse(X_68)))]]) ).
cnf(refute_0_549,plain,
add(inverse(X_47),multiply(inverse(inverse(X_47)),X_12)) = add(inverse(X_47),X_12),
inference(subst,[],[refute_0_29:[bind(X_10,$fot(inverse(X_47)))]]) ).
cnf(refute_0_550,plain,
X_47 = inverse(inverse(X_47)),
inference(subst,[],[refute_0_374:[bind(X_45,$fot(X_47))]]) ).
cnf(refute_0_551,plain,
( X_47 != inverse(inverse(X_47))
| inverse(inverse(X_47)) = X_47 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_47)),bind(Y0,$fot(inverse(inverse(X_47))))]]) ).
cnf(refute_0_552,plain,
inverse(inverse(X_47)) = X_47,
inference(resolve,[$cnf( $equal(X_47,inverse(inverse(X_47))) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
( add(inverse(X_47),multiply(inverse(inverse(X_47)),X_12)) != add(inverse(X_47),X_12)
| inverse(inverse(X_47)) != X_47
| add(inverse(X_47),multiply(X_47,X_12)) = add(inverse(X_47),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_47),multiply(inverse(inverse(X_47)),X_12)),add(inverse(X_47),X_12)) ),[0,1,0],$fot(X_47)]]) ).
cnf(refute_0_554,plain,
( add(inverse(X_47),multiply(inverse(inverse(X_47)),X_12)) != add(inverse(X_47),X_12)
| add(inverse(X_47),multiply(X_47,X_12)) = add(inverse(X_47),X_12) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_47)),X_47) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
add(inverse(X_47),multiply(X_47,X_12)) = add(inverse(X_47),X_12),
inference(resolve,[$cnf( $equal(add(inverse(X_47),multiply(inverse(inverse(X_47)),X_12)),add(inverse(X_47),X_12)) )],[refute_0_549,refute_0_554]) ).
cnf(refute_0_556,plain,
add(inverse(X_66),multiply(X_66,add(X_66,X_38))) = add(inverse(X_66),add(X_66,X_38)),
inference(subst,[],[refute_0_555:[bind(X_12,$fot(add(X_66,X_38))),bind(X_47,$fot(X_66))]]) ).
cnf(refute_0_557,plain,
X_66 = multiply(X_66,add(X_66,X_38)),
inference(subst,[],[refute_0_232:[bind(X_37,$fot(X_66))]]) ).
cnf(refute_0_558,plain,
( X_66 != multiply(X_66,add(X_66,X_38))
| multiply(X_66,add(X_66,X_38)) = X_66 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_66)),bind(Y0,$fot(multiply(X_66,add(X_66,X_38))))]]) ).
cnf(refute_0_559,plain,
multiply(X_66,add(X_66,X_38)) = X_66,
inference(resolve,[$cnf( $equal(X_66,multiply(X_66,add(X_66,X_38))) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
( multiply(X_66,add(X_66,X_38)) != X_66
| add(inverse(X_66),multiply(X_66,add(X_66,X_38))) != add(inverse(X_66),add(X_66,X_38))
| add(inverse(X_66),X_66) = add(inverse(X_66),add(X_66,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_66),multiply(X_66,add(X_66,X_38))),add(inverse(X_66),add(X_66,X_38))) ),[0,1],$fot(X_66)]]) ).
cnf(refute_0_561,plain,
( add(inverse(X_66),multiply(X_66,add(X_66,X_38))) != add(inverse(X_66),add(X_66,X_38))
| add(inverse(X_66),X_66) = add(inverse(X_66),add(X_66,X_38)) ),
inference(resolve,[$cnf( $equal(multiply(X_66,add(X_66,X_38)),X_66) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
add(inverse(X_66),X_66) = add(inverse(X_66),add(X_66,X_38)),
inference(resolve,[$cnf( $equal(add(inverse(X_66),multiply(X_66,add(X_66,X_38))),add(inverse(X_66),add(X_66,X_38))) )],[refute_0_556,refute_0_561]) ).
cnf(refute_0_563,plain,
add(X_66,inverse(X_66)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_564,plain,
add(inverse(X_66),X_66) = add(X_66,inverse(X_66)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_66)),bind(Y,$fot(inverse(X_66)))]]) ).
cnf(refute_0_565,plain,
( add(X_66,inverse(X_66)) != multiplicative_identity
| add(inverse(X_66),X_66) != add(X_66,inverse(X_66))
| add(inverse(X_66),X_66) = multiplicative_identity ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(inverse(X_66),X_66))),bind(Y0,$fot(add(X_66,inverse(X_66)))),bind(Z0,$fot(multiplicative_identity))]]) ).
cnf(refute_0_566,plain,
( add(X_66,inverse(X_66)) != multiplicative_identity
| add(inverse(X_66),X_66) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(inverse(X_66),X_66),add(X_66,inverse(X_66))) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
add(inverse(X_66),X_66) = multiplicative_identity,
inference(resolve,[$cnf( $equal(add(X_66,inverse(X_66)),multiplicative_identity) )],[refute_0_563,refute_0_566]) ).
cnf(refute_0_568,plain,
( add(inverse(X_66),X_66) != add(inverse(X_66),add(X_66,X_38))
| add(inverse(X_66),X_66) != multiplicative_identity
| multiplicative_identity = add(inverse(X_66),add(X_66,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_66),X_66),add(inverse(X_66),add(X_66,X_38))) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_569,plain,
( add(inverse(X_66),X_66) != add(inverse(X_66),add(X_66,X_38))
| multiplicative_identity = add(inverse(X_66),add(X_66,X_38)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_66),X_66),multiplicative_identity) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
multiplicative_identity = add(inverse(X_66),add(X_66,X_38)),
inference(resolve,[$cnf( $equal(add(inverse(X_66),X_66),add(inverse(X_66),add(X_66,X_38))) )],[refute_0_562,refute_0_569]) ).
cnf(refute_0_571,plain,
multiplicative_identity = add(inverse(X_68),add(X_68,X_67)),
inference(subst,[],[refute_0_570:[bind(X_38,$fot(X_67)),bind(X_66,$fot(X_68))]]) ).
cnf(refute_0_572,plain,
( multiplicative_identity != add(inverse(X_68),add(X_68,X_67))
| add(inverse(X_68),add(X_68,X_67)) = multiplicative_identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(inverse(X_68),add(X_68,X_67))))]]) ).
cnf(refute_0_573,plain,
add(inverse(X_68),add(X_68,X_67)) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(inverse(X_68),add(X_68,X_67))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
( add(add(X_68,X_67),multiply(inverse(X_68),X_12)) != multiply(add(inverse(X_68),add(X_68,X_67)),add(add(X_68,X_67),X_12))
| add(inverse(X_68),add(X_68,X_67)) != multiplicative_identity
| add(add(X_68,X_67),multiply(inverse(X_68),X_12)) = multiply(multiplicative_identity,add(add(X_68,X_67),X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_68,X_67),multiply(inverse(X_68),X_12)),multiply(add(inverse(X_68),add(X_68,X_67)),add(add(X_68,X_67),X_12))) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_575,plain,
( add(add(X_68,X_67),multiply(inverse(X_68),X_12)) != multiply(add(inverse(X_68),add(X_68,X_67)),add(add(X_68,X_67),X_12))
| add(add(X_68,X_67),multiply(inverse(X_68),X_12)) = multiply(multiplicative_identity,add(add(X_68,X_67),X_12)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_68),add(X_68,X_67)),multiplicative_identity) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
add(add(X_68,X_67),multiply(inverse(X_68),X_12)) = multiply(multiplicative_identity,add(add(X_68,X_67),X_12)),
inference(resolve,[$cnf( $equal(add(add(X_68,X_67),multiply(inverse(X_68),X_12)),multiply(add(inverse(X_68),add(X_68,X_67)),add(add(X_68,X_67),X_12))) )],[refute_0_548,refute_0_575]) ).
cnf(refute_0_577,plain,
multiply(multiplicative_identity,add(add(X_68,X_67),X_12)) = add(add(X_68,X_67),X_12),
inference(subst,[],[refute_0_25:[bind(X,$fot(add(add(X_68,X_67),X_12)))]]) ).
cnf(refute_0_578,plain,
( multiply(multiplicative_identity,add(add(X_68,X_67),X_12)) != add(add(X_68,X_67),X_12)
| add(add(X_68,X_67),multiply(inverse(X_68),X_12)) != multiply(multiplicative_identity,add(add(X_68,X_67),X_12))
| add(add(X_68,X_67),multiply(inverse(X_68),X_12)) = add(add(X_68,X_67),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_68,X_67),multiply(inverse(X_68),X_12)),multiply(multiplicative_identity,add(add(X_68,X_67),X_12))) ),[1],$fot(add(add(X_68,X_67),X_12))]]) ).
cnf(refute_0_579,plain,
( add(add(X_68,X_67),multiply(inverse(X_68),X_12)) != multiply(multiplicative_identity,add(add(X_68,X_67),X_12))
| add(add(X_68,X_67),multiply(inverse(X_68),X_12)) = add(add(X_68,X_67),X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(add(X_68,X_67),X_12)),add(add(X_68,X_67),X_12)) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
add(add(X_68,X_67),multiply(inverse(X_68),X_12)) = add(add(X_68,X_67),X_12),
inference(resolve,[$cnf( $equal(add(add(X_68,X_67),multiply(inverse(X_68),X_12)),multiply(multiplicative_identity,add(add(X_68,X_67),X_12))) )],[refute_0_576,refute_0_579]) ).
cnf(refute_0_581,plain,
add(add(X_55,X_12),multiply(inverse(X_55),X_12)) = add(add(X_55,X_12),X_12),
inference(subst,[],[refute_0_580:[bind(X_67,$fot(X_12)),bind(X_68,$fot(X_55))]]) ).
cnf(refute_0_582,plain,
( add(add(X_55,X_12),X_12) != add(X_12,X_55)
| add(add(X_55,X_12),multiply(inverse(X_55),X_12)) != add(add(X_55,X_12),X_12)
| add(add(X_55,X_12),multiply(inverse(X_55),X_12)) = add(X_12,X_55) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(X_55,X_12),multiply(inverse(X_55),X_12)))),bind(Y0,$fot(add(add(X_55,X_12),X_12))),bind(Z0,$fot(add(X_12,X_55)))]]) ).
cnf(refute_0_583,plain,
( add(add(X_55,X_12),X_12) != add(X_12,X_55)
| add(add(X_55,X_12),multiply(inverse(X_55),X_12)) = add(X_12,X_55) ),
inference(resolve,[$cnf( $equal(add(add(X_55,X_12),multiply(inverse(X_55),X_12)),add(add(X_55,X_12),X_12)) )],[refute_0_581,refute_0_582]) ).
cnf(refute_0_584,plain,
add(add(X_55,X_12),multiply(inverse(X_55),X_12)) = add(X_12,X_55),
inference(resolve,[$cnf( $equal(add(add(X_55,X_12),X_12),add(X_12,X_55)) )],[refute_0_547,refute_0_583]) ).
cnf(refute_0_585,plain,
( add(X_55,X_12) != add(add(X_55,X_12),multiply(inverse(X_55),X_12))
| add(add(X_55,X_12),multiply(inverse(X_55),X_12)) != add(X_12,X_55)
| add(X_55,X_12) = add(X_12,X_55) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_55,X_12),add(X_12,X_55)) ),[0],$fot(add(add(X_55,X_12),multiply(inverse(X_55),X_12)))]]) ).
cnf(refute_0_586,plain,
( add(X_55,X_12) != add(add(X_55,X_12),multiply(inverse(X_55),X_12))
| add(X_55,X_12) = add(X_12,X_55) ),
inference(resolve,[$cnf( $equal(add(add(X_55,X_12),multiply(inverse(X_55),X_12)),add(X_12,X_55)) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
add(X_55,X_12) = add(X_12,X_55),
inference(resolve,[$cnf( $equal(add(X_55,X_12),add(add(X_55,X_12),multiply(inverse(X_55),X_12))) )],[refute_0_542,refute_0_586]) ).
cnf(refute_0_588,plain,
( add(X_55,X_12) != add(X_12,X_55)
| add(X_12,X_55) = add(X_55,X_12) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_55,X_12))),bind(Y0,$fot(add(X_12,X_55)))]]) ).
cnf(refute_0_589,plain,
add(X_12,X_55) = add(X_55,X_12),
inference(resolve,[$cnf( $equal(add(X_55,X_12),add(X_12,X_55)) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
add(add(X_55,X_11),X_11) = add(X_11,add(X_55,X_11)),
inference(subst,[],[refute_0_589:[bind(X_12,$fot(add(X_55,X_11))),bind(X_55,$fot(X_11))]]) ).
cnf(refute_0_591,plain,
( add(X_11,add(X_55,X_11)) != add(X_11,X_55)
| add(add(X_55,X_11),X_11) != add(X_11,add(X_55,X_11))
| add(add(X_55,X_11),X_11) = add(X_11,X_55) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(X_55,X_11),X_11))),bind(Y0,$fot(add(X_11,add(X_55,X_11)))),bind(Z0,$fot(add(X_11,X_55)))]]) ).
cnf(refute_0_592,plain,
( add(X_11,add(X_55,X_11)) != add(X_11,X_55)
| add(add(X_55,X_11),X_11) = add(X_11,X_55) ),
inference(resolve,[$cnf( $equal(add(add(X_55,X_11),X_11),add(X_11,add(X_55,X_11))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
add(add(X_55,X_11),X_11) = add(X_11,X_55),
inference(resolve,[$cnf( $equal(add(X_11,add(X_55,X_11)),add(X_11,X_55)) )],[refute_0_526,refute_0_592]) ).
cnf(refute_0_594,plain,
add(add(X_68,X_67),multiply(X_11,inverse(X_68))) = multiply(add(add(X_68,X_67),X_11),add(inverse(X_68),add(X_68,X_67))),
inference(subst,[],[refute_0_405:[bind(X_10,$fot(add(X_68,X_67))),bind(X_12,$fot(inverse(X_68)))]]) ).
cnf(refute_0_595,plain,
( add(add(X_68,X_67),multiply(X_11,inverse(X_68))) != multiply(add(add(X_68,X_67),X_11),add(inverse(X_68),add(X_68,X_67)))
| add(inverse(X_68),add(X_68,X_67)) != multiplicative_identity
| add(add(X_68,X_67),multiply(X_11,inverse(X_68))) = multiply(add(add(X_68,X_67),X_11),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_68,X_67),multiply(X_11,inverse(X_68))),multiply(add(add(X_68,X_67),X_11),add(inverse(X_68),add(X_68,X_67)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_596,plain,
( add(add(X_68,X_67),multiply(X_11,inverse(X_68))) != multiply(add(add(X_68,X_67),X_11),add(inverse(X_68),add(X_68,X_67)))
| add(add(X_68,X_67),multiply(X_11,inverse(X_68))) = multiply(add(add(X_68,X_67),X_11),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(inverse(X_68),add(X_68,X_67)),multiplicative_identity) )],[refute_0_573,refute_0_595]) ).
cnf(refute_0_597,plain,
add(add(X_68,X_67),multiply(X_11,inverse(X_68))) = multiply(add(add(X_68,X_67),X_11),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(add(X_68,X_67),multiply(X_11,inverse(X_68))),multiply(add(add(X_68,X_67),X_11),add(inverse(X_68),add(X_68,X_67)))) )],[refute_0_594,refute_0_596]) ).
cnf(refute_0_598,plain,
multiply(add(add(X_68,X_67),X_11),multiplicative_identity) = add(add(X_68,X_67),X_11),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(add(X_68,X_67),X_11)))]]) ).
cnf(refute_0_599,plain,
( multiply(add(add(X_68,X_67),X_11),multiplicative_identity) != add(add(X_68,X_67),X_11)
| add(add(X_68,X_67),multiply(X_11,inverse(X_68))) != multiply(add(add(X_68,X_67),X_11),multiplicative_identity)
| add(add(X_68,X_67),multiply(X_11,inverse(X_68))) = add(add(X_68,X_67),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_68,X_67),multiply(X_11,inverse(X_68))),multiply(add(add(X_68,X_67),X_11),multiplicative_identity)) ),[1],$fot(add(add(X_68,X_67),X_11))]]) ).
cnf(refute_0_600,plain,
( add(add(X_68,X_67),multiply(X_11,inverse(X_68))) != multiply(add(add(X_68,X_67),X_11),multiplicative_identity)
| add(add(X_68,X_67),multiply(X_11,inverse(X_68))) = add(add(X_68,X_67),X_11) ),
inference(resolve,[$cnf( $equal(multiply(add(add(X_68,X_67),X_11),multiplicative_identity),add(add(X_68,X_67),X_11)) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
add(add(X_68,X_67),multiply(X_11,inverse(X_68))) = add(add(X_68,X_67),X_11),
inference(resolve,[$cnf( $equal(add(add(X_68,X_67),multiply(X_11,inverse(X_68))),multiply(add(add(X_68,X_67),X_11),multiplicative_identity)) )],[refute_0_597,refute_0_600]) ).
cnf(refute_0_602,plain,
add(add(X_55,X_11),multiply(X_11,inverse(X_55))) = add(add(X_55,X_11),X_11),
inference(subst,[],[refute_0_601:[bind(X_67,$fot(X_11)),bind(X_68,$fot(X_55))]]) ).
cnf(refute_0_603,plain,
( add(add(X_55,X_11),X_11) != add(X_11,X_55)
| add(add(X_55,X_11),multiply(X_11,inverse(X_55))) != add(add(X_55,X_11),X_11)
| add(add(X_55,X_11),multiply(X_11,inverse(X_55))) = add(X_11,X_55) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(X_55,X_11),multiply(X_11,inverse(X_55))))),bind(Y0,$fot(add(add(X_55,X_11),X_11))),bind(Z0,$fot(add(X_11,X_55)))]]) ).
cnf(refute_0_604,plain,
( add(add(X_55,X_11),X_11) != add(X_11,X_55)
| add(add(X_55,X_11),multiply(X_11,inverse(X_55))) = add(X_11,X_55) ),
inference(resolve,[$cnf( $equal(add(add(X_55,X_11),multiply(X_11,inverse(X_55))),add(add(X_55,X_11),X_11)) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
add(add(X_55,X_11),multiply(X_11,inverse(X_55))) = add(X_11,X_55),
inference(resolve,[$cnf( $equal(add(add(X_55,X_11),X_11),add(X_11,X_55)) )],[refute_0_593,refute_0_604]) ).
cnf(refute_0_606,plain,
( add(X_55,X_11) != add(add(X_55,X_11),multiply(X_11,inverse(X_55)))
| add(add(X_55,X_11),multiply(X_11,inverse(X_55))) != add(X_11,X_55)
| add(X_55,X_11) = add(X_11,X_55) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_55,X_11),add(X_11,X_55)) ),[0],$fot(add(add(X_55,X_11),multiply(X_11,inverse(X_55))))]]) ).
cnf(refute_0_607,plain,
( add(X_55,X_11) != add(add(X_55,X_11),multiply(X_11,inverse(X_55)))
| add(X_55,X_11) = add(X_11,X_55) ),
inference(resolve,[$cnf( $equal(add(add(X_55,X_11),multiply(X_11,inverse(X_55))),add(X_11,X_55)) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
add(X_55,X_11) = add(X_11,X_55),
inference(resolve,[$cnf( $equal(add(X_55,X_11),add(add(X_55,X_11),multiply(X_11,inverse(X_55)))) )],[refute_0_523,refute_0_607]) ).
cnf(refute_0_609,plain,
( add(X_55,X_11) != add(X_11,X_55)
| add(X_11,X_55) = add(X_55,X_11) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_55,X_11))),bind(Y0,$fot(add(X_11,X_55)))]]) ).
cnf(refute_0_610,plain,
add(X_11,X_55) = add(X_55,X_11),
inference(resolve,[$cnf( $equal(add(X_55,X_11),add(X_11,X_55)) )],[refute_0_608,refute_0_609]) ).
cnf(refute_0_611,plain,
add(add(add(Y,X_113),X_115),Y) = add(Y,add(add(Y,X_113),X_115)),
inference(subst,[],[refute_0_610:[bind(X_11,$fot(add(add(Y,X_113),X_115))),bind(X_55,$fot(Y))]]) ).
cnf(refute_0_612,plain,
( add(add(add(Y,X_113),X_115),Y) != add(Y,add(add(Y,X_113),X_115))
| add(add(add(Y,X_113),X_115),Y) != add(add(Y,X_113),X_115)
| add(Y,add(add(Y,X_113),X_115)) = add(add(Y,X_113),X_115) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(add(Y,X_113),X_115),Y),add(add(Y,X_113),X_115)) ),[0],$fot(add(Y,add(add(Y,X_113),X_115)))]]) ).
cnf(refute_0_613,plain,
( add(add(add(Y,X_113),X_115),Y) != add(add(Y,X_113),X_115)
| add(Y,add(add(Y,X_113),X_115)) = add(add(Y,X_113),X_115) ),
inference(resolve,[$cnf( $equal(add(add(add(Y,X_113),X_115),Y),add(Y,add(add(Y,X_113),X_115))) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
add(Y,add(add(Y,X_113),X_115)) = add(add(Y,X_113),X_115),
inference(resolve,[$cnf( $equal(add(add(add(Y,X_113),X_115),Y),add(add(Y,X_113),X_115)) )],[refute_0_479,refute_0_613]) ).
cnf(refute_0_615,plain,
add(X_10,multiply(inverse(X_10),add(add(X_124,inverse(inverse(X_10))),X_123))) = add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)),
inference(subst,[],[refute_0_29:[bind(X_12,$fot(add(add(X_124,inverse(inverse(X_10))),X_123)))]]) ).
cnf(refute_0_616,plain,
multiply(X,add(add(X_44,inverse(X)),Z)) = add(multiply(X,add(X_44,inverse(X))),multiply(X,Z)),
inference(subst,[],[distributivity2:[bind(Y,$fot(add(X_44,inverse(X))))]]) ).
cnf(refute_0_617,plain,
multiply(X,add(X_44,inverse(X))) = multiply(X,X_44),
inference(subst,[],[refute_0_488:[bind(X_37,$fot(X)),bind(X_38,$fot(X_44))]]) ).
cnf(refute_0_618,plain,
( multiply(X,add(X_44,inverse(X))) != multiply(X,X_44)
| multiply(X,add(add(X_44,inverse(X)),Z)) != add(multiply(X,add(X_44,inverse(X))),multiply(X,Z))
| multiply(X,add(add(X_44,inverse(X)),Z)) = add(multiply(X,X_44),multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,add(add(X_44,inverse(X)),Z)),add(multiply(X,add(X_44,inverse(X))),multiply(X,Z))) ),[1,0],$fot(multiply(X,X_44))]]) ).
cnf(refute_0_619,plain,
( multiply(X,add(add(X_44,inverse(X)),Z)) != add(multiply(X,add(X_44,inverse(X))),multiply(X,Z))
| multiply(X,add(add(X_44,inverse(X)),Z)) = add(multiply(X,X_44),multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,add(X_44,inverse(X))),multiply(X,X_44)) )],[refute_0_617,refute_0_618]) ).
cnf(refute_0_620,plain,
multiply(X,add(add(X_44,inverse(X)),Z)) = add(multiply(X,X_44),multiply(X,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(add(X_44,inverse(X)),Z)),add(multiply(X,add(X_44,inverse(X))),multiply(X,Z))) )],[refute_0_616,refute_0_619]) ).
cnf(refute_0_621,plain,
add(multiply(X,X_44),multiply(X,Z)) = multiply(X,add(X_44,Z)),
inference(subst,[],[refute_0_124:[bind(Y,$fot(X_44))]]) ).
cnf(refute_0_622,plain,
( multiply(X,add(add(X_44,inverse(X)),Z)) != add(multiply(X,X_44),multiply(X,Z))
| add(multiply(X,X_44),multiply(X,Z)) != multiply(X,add(X_44,Z))
| multiply(X,add(add(X_44,inverse(X)),Z)) = multiply(X,add(X_44,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,add(add(X_44,inverse(X)),Z)),multiply(X,add(X_44,Z))) ),[0],$fot(add(multiply(X,X_44),multiply(X,Z)))]]) ).
cnf(refute_0_623,plain,
( multiply(X,add(add(X_44,inverse(X)),Z)) != add(multiply(X,X_44),multiply(X,Z))
| multiply(X,add(add(X_44,inverse(X)),Z)) = multiply(X,add(X_44,Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X,X_44),multiply(X,Z)),multiply(X,add(X_44,Z))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
multiply(X,add(add(X_44,inverse(X)),Z)) = multiply(X,add(X_44,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(add(X_44,inverse(X)),Z)),add(multiply(X,X_44),multiply(X,Z))) )],[refute_0_620,refute_0_623]) ).
cnf(refute_0_625,plain,
multiply(inverse(X_10),add(add(X_124,inverse(inverse(X_10))),X_123)) = multiply(inverse(X_10),add(X_124,X_123)),
inference(subst,[],[refute_0_624:[bind(X,$fot(inverse(X_10))),bind(Z,$fot(X_123)),bind(X_44,$fot(X_124))]]) ).
cnf(refute_0_626,plain,
( multiply(inverse(X_10),add(add(X_124,inverse(inverse(X_10))),X_123)) != multiply(inverse(X_10),add(X_124,X_123))
| add(X_10,multiply(inverse(X_10),add(add(X_124,inverse(inverse(X_10))),X_123))) != add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))
| add(X_10,multiply(inverse(X_10),add(X_124,X_123))) = add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),add(add(X_124,inverse(inverse(X_10))),X_123))),add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))) ),[0,1],$fot(multiply(inverse(X_10),add(X_124,X_123)))]]) ).
cnf(refute_0_627,plain,
( add(X_10,multiply(inverse(X_10),add(add(X_124,inverse(inverse(X_10))),X_123))) != add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))
| add(X_10,multiply(inverse(X_10),add(X_124,X_123))) = add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_10),add(add(X_124,inverse(inverse(X_10))),X_123)),multiply(inverse(X_10),add(X_124,X_123))) )],[refute_0_625,refute_0_626]) ).
cnf(refute_0_628,plain,
add(X_10,multiply(inverse(X_10),add(X_124,X_123))) = add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),add(add(X_124,inverse(inverse(X_10))),X_123))),add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))) )],[refute_0_615,refute_0_627]) ).
cnf(refute_0_629,plain,
add(X_10,multiply(inverse(X_10),add(X_124,X_123))) = add(X_10,add(X_124,X_123)),
inference(subst,[],[refute_0_29:[bind(X_12,$fot(add(X_124,X_123)))]]) ).
cnf(refute_0_630,plain,
( add(X_10,multiply(inverse(X_10),add(X_124,X_123))) != add(X_10,add(X_124,X_123))
| add(X_10,multiply(inverse(X_10),add(X_124,X_123))) != add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))
| add(X_10,add(X_124,X_123)) = add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),add(X_124,X_123))),add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))) ),[0],$fot(add(X_10,add(X_124,X_123)))]]) ).
cnf(refute_0_631,plain,
( add(X_10,multiply(inverse(X_10),add(X_124,X_123))) != add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))
| add(X_10,add(X_124,X_123)) = add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) ),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),add(X_124,X_123))),add(X_10,add(X_124,X_123))) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
add(add(add(X_101,Y),X_103),multiply(Y,add(add(X_101,Y),X_103))) = add(add(X_101,Y),X_103),
inference(subst,[],[refute_0_447:[bind(Z,$fot(add(add(X_101,Y),X_103)))]]) ).
cnf(refute_0_633,plain,
multiply(X_37,add(add(X_21,X_37),X_39)) = add(multiply(X_37,add(X_21,X_37)),multiply(X_37,X_39)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_37)),bind(Y,$fot(add(X_21,X_37))),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_634,plain,
add(X_20,multiply(additive_identity,X_21)) = multiply(X_20,add(X_20,X_21)),
inference(subst,[],[refute_0_103:[bind(X_10,$fot(X_20)),bind(X_12,$fot(X_21))]]) ).
cnf(refute_0_635,plain,
add(X_21,X_20) = add(X_20,X_21),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_21)),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_636,plain,
( add(X_21,X_20) != add(X_20,X_21)
| add(X_20,X_21) = add(X_21,X_20) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_21,X_20))),bind(Y0,$fot(add(X_20,X_21)))]]) ).
cnf(refute_0_637,plain,
add(X_20,X_21) = add(X_21,X_20),
inference(resolve,[$cnf( $equal(add(X_21,X_20),add(X_20,X_21)) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
( add(X_20,X_21) != add(X_21,X_20)
| add(X_20,multiply(additive_identity,X_21)) != multiply(X_20,add(X_20,X_21))
| add(X_20,multiply(additive_identity,X_21)) = multiply(X_20,add(X_21,X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(additive_identity,X_21)),multiply(X_20,add(X_20,X_21))) ),[1,1],$fot(add(X_21,X_20))]]) ).
cnf(refute_0_639,plain,
( add(X_20,multiply(additive_identity,X_21)) != multiply(X_20,add(X_20,X_21))
| add(X_20,multiply(additive_identity,X_21)) = multiply(X_20,add(X_21,X_20)) ),
inference(resolve,[$cnf( $equal(add(X_20,X_21),add(X_21,X_20)) )],[refute_0_637,refute_0_638]) ).
cnf(refute_0_640,plain,
add(X_20,multiply(additive_identity,X_21)) = multiply(X_20,add(X_21,X_20)),
inference(resolve,[$cnf( $equal(add(X_20,multiply(additive_identity,X_21)),multiply(X_20,add(X_20,X_21))) )],[refute_0_634,refute_0_639]) ).
cnf(refute_0_641,plain,
add(X_37,multiply(additive_identity,X_21)) = multiply(X_37,add(X_21,X_37)),
inference(subst,[],[refute_0_640:[bind(X_20,$fot(X_37))]]) ).
cnf(refute_0_642,plain,
( add(X_37,multiply(additive_identity,X_21)) != multiply(X_37,add(X_21,X_37))
| multiply(X_37,add(X_21,X_37)) = add(X_37,multiply(additive_identity,X_21)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_37,multiply(additive_identity,X_21)))),bind(Y0,$fot(multiply(X_37,add(X_21,X_37))))]]) ).
cnf(refute_0_643,plain,
multiply(X_37,add(X_21,X_37)) = add(X_37,multiply(additive_identity,X_21)),
inference(resolve,[$cnf( $equal(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,add(X_21,X_37))) )],[refute_0_641,refute_0_642]) ).
cnf(refute_0_644,plain,
( multiply(X_37,add(X_21,X_37)) != add(X_37,multiply(additive_identity,X_21))
| multiply(X_37,add(add(X_21,X_37),X_39)) != add(multiply(X_37,add(X_21,X_37)),multiply(X_37,X_39))
| multiply(X_37,add(add(X_21,X_37),X_39)) = add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,add(add(X_21,X_37),X_39)),add(multiply(X_37,add(X_21,X_37)),multiply(X_37,X_39))) ),[1,0],$fot(add(X_37,multiply(additive_identity,X_21)))]]) ).
cnf(refute_0_645,plain,
( multiply(X_37,add(add(X_21,X_37),X_39)) != add(multiply(X_37,add(X_21,X_37)),multiply(X_37,X_39))
| multiply(X_37,add(add(X_21,X_37),X_39)) = add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) ),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_21,X_37)),add(X_37,multiply(additive_identity,X_21))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
multiply(X_37,add(add(X_21,X_37),X_39)) = add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)),
inference(resolve,[$cnf( $equal(multiply(X_37,add(add(X_21,X_37),X_39)),add(multiply(X_37,add(X_21,X_37)),multiply(X_37,X_39))) )],[refute_0_633,refute_0_645]) ).
cnf(refute_0_647,plain,
add(X_37,additive_identity) = X_37,
inference(subst,[],[additive_id1:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_648,plain,
add(X_37,multiply(additive_identity,X_21)) = add(X_37,multiply(additive_identity,X_21)),
introduced(tautology,[refl,[$fot(add(X_37,multiply(additive_identity,X_21)))]]) ).
cnf(refute_0_649,plain,
( multiply(additive_identity,X_21) != additive_identity
| add(X_37,multiply(additive_identity,X_21)) != add(X_37,multiply(additive_identity,X_21))
| add(X_37,multiply(additive_identity,X_21)) = add(X_37,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_37,multiply(additive_identity,X_21)),add(X_37,multiply(additive_identity,X_21))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_650,plain,
( multiply(additive_identity,X_21) != additive_identity
| add(X_37,multiply(additive_identity,X_21)) = add(X_37,additive_identity) ),
inference(resolve,[$cnf( $equal(add(X_37,multiply(additive_identity,X_21)),add(X_37,multiply(additive_identity,X_21))) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
add(X_37,multiply(additive_identity,X_21)) = add(X_37,additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_21),additive_identity) )],[refute_0_458,refute_0_650]) ).
cnf(refute_0_652,plain,
( add(X_37,multiply(additive_identity,X_21)) != add(X_37,additive_identity)
| add(X_37,additive_identity) != X_37
| add(X_37,multiply(additive_identity,X_21)) = X_37 ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(X_37,multiply(additive_identity,X_21)))),bind(Y0,$fot(add(X_37,additive_identity))),bind(Z0,$fot(X_37))]]) ).
cnf(refute_0_653,plain,
( add(X_37,additive_identity) != X_37
| add(X_37,multiply(additive_identity,X_21)) = X_37 ),
inference(resolve,[$cnf( $equal(add(X_37,multiply(additive_identity,X_21)),add(X_37,additive_identity)) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
add(X_37,multiply(additive_identity,X_21)) = X_37,
inference(resolve,[$cnf( $equal(add(X_37,additive_identity),X_37) )],[refute_0_647,refute_0_653]) ).
cnf(refute_0_655,plain,
add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) = add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)),
introduced(tautology,[refl,[$fot(add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)))]]) ).
cnf(refute_0_656,plain,
( add(X_37,multiply(additive_identity,X_21)) != X_37
| add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) != add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39))
| add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) = add(X_37,multiply(X_37,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)),add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39))) ),[1,0],$fot(X_37)]]) ).
cnf(refute_0_657,plain,
( add(X_37,multiply(additive_identity,X_21)) != X_37
| add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) = add(X_37,multiply(X_37,X_39)) ),
inference(resolve,[$cnf( $equal(add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)),add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39))) )],[refute_0_655,refute_0_656]) ).
cnf(refute_0_658,plain,
add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) = add(X_37,multiply(X_37,X_39)),
inference(resolve,[$cnf( $equal(add(X_37,multiply(additive_identity,X_21)),X_37) )],[refute_0_654,refute_0_657]) ).
cnf(refute_0_659,plain,
( add(X_37,multiply(X_37,X_39)) != X_37
| add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) != add(X_37,multiply(X_37,X_39))
| add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) = X_37 ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)))),bind(Y0,$fot(add(X_37,multiply(X_37,X_39)))),bind(Z0,$fot(X_37))]]) ).
cnf(refute_0_660,plain,
( add(X_37,multiply(X_37,X_39)) != X_37
| add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) = X_37 ),
inference(resolve,[$cnf( $equal(add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)),add(X_37,multiply(X_37,X_39))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) = X_37,
inference(resolve,[$cnf( $equal(add(X_37,multiply(X_37,X_39)),X_37) )],[refute_0_456,refute_0_660]) ).
cnf(refute_0_662,plain,
( multiply(X_37,add(add(X_21,X_37),X_39)) != add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39))
| add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)) != X_37
| multiply(X_37,add(add(X_21,X_37),X_39)) = X_37 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_37,add(add(X_21,X_37),X_39)),X_37) ),[0],$fot(add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)))]]) ).
cnf(refute_0_663,plain,
( multiply(X_37,add(add(X_21,X_37),X_39)) != add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39))
| multiply(X_37,add(add(X_21,X_37),X_39)) = X_37 ),
inference(resolve,[$cnf( $equal(add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39)),X_37) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
multiply(X_37,add(add(X_21,X_37),X_39)) = X_37,
inference(resolve,[$cnf( $equal(multiply(X_37,add(add(X_21,X_37),X_39)),add(add(X_37,multiply(additive_identity,X_21)),multiply(X_37,X_39))) )],[refute_0_646,refute_0_663]) ).
cnf(refute_0_665,plain,
multiply(Y,add(add(X_101,Y),X_103)) = Y,
inference(subst,[],[refute_0_664:[bind(X_21,$fot(X_101)),bind(X_37,$fot(Y)),bind(X_39,$fot(X_103))]]) ).
cnf(refute_0_666,plain,
( multiply(Y,add(add(X_101,Y),X_103)) != Y
| add(add(add(X_101,Y),X_103),multiply(Y,add(add(X_101,Y),X_103))) != add(add(X_101,Y),X_103)
| add(add(add(X_101,Y),X_103),Y) = add(add(X_101,Y),X_103) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(add(X_101,Y),X_103),multiply(Y,add(add(X_101,Y),X_103))),add(add(X_101,Y),X_103)) ),[0,1],$fot(Y)]]) ).
cnf(refute_0_667,plain,
( add(add(add(X_101,Y),X_103),multiply(Y,add(add(X_101,Y),X_103))) != add(add(X_101,Y),X_103)
| add(add(add(X_101,Y),X_103),Y) = add(add(X_101,Y),X_103) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(add(X_101,Y),X_103)),Y) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
add(add(add(X_101,Y),X_103),Y) = add(add(X_101,Y),X_103),
inference(resolve,[$cnf( $equal(add(add(add(X_101,Y),X_103),multiply(Y,add(add(X_101,Y),X_103))),add(add(X_101,Y),X_103)) )],[refute_0_632,refute_0_667]) ).
cnf(refute_0_669,plain,
add(add(add(X_101,Y),X_103),Y) = add(Y,add(add(X_101,Y),X_103)),
inference(subst,[],[refute_0_610:[bind(X_11,$fot(add(add(X_101,Y),X_103))),bind(X_55,$fot(Y))]]) ).
cnf(refute_0_670,plain,
( add(add(add(X_101,Y),X_103),Y) != add(Y,add(add(X_101,Y),X_103))
| add(add(add(X_101,Y),X_103),Y) != add(add(X_101,Y),X_103)
| add(Y,add(add(X_101,Y),X_103)) = add(add(X_101,Y),X_103) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(add(X_101,Y),X_103),Y),add(add(X_101,Y),X_103)) ),[0],$fot(add(Y,add(add(X_101,Y),X_103)))]]) ).
cnf(refute_0_671,plain,
( add(add(add(X_101,Y),X_103),Y) != add(add(X_101,Y),X_103)
| add(Y,add(add(X_101,Y),X_103)) = add(add(X_101,Y),X_103) ),
inference(resolve,[$cnf( $equal(add(add(add(X_101,Y),X_103),Y),add(Y,add(add(X_101,Y),X_103))) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
add(Y,add(add(X_101,Y),X_103)) = add(add(X_101,Y),X_103),
inference(resolve,[$cnf( $equal(add(add(add(X_101,Y),X_103),Y),add(add(X_101,Y),X_103)) )],[refute_0_668,refute_0_671]) ).
cnf(refute_0_673,plain,
add(X_10,add(add(X_124,X_10),X_123)) = add(add(X_124,X_10),X_123),
inference(subst,[],[refute_0_672:[bind(Y,$fot(X_10)),bind(X_101,$fot(X_124)),bind(X_103,$fot(X_123))]]) ).
cnf(refute_0_674,plain,
add(X_124,inverse(inverse(X_10))) = add(X_124,inverse(inverse(X_10))),
introduced(tautology,[refl,[$fot(add(X_124,inverse(inverse(X_10))))]]) ).
cnf(refute_0_675,plain,
( add(X_124,inverse(inverse(X_10))) != add(X_124,inverse(inverse(X_10)))
| inverse(inverse(X_10)) != X_10
| add(X_124,inverse(inverse(X_10))) = add(X_124,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_124,inverse(inverse(X_10))),add(X_124,inverse(inverse(X_10)))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_676,plain,
( inverse(inverse(X_10)) != X_10
| add(X_124,inverse(inverse(X_10))) = add(X_124,X_10) ),
inference(resolve,[$cnf( $equal(add(X_124,inverse(inverse(X_10))),add(X_124,inverse(inverse(X_10)))) )],[refute_0_674,refute_0_675]) ).
cnf(refute_0_677,plain,
add(X_124,inverse(inverse(X_10))) = add(X_124,X_10),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),X_10) )],[refute_0_377,refute_0_676]) ).
cnf(refute_0_678,plain,
add(add(X_124,inverse(inverse(X_10))),X_123) = add(add(X_124,inverse(inverse(X_10))),X_123),
introduced(tautology,[refl,[$fot(add(add(X_124,inverse(inverse(X_10))),X_123))]]) ).
cnf(refute_0_679,plain,
( add(X_124,inverse(inverse(X_10))) != add(X_124,X_10)
| add(add(X_124,inverse(inverse(X_10))),X_123) != add(add(X_124,inverse(inverse(X_10))),X_123)
| add(add(X_124,inverse(inverse(X_10))),X_123) = add(add(X_124,X_10),X_123) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_124,inverse(inverse(X_10))),X_123),add(add(X_124,inverse(inverse(X_10))),X_123)) ),[1,0],$fot(add(X_124,X_10))]]) ).
cnf(refute_0_680,plain,
( add(X_124,inverse(inverse(X_10))) != add(X_124,X_10)
| add(add(X_124,inverse(inverse(X_10))),X_123) = add(add(X_124,X_10),X_123) ),
inference(resolve,[$cnf( $equal(add(add(X_124,inverse(inverse(X_10))),X_123),add(add(X_124,inverse(inverse(X_10))),X_123)) )],[refute_0_678,refute_0_679]) ).
cnf(refute_0_681,plain,
add(add(X_124,inverse(inverse(X_10))),X_123) = add(add(X_124,X_10),X_123),
inference(resolve,[$cnf( $equal(add(X_124,inverse(inverse(X_10))),add(X_124,X_10)) )],[refute_0_677,refute_0_680]) ).
cnf(refute_0_682,plain,
add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) = add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)),
introduced(tautology,[refl,[$fot(add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)))]]) ).
cnf(refute_0_683,plain,
( add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) != add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))
| add(add(X_124,inverse(inverse(X_10))),X_123) != add(add(X_124,X_10),X_123)
| add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) = add(X_10,add(add(X_124,X_10),X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)),add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))) ),[1,1],$fot(add(add(X_124,X_10),X_123))]]) ).
cnf(refute_0_684,plain,
( add(add(X_124,inverse(inverse(X_10))),X_123) != add(add(X_124,X_10),X_123)
| add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) = add(X_10,add(add(X_124,X_10),X_123)) ),
inference(resolve,[$cnf( $equal(add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)),add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))) )],[refute_0_682,refute_0_683]) ).
cnf(refute_0_685,plain,
add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) = add(X_10,add(add(X_124,X_10),X_123)),
inference(resolve,[$cnf( $equal(add(add(X_124,inverse(inverse(X_10))),X_123),add(add(X_124,X_10),X_123)) )],[refute_0_681,refute_0_684]) ).
cnf(refute_0_686,plain,
( add(X_10,add(add(X_124,X_10),X_123)) != add(add(X_124,X_10),X_123)
| add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) != add(X_10,add(add(X_124,X_10),X_123))
| add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) = add(add(X_124,X_10),X_123) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)))),bind(Y0,$fot(add(X_10,add(add(X_124,X_10),X_123)))),bind(Z0,$fot(add(add(X_124,X_10),X_123)))]]) ).
cnf(refute_0_687,plain,
( add(X_10,add(add(X_124,X_10),X_123)) != add(add(X_124,X_10),X_123)
| add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) = add(add(X_124,X_10),X_123) ),
inference(resolve,[$cnf( $equal(add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)),add(X_10,add(add(X_124,X_10),X_123))) )],[refute_0_685,refute_0_686]) ).
cnf(refute_0_688,plain,
add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) = add(add(X_124,X_10),X_123),
inference(resolve,[$cnf( $equal(add(X_10,add(add(X_124,X_10),X_123)),add(add(X_124,X_10),X_123)) )],[refute_0_673,refute_0_687]) ).
cnf(refute_0_689,plain,
( add(X_10,add(X_124,X_123)) != add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))
| add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)) != add(add(X_124,X_10),X_123)
| add(X_10,add(X_124,X_123)) = add(add(X_124,X_10),X_123) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_10,add(X_124,X_123)),add(add(X_124,X_10),X_123)) ),[0],$fot(add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)))]]) ).
cnf(refute_0_690,plain,
( add(X_10,add(X_124,X_123)) != add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))
| add(X_10,add(X_124,X_123)) = add(add(X_124,X_10),X_123) ),
inference(resolve,[$cnf( $equal(add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123)),add(add(X_124,X_10),X_123)) )],[refute_0_688,refute_0_689]) ).
cnf(refute_0_691,plain,
( add(X_10,multiply(inverse(X_10),add(X_124,X_123))) != add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))
| add(X_10,add(X_124,X_123)) = add(add(X_124,X_10),X_123) ),
inference(resolve,[$cnf( $equal(add(X_10,add(X_124,X_123)),add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))) )],[refute_0_631,refute_0_690]) ).
cnf(refute_0_692,plain,
add(X_10,add(X_124,X_123)) = add(add(X_124,X_10),X_123),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),add(X_124,X_123))),add(X_10,add(add(X_124,inverse(inverse(X_10))),X_123))) )],[refute_0_628,refute_0_691]) ).
cnf(refute_0_693,plain,
( add(X_10,add(X_124,X_123)) != add(add(X_124,X_10),X_123)
| add(add(X_124,X_10),X_123) = add(X_10,add(X_124,X_123)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_10,add(X_124,X_123)))),bind(Y0,$fot(add(add(X_124,X_10),X_123)))]]) ).
cnf(refute_0_694,plain,
add(add(X_124,X_10),X_123) = add(X_10,add(X_124,X_123)),
inference(resolve,[$cnf( $equal(add(X_10,add(X_124,X_123)),add(add(X_124,X_10),X_123)) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
add(add(Y,X_113),X_115) = add(X_113,add(Y,X_115)),
inference(subst,[],[refute_0_694:[bind(X_10,$fot(X_113)),bind(X_123,$fot(X_115)),bind(X_124,$fot(Y))]]) ).
cnf(refute_0_696,plain,
add(Y,add(add(Y,X_113),X_115)) = add(Y,add(add(Y,X_113),X_115)),
introduced(tautology,[refl,[$fot(add(Y,add(add(Y,X_113),X_115)))]]) ).
cnf(refute_0_697,plain,
( add(Y,add(add(Y,X_113),X_115)) != add(Y,add(add(Y,X_113),X_115))
| add(add(Y,X_113),X_115) != add(X_113,add(Y,X_115))
| add(Y,add(add(Y,X_113),X_115)) = add(Y,add(X_113,add(Y,X_115))) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,add(add(Y,X_113),X_115)),add(Y,add(add(Y,X_113),X_115))) ),[1,1],$fot(add(X_113,add(Y,X_115)))]]) ).
cnf(refute_0_698,plain,
( add(add(Y,X_113),X_115) != add(X_113,add(Y,X_115))
| add(Y,add(add(Y,X_113),X_115)) = add(Y,add(X_113,add(Y,X_115))) ),
inference(resolve,[$cnf( $equal(add(Y,add(add(Y,X_113),X_115)),add(Y,add(add(Y,X_113),X_115))) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
add(Y,add(add(Y,X_113),X_115)) = add(Y,add(X_113,add(Y,X_115))),
inference(resolve,[$cnf( $equal(add(add(Y,X_113),X_115),add(X_113,add(Y,X_115))) )],[refute_0_695,refute_0_698]) ).
cnf(refute_0_700,plain,
( add(Y,add(add(Y,X_113),X_115)) != add(Y,add(X_113,add(Y,X_115)))
| add(Y,add(add(Y,X_113),X_115)) != add(add(Y,X_113),X_115)
| add(Y,add(X_113,add(Y,X_115))) = add(add(Y,X_113),X_115) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,add(add(Y,X_113),X_115)),add(add(Y,X_113),X_115)) ),[0],$fot(add(Y,add(X_113,add(Y,X_115))))]]) ).
cnf(refute_0_701,plain,
( add(Y,add(add(Y,X_113),X_115)) != add(add(Y,X_113),X_115)
| add(Y,add(X_113,add(Y,X_115))) = add(add(Y,X_113),X_115) ),
inference(resolve,[$cnf( $equal(add(Y,add(add(Y,X_113),X_115)),add(Y,add(X_113,add(Y,X_115)))) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
( add(Y,add(X_113,add(Y,X_115))) != add(add(Y,X_113),X_115)
| add(add(Y,X_113),X_115) != add(X_113,add(Y,X_115))
| add(Y,add(X_113,add(Y,X_115))) = add(X_113,add(Y,X_115)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(Y,add(X_113,add(Y,X_115))),add(X_113,add(Y,X_115))) ),[0],$fot(add(add(Y,X_113),X_115))]]) ).
cnf(refute_0_703,plain,
( add(Y,add(X_113,add(Y,X_115))) != add(add(Y,X_113),X_115)
| add(Y,add(X_113,add(Y,X_115))) = add(X_113,add(Y,X_115)) ),
inference(resolve,[$cnf( $equal(add(add(Y,X_113),X_115),add(X_113,add(Y,X_115))) )],[refute_0_695,refute_0_702]) ).
cnf(refute_0_704,plain,
( add(Y,add(add(Y,X_113),X_115)) != add(add(Y,X_113),X_115)
| add(Y,add(X_113,add(Y,X_115))) = add(X_113,add(Y,X_115)) ),
inference(resolve,[$cnf( $equal(add(Y,add(X_113,add(Y,X_115))),add(add(Y,X_113),X_115)) )],[refute_0_701,refute_0_703]) ).
cnf(refute_0_705,plain,
add(Y,add(X_113,add(Y,X_115))) = add(X_113,add(Y,X_115)),
inference(resolve,[$cnf( $equal(add(Y,add(add(Y,X_113),X_115)),add(add(Y,X_113),X_115)) )],[refute_0_614,refute_0_704]) ).
cnf(refute_0_706,plain,
add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_116,add(X_10,multiply(X_11,X_12))),
inference(subst,[],[refute_0_705:[bind(Y,$fot(X_10)),bind(X_113,$fot(X_116)),bind(X_115,$fot(multiply(X_11,X_12)))]]) ).
cnf(refute_0_707,plain,
add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) = add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))),
introduced(tautology,[refl,[$fot(add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))))]]) ).
cnf(refute_0_708,plain,
( add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))) != add(X_116,add(X_10,multiply(X_11,X_12)))
| add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) != add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))
| add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) = add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))),add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))) ),[1,1],$fot(add(X_116,add(X_10,multiply(X_11,X_12))))]]) ).
cnf(refute_0_709,plain,
( add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))) != add(X_116,add(X_10,multiply(X_11,X_12)))
| add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) = add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) ),
inference(resolve,[$cnf( $equal(add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))),add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) = add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))),
inference(resolve,[$cnf( $equal(add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))),add(X_116,add(X_10,multiply(X_11,X_12)))) )],[refute_0_706,refute_0_709]) ).
cnf(refute_0_711,plain,
add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))),
inference(subst,[],[refute_0_694:[bind(X_10,$fot(X_11)),bind(X_123,$fot(add(X_116,add(X_10,multiply(X_11,X_12))))),bind(X_124,$fot(X_10))]]) ).
cnf(refute_0_712,plain,
add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))) = add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12)))),
inference(subst,[],[refute_0_705:[bind(Y,$fot(X_116)),bind(X_113,$fot(add(X_10,X_11))),bind(X_115,$fot(add(X_10,multiply(X_11,X_12))))]]) ).
cnf(refute_0_713,plain,
( add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))) != add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))
| add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12)))) != add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))
| add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))) = add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))))),bind(Y0,$fot(add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12)))))),bind(Z0,$fot(add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))))]]) ).
cnf(refute_0_714,plain,
( add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12)))) != add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))
| add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))) = add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) ),
inference(resolve,[$cnf( $equal(add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))),add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))) )],[refute_0_712,refute_0_713]) ).
cnf(refute_0_715,plain,
add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))) = add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))),
inference(resolve,[$cnf( $equal(add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12)))),add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))) )],[refute_0_711,refute_0_714]) ).
cnf(refute_0_716,plain,
add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))),
inference(subst,[],[refute_0_694:[bind(X_10,$fot(X_116)),bind(X_123,$fot(add(X_116,add(X_10,multiply(X_11,X_12))))),bind(X_124,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_717,plain,
( add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))) != add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))
| add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) != add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12)))))
| add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))))),bind(Y0,$fot(add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))))),bind(Z0,$fot(add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))))]]) ).
cnf(refute_0_718,plain,
( add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))) != add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))
| add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) ),
inference(resolve,[$cnf( $equal(add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))),add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12)))))) )],[refute_0_716,refute_0_717]) ).
cnf(refute_0_719,plain,
add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))),
inference(resolve,[$cnf( $equal(add(X_116,add(add(X_10,X_11),add(X_116,add(X_10,multiply(X_11,X_12))))),add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))) )],[refute_0_715,refute_0_718]) ).
cnf(refute_0_720,plain,
( add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) != add(X_11,add(X_116,add(X_10,multiply(X_11,X_12))))
| add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) != add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))
| add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))))),bind(Y0,$fot(add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))))),bind(Z0,$fot(add(X_11,add(X_116,add(X_10,multiply(X_11,X_12))))))]]) ).
cnf(refute_0_721,plain,
( add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))) != add(X_11,add(X_116,add(X_10,multiply(X_11,X_12))))
| add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) ),
inference(resolve,[$cnf( $equal(add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))),add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12)))))) )],[refute_0_719,refute_0_720]) ).
cnf(refute_0_722,plain,
add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))),
inference(resolve,[$cnf( $equal(add(X_11,add(X_10,add(X_116,add(X_10,multiply(X_11,X_12))))),add(X_11,add(X_116,add(X_10,multiply(X_11,X_12))))) )],[refute_0_710,refute_0_721]) ).
cnf(refute_0_723,plain,
( add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) != add(X_11,add(X_116,add(X_10,multiply(X_11,X_12))))
| add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) != add(add(X_10,X_11),X_116)
| add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) = add(add(X_10,X_11),X_116) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))),add(add(X_10,X_11),X_116)) ),[0],$fot(add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))))]]) ).
cnf(refute_0_724,plain,
( add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) != add(add(X_10,X_11),X_116)
| add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) = add(add(X_10,X_11),X_116) ),
inference(resolve,[$cnf( $equal(add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))),add(X_11,add(X_116,add(X_10,multiply(X_11,X_12))))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
add(add(X_10,X_11),X_116) = add(X_11,add(X_10,X_116)),
inference(subst,[],[refute_0_694:[bind(X_10,$fot(X_11)),bind(X_123,$fot(X_116)),bind(X_124,$fot(X_10))]]) ).
cnf(refute_0_726,plain,
( add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) != add(add(X_10,X_11),X_116)
| add(add(X_10,X_11),X_116) != add(X_11,add(X_10,X_116))
| add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_10,X_116)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))),add(X_11,add(X_10,X_116))) ),[0],$fot(add(add(X_10,X_11),X_116))]]) ).
cnf(refute_0_727,plain,
( add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) != add(add(X_10,X_11),X_116)
| add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_10,X_116)) ),
inference(resolve,[$cnf( $equal(add(add(X_10,X_11),X_116),add(X_11,add(X_10,X_116))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
( add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))) != add(add(X_10,X_11),X_116)
| add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_10,X_116)) ),
inference(resolve,[$cnf( $equal(add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))),add(add(X_10,X_11),X_116)) )],[refute_0_724,refute_0_727]) ).
cnf(refute_0_729,plain,
add(X_11,add(X_116,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_10,X_116)),
inference(resolve,[$cnf( $equal(add(add(add(X_10,X_11),X_116),add(X_116,add(X_10,multiply(X_11,X_12)))),add(add(X_10,X_11),X_116)) )],[refute_0_432,refute_0_728]) ).
cnf(refute_0_730,plain,
add(X_11,add(X_10,add(X_10,multiply(X_11,X_12)))) = add(X_11,add(X_10,X_10)),
inference(subst,[],[refute_0_729:[bind(X_116,$fot(X_10))]]) ).
cnf(refute_0_731,plain,
add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) = add(X_11,add(X_10,add(X_10,multiply(X_11,X_12)))),
inference(subst,[],[refute_0_694:[bind(X_10,$fot(X_11)),bind(X_123,$fot(add(X_10,multiply(X_11,X_12)))),bind(X_124,$fot(X_10))]]) ).
cnf(refute_0_732,plain,
( add(X_11,add(X_10,add(X_10,multiply(X_11,X_12)))) != add(X_11,add(X_10,X_10))
| add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) != add(X_11,add(X_10,add(X_10,multiply(X_11,X_12))))
| add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) = add(X_11,add(X_10,X_10)) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))))),bind(Y0,$fot(add(X_11,add(X_10,add(X_10,multiply(X_11,X_12)))))),bind(Z0,$fot(add(X_11,add(X_10,X_10))))]]) ).
cnf(refute_0_733,plain,
( add(X_11,add(X_10,add(X_10,multiply(X_11,X_12)))) != add(X_11,add(X_10,X_10))
| add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) = add(X_11,add(X_10,X_10)) ),
inference(resolve,[$cnf( $equal(add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))),add(X_11,add(X_10,add(X_10,multiply(X_11,X_12))))) )],[refute_0_731,refute_0_732]) ).
cnf(refute_0_734,plain,
add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) = add(X_11,add(X_10,X_10)),
inference(resolve,[$cnf( $equal(add(X_11,add(X_10,add(X_10,multiply(X_11,X_12)))),add(X_11,add(X_10,X_10))) )],[refute_0_730,refute_0_733]) ).
cnf(refute_0_735,plain,
( add(X_11,add(X_10,X_10)) != add(X_11,X_10)
| add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) != add(X_11,add(X_10,X_10))
| add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) = add(X_11,X_10) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))))),bind(Y0,$fot(add(X_11,add(X_10,X_10)))),bind(Z0,$fot(add(X_11,X_10)))]]) ).
cnf(refute_0_736,plain,
( add(X_11,add(X_10,X_10)) != add(X_11,X_10)
| add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) = add(X_11,X_10) ),
inference(resolve,[$cnf( $equal(add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))),add(X_11,add(X_10,X_10))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) = add(X_11,X_10),
inference(resolve,[$cnf( $equal(add(X_11,add(X_10,X_10)),add(X_11,X_10)) )],[refute_0_417,refute_0_736]) ).
cnf(refute_0_738,plain,
add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))) = add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))),
introduced(tautology,[refl,[$fot(add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))))]]) ).
cnf(refute_0_739,plain,
( add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))) != add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))))
| add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) != add(X_11,X_10)
| add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))) = add(X_121,add(X_11,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))),add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))))) ),[1,1],$fot(add(X_11,X_10))]]) ).
cnf(refute_0_740,plain,
( add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))) != add(X_11,X_10)
| add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))) = add(X_121,add(X_11,X_10)) ),
inference(resolve,[$cnf( $equal(add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))),add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))))) )],[refute_0_738,refute_0_739]) ).
cnf(refute_0_741,plain,
add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))) = add(X_121,add(X_11,X_10)),
inference(resolve,[$cnf( $equal(add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))),add(X_11,X_10)) )],[refute_0_737,refute_0_740]) ).
cnf(refute_0_742,plain,
add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) = add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))),
inference(subst,[],[refute_0_694:[bind(X_10,$fot(X_121)),bind(X_123,$fot(add(X_10,multiply(X_11,X_12)))),bind(X_124,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_743,plain,
( add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))) != add(X_121,add(X_11,X_10))
| add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) != add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))))
| add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) = add(X_121,add(X_11,X_10)) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))))),bind(Y0,$fot(add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))))),bind(Z0,$fot(add(X_121,add(X_11,X_10))))]]) ).
cnf(refute_0_744,plain,
( add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))) != add(X_121,add(X_11,X_10))
| add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) = add(X_121,add(X_11,X_10)) ),
inference(resolve,[$cnf( $equal(add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))),add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12))))) )],[refute_0_742,refute_0_743]) ).
cnf(refute_0_745,plain,
add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) = add(X_121,add(X_11,X_10)),
inference(resolve,[$cnf( $equal(add(X_121,add(add(X_10,X_11),add(X_10,multiply(X_11,X_12)))),add(X_121,add(X_11,X_10))) )],[refute_0_741,refute_0_744]) ).
cnf(refute_0_746,plain,
( add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) != add(X_121,add(X_11,X_10))
| add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) != add(add(X_10,X_11),X_121)
| add(X_121,add(X_11,X_10)) = add(add(X_10,X_11),X_121) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))),add(add(X_10,X_11),X_121)) ),[0],$fot(add(X_121,add(X_11,X_10)))]]) ).
cnf(refute_0_747,plain,
( add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) != add(add(X_10,X_11),X_121)
| add(X_121,add(X_11,X_10)) = add(add(X_10,X_11),X_121) ),
inference(resolve,[$cnf( $equal(add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))),add(X_121,add(X_11,X_10))) )],[refute_0_745,refute_0_746]) ).
cnf(refute_0_748,plain,
add(add(X_10,X_11),X_121) = add(X_11,add(X_10,X_121)),
inference(subst,[],[refute_0_694:[bind(X_10,$fot(X_11)),bind(X_123,$fot(X_121)),bind(X_124,$fot(X_10))]]) ).
cnf(refute_0_749,plain,
( add(X_121,add(X_11,X_10)) != add(add(X_10,X_11),X_121)
| add(add(X_10,X_11),X_121) != add(X_11,add(X_10,X_121))
| add(X_121,add(X_11,X_10)) = add(X_11,add(X_10,X_121)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_121,add(X_11,X_10)),add(X_11,add(X_10,X_121))) ),[0],$fot(add(add(X_10,X_11),X_121))]]) ).
cnf(refute_0_750,plain,
( add(X_121,add(X_11,X_10)) != add(add(X_10,X_11),X_121)
| add(X_121,add(X_11,X_10)) = add(X_11,add(X_10,X_121)) ),
inference(resolve,[$cnf( $equal(add(add(X_10,X_11),X_121),add(X_11,add(X_10,X_121))) )],[refute_0_748,refute_0_749]) ).
cnf(refute_0_751,plain,
( add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))) != add(add(X_10,X_11),X_121)
| add(X_121,add(X_11,X_10)) = add(X_11,add(X_10,X_121)) ),
inference(resolve,[$cnf( $equal(add(X_121,add(X_11,X_10)),add(add(X_10,X_11),X_121)) )],[refute_0_747,refute_0_750]) ).
cnf(refute_0_752,plain,
add(X_121,add(X_11,X_10)) = add(X_11,add(X_10,X_121)),
inference(resolve,[$cnf( $equal(add(add(add(X_10,X_11),X_121),add(X_10,multiply(X_11,X_12))),add(add(X_10,X_11),X_121)) )],[refute_0_410,refute_0_751]) ).
cnf(refute_0_753,plain,
( add(X_121,add(X_11,X_10)) != add(X_11,add(X_10,X_121))
| add(X_11,add(X_10,X_121)) = add(X_121,add(X_11,X_10)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_121,add(X_11,X_10)))),bind(Y0,$fot(add(X_11,add(X_10,X_121))))]]) ).
cnf(refute_0_754,plain,
add(X_11,add(X_10,X_121)) = add(X_121,add(X_11,X_10)),
inference(resolve,[$cnf( $equal(add(X_121,add(X_11,X_10)),add(X_11,add(X_10,X_121))) )],[refute_0_752,refute_0_753]) ).
cnf(refute_0_755,plain,
add(b,add(c,a)) = add(a,add(b,c)),
inference(subst,[],[refute_0_754:[bind(X_10,$fot(c)),bind(X_11,$fot(b)),bind(X_121,$fot(a))]]) ).
cnf(refute_0_756,plain,
add(c,add(a,b)) = add(b,add(c,a)),
inference(subst,[],[refute_0_754:[bind(X_10,$fot(a)),bind(X_11,$fot(c)),bind(X_121,$fot(b))]]) ).
cnf(refute_0_757,plain,
( add(b,add(c,a)) != add(a,add(b,c))
| add(c,add(a,b)) != add(b,add(c,a))
| add(c,add(a,b)) = add(a,add(b,c)) ),
inference(subst,[],[refute_0_194:[bind(X0,$fot(add(c,add(a,b)))),bind(Y0,$fot(add(b,add(c,a)))),bind(Z0,$fot(add(a,add(b,c))))]]) ).
cnf(refute_0_758,plain,
( add(b,add(c,a)) != add(a,add(b,c))
| add(c,add(a,b)) = add(a,add(b,c)) ),
inference(resolve,[$cnf( $equal(add(c,add(a,b)),add(b,add(c,a))) )],[refute_0_756,refute_0_757]) ).
cnf(refute_0_759,plain,
add(c,add(a,b)) = add(a,add(b,c)),
inference(resolve,[$cnf( $equal(add(b,add(c,a)),add(a,add(b,c))) )],[refute_0_755,refute_0_758]) ).
cnf(refute_0_760,plain,
( add(a,add(b,c)) != add(a,add(b,c))
| add(c,add(a,b)) != add(a,add(b,c))
| add(a,add(b,c)) = add(c,add(a,b)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(a,add(b,c)),add(c,add(a,b))) ),[1],$fot(add(a,add(b,c)))]]) ).
cnf(refute_0_761,plain,
( add(a,add(b,c)) != add(a,add(b,c))
| add(a,add(b,c)) = add(c,add(a,b)) ),
inference(resolve,[$cnf( $equal(add(c,add(a,b)),add(a,add(b,c))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
add(a,add(b,c)) != add(a,add(b,c)),
inference(resolve,[$cnf( $equal(add(a,add(b,c)),add(c,add(a,b))) )],[refute_0_761,refute_0_8]) ).
cnf(refute_0_763,plain,
add(a,add(b,c)) = add(a,add(b,c)),
introduced(tautology,[refl,[$fot(add(a,add(b,c)))]]) ).
cnf(refute_0_764,plain,
$false,
inference(resolve,[$cnf( $equal(add(a,add(b,c)),add(a,add(b,c))) )],[refute_0_763,refute_0_762]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO008-4 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n026.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 : Wed Jun 1 16:43:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.07/1.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.07/1.24
% 1.07/1.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.07/1.32
%------------------------------------------------------------------------------