TSTP Solution File: BOO013-4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 23:44:35 EDT 2022
% Result : Unsatisfiable 0.62s 0.84s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 112
% Syntax : Number of clauses : 512 ( 264 unt; 0 nHn; 274 RR)
% Number of literals : 866 ( 865 equ; 355 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 636 ( 19 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(b_a_multiplicative_identity,hypothesis,
add(a,b) = multiplicative_identity ).
cnf(b_an_additive_identity,hypothesis,
multiply(a,b) = additive_identity ).
cnf(prove_a_inverse_is_b,negated_conjecture,
b != inverse(a) ).
cnf(refute_0_0,plain,
multiply(X_45,add(inverse(X_45),X_47)) = add(multiply(X_45,inverse(X_45)),multiply(X_45,X_47)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_45)),bind(Y,$fot(inverse(X_45))),bind(Z,$fot(X_47))]]) ).
cnf(refute_0_1,plain,
multiply(X_45,inverse(X_45)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_45))]]) ).
cnf(refute_0_2,plain,
( multiply(X_45,add(inverse(X_45),X_47)) != add(multiply(X_45,inverse(X_45)),multiply(X_45,X_47))
| multiply(X_45,inverse(X_45)) != additive_identity
| multiply(X_45,add(inverse(X_45),X_47)) = add(additive_identity,multiply(X_45,X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_45,add(inverse(X_45),X_47)),add(multiply(X_45,inverse(X_45)),multiply(X_45,X_47))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_3,plain,
( multiply(X_45,add(inverse(X_45),X_47)) != add(multiply(X_45,inverse(X_45)),multiply(X_45,X_47))
| multiply(X_45,add(inverse(X_45),X_47)) = add(additive_identity,multiply(X_45,X_47)) ),
inference(resolve,[$cnf( $equal(multiply(X_45,inverse(X_45)),additive_identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(X_45,add(inverse(X_45),X_47)) = add(additive_identity,multiply(X_45,X_47)),
inference(resolve,[$cnf( $equal(multiply(X_45,add(inverse(X_45),X_47)),add(multiply(X_45,inverse(X_45)),multiply(X_45,X_47))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
add(X,additive_identity) = add(additive_identity,X),
inference(subst,[],[commutativity_of_add:[bind(Y,$fot(additive_identity))]]) ).
cnf(refute_0_6,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_7,plain,
( add(X,additive_identity) != X
| add(additive_identity,X) = X ),
inference(resolve,[$cnf( $equal(add(X,additive_identity),add(additive_identity,X)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
add(additive_identity,X) = X,
inference(resolve,[$cnf( $equal(add(X,additive_identity),X) )],[additive_id1,refute_0_7]) ).
cnf(refute_0_9,plain,
add(additive_identity,multiply(X_45,X_47)) = multiply(X_45,X_47),
inference(subst,[],[refute_0_8:[bind(X,$fot(multiply(X_45,X_47)))]]) ).
cnf(refute_0_10,plain,
( multiply(X_45,add(inverse(X_45),X_47)) != add(additive_identity,multiply(X_45,X_47))
| add(additive_identity,multiply(X_45,X_47)) != multiply(X_45,X_47)
| multiply(X_45,add(inverse(X_45),X_47)) = multiply(X_45,X_47) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_45,add(inverse(X_45),X_47)),multiply(X_45,X_47)) ),[0],$fot(add(additive_identity,multiply(X_45,X_47)))]]) ).
cnf(refute_0_11,plain,
( multiply(X_45,add(inverse(X_45),X_47)) != add(additive_identity,multiply(X_45,X_47))
| multiply(X_45,add(inverse(X_45),X_47)) = multiply(X_45,X_47) ),
inference(resolve,[$cnf( $equal(add(additive_identity,multiply(X_45,X_47)),multiply(X_45,X_47)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
multiply(X_45,add(inverse(X_45),X_47)) = multiply(X_45,X_47),
inference(resolve,[$cnf( $equal(multiply(X_45,add(inverse(X_45),X_47)),add(additive_identity,multiply(X_45,X_47))) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(X_104,add(inverse(X_104),inverse(inverse(X_104)))) = multiply(X_104,inverse(inverse(X_104))),
inference(subst,[],[refute_0_12:[bind(X_45,$fot(X_104)),bind(X_47,$fot(inverse(inverse(X_104))))]]) ).
cnf(refute_0_14,plain,
add(inverse(X_104),inverse(inverse(X_104))) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(inverse(X_104)))]]) ).
cnf(refute_0_15,plain,
( multiply(X_104,add(inverse(X_104),inverse(inverse(X_104)))) != multiply(X_104,inverse(inverse(X_104)))
| add(inverse(X_104),inverse(inverse(X_104))) != multiplicative_identity
| multiply(X_104,multiplicative_identity) = multiply(X_104,inverse(inverse(X_104))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_104,add(inverse(X_104),inverse(inverse(X_104)))),multiply(X_104,inverse(inverse(X_104)))) ),[0,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_16,plain,
( multiply(X_104,add(inverse(X_104),inverse(inverse(X_104)))) != multiply(X_104,inverse(inverse(X_104)))
| multiply(X_104,multiplicative_identity) = multiply(X_104,inverse(inverse(X_104))) ),
inference(resolve,[$cnf( $equal(add(inverse(X_104),inverse(inverse(X_104))),multiplicative_identity) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(X_104,multiplicative_identity) = multiply(X_104,inverse(inverse(X_104))),
inference(resolve,[$cnf( $equal(multiply(X_104,add(inverse(X_104),inverse(inverse(X_104)))),multiply(X_104,inverse(inverse(X_104)))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(X_104,multiplicative_identity) = X_104,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(X_104))]]) ).
cnf(refute_0_19,plain,
( multiply(X_104,multiplicative_identity) != X_104
| multiply(X_104,multiplicative_identity) != multiply(X_104,inverse(inverse(X_104)))
| X_104 = multiply(X_104,inverse(inverse(X_104))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_104,multiplicative_identity),multiply(X_104,inverse(inverse(X_104)))) ),[0],$fot(X_104)]]) ).
cnf(refute_0_20,plain,
( multiply(X_104,multiplicative_identity) != multiply(X_104,inverse(inverse(X_104)))
| X_104 = multiply(X_104,inverse(inverse(X_104))) ),
inference(resolve,[$cnf( $equal(multiply(X_104,multiplicative_identity),X_104) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),add(X_10,additive_identity)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_22,plain,
add(X_10,additive_identity) = X_10,
inference(subst,[],[additive_id1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_23,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),add(X_10,additive_identity))
| add(X_10,additive_identity) != X_10
| add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10) ),
introduced(tautology,[equality,[$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_24,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( $equal(add(X_10,additive_identity),X_10) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),add(X_10,additive_identity))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_28,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( multiply(X,Y) != multiply(Y,X)
| multiply(Y,X) = multiply(X,Y) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_30,plain,
multiply(Y,X) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(Y,X)) )],[commutativity_of_multiply,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(add(X_10,X_11),X_10) = multiply(X_10,add(X_10,X_11)),
inference(subst,[],[refute_0_30:[bind(X,$fot(X_10)),bind(Y,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_32,plain,
( multiply(add(X_10,X_11),X_10) != multiply(X_10,add(X_10,X_11))
| add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),X_10)
| add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)) ),
introduced(tautology,[equality,[$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_33,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( $equal(multiply(add(X_10,X_11),X_10),multiply(X_10,add(X_10,X_11))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),X_10)) )],[refute_0_25,refute_0_33]) ).
cnf(refute_0_35,plain,
add(X_20,multiply(X_21,additive_identity)) = multiply(X_20,add(X_20,X_21)),
inference(subst,[],[refute_0_34:[bind(X_10,$fot(X_20)),bind(X_11,$fot(X_21))]]) ).
cnf(refute_0_36,plain,
add(X_21,X_20) = add(X_20,X_21),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_21)),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_37,plain,
( add(X_21,X_20) != add(X_20,X_21)
| add(X_20,X_21) = add(X_21,X_20) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(add(X_21,X_20))),bind(Y0,$fot(add(X_20,X_21)))]]) ).
cnf(refute_0_38,plain,
add(X_20,X_21) = add(X_21,X_20),
inference(resolve,[$cnf( $equal(add(X_21,X_20),add(X_20,X_21)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( add(X_20,X_21) != add(X_21,X_20)
| add(X_20,multiply(X_21,additive_identity)) != multiply(X_20,add(X_20,X_21))
| add(X_20,multiply(X_21,additive_identity)) = multiply(X_20,add(X_21,X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(X_20,add(X_20,X_21))) ),[1,1],$fot(add(X_21,X_20))]]) ).
cnf(refute_0_40,plain,
( add(X_20,multiply(X_21,additive_identity)) != multiply(X_20,add(X_20,X_21))
| add(X_20,multiply(X_21,additive_identity)) = multiply(X_20,add(X_21,X_20)) ),
inference(resolve,[$cnf( $equal(add(X_20,X_21),add(X_21,X_20)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
add(X_20,multiply(X_21,additive_identity)) = multiply(X_20,add(X_21,X_20)),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(X_20,add(X_20,X_21))) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
add(X_20,additive_identity) = X_20,
inference(subst,[],[additive_id1:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_43,plain,
add(multiply(X_21,additive_identity),Y) = add(Y,multiply(X_21,additive_identity)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(X_21,additive_identity)))]]) ).
cnf(refute_0_44,plain,
add(Y,multiply(X_21,additive_identity)) = multiply(Y,add(Y,X_21)),
inference(subst,[],[refute_0_34:[bind(X_10,$fot(Y)),bind(X_11,$fot(X_21))]]) ).
cnf(refute_0_45,plain,
( add(Y,multiply(X_21,additive_identity)) != multiply(Y,add(Y,X_21))
| add(multiply(X_21,additive_identity),Y) != add(Y,multiply(X_21,additive_identity))
| add(multiply(X_21,additive_identity),Y) = multiply(Y,add(Y,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_21,additive_identity),Y),add(Y,multiply(X_21,additive_identity))) ),[1],$fot(multiply(Y,add(Y,X_21)))]]) ).
cnf(refute_0_46,plain,
( add(multiply(X_21,additive_identity),Y) != add(Y,multiply(X_21,additive_identity))
| add(multiply(X_21,additive_identity),Y) = multiply(Y,add(Y,X_21)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(X_21,additive_identity)),multiply(Y,add(Y,X_21))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
add(multiply(X_21,additive_identity),Y) = multiply(Y,add(Y,X_21)),
inference(resolve,[$cnf( $equal(add(multiply(X_21,additive_identity),Y),add(Y,multiply(X_21,additive_identity))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) = multiply(multiply(X_37,additive_identity),add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37)))),
inference(subst,[],[refute_0_47:[bind(Y,$fot(multiply(X_37,additive_identity))),bind(X_21,$fot(inverse(multiply(additive_identity,X_37))))]]) ).
cnf(refute_0_49,plain,
add(multiply(additive_identity,X_23),Y) = add(Y,multiply(additive_identity,X_23)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,X_23)))]]) ).
cnf(refute_0_50,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,$fot(X_12))]]) ).
cnf(refute_0_51,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
| add(X_10,additive_identity) != X_10
| add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
introduced(tautology,[equality,[$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_52,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( $equal(add(X_10,additive_identity),X_10) )],[refute_0_22,refute_0_51]) ).
cnf(refute_0_53,plain,
add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) )],[refute_0_50,refute_0_52]) ).
cnf(refute_0_54,plain,
add(Y,multiply(additive_identity,X_23)) = multiply(Y,add(Y,X_23)),
inference(subst,[],[refute_0_53:[bind(X_10,$fot(Y)),bind(X_12,$fot(X_23))]]) ).
cnf(refute_0_55,plain,
( add(Y,multiply(additive_identity,X_23)) != multiply(Y,add(Y,X_23))
| add(multiply(additive_identity,X_23),Y) != add(Y,multiply(additive_identity,X_23))
| add(multiply(additive_identity,X_23),Y) = multiply(Y,add(Y,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_23),Y),add(Y,multiply(additive_identity,X_23))) ),[1],$fot(multiply(Y,add(Y,X_23)))]]) ).
cnf(refute_0_56,plain,
( add(multiply(additive_identity,X_23),Y) != add(Y,multiply(additive_identity,X_23))
| add(multiply(additive_identity,X_23),Y) = multiply(Y,add(Y,X_23)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,X_23)),multiply(Y,add(Y,X_23))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
add(multiply(additive_identity,X_23),Y) = multiply(Y,add(Y,X_23)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_23),Y),add(Y,multiply(additive_identity,X_23))) )],[refute_0_49,refute_0_56]) ).
cnf(refute_0_58,plain,
add(multiply(additive_identity,X_36),inverse(multiply(additive_identity,X_36))) = multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)),
inference(subst,[],[refute_0_57:[bind(Y,$fot(inverse(multiply(additive_identity,X_36)))),bind(X_23,$fot(X_36))]]) ).
cnf(refute_0_59,plain,
add(multiply(additive_identity,X_36),inverse(multiply(additive_identity,X_36))) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(multiply(additive_identity,X_36)))]]) ).
cnf(refute_0_60,plain,
( add(multiply(additive_identity,X_36),inverse(multiply(additive_identity,X_36))) != multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36))
| add(multiply(additive_identity,X_36),inverse(multiply(additive_identity,X_36))) != multiplicative_identity
| multiplicative_identity = multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_36),inverse(multiply(additive_identity,X_36))),multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36))) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_61,plain,
( add(multiply(additive_identity,X_36),inverse(multiply(additive_identity,X_36))) != multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36))
| multiplicative_identity = multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_36),inverse(multiply(additive_identity,X_36))),multiplicative_identity) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiplicative_identity = multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_36),inverse(multiply(additive_identity,X_36))),multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
add(multiply(X_12,additive_identity),X_10) = multiply(X_10,add(X_10,X_12)),
inference(subst,[],[refute_0_47:[bind(Y,$fot(X_10)),bind(X_21,$fot(X_12))]]) ).
cnf(refute_0_64,plain,
( add(multiply(X_12,additive_identity),X_10) != multiply(X_10,add(X_10,X_12))
| multiply(X_10,add(X_10,X_12)) = add(multiply(X_12,additive_identity),X_10) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(add(multiply(X_12,additive_identity),X_10))),bind(Y0,$fot(multiply(X_10,add(X_10,X_12))))]]) ).
cnf(refute_0_65,plain,
multiply(X_10,add(X_10,X_12)) = add(multiply(X_12,additive_identity),X_10),
inference(resolve,[$cnf( $equal(add(multiply(X_12,additive_identity),X_10),multiply(X_10,add(X_10,X_12))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( multiply(X_10,add(X_10,X_12)) != add(multiply(X_12,additive_identity),X_10)
| add(X_10,multiply(additive_identity,X_12)) != multiply(X_10,add(X_10,X_12))
| add(X_10,multiply(additive_identity,X_12)) = add(multiply(X_12,additive_identity),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(X_10,add(X_10,X_12))) ),[1],$fot(add(multiply(X_12,additive_identity),X_10))]]) ).
cnf(refute_0_67,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(X_10,add(X_10,X_12))
| add(X_10,multiply(additive_identity,X_12)) = add(multiply(X_12,additive_identity),X_10) ),
inference(resolve,[$cnf( $equal(multiply(X_10,add(X_10,X_12)),add(multiply(X_12,additive_identity),X_10)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
add(X_10,multiply(additive_identity,X_12)) = add(multiply(X_12,additive_identity),X_10),
inference(resolve,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(X_10,add(X_10,X_12))) )],[refute_0_53,refute_0_67]) ).
cnf(refute_0_69,plain,
add(inverse(multiply(additive_identity,X_36)),multiply(additive_identity,X_36)) = add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))),
inference(subst,[],[refute_0_68:[bind(X_10,$fot(inverse(multiply(additive_identity,X_36)))),bind(X_12,$fot(X_36))]]) ).
cnf(refute_0_70,plain,
add(X_33,multiply(X_34,additive_identity)) = multiply(X_33,add(X_34,X_33)),
inference(subst,[],[refute_0_41:[bind(X_20,$fot(X_33)),bind(X_21,$fot(X_34))]]) ).
cnf(refute_0_71,plain,
multiply(additive_identity,X_34) = multiply(X_34,additive_identity),
inference(subst,[],[commutativity_of_multiply:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_34))]]) ).
cnf(refute_0_72,plain,
( multiply(additive_identity,X_34) != multiply(X_34,additive_identity)
| multiply(X_34,additive_identity) = multiply(additive_identity,X_34) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(additive_identity,X_34))),bind(Y0,$fot(multiply(X_34,additive_identity)))]]) ).
cnf(refute_0_73,plain,
multiply(X_34,additive_identity) = multiply(additive_identity,X_34),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_34),multiply(X_34,additive_identity)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( multiply(X_34,additive_identity) != multiply(additive_identity,X_34)
| add(X_33,multiply(X_34,additive_identity)) != multiply(X_33,add(X_34,X_33))
| add(X_33,multiply(additive_identity,X_34)) = multiply(X_33,add(X_34,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_33,multiply(X_34,additive_identity)),multiply(X_33,add(X_34,X_33))) ),[0,1],$fot(multiply(additive_identity,X_34))]]) ).
cnf(refute_0_75,plain,
( add(X_33,multiply(X_34,additive_identity)) != multiply(X_33,add(X_34,X_33))
| add(X_33,multiply(additive_identity,X_34)) = multiply(X_33,add(X_34,X_33)) ),
inference(resolve,[$cnf( $equal(multiply(X_34,additive_identity),multiply(additive_identity,X_34)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
add(X_33,multiply(additive_identity,X_34)) = multiply(X_33,add(X_34,X_33)),
inference(resolve,[$cnf( $equal(add(X_33,multiply(X_34,additive_identity)),multiply(X_33,add(X_34,X_33))) )],[refute_0_70,refute_0_75]) ).
cnf(refute_0_77,plain,
( add(X_33,multiply(additive_identity,X_34)) != multiply(X_33,add(X_34,X_33))
| multiply(X_33,add(X_34,X_33)) = add(X_33,multiply(additive_identity,X_34)) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(add(X_33,multiply(additive_identity,X_34)))),bind(Y0,$fot(multiply(X_33,add(X_34,X_33))))]]) ).
cnf(refute_0_78,plain,
multiply(X_33,add(X_34,X_33)) = add(X_33,multiply(additive_identity,X_34)),
inference(resolve,[$cnf( $equal(add(X_33,multiply(additive_identity,X_34)),multiply(X_33,add(X_34,X_33))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))) = add(inverse(multiply(additive_identity,X_36)),multiply(additive_identity,X_36)),
inference(subst,[],[refute_0_78:[bind(X_33,$fot(inverse(multiply(additive_identity,X_36)))),bind(X_34,$fot(X_36))]]) ).
cnf(refute_0_80,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_81,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_28,refute_0_80]) ).
cnf(refute_0_82,plain,
( multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))) != add(inverse(multiply(additive_identity,X_36)),multiply(additive_identity,X_36))
| add(inverse(multiply(additive_identity,X_36)),multiply(additive_identity,X_36)) != add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36)))
| multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))) = add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))) ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))))),bind(Y0,$fot(add(inverse(multiply(additive_identity,X_36)),multiply(additive_identity,X_36)))),bind(Z0,$fot(add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36)))))]]) ).
cnf(refute_0_83,plain,
( add(inverse(multiply(additive_identity,X_36)),multiply(additive_identity,X_36)) != add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36)))
| multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))) = add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))),add(inverse(multiply(additive_identity,X_36)),multiply(additive_identity,X_36))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))) = add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))),
inference(resolve,[$cnf( $equal(add(inverse(multiply(additive_identity,X_36)),multiply(additive_identity,X_36)),add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36)))) )],[refute_0_69,refute_0_83]) ).
cnf(refute_0_85,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_11,X_10)),
inference(subst,[],[refute_0_41:[bind(X_20,$fot(X_10)),bind(X_21,$fot(X_11))]]) ).
cnf(refute_0_86,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(X_10,add(X_10,X_11))
| add(X_10,multiply(X_11,additive_identity)) != multiply(X_10,add(X_11,X_10))
| multiply(X_10,add(X_11,X_10)) = multiply(X_10,add(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(X_10,add(X_10,X_11))) ),[0],$fot(multiply(X_10,add(X_11,X_10)))]]) ).
cnf(refute_0_87,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(X_10,add(X_10,X_11))
| multiply(X_10,add(X_11,X_10)) = multiply(X_10,add(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(X_10,add(X_11,X_10))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
multiply(X_10,add(X_11,X_10)) = multiply(X_10,add(X_10,X_11)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(X_10,add(X_10,X_11))) )],[refute_0_34,refute_0_87]) ).
cnf(refute_0_89,plain,
( multiply(X_10,add(X_11,X_10)) != multiply(X_10,add(X_10,X_11))
| multiply(X_10,add(X_10,X_11)) = multiply(X_10,add(X_11,X_10)) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X_10,add(X_11,X_10)))),bind(Y0,$fot(multiply(X_10,add(X_10,X_11))))]]) ).
cnf(refute_0_90,plain,
multiply(X_10,add(X_10,X_11)) = multiply(X_10,add(X_11,X_10)),
inference(resolve,[$cnf( $equal(multiply(X_10,add(X_11,X_10)),multiply(X_10,add(X_10,X_11))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)) = multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))),
inference(subst,[],[refute_0_90:[bind(X_10,$fot(inverse(multiply(additive_identity,X_36)))),bind(X_11,$fot(X_36))]]) ).
cnf(refute_0_92,plain,
( multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))) != add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36)))
| multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)) != multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36))))
| multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)) = add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))) ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)))),bind(Y0,$fot(multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))))),bind(Z0,$fot(add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36)))))]]) ).
cnf(refute_0_93,plain,
( multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))) != add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36)))
| multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)) = add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)),multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36))))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)) = add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(additive_identity,X_36)),add(X_36,inverse(multiply(additive_identity,X_36)))),add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36)))) )],[refute_0_84,refute_0_93]) ).
cnf(refute_0_95,plain,
( multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)) != add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36)))
| multiplicative_identity != multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36))
| multiplicative_identity = add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplicative_identity,multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36))) ),[1],$fot(add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))))]]) ).
cnf(refute_0_96,plain,
( multiplicative_identity != multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36))
| multiplicative_identity = add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36)),add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
multiplicative_identity = add(multiply(X_36,additive_identity),inverse(multiply(additive_identity,X_36))),
inference(resolve,[$cnf( $equal(multiplicative_identity,multiply(inverse(multiply(additive_identity,X_36)),add(inverse(multiply(additive_identity,X_36)),X_36))) )],[refute_0_62,refute_0_96]) ).
cnf(refute_0_98,plain,
multiplicative_identity = add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37))),
inference(subst,[],[refute_0_97:[bind(X_36,$fot(X_37))]]) ).
cnf(refute_0_99,plain,
( multiplicative_identity != add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37)))
| add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37))) = multiplicative_identity ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37)))))]]) ).
cnf(refute_0_100,plain,
add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37))) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37)))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37))) != multiplicative_identity
| add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) != multiply(multiply(X_37,additive_identity),add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37))))
| add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) = multiply(multiply(X_37,additive_identity),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)),multiply(multiply(X_37,additive_identity),add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37))))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_102,plain,
( add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) != multiply(multiply(X_37,additive_identity),add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37))))
| add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) = multiply(multiply(X_37,additive_identity),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37))),multiplicative_identity) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) = multiply(multiply(X_37,additive_identity),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)),multiply(multiply(X_37,additive_identity),add(multiply(X_37,additive_identity),inverse(multiply(additive_identity,X_37))))) )],[refute_0_48,refute_0_102]) ).
cnf(refute_0_104,plain,
add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) = multiply(multiply(X_21,additive_identity),add(multiply(X_21,additive_identity),X_36)),
inference(subst,[],[refute_0_57:[bind(Y,$fot(multiply(X_21,additive_identity))),bind(X_23,$fot(X_36))]]) ).
cnf(refute_0_105,plain,
add(multiply(X_21,additive_identity),X_36) = multiply(X_36,add(X_36,X_21)),
inference(subst,[],[refute_0_47:[bind(Y,$fot(X_36))]]) ).
cnf(refute_0_106,plain,
( add(multiply(X_21,additive_identity),X_36) != multiply(X_36,add(X_36,X_21))
| add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) != multiply(multiply(X_21,additive_identity),add(multiply(X_21,additive_identity),X_36))
| add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) = multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)),multiply(multiply(X_21,additive_identity),add(multiply(X_21,additive_identity),X_36))) ),[1,1],$fot(multiply(X_36,add(X_36,X_21)))]]) ).
cnf(refute_0_107,plain,
( add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) != multiply(multiply(X_21,additive_identity),add(multiply(X_21,additive_identity),X_36))
| add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) = multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_21,additive_identity),X_36),multiply(X_36,add(X_36,X_21))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) = multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)),multiply(multiply(X_21,additive_identity),add(multiply(X_21,additive_identity),X_36))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) = multiply(multiply(additive_identity,X_36),add(multiply(additive_identity,X_36),X_23)),
inference(subst,[],[refute_0_57:[bind(Y,$fot(multiply(additive_identity,X_36)))]]) ).
cnf(refute_0_110,plain,
add(multiply(additive_identity,X_36),X_23) = multiply(X_23,add(X_23,X_36)),
inference(subst,[],[refute_0_57:[bind(Y,$fot(X_23)),bind(X_23,$fot(X_36))]]) ).
cnf(refute_0_111,plain,
( add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) != multiply(multiply(additive_identity,X_36),add(multiply(additive_identity,X_36),X_23))
| add(multiply(additive_identity,X_36),X_23) != multiply(X_23,add(X_23,X_36))
| add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) = multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)),multiply(multiply(additive_identity,X_36),add(multiply(additive_identity,X_36),X_23))) ),[1,1],$fot(multiply(X_23,add(X_23,X_36)))]]) ).
cnf(refute_0_112,plain,
( add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) != multiply(multiply(additive_identity,X_36),add(multiply(additive_identity,X_36),X_23))
| add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) = multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_36),X_23),multiply(X_23,add(X_23,X_36))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) = multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)),multiply(multiply(additive_identity,X_36),add(multiply(additive_identity,X_36),X_23))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( multiply(X,add(Y,Z)) != add(multiply(X,Y),multiply(X,Z))
| add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_115,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[distributivity2,refute_0_114]) ).
cnf(refute_0_116,plain,
add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) = multiply(additive_identity,add(X_23,X_36)),
inference(subst,[],[refute_0_115:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_23)),bind(Z,$fot(X_36))]]) ).
cnf(refute_0_117,plain,
( add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) != multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36)))
| add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) != multiply(additive_identity,add(X_23,X_36))
| multiply(additive_identity,add(X_23,X_36)) = multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)),multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36)))) ),[0],$fot(multiply(additive_identity,add(X_23,X_36)))]]) ).
cnf(refute_0_118,plain,
( add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) != multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36)))
| multiply(additive_identity,add(X_23,X_36)) = multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)),multiply(additive_identity,add(X_23,X_36))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)) = multiply(multiply(additive_identity,X_12),add(X_34,multiply(additive_identity,X_12))),
inference(subst,[],[refute_0_41:[bind(X_20,$fot(multiply(additive_identity,X_12))),bind(X_21,$fot(X_34))]]) ).
cnf(refute_0_120,plain,
add(X_34,multiply(additive_identity,X_12)) = multiply(X_34,add(X_34,X_12)),
inference(subst,[],[refute_0_53:[bind(X_10,$fot(X_34))]]) ).
cnf(refute_0_121,plain,
( add(X_34,multiply(additive_identity,X_12)) != multiply(X_34,add(X_34,X_12))
| add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)) != multiply(multiply(additive_identity,X_12),add(X_34,multiply(additive_identity,X_12)))
| add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)) = multiply(multiply(additive_identity,X_12),multiply(X_34,add(X_34,X_12))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)),multiply(multiply(additive_identity,X_12),add(X_34,multiply(additive_identity,X_12)))) ),[1,1],$fot(multiply(X_34,add(X_34,X_12)))]]) ).
cnf(refute_0_122,plain,
( add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)) != multiply(multiply(additive_identity,X_12),add(X_34,multiply(additive_identity,X_12)))
| add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)) = multiply(multiply(additive_identity,X_12),multiply(X_34,add(X_34,X_12))) ),
inference(resolve,[$cnf( $equal(add(X_34,multiply(additive_identity,X_12)),multiply(X_34,add(X_34,X_12))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)) = multiply(multiply(additive_identity,X_12),multiply(X_34,add(X_34,X_12))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)),multiply(multiply(additive_identity,X_12),add(X_34,multiply(additive_identity,X_12)))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
( add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)) != multiply(multiply(additive_identity,X_12),multiply(X_34,add(X_34,X_12)))
| multiply(multiply(additive_identity,X_12),multiply(X_34,add(X_34,X_12))) = add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)))),bind(Y0,$fot(multiply(multiply(additive_identity,X_12),multiply(X_34,add(X_34,X_12)))))]]) ).
cnf(refute_0_125,plain,
multiply(multiply(additive_identity,X_12),multiply(X_34,add(X_34,X_12))) = add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_12),multiply(X_34,additive_identity)),multiply(multiply(additive_identity,X_12),multiply(X_34,add(X_34,X_12)))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36))) = add(multiply(additive_identity,X_36),multiply(X_23,additive_identity)),
inference(subst,[],[refute_0_125:[bind(X_12,$fot(X_36)),bind(X_34,$fot(X_23))]]) ).
cnf(refute_0_127,plain,
( multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36))) != add(multiply(additive_identity,X_36),multiply(X_23,additive_identity))
| multiply(additive_identity,add(X_23,X_36)) != multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36)))
| multiply(additive_identity,add(X_23,X_36)) = add(multiply(additive_identity,X_36),multiply(X_23,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_23,X_36)),multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36)))) ),[1],$fot(add(multiply(additive_identity,X_36),multiply(X_23,additive_identity)))]]) ).
cnf(refute_0_128,plain,
( multiply(additive_identity,add(X_23,X_36)) != multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36)))
| multiply(additive_identity,add(X_23,X_36)) = add(multiply(additive_identity,X_36),multiply(X_23,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36))),add(multiply(additive_identity,X_36),multiply(X_23,additive_identity))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
( add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)) != multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36)))
| multiply(additive_identity,add(X_23,X_36)) = add(multiply(additive_identity,X_36),multiply(X_23,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_23,X_36)),multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36)))) )],[refute_0_118,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(additive_identity,add(X_23,X_36)) = add(multiply(additive_identity,X_36),multiply(X_23,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_23),multiply(additive_identity,X_36)),multiply(multiply(additive_identity,X_36),multiply(X_23,add(X_23,X_36)))) )],[refute_0_113,refute_0_129]) ).
cnf(refute_0_131,plain,
( multiply(additive_identity,add(X_23,X_36)) != add(multiply(additive_identity,X_36),multiply(X_23,additive_identity))
| add(multiply(additive_identity,X_36),multiply(X_23,additive_identity)) = multiply(additive_identity,add(X_23,X_36)) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(additive_identity,add(X_23,X_36)))),bind(Y0,$fot(add(multiply(additive_identity,X_36),multiply(X_23,additive_identity))))]]) ).
cnf(refute_0_132,plain,
add(multiply(additive_identity,X_36),multiply(X_23,additive_identity)) = multiply(additive_identity,add(X_23,X_36)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_23,X_36)),add(multiply(additive_identity,X_36),multiply(X_23,additive_identity))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) = multiply(additive_identity,add(X_21,X_36)),
inference(subst,[],[refute_0_132:[bind(X_23,$fot(X_21))]]) ).
cnf(refute_0_134,plain,
( add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) != multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))
| add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) != multiply(additive_identity,add(X_21,X_36))
| multiply(additive_identity,add(X_21,X_36)) = multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)),multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))) ),[0],$fot(multiply(additive_identity,add(X_21,X_36)))]]) ).
cnf(refute_0_135,plain,
( add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) != multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))
| multiply(additive_identity,add(X_21,X_36)) = multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)),multiply(additive_identity,add(X_21,X_36))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)) = multiply(multiply(X_31,additive_identity),add(multiply(X_31,additive_identity),X_21)),
inference(subst,[],[refute_0_47:[bind(Y,$fot(multiply(X_31,additive_identity)))]]) ).
cnf(refute_0_137,plain,
add(multiply(X_31,additive_identity),X_21) = multiply(X_21,add(X_21,X_31)),
inference(subst,[],[refute_0_47:[bind(Y,$fot(X_21)),bind(X_21,$fot(X_31))]]) ).
cnf(refute_0_138,plain,
( add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)) != multiply(multiply(X_31,additive_identity),add(multiply(X_31,additive_identity),X_21))
| add(multiply(X_31,additive_identity),X_21) != multiply(X_21,add(X_21,X_31))
| add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)) = multiply(multiply(X_31,additive_identity),multiply(X_21,add(X_21,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)),multiply(multiply(X_31,additive_identity),add(multiply(X_31,additive_identity),X_21))) ),[1,1],$fot(multiply(X_21,add(X_21,X_31)))]]) ).
cnf(refute_0_139,plain,
( add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)) != multiply(multiply(X_31,additive_identity),add(multiply(X_31,additive_identity),X_21))
| add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)) = multiply(multiply(X_31,additive_identity),multiply(X_21,add(X_21,X_31))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),X_21),multiply(X_21,add(X_21,X_31))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)) = multiply(multiply(X_31,additive_identity),multiply(X_21,add(X_21,X_31))),
inference(resolve,[$cnf( $equal(add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)),multiply(multiply(X_31,additive_identity),add(multiply(X_31,additive_identity),X_21))) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
( add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)) != multiply(multiply(X_31,additive_identity),multiply(X_21,add(X_21,X_31)))
| multiply(multiply(X_31,additive_identity),multiply(X_21,add(X_21,X_31))) = add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)))),bind(Y0,$fot(multiply(multiply(X_31,additive_identity),multiply(X_21,add(X_21,X_31)))))]]) ).
cnf(refute_0_142,plain,
multiply(multiply(X_31,additive_identity),multiply(X_21,add(X_21,X_31))) = add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(X_21,additive_identity),multiply(X_31,additive_identity)),multiply(multiply(X_31,additive_identity),multiply(X_21,add(X_21,X_31)))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) = add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)),
inference(subst,[],[refute_0_142:[bind(X_21,$fot(X_36)),bind(X_31,$fot(X_21))]]) ).
cnf(refute_0_144,plain,
( multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) != add(multiply(X_36,additive_identity),multiply(X_21,additive_identity))
| multiply(additive_identity,add(X_21,X_36)) != multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))
| multiply(additive_identity,add(X_21,X_36)) = add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_21,X_36)),multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))) ),[1],$fot(add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)))]]) ).
cnf(refute_0_145,plain,
( multiply(additive_identity,add(X_21,X_36)) != multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))
| multiply(additive_identity,add(X_21,X_36)) = add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))),add(multiply(X_36,additive_identity),multiply(X_21,additive_identity))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
( add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) != multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))
| multiply(additive_identity,add(X_21,X_36)) = add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_21,X_36)),multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))) )],[refute_0_135,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(additive_identity,add(X_21,X_36)) = add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)),multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))) )],[refute_0_108,refute_0_146]) ).
cnf(refute_0_148,plain,
( multiply(additive_identity,add(X_21,X_36)) != add(multiply(X_36,additive_identity),multiply(X_21,additive_identity))
| add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) = multiply(additive_identity,add(X_21,X_36)) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(additive_identity,add(X_21,X_36)))),bind(Y0,$fot(add(multiply(X_36,additive_identity),multiply(X_21,additive_identity))))]]) ).
cnf(refute_0_149,plain,
add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) = multiply(additive_identity,add(X_21,X_36)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_21,X_36)),add(multiply(X_36,additive_identity),multiply(X_21,additive_identity))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) = multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))),
inference(subst,[],[refute_0_149:[bind(X_21,$fot(X_37)),bind(X_36,$fot(inverse(multiply(additive_identity,X_37))))]]) ).
cnf(refute_0_151,plain,
( add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) != multiply(multiply(X_37,additive_identity),multiplicative_identity)
| add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) != multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37))))
| multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) = multiply(multiply(X_37,additive_identity),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)),multiply(multiply(X_37,additive_identity),multiplicative_identity)) ),[0],$fot(multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))))]]) ).
cnf(refute_0_152,plain,
( add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) != multiply(multiply(X_37,additive_identity),multiplicative_identity)
| multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) = multiply(multiply(X_37,additive_identity),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)),multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37))))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
multiply(multiply(X_37,additive_identity),multiplicative_identity) = multiply(X_37,additive_identity),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(multiply(X_37,additive_identity)))]]) ).
cnf(refute_0_154,plain,
( multiply(multiply(X_37,additive_identity),multiplicative_identity) != multiply(X_37,additive_identity)
| multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) != multiply(multiply(X_37,additive_identity),multiplicative_identity)
| multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) = multiply(X_37,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))),multiply(multiply(X_37,additive_identity),multiplicative_identity)) ),[1],$fot(multiply(X_37,additive_identity))]]) ).
cnf(refute_0_155,plain,
( multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) != multiply(multiply(X_37,additive_identity),multiplicative_identity)
| multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) = multiply(X_37,additive_identity) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_37,additive_identity),multiplicative_identity),multiply(X_37,additive_identity)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)) != multiply(multiply(X_37,additive_identity),multiplicative_identity)
| multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) = multiply(X_37,additive_identity) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))),multiply(multiply(X_37,additive_identity),multiplicative_identity)) )],[refute_0_152,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) = multiply(X_37,additive_identity),
inference(resolve,[$cnf( $equal(add(multiply(inverse(multiply(additive_identity,X_37)),additive_identity),multiply(X_37,additive_identity)),multiply(multiply(X_37,additive_identity),multiplicative_identity)) )],[refute_0_103,refute_0_156]) ).
cnf(refute_0_158,plain,
multiply(additive_identity,add(additive_identity,X_47)) = add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_47)),
inference(subst,[],[distributivity2:[bind(X,$fot(additive_identity)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_47))]]) ).
cnf(refute_0_159,plain,
add(multiply(additive_identity,additive_identity),Y) = add(Y,multiply(additive_identity,additive_identity)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_160,plain,
add(X_20,multiply(additive_identity,additive_identity)) = multiply(X_20,add(X_20,additive_identity)),
inference(subst,[],[refute_0_34:[bind(X_10,$fot(X_20)),bind(X_11,$fot(additive_identity))]]) ).
cnf(refute_0_161,plain,
( add(X_20,multiply(additive_identity,additive_identity)) != multiply(X_20,add(X_20,additive_identity))
| add(X_20,additive_identity) != X_20
| add(X_20,multiply(additive_identity,additive_identity)) = multiply(X_20,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(additive_identity,additive_identity)),multiply(X_20,add(X_20,additive_identity))) ),[1,1],$fot(X_20)]]) ).
cnf(refute_0_162,plain,
( add(X_20,multiply(additive_identity,additive_identity)) != multiply(X_20,add(X_20,additive_identity))
| add(X_20,multiply(additive_identity,additive_identity)) = multiply(X_20,X_20) ),
inference(resolve,[$cnf( $equal(add(X_20,additive_identity),X_20) )],[refute_0_42,refute_0_161]) ).
cnf(refute_0_163,plain,
add(X_20,multiply(additive_identity,additive_identity)) = multiply(X_20,X_20),
inference(resolve,[$cnf( $equal(add(X_20,multiply(additive_identity,additive_identity)),multiply(X_20,add(X_20,additive_identity))) )],[refute_0_160,refute_0_162]) ).
cnf(refute_0_164,plain,
add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y),
inference(subst,[],[refute_0_163:[bind(X_20,$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( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_159,refute_0_166]) ).
cnf(refute_0_168,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_47)) = multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47)),
inference(subst,[],[refute_0_167:[bind(Y,$fot(multiply(additive_identity,X_47)))]]) ).
cnf(refute_0_169,plain,
( multiply(additive_identity,add(additive_identity,X_47)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_47))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_47)) != multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))
| multiply(additive_identity,add(additive_identity,X_47)) = multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(additive_identity,add(additive_identity,X_47)),multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))) ),[0],$fot(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_47)))]]) ).
cnf(refute_0_170,plain,
( multiply(additive_identity,add(additive_identity,X_47)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_47))
| multiply(additive_identity,add(additive_identity,X_47)) = multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_47)),multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
multiply(additive_identity,add(additive_identity,X_47)) = multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_47)),add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_47))) )],[refute_0_158,refute_0_170]) ).
cnf(refute_0_172,plain,
multiply(X_45,add(X_46,multiplicative_identity)) = add(multiply(X_45,X_46),multiply(X_45,multiplicative_identity)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_45)),bind(Y,$fot(X_46)),bind(Z,$fot(multiplicative_identity))]]) ).
cnf(refute_0_173,plain,
multiply(X_45,multiplicative_identity) = X_45,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(X_45))]]) ).
cnf(refute_0_174,plain,
( multiply(X_45,add(X_46,multiplicative_identity)) != add(multiply(X_45,X_46),multiply(X_45,multiplicative_identity))
| multiply(X_45,multiplicative_identity) != X_45
| multiply(X_45,add(X_46,multiplicative_identity)) = add(multiply(X_45,X_46),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_45,add(X_46,multiplicative_identity)),add(multiply(X_45,X_46),multiply(X_45,multiplicative_identity))) ),[1,1],$fot(X_45)]]) ).
cnf(refute_0_175,plain,
( multiply(X_45,add(X_46,multiplicative_identity)) != add(multiply(X_45,X_46),multiply(X_45,multiplicative_identity))
| multiply(X_45,add(X_46,multiplicative_identity)) = add(multiply(X_45,X_46),X_45) ),
inference(resolve,[$cnf( $equal(multiply(X_45,multiplicative_identity),X_45) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(X_45,add(X_46,multiplicative_identity)) = add(multiply(X_45,X_46),X_45),
inference(resolve,[$cnf( $equal(multiply(X_45,add(X_46,multiplicative_identity)),add(multiply(X_45,X_46),multiply(X_45,multiplicative_identity))) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),add(X_10,inverse(X_10))),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(inverse(X_10)))]]) ).
cnf(refute_0_178,plain,
add(X_10,inverse(X_10)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_179,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),add(X_10,inverse(X_10)))
| add(X_10,inverse(X_10)) != multiplicative_identity
| add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity) ),
introduced(tautology,[equality,[$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_180,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( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) )],[refute_0_177,refute_0_180]) ).
cnf(refute_0_182,plain,
multiply(add(X_10,X_11),multiplicative_identity) = add(X_10,X_11),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_183,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_184,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( $equal(multiply(add(X_10,X_11),multiplicative_identity),add(X_10,X_11)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
add(X_15,multiply(multiplicative_identity,inverse(X_15))) = add(X_15,multiplicative_identity),
inference(subst,[],[refute_0_185:[bind(X_10,$fot(X_15)),bind(X_11,$fot(multiplicative_identity))]]) ).
cnf(refute_0_187,plain,
multiply(X,multiplicative_identity) = multiply(multiplicative_identity,X),
inference(subst,[],[commutativity_of_multiply:[bind(Y,$fot(multiplicative_identity))]]) ).
cnf(refute_0_188,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_189,plain,
( multiply(X,multiplicative_identity) != X
| multiply(multiplicative_identity,X) = X ),
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),multiply(multiplicative_identity,X)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
multiply(multiplicative_identity,X) = X,
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),X) )],[multiplicative_id1,refute_0_189]) ).
cnf(refute_0_191,plain,
multiply(multiplicative_identity,inverse(X_15)) = inverse(X_15),
inference(subst,[],[refute_0_190:[bind(X,$fot(inverse(X_15)))]]) ).
cnf(refute_0_192,plain,
( multiply(multiplicative_identity,inverse(X_15)) != inverse(X_15)
| add(X_15,multiply(multiplicative_identity,inverse(X_15))) != add(X_15,multiplicative_identity)
| add(X_15,inverse(X_15)) = add(X_15,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_15,multiply(multiplicative_identity,inverse(X_15))),add(X_15,multiplicative_identity)) ),[0,1],$fot(inverse(X_15))]]) ).
cnf(refute_0_193,plain,
( add(X_15,multiply(multiplicative_identity,inverse(X_15))) != add(X_15,multiplicative_identity)
| add(X_15,inverse(X_15)) = add(X_15,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(X_15)),inverse(X_15)) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
add(X_15,inverse(X_15)) = add(X_15,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_15,multiply(multiplicative_identity,inverse(X_15))),add(X_15,multiplicative_identity)) )],[refute_0_186,refute_0_193]) ).
cnf(refute_0_195,plain,
add(X_15,inverse(X_15)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_196,plain,
( add(X_15,inverse(X_15)) != add(X_15,multiplicative_identity)
| add(X_15,inverse(X_15)) != multiplicative_identity
| multiplicative_identity = add(X_15,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_15,inverse(X_15)),add(X_15,multiplicative_identity)) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_197,plain,
( add(X_15,inverse(X_15)) != add(X_15,multiplicative_identity)
| multiplicative_identity = add(X_15,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_15,inverse(X_15)),multiplicative_identity) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
multiplicative_identity = add(X_15,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_15,inverse(X_15)),add(X_15,multiplicative_identity)) )],[refute_0_194,refute_0_197]) ).
cnf(refute_0_199,plain,
( multiplicative_identity != add(X_15,multiplicative_identity)
| add(X_15,multiplicative_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_15,multiplicative_identity)))]]) ).
cnf(refute_0_200,plain,
add(X_15,multiplicative_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_15,multiplicative_identity)) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
add(X_46,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[refute_0_200:[bind(X_15,$fot(X_46))]]) ).
cnf(refute_0_202,plain,
multiply(X_45,add(X_46,multiplicative_identity)) = multiply(X_45,add(X_46,multiplicative_identity)),
introduced(tautology,[refl,[$fot(multiply(X_45,add(X_46,multiplicative_identity)))]]) ).
cnf(refute_0_203,plain,
( multiply(X_45,add(X_46,multiplicative_identity)) != multiply(X_45,add(X_46,multiplicative_identity))
| add(X_46,multiplicative_identity) != multiplicative_identity
| multiply(X_45,add(X_46,multiplicative_identity)) = multiply(X_45,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_45,add(X_46,multiplicative_identity)),multiply(X_45,add(X_46,multiplicative_identity))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_204,plain,
( add(X_46,multiplicative_identity) != multiplicative_identity
| multiply(X_45,add(X_46,multiplicative_identity)) = multiply(X_45,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(X_45,add(X_46,multiplicative_identity)),multiply(X_45,add(X_46,multiplicative_identity))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
multiply(X_45,add(X_46,multiplicative_identity)) = multiply(X_45,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_46,multiplicative_identity),multiplicative_identity) )],[refute_0_201,refute_0_204]) ).
cnf(refute_0_206,plain,
( multiply(X_45,add(X_46,multiplicative_identity)) != multiply(X_45,multiplicative_identity)
| multiply(X_45,multiplicative_identity) != X_45
| multiply(X_45,add(X_46,multiplicative_identity)) = X_45 ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(multiply(X_45,add(X_46,multiplicative_identity)))),bind(Y0,$fot(multiply(X_45,multiplicative_identity))),bind(Z0,$fot(X_45))]]) ).
cnf(refute_0_207,plain,
( multiply(X_45,multiplicative_identity) != X_45
| multiply(X_45,add(X_46,multiplicative_identity)) = X_45 ),
inference(resolve,[$cnf( $equal(multiply(X_45,add(X_46,multiplicative_identity)),multiply(X_45,multiplicative_identity)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
multiply(X_45,add(X_46,multiplicative_identity)) = X_45,
inference(resolve,[$cnf( $equal(multiply(X_45,multiplicative_identity),X_45) )],[refute_0_173,refute_0_207]) ).
cnf(refute_0_209,plain,
( multiply(X_45,add(X_46,multiplicative_identity)) != X_45
| multiply(X_45,add(X_46,multiplicative_identity)) != add(multiply(X_45,X_46),X_45)
| X_45 = add(multiply(X_45,X_46),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_45,add(X_46,multiplicative_identity)),add(multiply(X_45,X_46),X_45)) ),[0],$fot(X_45)]]) ).
cnf(refute_0_210,plain,
( multiply(X_45,add(X_46,multiplicative_identity)) != add(multiply(X_45,X_46),X_45)
| X_45 = add(multiply(X_45,X_46),X_45) ),
inference(resolve,[$cnf( $equal(multiply(X_45,add(X_46,multiplicative_identity)),X_45) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
add(Y,multiply(Y,Z)) = multiply(add(Y,Y),add(Y,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_212,plain,
add(X_15,multiply(X_15,inverse(X_15))) = add(X_15,X_15),
inference(subst,[],[refute_0_185:[bind(X_10,$fot(X_15)),bind(X_11,$fot(X_15))]]) ).
cnf(refute_0_213,plain,
multiply(X_15,inverse(X_15)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_214,plain,
( multiply(X_15,inverse(X_15)) != additive_identity
| add(X_15,multiply(X_15,inverse(X_15))) != add(X_15,X_15)
| add(X_15,additive_identity) = add(X_15,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_15,multiply(X_15,inverse(X_15))),add(X_15,X_15)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_215,plain,
( add(X_15,multiply(X_15,inverse(X_15))) != add(X_15,X_15)
| add(X_15,additive_identity) = add(X_15,X_15) ),
inference(resolve,[$cnf( $equal(multiply(X_15,inverse(X_15)),additive_identity) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
add(X_15,additive_identity) = add(X_15,X_15),
inference(resolve,[$cnf( $equal(add(X_15,multiply(X_15,inverse(X_15))),add(X_15,X_15)) )],[refute_0_212,refute_0_215]) ).
cnf(refute_0_217,plain,
add(X_15,additive_identity) = X_15,
inference(subst,[],[additive_id1:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_218,plain,
( add(X_15,additive_identity) != X_15
| add(X_15,additive_identity) != add(X_15,X_15)
| X_15 = add(X_15,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_15,additive_identity),add(X_15,X_15)) ),[0],$fot(X_15)]]) ).
cnf(refute_0_219,plain,
( add(X_15,additive_identity) != add(X_15,X_15)
| X_15 = add(X_15,X_15) ),
inference(resolve,[$cnf( $equal(add(X_15,additive_identity),X_15) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
X_15 = add(X_15,X_15),
inference(resolve,[$cnf( $equal(add(X_15,additive_identity),add(X_15,X_15)) )],[refute_0_216,refute_0_219]) ).
cnf(refute_0_221,plain,
Y = add(Y,Y),
inference(subst,[],[refute_0_220:[bind(X_15,$fot(Y))]]) ).
cnf(refute_0_222,plain,
( Y != add(Y,Y)
| add(Y,Y) = Y ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(Y)),bind(Y0,$fot(add(Y,Y)))]]) ).
cnf(refute_0_223,plain,
add(Y,Y) = Y,
inference(resolve,[$cnf( $equal(Y,add(Y,Y)) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
( add(Y,Y) != Y
| add(Y,multiply(Y,Z)) != multiply(add(Y,Y),add(Y,Z))
| add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_225,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( $equal(add(Y,Y),Y) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) )],[refute_0_211,refute_0_225]) ).
cnf(refute_0_227,plain,
add(X_45,multiply(X_45,X_46)) = multiply(X_45,add(X_45,X_46)),
inference(subst,[],[refute_0_226:[bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).
cnf(refute_0_228,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_229,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_228]) ).
cnf(refute_0_230,plain,
add(multiply(X_45,X_46),X_45) = add(X_45,multiply(X_45,X_46)),
inference(subst,[],[refute_0_229:[bind(X,$fot(X_45)),bind(Y,$fot(multiply(X_45,X_46)))]]) ).
cnf(refute_0_231,plain,
( add(X_45,multiply(X_45,X_46)) != multiply(X_45,add(X_45,X_46))
| add(multiply(X_45,X_46),X_45) != add(X_45,multiply(X_45,X_46))
| add(multiply(X_45,X_46),X_45) = multiply(X_45,add(X_45,X_46)) ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(add(multiply(X_45,X_46),X_45))),bind(Y0,$fot(add(X_45,multiply(X_45,X_46)))),bind(Z0,$fot(multiply(X_45,add(X_45,X_46))))]]) ).
cnf(refute_0_232,plain,
( add(X_45,multiply(X_45,X_46)) != multiply(X_45,add(X_45,X_46))
| add(multiply(X_45,X_46),X_45) = multiply(X_45,add(X_45,X_46)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_45,X_46),X_45),add(X_45,multiply(X_45,X_46))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
add(multiply(X_45,X_46),X_45) = multiply(X_45,add(X_45,X_46)),
inference(resolve,[$cnf( $equal(add(X_45,multiply(X_45,X_46)),multiply(X_45,add(X_45,X_46))) )],[refute_0_227,refute_0_232]) ).
cnf(refute_0_234,plain,
( X_45 != add(multiply(X_45,X_46),X_45)
| add(multiply(X_45,X_46),X_45) != multiply(X_45,add(X_45,X_46))
| X_45 = multiply(X_45,add(X_45,X_46)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_45,multiply(X_45,add(X_45,X_46))) ),[0],$fot(add(multiply(X_45,X_46),X_45))]]) ).
cnf(refute_0_235,plain,
( X_45 != add(multiply(X_45,X_46),X_45)
| X_45 = multiply(X_45,add(X_45,X_46)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_45,X_46),X_45),multiply(X_45,add(X_45,X_46))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
( multiply(X_45,add(X_46,multiplicative_identity)) != add(multiply(X_45,X_46),X_45)
| X_45 = multiply(X_45,add(X_45,X_46)) ),
inference(resolve,[$cnf( $equal(X_45,add(multiply(X_45,X_46),X_45)) )],[refute_0_210,refute_0_235]) ).
cnf(refute_0_237,plain,
X_45 = multiply(X_45,add(X_45,X_46)),
inference(resolve,[$cnf( $equal(multiply(X_45,add(X_46,multiplicative_identity)),add(multiply(X_45,X_46),X_45)) )],[refute_0_176,refute_0_236]) ).
cnf(refute_0_238,plain,
( X_45 != multiply(X_45,add(X_45,X_46))
| multiply(X_45,add(X_45,X_46)) = X_45 ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(X_45)),bind(Y0,$fot(multiply(X_45,add(X_45,X_46))))]]) ).
cnf(refute_0_239,plain,
multiply(X_45,add(X_45,X_46)) = X_45,
inference(resolve,[$cnf( $equal(X_45,multiply(X_45,add(X_45,X_46))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
multiply(additive_identity,add(additive_identity,X_47)) = additive_identity,
inference(subst,[],[refute_0_239:[bind(X_45,$fot(additive_identity)),bind(X_46,$fot(X_47))]]) ).
cnf(refute_0_241,plain,
( multiply(additive_identity,add(additive_identity,X_47)) != multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))
| multiply(additive_identity,add(additive_identity,X_47)) != additive_identity
| additive_identity = multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_47)),multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_242,plain,
( multiply(additive_identity,add(additive_identity,X_47)) != multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))
| additive_identity = multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_47)),additive_identity) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),
inference(subst,[],[refute_0_53:[bind(X_10,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_244,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,$fot(multiply(additive_identity,X_12)))]]) ).
cnf(refute_0_245,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) ),
introduced(tautology,[equality,[$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_246,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( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
add(X_12,additive_identity) = X_12,
inference(subst,[],[additive_id1:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_249,plain,
multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,add(X_12,additive_identity)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(X_12,additive_identity)))]]) ).
cnf(refute_0_250,plain,
( multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| add(X_12,additive_identity) != X_12
| multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12) ),
introduced(tautology,[equality,[$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_251,plain,
( add(X_12,additive_identity) != X_12
| multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(add(X_12,additive_identity),X_12) )],[refute_0_248,refute_0_251]) ).
cnf(refute_0_253,plain,
add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) = multiply(additive_identity,add(X_12,additive_identity)),
inference(subst,[],[refute_0_115:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_12)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_254,plain,
( add(multiply(additive_identity,X_23),Y) != multiply(Y,add(Y,X_23))
| multiply(Y,add(Y,X_23)) = add(multiply(additive_identity,X_23),Y) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(add(multiply(additive_identity,X_23),Y))),bind(Y0,$fot(multiply(Y,add(Y,X_23))))]]) ).
cnf(refute_0_255,plain,
multiply(Y,add(Y,X_23)) = add(multiply(additive_identity,X_23),Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_23),Y),multiply(Y,add(Y,X_23))) )],[refute_0_57,refute_0_254]) ).
cnf(refute_0_256,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)),
inference(subst,[],[refute_0_255:[bind(Y,$fot(multiply(additive_identity,additive_identity))),bind(X_23,$fot(X_12))]]) ).
cnf(refute_0_257,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)) ),
inference(subst,[],[refute_0_81:[bind(X0,$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_258,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( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_253,refute_0_258]) ).
cnf(refute_0_260,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12) ),
inference(subst,[],[refute_0_81:[bind(X0,$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_261,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( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,X_12)) )],[refute_0_252,refute_0_261]) ).
cnf(refute_0_263,plain,
( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
introduced(tautology,[equality,[$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_264,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( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),multiply(additive_identity,X_12)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_247,refute_0_264]) ).
cnf(refute_0_266,plain,
multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47)) = multiply(additive_identity,X_47),
inference(subst,[],[refute_0_265:[bind(X_12,$fot(X_47))]]) ).
cnf(refute_0_267,plain,
( multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47)) != multiply(additive_identity,X_47)
| additive_identity != multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))
| additive_identity = multiply(additive_identity,X_47) ),
introduced(tautology,[equality,[$cnf( $equal(additive_identity,multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))) ),[1],$fot(multiply(additive_identity,X_47))]]) ).
cnf(refute_0_268,plain,
( additive_identity != multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))
| additive_identity = multiply(additive_identity,X_47) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47)),multiply(additive_identity,X_47)) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
( multiply(additive_identity,add(additive_identity,X_47)) != multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))
| additive_identity = multiply(additive_identity,X_47) ),
inference(resolve,[$cnf( $equal(additive_identity,multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))) )],[refute_0_242,refute_0_268]) ).
cnf(refute_0_270,plain,
additive_identity = multiply(additive_identity,X_47),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_47)),multiply(multiply(additive_identity,X_47),multiply(additive_identity,X_47))) )],[refute_0_171,refute_0_269]) ).
cnf(refute_0_271,plain,
( additive_identity != multiply(additive_identity,X_47)
| multiply(additive_identity,X_47) = additive_identity ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(additive_identity,X_47)))]]) ).
cnf(refute_0_272,plain,
multiply(additive_identity,X_47) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(additive_identity,X_47)) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) = additive_identity,
inference(subst,[],[refute_0_272:[bind(X_47,$fot(add(X_37,inverse(multiply(additive_identity,X_37)))))]]) ).
cnf(refute_0_274,plain,
( multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) != multiply(X_37,additive_identity)
| multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) != additive_identity
| additive_identity = multiply(X_37,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))),multiply(X_37,additive_identity)) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_275,plain,
( multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))) != multiply(X_37,additive_identity)
| additive_identity = multiply(X_37,additive_identity) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))),additive_identity) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
additive_identity = multiply(X_37,additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_37,inverse(multiply(additive_identity,X_37)))),multiply(X_37,additive_identity)) )],[refute_0_157,refute_0_275]) ).
cnf(refute_0_277,plain,
( additive_identity != multiply(X_37,additive_identity)
| multiply(X_37,additive_identity) = additive_identity ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(X_37,additive_identity)))]]) ).
cnf(refute_0_278,plain,
multiply(X_37,additive_identity) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(X_37,additive_identity)) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
multiply(X_21,additive_identity) = additive_identity,
inference(subst,[],[refute_0_278:[bind(X_37,$fot(X_21))]]) ).
cnf(refute_0_280,plain,
add(X_20,multiply(X_21,additive_identity)) = add(X_20,multiply(X_21,additive_identity)),
introduced(tautology,[refl,[$fot(add(X_20,multiply(X_21,additive_identity)))]]) ).
cnf(refute_0_281,plain,
( multiply(X_21,additive_identity) != additive_identity
| add(X_20,multiply(X_21,additive_identity)) != add(X_20,multiply(X_21,additive_identity))
| add(X_20,multiply(X_21,additive_identity)) = add(X_20,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),add(X_20,multiply(X_21,additive_identity))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_282,plain,
( multiply(X_21,additive_identity) != additive_identity
| add(X_20,multiply(X_21,additive_identity)) = add(X_20,additive_identity) ),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),add(X_20,multiply(X_21,additive_identity))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
add(X_20,multiply(X_21,additive_identity)) = add(X_20,additive_identity),
inference(resolve,[$cnf( $equal(multiply(X_21,additive_identity),additive_identity) )],[refute_0_279,refute_0_282]) ).
cnf(refute_0_284,plain,
( add(X_20,multiply(X_21,additive_identity)) != add(X_20,additive_identity)
| add(X_20,additive_identity) != X_20
| add(X_20,multiply(X_21,additive_identity)) = X_20 ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(add(X_20,multiply(X_21,additive_identity)))),bind(Y0,$fot(add(X_20,additive_identity))),bind(Z0,$fot(X_20))]]) ).
cnf(refute_0_285,plain,
( add(X_20,additive_identity) != X_20
| add(X_20,multiply(X_21,additive_identity)) = X_20 ),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),add(X_20,additive_identity)) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
add(X_20,multiply(X_21,additive_identity)) = X_20,
inference(resolve,[$cnf( $equal(add(X_20,additive_identity),X_20) )],[refute_0_42,refute_0_285]) ).
cnf(refute_0_287,plain,
( add(X_20,multiply(X_21,additive_identity)) != X_20
| add(X_20,multiply(X_21,additive_identity)) != multiply(X_20,add(X_21,X_20))
| X_20 = multiply(X_20,add(X_21,X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(X_20,add(X_21,X_20))) ),[0],$fot(X_20)]]) ).
cnf(refute_0_288,plain,
( add(X_20,multiply(X_21,additive_identity)) != multiply(X_20,add(X_21,X_20))
| X_20 = multiply(X_20,add(X_21,X_20)) ),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),X_20) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
X_20 = multiply(X_20,add(X_21,X_20)),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(X_20,add(X_21,X_20))) )],[refute_0_41,refute_0_288]) ).
cnf(refute_0_290,plain,
inverse(inverse(X_21)) = multiply(inverse(inverse(X_21)),add(X_21,inverse(inverse(X_21)))),
inference(subst,[],[refute_0_289:[bind(X_20,$fot(inverse(inverse(X_21))))]]) ).
cnf(refute_0_291,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,$fot(X_12))]]) ).
cnf(refute_0_292,plain,
( add(X_10,multiply(inverse(X_10),X_12)) != multiply(add(X_10,inverse(X_10)),add(X_10,X_12))
| add(X_10,inverse(X_10)) != multiplicative_identity
| add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)) ),
introduced(tautology,[equality,[$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_293,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( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_178,refute_0_292]) ).
cnf(refute_0_294,plain,
add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(add(X_10,inverse(X_10)),add(X_10,X_12))) )],[refute_0_291,refute_0_293]) ).
cnf(refute_0_295,plain,
multiply(multiplicative_identity,add(X_10,X_12)) = add(X_10,X_12),
inference(subst,[],[refute_0_190:[bind(X,$fot(add(X_10,X_12)))]]) ).
cnf(refute_0_296,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_297,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( $equal(multiply(multiplicative_identity,add(X_10,X_12)),add(X_10,X_12)) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
add(X_10,multiply(inverse(X_10),X_12)) = add(X_10,X_12),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(multiplicative_identity,add(X_10,X_12))) )],[refute_0_294,refute_0_297]) ).
cnf(refute_0_299,plain,
add(X_78,multiply(inverse(X_78),inverse(inverse(X_78)))) = add(X_78,inverse(inverse(X_78))),
inference(subst,[],[refute_0_298:[bind(X_10,$fot(X_78)),bind(X_12,$fot(inverse(inverse(X_78))))]]) ).
cnf(refute_0_300,plain,
multiply(inverse(X_78),inverse(inverse(X_78))) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(inverse(X_78)))]]) ).
cnf(refute_0_301,plain,
( multiply(inverse(X_78),inverse(inverse(X_78))) != additive_identity
| add(X_78,multiply(inverse(X_78),inverse(inverse(X_78)))) != add(X_78,inverse(inverse(X_78)))
| add(X_78,additive_identity) = add(X_78,inverse(inverse(X_78))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_78,multiply(inverse(X_78),inverse(inverse(X_78)))),add(X_78,inverse(inverse(X_78)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_302,plain,
( add(X_78,multiply(inverse(X_78),inverse(inverse(X_78)))) != add(X_78,inverse(inverse(X_78)))
| add(X_78,additive_identity) = add(X_78,inverse(inverse(X_78))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_78),inverse(inverse(X_78))),additive_identity) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
add(X_78,additive_identity) = add(X_78,inverse(inverse(X_78))),
inference(resolve,[$cnf( $equal(add(X_78,multiply(inverse(X_78),inverse(inverse(X_78)))),add(X_78,inverse(inverse(X_78)))) )],[refute_0_299,refute_0_302]) ).
cnf(refute_0_304,plain,
add(X_78,additive_identity) = X_78,
inference(subst,[],[additive_id1:[bind(X,$fot(X_78))]]) ).
cnf(refute_0_305,plain,
( add(X_78,additive_identity) != X_78
| add(X_78,additive_identity) != add(X_78,inverse(inverse(X_78)))
| X_78 = add(X_78,inverse(inverse(X_78))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_78,additive_identity),add(X_78,inverse(inverse(X_78)))) ),[0],$fot(X_78)]]) ).
cnf(refute_0_306,plain,
( add(X_78,additive_identity) != add(X_78,inverse(inverse(X_78)))
| X_78 = add(X_78,inverse(inverse(X_78))) ),
inference(resolve,[$cnf( $equal(add(X_78,additive_identity),X_78) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
X_78 = add(X_78,inverse(inverse(X_78))),
inference(resolve,[$cnf( $equal(add(X_78,additive_identity),add(X_78,inverse(inverse(X_78)))) )],[refute_0_303,refute_0_306]) ).
cnf(refute_0_308,plain,
X_21 = add(X_21,inverse(inverse(X_21))),
inference(subst,[],[refute_0_307:[bind(X_78,$fot(X_21))]]) ).
cnf(refute_0_309,plain,
( X_21 != add(X_21,inverse(inverse(X_21)))
| add(X_21,inverse(inverse(X_21))) = X_21 ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(X_21)),bind(Y0,$fot(add(X_21,inverse(inverse(X_21)))))]]) ).
cnf(refute_0_310,plain,
add(X_21,inverse(inverse(X_21))) = X_21,
inference(resolve,[$cnf( $equal(X_21,add(X_21,inverse(inverse(X_21)))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
( add(X_21,inverse(inverse(X_21))) != X_21
| inverse(inverse(X_21)) != multiply(inverse(inverse(X_21)),add(X_21,inverse(inverse(X_21))))
| inverse(inverse(X_21)) = multiply(inverse(inverse(X_21)),X_21) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_21)),multiply(inverse(inverse(X_21)),add(X_21,inverse(inverse(X_21))))) ),[1,1],$fot(X_21)]]) ).
cnf(refute_0_312,plain,
( inverse(inverse(X_21)) != multiply(inverse(inverse(X_21)),add(X_21,inverse(inverse(X_21))))
| inverse(inverse(X_21)) = multiply(inverse(inverse(X_21)),X_21) ),
inference(resolve,[$cnf( $equal(add(X_21,inverse(inverse(X_21))),X_21) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
inverse(inverse(X_21)) = multiply(inverse(inverse(X_21)),X_21),
inference(resolve,[$cnf( $equal(inverse(inverse(X_21)),multiply(inverse(inverse(X_21)),add(X_21,inverse(inverse(X_21))))) )],[refute_0_290,refute_0_312]) ).
cnf(refute_0_314,plain,
multiply(inverse(inverse(X_21)),X_21) = multiply(X_21,inverse(inverse(X_21))),
inference(subst,[],[refute_0_30:[bind(X,$fot(X_21)),bind(Y,$fot(inverse(inverse(X_21))))]]) ).
cnf(refute_0_315,plain,
( multiply(inverse(inverse(X_21)),X_21) != multiply(X_21,inverse(inverse(X_21)))
| inverse(inverse(X_21)) != multiply(inverse(inverse(X_21)),X_21)
| inverse(inverse(X_21)) = multiply(X_21,inverse(inverse(X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_21)),multiply(inverse(inverse(X_21)),X_21)) ),[1],$fot(multiply(X_21,inverse(inverse(X_21))))]]) ).
cnf(refute_0_316,plain,
( inverse(inverse(X_21)) != multiply(inverse(inverse(X_21)),X_21)
| inverse(inverse(X_21)) = multiply(X_21,inverse(inverse(X_21))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_21)),X_21),multiply(X_21,inverse(inverse(X_21)))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
inverse(inverse(X_21)) = multiply(X_21,inverse(inverse(X_21))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_21)),multiply(inverse(inverse(X_21)),X_21)) )],[refute_0_313,refute_0_316]) ).
cnf(refute_0_318,plain,
( inverse(inverse(X_21)) != multiply(X_21,inverse(inverse(X_21)))
| multiply(X_21,inverse(inverse(X_21))) = inverse(inverse(X_21)) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(inverse(inverse(X_21)))),bind(Y0,$fot(multiply(X_21,inverse(inverse(X_21)))))]]) ).
cnf(refute_0_319,plain,
multiply(X_21,inverse(inverse(X_21))) = inverse(inverse(X_21)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_21)),multiply(X_21,inverse(inverse(X_21)))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
multiply(X_104,inverse(inverse(X_104))) = inverse(inverse(X_104)),
inference(subst,[],[refute_0_319:[bind(X_21,$fot(X_104))]]) ).
cnf(refute_0_321,plain,
( X_104 != multiply(X_104,inverse(inverse(X_104)))
| multiply(X_104,inverse(inverse(X_104))) != inverse(inverse(X_104))
| X_104 = inverse(inverse(X_104)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_104,inverse(inverse(X_104))) ),[0],$fot(multiply(X_104,inverse(inverse(X_104))))]]) ).
cnf(refute_0_322,plain,
( X_104 != multiply(X_104,inverse(inverse(X_104)))
| X_104 = inverse(inverse(X_104)) ),
inference(resolve,[$cnf( $equal(multiply(X_104,inverse(inverse(X_104))),inverse(inverse(X_104))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
( multiply(X_104,multiplicative_identity) != multiply(X_104,inverse(inverse(X_104)))
| X_104 = inverse(inverse(X_104)) ),
inference(resolve,[$cnf( $equal(X_104,multiply(X_104,inverse(inverse(X_104)))) )],[refute_0_20,refute_0_322]) ).
cnf(refute_0_324,plain,
X_104 = inverse(inverse(X_104)),
inference(resolve,[$cnf( $equal(multiply(X_104,multiplicative_identity),multiply(X_104,inverse(inverse(X_104)))) )],[refute_0_17,refute_0_323]) ).
cnf(refute_0_325,plain,
b = inverse(inverse(b)),
inference(subst,[],[refute_0_324:[bind(X_104,$fot(b))]]) ).
cnf(refute_0_326,plain,
multiply(a,add(b,X_47)) = add(multiply(a,b),multiply(a,X_47)),
inference(subst,[],[distributivity2:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_47))]]) ).
cnf(refute_0_327,plain,
( multiply(a,add(b,X_47)) != add(multiply(a,b),multiply(a,X_47))
| multiply(a,b) != additive_identity
| multiply(a,add(b,X_47)) = add(additive_identity,multiply(a,X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,add(b,X_47)),add(multiply(a,b),multiply(a,X_47))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_328,plain,
( multiply(a,add(b,X_47)) != add(multiply(a,b),multiply(a,X_47))
| multiply(a,add(b,X_47)) = add(additive_identity,multiply(a,X_47)) ),
inference(resolve,[$cnf( $equal(multiply(a,b),additive_identity) )],[b_an_additive_identity,refute_0_327]) ).
cnf(refute_0_329,plain,
multiply(a,add(b,X_47)) = add(additive_identity,multiply(a,X_47)),
inference(resolve,[$cnf( $equal(multiply(a,add(b,X_47)),add(multiply(a,b),multiply(a,X_47))) )],[refute_0_326,refute_0_328]) ).
cnf(refute_0_330,plain,
add(additive_identity,multiply(a,X_47)) = multiply(a,X_47),
inference(subst,[],[refute_0_8:[bind(X,$fot(multiply(a,X_47)))]]) ).
cnf(refute_0_331,plain,
( multiply(a,add(b,X_47)) != add(additive_identity,multiply(a,X_47))
| add(additive_identity,multiply(a,X_47)) != multiply(a,X_47)
| multiply(a,add(b,X_47)) = multiply(a,X_47) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,add(b,X_47)),multiply(a,X_47)) ),[0],$fot(add(additive_identity,multiply(a,X_47)))]]) ).
cnf(refute_0_332,plain,
( multiply(a,add(b,X_47)) != add(additive_identity,multiply(a,X_47))
| multiply(a,add(b,X_47)) = multiply(a,X_47) ),
inference(resolve,[$cnf( $equal(add(additive_identity,multiply(a,X_47)),multiply(a,X_47)) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
multiply(a,add(b,X_47)) = multiply(a,X_47),
inference(resolve,[$cnf( $equal(multiply(a,add(b,X_47)),add(additive_identity,multiply(a,X_47))) )],[refute_0_329,refute_0_332]) ).
cnf(refute_0_334,plain,
multiply(a,add(b,inverse(b))) = multiply(a,inverse(b)),
inference(subst,[],[refute_0_333:[bind(X_47,$fot(inverse(b)))]]) ).
cnf(refute_0_335,plain,
add(inverse(b),multiply(a,additive_identity)) = multiply(inverse(b),add(a,inverse(b))),
inference(subst,[],[refute_0_41:[bind(X_20,$fot(inverse(b))),bind(X_21,$fot(a))]]) ).
cnf(refute_0_336,plain,
add(a,multiply(b,X_12)) = multiply(add(a,b),add(a,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_337,plain,
( add(a,multiply(b,X_12)) != multiply(add(a,b),add(a,X_12))
| add(a,b) != multiplicative_identity
| add(a,multiply(b,X_12)) = multiply(multiplicative_identity,add(a,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,multiply(b,X_12)),multiply(add(a,b),add(a,X_12))) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_338,plain,
( add(a,multiply(b,X_12)) != multiply(add(a,b),add(a,X_12))
| add(a,multiply(b,X_12)) = multiply(multiplicative_identity,add(a,X_12)) ),
inference(resolve,[$cnf( $equal(add(a,b),multiplicative_identity) )],[b_a_multiplicative_identity,refute_0_337]) ).
cnf(refute_0_339,plain,
add(a,multiply(b,X_12)) = multiply(multiplicative_identity,add(a,X_12)),
inference(resolve,[$cnf( $equal(add(a,multiply(b,X_12)),multiply(add(a,b),add(a,X_12))) )],[refute_0_336,refute_0_338]) ).
cnf(refute_0_340,plain,
multiply(multiplicative_identity,add(a,X_12)) = add(a,X_12),
inference(subst,[],[refute_0_190:[bind(X,$fot(add(a,X_12)))]]) ).
cnf(refute_0_341,plain,
( multiply(multiplicative_identity,add(a,X_12)) != add(a,X_12)
| add(a,multiply(b,X_12)) != multiply(multiplicative_identity,add(a,X_12))
| add(a,multiply(b,X_12)) = add(a,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,multiply(b,X_12)),multiply(multiplicative_identity,add(a,X_12))) ),[1],$fot(add(a,X_12))]]) ).
cnf(refute_0_342,plain,
( add(a,multiply(b,X_12)) != multiply(multiplicative_identity,add(a,X_12))
| add(a,multiply(b,X_12)) = add(a,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(a,X_12)),add(a,X_12)) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
add(a,multiply(b,X_12)) = add(a,X_12),
inference(resolve,[$cnf( $equal(add(a,multiply(b,X_12)),multiply(multiplicative_identity,add(a,X_12))) )],[refute_0_339,refute_0_342]) ).
cnf(refute_0_344,plain,
add(a,multiply(b,inverse(b))) = add(a,inverse(b)),
inference(subst,[],[refute_0_343:[bind(X_12,$fot(inverse(b)))]]) ).
cnf(refute_0_345,plain,
multiply(b,inverse(b)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(b))]]) ).
cnf(refute_0_346,plain,
( multiply(b,inverse(b)) != additive_identity
| add(a,multiply(b,inverse(b))) != add(a,inverse(b))
| add(a,additive_identity) = add(a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,multiply(b,inverse(b))),add(a,inverse(b))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_347,plain,
( add(a,multiply(b,inverse(b))) != add(a,inverse(b))
| add(a,additive_identity) = add(a,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(b)),additive_identity) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
add(a,additive_identity) = add(a,inverse(b)),
inference(resolve,[$cnf( $equal(add(a,multiply(b,inverse(b))),add(a,inverse(b))) )],[refute_0_344,refute_0_347]) ).
cnf(refute_0_349,plain,
add(a,additive_identity) = a,
inference(subst,[],[additive_id1:[bind(X,$fot(a))]]) ).
cnf(refute_0_350,plain,
( add(a,additive_identity) != add(a,inverse(b))
| add(a,additive_identity) != a
| a = add(a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,additive_identity),add(a,inverse(b))) ),[0],$fot(a)]]) ).
cnf(refute_0_351,plain,
( add(a,additive_identity) != add(a,inverse(b))
| a = add(a,inverse(b)) ),
inference(resolve,[$cnf( $equal(add(a,additive_identity),a) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
a = add(a,inverse(b)),
inference(resolve,[$cnf( $equal(add(a,additive_identity),add(a,inverse(b))) )],[refute_0_348,refute_0_351]) ).
cnf(refute_0_353,plain,
( a != add(a,inverse(b))
| add(a,inverse(b)) = a ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(a)),bind(Y0,$fot(add(a,inverse(b))))]]) ).
cnf(refute_0_354,plain,
add(a,inverse(b)) = a,
inference(resolve,[$cnf( $equal(a,add(a,inverse(b))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
( add(a,inverse(b)) != a
| add(inverse(b),multiply(a,additive_identity)) != multiply(inverse(b),add(a,inverse(b)))
| add(inverse(b),multiply(a,additive_identity)) = multiply(inverse(b),a) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(b),multiply(a,additive_identity)),multiply(inverse(b),add(a,inverse(b)))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_356,plain,
( add(inverse(b),multiply(a,additive_identity)) != multiply(inverse(b),add(a,inverse(b)))
| add(inverse(b),multiply(a,additive_identity)) = multiply(inverse(b),a) ),
inference(resolve,[$cnf( $equal(add(a,inverse(b)),a) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
add(inverse(b),multiply(a,additive_identity)) = multiply(inverse(b),a),
inference(resolve,[$cnf( $equal(add(inverse(b),multiply(a,additive_identity)),multiply(inverse(b),add(a,inverse(b)))) )],[refute_0_335,refute_0_356]) ).
cnf(refute_0_358,plain,
multiply(inverse(b),a) = multiply(a,inverse(b)),
inference(subst,[],[refute_0_30:[bind(X,$fot(a)),bind(Y,$fot(inverse(b)))]]) ).
cnf(refute_0_359,plain,
( multiply(inverse(b),a) != multiply(a,inverse(b))
| add(inverse(b),multiply(a,additive_identity)) != multiply(inverse(b),a)
| add(inverse(b),multiply(a,additive_identity)) = multiply(a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(b),multiply(a,additive_identity)),multiply(inverse(b),a)) ),[1],$fot(multiply(a,inverse(b)))]]) ).
cnf(refute_0_360,plain,
( add(inverse(b),multiply(a,additive_identity)) != multiply(inverse(b),a)
| add(inverse(b),multiply(a,additive_identity)) = multiply(a,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),a),multiply(a,inverse(b))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
add(inverse(b),multiply(a,additive_identity)) = multiply(a,inverse(b)),
inference(resolve,[$cnf( $equal(add(inverse(b),multiply(a,additive_identity)),multiply(inverse(b),a)) )],[refute_0_357,refute_0_360]) ).
cnf(refute_0_362,plain,
add(inverse(b),additive_identity) = inverse(b),
inference(subst,[],[additive_id1:[bind(X,$fot(inverse(b)))]]) ).
cnf(refute_0_363,plain,
multiply(a,additive_identity) = additive_identity,
inference(subst,[],[refute_0_278:[bind(X_37,$fot(a))]]) ).
cnf(refute_0_364,plain,
add(inverse(b),multiply(a,additive_identity)) = add(inverse(b),multiply(a,additive_identity)),
introduced(tautology,[refl,[$fot(add(inverse(b),multiply(a,additive_identity)))]]) ).
cnf(refute_0_365,plain,
( multiply(a,additive_identity) != additive_identity
| add(inverse(b),multiply(a,additive_identity)) != add(inverse(b),multiply(a,additive_identity))
| add(inverse(b),multiply(a,additive_identity)) = add(inverse(b),additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(b),multiply(a,additive_identity)),add(inverse(b),multiply(a,additive_identity))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_366,plain,
( multiply(a,additive_identity) != additive_identity
| add(inverse(b),multiply(a,additive_identity)) = add(inverse(b),additive_identity) ),
inference(resolve,[$cnf( $equal(add(inverse(b),multiply(a,additive_identity)),add(inverse(b),multiply(a,additive_identity))) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
add(inverse(b),multiply(a,additive_identity)) = add(inverse(b),additive_identity),
inference(resolve,[$cnf( $equal(multiply(a,additive_identity),additive_identity) )],[refute_0_363,refute_0_366]) ).
cnf(refute_0_368,plain,
( add(inverse(b),multiply(a,additive_identity)) != add(inverse(b),additive_identity)
| add(inverse(b),additive_identity) != inverse(b)
| add(inverse(b),multiply(a,additive_identity)) = inverse(b) ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(add(inverse(b),multiply(a,additive_identity)))),bind(Y0,$fot(add(inverse(b),additive_identity))),bind(Z0,$fot(inverse(b)))]]) ).
cnf(refute_0_369,plain,
( add(inverse(b),additive_identity) != inverse(b)
| add(inverse(b),multiply(a,additive_identity)) = inverse(b) ),
inference(resolve,[$cnf( $equal(add(inverse(b),multiply(a,additive_identity)),add(inverse(b),additive_identity)) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
add(inverse(b),multiply(a,additive_identity)) = inverse(b),
inference(resolve,[$cnf( $equal(add(inverse(b),additive_identity),inverse(b)) )],[refute_0_362,refute_0_369]) ).
cnf(refute_0_371,plain,
( add(inverse(b),multiply(a,additive_identity)) != multiply(a,inverse(b))
| add(inverse(b),multiply(a,additive_identity)) != inverse(b)
| inverse(b) = multiply(a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(b),multiply(a,additive_identity)),multiply(a,inverse(b))) ),[0],$fot(inverse(b))]]) ).
cnf(refute_0_372,plain,
( add(inverse(b),multiply(a,additive_identity)) != multiply(a,inverse(b))
| inverse(b) = multiply(a,inverse(b)) ),
inference(resolve,[$cnf( $equal(add(inverse(b),multiply(a,additive_identity)),inverse(b)) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
inverse(b) = multiply(a,inverse(b)),
inference(resolve,[$cnf( $equal(add(inverse(b),multiply(a,additive_identity)),multiply(a,inverse(b))) )],[refute_0_361,refute_0_372]) ).
cnf(refute_0_374,plain,
( inverse(b) != multiply(a,inverse(b))
| multiply(a,inverse(b)) = inverse(b) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(inverse(b))),bind(Y0,$fot(multiply(a,inverse(b))))]]) ).
cnf(refute_0_375,plain,
multiply(a,inverse(b)) = inverse(b),
inference(resolve,[$cnf( $equal(inverse(b),multiply(a,inverse(b))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
( multiply(a,add(b,inverse(b))) != multiply(a,inverse(b))
| multiply(a,inverse(b)) != inverse(b)
| multiply(a,add(b,inverse(b))) = inverse(b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,add(b,inverse(b))),inverse(b)) ),[0],$fot(multiply(a,inverse(b)))]]) ).
cnf(refute_0_377,plain,
( multiply(a,add(b,inverse(b))) != multiply(a,inverse(b))
| multiply(a,add(b,inverse(b))) = inverse(b) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),inverse(b)) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
multiply(a,add(b,inverse(b))) = inverse(b),
inference(resolve,[$cnf( $equal(multiply(a,add(b,inverse(b))),multiply(a,inverse(b))) )],[refute_0_334,refute_0_377]) ).
cnf(refute_0_379,plain,
add(Z,multiply(Y,Z)) = multiply(add(Z,Y),add(Z,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Z))]]) ).
cnf(refute_0_380,plain,
Z = add(Z,Z),
inference(subst,[],[refute_0_220:[bind(X_15,$fot(Z))]]) ).
cnf(refute_0_381,plain,
( Z != add(Z,Z)
| add(Z,Z) = Z ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(Z)),bind(Y0,$fot(add(Z,Z)))]]) ).
cnf(refute_0_382,plain,
add(Z,Z) = Z,
inference(resolve,[$cnf( $equal(Z,add(Z,Z)) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
( add(Z,Z) != Z
| add(Z,multiply(Y,Z)) != multiply(add(Z,Y),add(Z,Z))
| add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),add(Z,Z))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_384,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( $equal(add(Z,Z),Z) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z),
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),add(Z,Z))) )],[refute_0_379,refute_0_384]) ).
cnf(refute_0_386,plain,
multiply(add(Z,Y),Z) = multiply(Z,add(Z,Y)),
inference(subst,[],[refute_0_30:[bind(X,$fot(Z)),bind(Y,$fot(add(Z,Y)))]]) ).
cnf(refute_0_387,plain,
( multiply(add(Z,Y),Z) != multiply(Z,add(Z,Y))
| add(Z,multiply(Y,Z)) != multiply(add(Z,Y),Z)
| add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),Z)) ),[1],$fot(multiply(Z,add(Z,Y)))]]) ).
cnf(refute_0_388,plain,
( add(Z,multiply(Y,Z)) != multiply(add(Z,Y),Z)
| add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(add(Z,Y),Z),multiply(Z,add(Z,Y))) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)),
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),Z)) )],[refute_0_385,refute_0_388]) ).
cnf(refute_0_390,plain,
add(X_29,multiply(X_29,X_29)) = multiply(X_29,add(X_29,X_29)),
inference(subst,[],[refute_0_389:[bind(Y,$fot(X_29)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_391,plain,
add(multiply(additive_identity,additive_identity),X_29) = multiply(X_29,X_29),
inference(subst,[],[refute_0_167:[bind(Y,$fot(X_29))]]) ).
cnf(refute_0_392,plain,
( add(multiply(additive_identity,additive_identity),X_29) != multiply(X_29,X_29)
| multiply(X_29,X_29) = add(multiply(additive_identity,additive_identity),X_29) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),X_29))),bind(Y0,$fot(multiply(X_29,X_29)))]]) ).
cnf(refute_0_393,plain,
multiply(X_29,X_29) = add(multiply(additive_identity,additive_identity),X_29),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_29),multiply(X_29,X_29)) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
( multiply(X_29,X_29) != add(multiply(additive_identity,additive_identity),X_29)
| add(X_29,multiply(X_29,X_29)) != multiply(X_29,add(X_29,X_29))
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = multiply(X_29,add(X_29,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_29,multiply(X_29,X_29)),multiply(X_29,add(X_29,X_29))) ),[0,1],$fot(add(multiply(additive_identity,additive_identity),X_29))]]) ).
cnf(refute_0_395,plain,
( add(X_29,multiply(X_29,X_29)) != multiply(X_29,add(X_29,X_29))
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = multiply(X_29,add(X_29,X_29)) ),
inference(resolve,[$cnf( $equal(multiply(X_29,X_29),add(multiply(additive_identity,additive_identity),X_29)) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = multiply(X_29,add(X_29,X_29)),
inference(resolve,[$cnf( $equal(add(X_29,multiply(X_29,X_29)),multiply(X_29,add(X_29,X_29))) )],[refute_0_390,refute_0_395]) ).
cnf(refute_0_397,plain,
( X_15 != add(X_15,X_15)
| add(X_15,X_15) = X_15 ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(X_15)),bind(Y0,$fot(add(X_15,X_15)))]]) ).
cnf(refute_0_398,plain,
add(X_15,X_15) = X_15,
inference(resolve,[$cnf( $equal(X_15,add(X_15,X_15)) )],[refute_0_220,refute_0_397]) ).
cnf(refute_0_399,plain,
add(X_29,X_29) = X_29,
inference(subst,[],[refute_0_398:[bind(X_15,$fot(X_29))]]) ).
cnf(refute_0_400,plain,
multiply(X_29,add(X_29,X_29)) = multiply(X_29,add(X_29,X_29)),
introduced(tautology,[refl,[$fot(multiply(X_29,add(X_29,X_29)))]]) ).
cnf(refute_0_401,plain,
( multiply(X_29,add(X_29,X_29)) != multiply(X_29,add(X_29,X_29))
| add(X_29,X_29) != X_29
| multiply(X_29,add(X_29,X_29)) = multiply(X_29,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_29,add(X_29,X_29)),multiply(X_29,add(X_29,X_29))) ),[1,1],$fot(X_29)]]) ).
cnf(refute_0_402,plain,
( add(X_29,X_29) != X_29
| multiply(X_29,add(X_29,X_29)) = multiply(X_29,X_29) ),
inference(resolve,[$cnf( $equal(multiply(X_29,add(X_29,X_29)),multiply(X_29,add(X_29,X_29))) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
multiply(X_29,add(X_29,X_29)) = multiply(X_29,X_29),
inference(resolve,[$cnf( $equal(add(X_29,X_29),X_29) )],[refute_0_399,refute_0_402]) ).
cnf(refute_0_404,plain,
( multiply(X_29,add(X_29,X_29)) != multiply(X_29,X_29)
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) != multiply(X_29,add(X_29,X_29))
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = multiply(X_29,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_29,add(multiply(additive_identity,additive_identity),X_29)),multiply(X_29,add(X_29,X_29))) ),[1],$fot(multiply(X_29,X_29))]]) ).
cnf(refute_0_405,plain,
( add(X_29,add(multiply(additive_identity,additive_identity),X_29)) != multiply(X_29,add(X_29,X_29))
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = multiply(X_29,X_29) ),
inference(resolve,[$cnf( $equal(multiply(X_29,add(X_29,X_29)),multiply(X_29,X_29)) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = multiply(X_29,X_29),
inference(resolve,[$cnf( $equal(add(X_29,add(multiply(additive_identity,additive_identity),X_29)),multiply(X_29,add(X_29,X_29))) )],[refute_0_396,refute_0_405]) ).
cnf(refute_0_407,plain,
add(additive_identity,X_29) = X_29,
inference(subst,[],[refute_0_8:[bind(X,$fot(X_29))]]) ).
cnf(refute_0_408,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(subst,[],[refute_0_272:[bind(X_47,$fot(additive_identity))]]) ).
cnf(refute_0_409,plain,
add(multiply(additive_identity,additive_identity),X_29) = add(multiply(additive_identity,additive_identity),X_29),
introduced(tautology,[refl,[$fot(add(multiply(additive_identity,additive_identity),X_29))]]) ).
cnf(refute_0_410,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(multiply(additive_identity,additive_identity),X_29) != add(multiply(additive_identity,additive_identity),X_29)
| add(multiply(additive_identity,additive_identity),X_29) = add(additive_identity,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_29),add(multiply(additive_identity,additive_identity),X_29)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_411,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(multiply(additive_identity,additive_identity),X_29) = add(additive_identity,X_29) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_29),add(multiply(additive_identity,additive_identity),X_29)) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
add(multiply(additive_identity,additive_identity),X_29) = add(additive_identity,X_29),
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),additive_identity) )],[refute_0_408,refute_0_411]) ).
cnf(refute_0_413,plain,
( add(multiply(additive_identity,additive_identity),X_29) != add(additive_identity,X_29)
| add(additive_identity,X_29) != X_29
| add(multiply(additive_identity,additive_identity),X_29) = X_29 ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),X_29))),bind(Y0,$fot(add(additive_identity,X_29))),bind(Z0,$fot(X_29))]]) ).
cnf(refute_0_414,plain,
( add(additive_identity,X_29) != X_29
| add(multiply(additive_identity,additive_identity),X_29) = X_29 ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_29),add(additive_identity,X_29)) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
add(multiply(additive_identity,additive_identity),X_29) = X_29,
inference(resolve,[$cnf( $equal(add(additive_identity,X_29),X_29) )],[refute_0_407,refute_0_414]) ).
cnf(refute_0_416,plain,
add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = add(X_29,add(multiply(additive_identity,additive_identity),X_29)),
introduced(tautology,[refl,[$fot(add(X_29,add(multiply(additive_identity,additive_identity),X_29)))]]) ).
cnf(refute_0_417,plain,
( add(X_29,add(multiply(additive_identity,additive_identity),X_29)) != add(X_29,add(multiply(additive_identity,additive_identity),X_29))
| add(multiply(additive_identity,additive_identity),X_29) != X_29
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = add(X_29,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_29,add(multiply(additive_identity,additive_identity),X_29)),add(X_29,add(multiply(additive_identity,additive_identity),X_29))) ),[1,1],$fot(X_29)]]) ).
cnf(refute_0_418,plain,
( add(multiply(additive_identity,additive_identity),X_29) != X_29
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = add(X_29,X_29) ),
inference(resolve,[$cnf( $equal(add(X_29,add(multiply(additive_identity,additive_identity),X_29)),add(X_29,add(multiply(additive_identity,additive_identity),X_29))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = add(X_29,X_29),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_29),X_29) )],[refute_0_415,refute_0_418]) ).
cnf(refute_0_420,plain,
( add(X_29,X_29) != X_29
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) != add(X_29,X_29)
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = X_29 ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(add(X_29,add(multiply(additive_identity,additive_identity),X_29)))),bind(Y0,$fot(add(X_29,X_29))),bind(Z0,$fot(X_29))]]) ).
cnf(refute_0_421,plain,
( add(X_29,X_29) != X_29
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = X_29 ),
inference(resolve,[$cnf( $equal(add(X_29,add(multiply(additive_identity,additive_identity),X_29)),add(X_29,X_29)) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
add(X_29,add(multiply(additive_identity,additive_identity),X_29)) = X_29,
inference(resolve,[$cnf( $equal(add(X_29,X_29),X_29) )],[refute_0_399,refute_0_421]) ).
cnf(refute_0_423,plain,
( add(X_29,add(multiply(additive_identity,additive_identity),X_29)) != X_29
| add(X_29,add(multiply(additive_identity,additive_identity),X_29)) != multiply(X_29,X_29)
| X_29 = multiply(X_29,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_29,add(multiply(additive_identity,additive_identity),X_29)),multiply(X_29,X_29)) ),[0],$fot(X_29)]]) ).
cnf(refute_0_424,plain,
( add(X_29,add(multiply(additive_identity,additive_identity),X_29)) != multiply(X_29,X_29)
| X_29 = multiply(X_29,X_29) ),
inference(resolve,[$cnf( $equal(add(X_29,add(multiply(additive_identity,additive_identity),X_29)),X_29) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
X_29 = multiply(X_29,X_29),
inference(resolve,[$cnf( $equal(add(X_29,add(multiply(additive_identity,additive_identity),X_29)),multiply(X_29,X_29)) )],[refute_0_406,refute_0_424]) ).
cnf(refute_0_426,plain,
( X_29 != multiply(X_29,X_29)
| multiply(X_29,X_29) = X_29 ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(X_29)),bind(Y0,$fot(multiply(X_29,X_29)))]]) ).
cnf(refute_0_427,plain,
multiply(X_29,X_29) = X_29,
inference(resolve,[$cnf( $equal(X_29,multiply(X_29,X_29)) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
multiply(a,a) = a,
inference(subst,[],[refute_0_427:[bind(X_29,$fot(a))]]) ).
cnf(refute_0_429,plain,
multiply(a,add(b,multiply(X_11,inverse(b)))) = multiply(a,multiply(X_11,inverse(b))),
inference(subst,[],[refute_0_333:[bind(X_47,$fot(multiply(X_11,inverse(b))))]]) ).
cnf(refute_0_430,plain,
add(b,multiply(X_11,inverse(b))) = add(b,X_11),
inference(subst,[],[refute_0_185:[bind(X_10,$fot(b))]]) ).
cnf(refute_0_431,plain,
( multiply(a,add(b,multiply(X_11,inverse(b)))) != multiply(a,multiply(X_11,inverse(b)))
| add(b,multiply(X_11,inverse(b))) != add(b,X_11)
| multiply(a,add(b,X_11)) = multiply(a,multiply(X_11,inverse(b))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,add(b,multiply(X_11,inverse(b)))),multiply(a,multiply(X_11,inverse(b)))) ),[0,1],$fot(add(b,X_11))]]) ).
cnf(refute_0_432,plain,
( multiply(a,add(b,multiply(X_11,inverse(b)))) != multiply(a,multiply(X_11,inverse(b)))
| multiply(a,add(b,X_11)) = multiply(a,multiply(X_11,inverse(b))) ),
inference(resolve,[$cnf( $equal(add(b,multiply(X_11,inverse(b))),add(b,X_11)) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
multiply(a,add(b,X_11)) = multiply(a,multiply(X_11,inverse(b))),
inference(resolve,[$cnf( $equal(multiply(a,add(b,multiply(X_11,inverse(b)))),multiply(a,multiply(X_11,inverse(b)))) )],[refute_0_429,refute_0_432]) ).
cnf(refute_0_434,plain,
multiply(a,add(b,X_11)) = multiply(a,X_11),
inference(subst,[],[refute_0_333:[bind(X_47,$fot(X_11))]]) ).
cnf(refute_0_435,plain,
( multiply(a,add(b,X_11)) != multiply(a,X_11)
| multiply(a,add(b,X_11)) != multiply(a,multiply(X_11,inverse(b)))
| multiply(a,X_11) = multiply(a,multiply(X_11,inverse(b))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,add(b,X_11)),multiply(a,multiply(X_11,inverse(b)))) ),[0],$fot(multiply(a,X_11))]]) ).
cnf(refute_0_436,plain,
( multiply(a,add(b,X_11)) != multiply(a,multiply(X_11,inverse(b)))
| multiply(a,X_11) = multiply(a,multiply(X_11,inverse(b))) ),
inference(resolve,[$cnf( $equal(multiply(a,add(b,X_11)),multiply(a,X_11)) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
add(multiply(Y,inverse(b)),multiply(a,additive_identity)) = multiply(multiply(Y,inverse(b)),add(a,multiply(Y,inverse(b)))),
inference(subst,[],[refute_0_41:[bind(X_20,$fot(multiply(Y,inverse(b)))),bind(X_21,$fot(a))]]) ).
cnf(refute_0_438,plain,
add(a,multiply(Y,inverse(b))) = multiply(add(a,Y),add(a,inverse(b))),
inference(subst,[],[distributivity1:[bind(X,$fot(a)),bind(Z,$fot(inverse(b)))]]) ).
cnf(refute_0_439,plain,
( add(a,multiply(Y,inverse(b))) != multiply(add(a,Y),add(a,inverse(b)))
| add(a,inverse(b)) != a
| add(a,multiply(Y,inverse(b))) = multiply(add(a,Y),a) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,multiply(Y,inverse(b))),multiply(add(a,Y),add(a,inverse(b)))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_440,plain,
( add(a,multiply(Y,inverse(b))) != multiply(add(a,Y),add(a,inverse(b)))
| add(a,multiply(Y,inverse(b))) = multiply(add(a,Y),a) ),
inference(resolve,[$cnf( $equal(add(a,inverse(b)),a) )],[refute_0_354,refute_0_439]) ).
cnf(refute_0_441,plain,
add(a,multiply(Y,inverse(b))) = multiply(add(a,Y),a),
inference(resolve,[$cnf( $equal(add(a,multiply(Y,inverse(b))),multiply(add(a,Y),add(a,inverse(b)))) )],[refute_0_438,refute_0_440]) ).
cnf(refute_0_442,plain,
multiply(add(a,Y),a) = multiply(a,add(a,Y)),
inference(subst,[],[refute_0_30:[bind(X,$fot(a)),bind(Y,$fot(add(a,Y)))]]) ).
cnf(refute_0_443,plain,
( multiply(add(a,Y),a) != multiply(a,add(a,Y))
| add(a,multiply(Y,inverse(b))) != multiply(add(a,Y),a)
| add(a,multiply(Y,inverse(b))) = multiply(a,add(a,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,multiply(Y,inverse(b))),multiply(add(a,Y),a)) ),[1],$fot(multiply(a,add(a,Y)))]]) ).
cnf(refute_0_444,plain,
( add(a,multiply(Y,inverse(b))) != multiply(add(a,Y),a)
| add(a,multiply(Y,inverse(b))) = multiply(a,add(a,Y)) ),
inference(resolve,[$cnf( $equal(multiply(add(a,Y),a),multiply(a,add(a,Y))) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
add(a,multiply(Y,inverse(b))) = multiply(a,add(a,Y)),
inference(resolve,[$cnf( $equal(add(a,multiply(Y,inverse(b))),multiply(add(a,Y),a)) )],[refute_0_441,refute_0_444]) ).
cnf(refute_0_446,plain,
( add(multiply(Y,inverse(b)),multiply(a,additive_identity)) != multiply(multiply(Y,inverse(b)),add(a,multiply(Y,inverse(b))))
| add(a,multiply(Y,inverse(b))) != multiply(a,add(a,Y))
| add(multiply(Y,inverse(b)),multiply(a,additive_identity)) = multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,inverse(b)),multiply(a,additive_identity)),multiply(multiply(Y,inverse(b)),add(a,multiply(Y,inverse(b))))) ),[1,1],$fot(multiply(a,add(a,Y)))]]) ).
cnf(refute_0_447,plain,
( add(multiply(Y,inverse(b)),multiply(a,additive_identity)) != multiply(multiply(Y,inverse(b)),add(a,multiply(Y,inverse(b))))
| add(multiply(Y,inverse(b)),multiply(a,additive_identity)) = multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) ),
inference(resolve,[$cnf( $equal(add(a,multiply(Y,inverse(b))),multiply(a,add(a,Y))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
add(multiply(Y,inverse(b)),multiply(a,additive_identity)) = multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))),
inference(resolve,[$cnf( $equal(add(multiply(Y,inverse(b)),multiply(a,additive_identity)),multiply(multiply(Y,inverse(b)),add(a,multiply(Y,inverse(b))))) )],[refute_0_437,refute_0_447]) ).
cnf(refute_0_449,plain,
add(multiply(Y,inverse(b)),multiply(a,additive_identity)) = add(multiply(a,additive_identity),multiply(Y,inverse(b))),
inference(subst,[],[refute_0_229:[bind(X,$fot(multiply(a,additive_identity))),bind(Y,$fot(multiply(Y,inverse(b))))]]) ).
cnf(refute_0_450,plain,
( add(multiply(Y,inverse(b)),multiply(a,additive_identity)) != multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))
| add(multiply(Y,inverse(b)),multiply(a,additive_identity)) != add(multiply(a,additive_identity),multiply(Y,inverse(b)))
| add(multiply(a,additive_identity),multiply(Y,inverse(b))) = multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,inverse(b)),multiply(a,additive_identity)),multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))) ),[0],$fot(add(multiply(a,additive_identity),multiply(Y,inverse(b))))]]) ).
cnf(refute_0_451,plain,
( add(multiply(Y,inverse(b)),multiply(a,additive_identity)) != multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))
| add(multiply(a,additive_identity),multiply(Y,inverse(b))) = multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,inverse(b)),multiply(a,additive_identity)),add(multiply(a,additive_identity),multiply(Y,inverse(b)))) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
add(multiply(a,additive_identity),multiply(Y,inverse(b))) = multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))),
inference(resolve,[$cnf( $equal(add(multiply(Y,inverse(b)),multiply(a,additive_identity)),multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))) )],[refute_0_448,refute_0_451]) ).
cnf(refute_0_453,plain,
add(additive_identity,multiply(Y,inverse(b))) = multiply(Y,inverse(b)),
inference(subst,[],[refute_0_8:[bind(X,$fot(multiply(Y,inverse(b))))]]) ).
cnf(refute_0_454,plain,
add(multiply(a,additive_identity),multiply(Y,inverse(b))) = add(multiply(a,additive_identity),multiply(Y,inverse(b))),
introduced(tautology,[refl,[$fot(add(multiply(a,additive_identity),multiply(Y,inverse(b))))]]) ).
cnf(refute_0_455,plain,
( multiply(a,additive_identity) != additive_identity
| add(multiply(a,additive_identity),multiply(Y,inverse(b))) != add(multiply(a,additive_identity),multiply(Y,inverse(b)))
| add(multiply(a,additive_identity),multiply(Y,inverse(b))) = add(additive_identity,multiply(Y,inverse(b))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(a,additive_identity),multiply(Y,inverse(b))),add(multiply(a,additive_identity),multiply(Y,inverse(b)))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_456,plain,
( multiply(a,additive_identity) != additive_identity
| add(multiply(a,additive_identity),multiply(Y,inverse(b))) = add(additive_identity,multiply(Y,inverse(b))) ),
inference(resolve,[$cnf( $equal(add(multiply(a,additive_identity),multiply(Y,inverse(b))),add(multiply(a,additive_identity),multiply(Y,inverse(b)))) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
add(multiply(a,additive_identity),multiply(Y,inverse(b))) = add(additive_identity,multiply(Y,inverse(b))),
inference(resolve,[$cnf( $equal(multiply(a,additive_identity),additive_identity) )],[refute_0_363,refute_0_456]) ).
cnf(refute_0_458,plain,
( add(multiply(a,additive_identity),multiply(Y,inverse(b))) != add(additive_identity,multiply(Y,inverse(b)))
| add(additive_identity,multiply(Y,inverse(b))) != multiply(Y,inverse(b))
| add(multiply(a,additive_identity),multiply(Y,inverse(b))) = multiply(Y,inverse(b)) ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(add(multiply(a,additive_identity),multiply(Y,inverse(b))))),bind(Y0,$fot(add(additive_identity,multiply(Y,inverse(b))))),bind(Z0,$fot(multiply(Y,inverse(b))))]]) ).
cnf(refute_0_459,plain,
( add(additive_identity,multiply(Y,inverse(b))) != multiply(Y,inverse(b))
| add(multiply(a,additive_identity),multiply(Y,inverse(b))) = multiply(Y,inverse(b)) ),
inference(resolve,[$cnf( $equal(add(multiply(a,additive_identity),multiply(Y,inverse(b))),add(additive_identity,multiply(Y,inverse(b)))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
add(multiply(a,additive_identity),multiply(Y,inverse(b))) = multiply(Y,inverse(b)),
inference(resolve,[$cnf( $equal(add(additive_identity,multiply(Y,inverse(b))),multiply(Y,inverse(b))) )],[refute_0_453,refute_0_459]) ).
cnf(refute_0_461,plain,
( add(multiply(a,additive_identity),multiply(Y,inverse(b))) != multiply(Y,inverse(b))
| add(multiply(a,additive_identity),multiply(Y,inverse(b))) != multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))
| multiply(Y,inverse(b)) = multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(a,additive_identity),multiply(Y,inverse(b))),multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))) ),[0],$fot(multiply(Y,inverse(b)))]]) ).
cnf(refute_0_462,plain,
( add(multiply(a,additive_identity),multiply(Y,inverse(b))) != multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))
| multiply(Y,inverse(b)) = multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) ),
inference(resolve,[$cnf( $equal(add(multiply(a,additive_identity),multiply(Y,inverse(b))),multiply(Y,inverse(b))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
multiply(multiply(Y,inverse(b)),a) = multiply(a,multiply(Y,inverse(b))),
inference(subst,[],[refute_0_30:[bind(X,$fot(a)),bind(Y,$fot(multiply(Y,inverse(b))))]]) ).
cnf(refute_0_464,plain,
multiply(a,add(a,Y)) = a,
inference(subst,[],[refute_0_239:[bind(X_45,$fot(a)),bind(X_46,$fot(Y))]]) ).
cnf(refute_0_465,plain,
multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) = multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))),
introduced(tautology,[refl,[$fot(multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))))]]) ).
cnf(refute_0_466,plain,
( multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) != multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))
| multiply(a,add(a,Y)) != a
| multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) = multiply(multiply(Y,inverse(b)),a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))),multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_467,plain,
( multiply(a,add(a,Y)) != a
| multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) = multiply(multiply(Y,inverse(b)),a) ),
inference(resolve,[$cnf( $equal(multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))),multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) = multiply(multiply(Y,inverse(b)),a),
inference(resolve,[$cnf( $equal(multiply(a,add(a,Y)),a) )],[refute_0_464,refute_0_467]) ).
cnf(refute_0_469,plain,
( multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) != multiply(multiply(Y,inverse(b)),a)
| multiply(multiply(Y,inverse(b)),a) != multiply(a,multiply(Y,inverse(b)))
| multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) = multiply(a,multiply(Y,inverse(b))) ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))))),bind(Y0,$fot(multiply(multiply(Y,inverse(b)),a))),bind(Z0,$fot(multiply(a,multiply(Y,inverse(b)))))]]) ).
cnf(refute_0_470,plain,
( multiply(multiply(Y,inverse(b)),a) != multiply(a,multiply(Y,inverse(b)))
| multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) = multiply(a,multiply(Y,inverse(b))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))),multiply(multiply(Y,inverse(b)),a)) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) = multiply(a,multiply(Y,inverse(b))),
inference(resolve,[$cnf( $equal(multiply(multiply(Y,inverse(b)),a),multiply(a,multiply(Y,inverse(b)))) )],[refute_0_463,refute_0_470]) ).
cnf(refute_0_472,plain,
( multiply(Y,inverse(b)) != multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))
| multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))) != multiply(a,multiply(Y,inverse(b)))
| multiply(Y,inverse(b)) = multiply(a,multiply(Y,inverse(b))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(Y,inverse(b)),multiply(a,multiply(Y,inverse(b)))) ),[0],$fot(multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))))]]) ).
cnf(refute_0_473,plain,
( multiply(Y,inverse(b)) != multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))
| multiply(Y,inverse(b)) = multiply(a,multiply(Y,inverse(b))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y))),multiply(a,multiply(Y,inverse(b)))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
( add(multiply(a,additive_identity),multiply(Y,inverse(b))) != multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))
| multiply(Y,inverse(b)) = multiply(a,multiply(Y,inverse(b))) ),
inference(resolve,[$cnf( $equal(multiply(Y,inverse(b)),multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))) )],[refute_0_462,refute_0_473]) ).
cnf(refute_0_475,plain,
multiply(Y,inverse(b)) = multiply(a,multiply(Y,inverse(b))),
inference(resolve,[$cnf( $equal(add(multiply(a,additive_identity),multiply(Y,inverse(b))),multiply(multiply(Y,inverse(b)),multiply(a,add(a,Y)))) )],[refute_0_452,refute_0_474]) ).
cnf(refute_0_476,plain,
( multiply(Y,inverse(b)) != multiply(a,multiply(Y,inverse(b)))
| multiply(a,multiply(Y,inverse(b))) = multiply(Y,inverse(b)) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(Y,inverse(b)))),bind(Y0,$fot(multiply(a,multiply(Y,inverse(b)))))]]) ).
cnf(refute_0_477,plain,
multiply(a,multiply(Y,inverse(b))) = multiply(Y,inverse(b)),
inference(resolve,[$cnf( $equal(multiply(Y,inverse(b)),multiply(a,multiply(Y,inverse(b)))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
multiply(a,multiply(X_11,inverse(b))) = multiply(X_11,inverse(b)),
inference(subst,[],[refute_0_477:[bind(Y,$fot(X_11))]]) ).
cnf(refute_0_479,plain,
( multiply(a,X_11) != multiply(a,multiply(X_11,inverse(b)))
| multiply(a,multiply(X_11,inverse(b))) != multiply(X_11,inverse(b))
| multiply(a,X_11) = multiply(X_11,inverse(b)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,X_11),multiply(X_11,inverse(b))) ),[0],$fot(multiply(a,multiply(X_11,inverse(b))))]]) ).
cnf(refute_0_480,plain,
( multiply(a,X_11) != multiply(a,multiply(X_11,inverse(b)))
| multiply(a,X_11) = multiply(X_11,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(a,multiply(X_11,inverse(b))),multiply(X_11,inverse(b))) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
( multiply(a,add(b,X_11)) != multiply(a,multiply(X_11,inverse(b)))
| multiply(a,X_11) = multiply(X_11,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(a,X_11),multiply(a,multiply(X_11,inverse(b)))) )],[refute_0_436,refute_0_480]) ).
cnf(refute_0_482,plain,
multiply(a,X_11) = multiply(X_11,inverse(b)),
inference(resolve,[$cnf( $equal(multiply(a,add(b,X_11)),multiply(a,multiply(X_11,inverse(b)))) )],[refute_0_433,refute_0_481]) ).
cnf(refute_0_483,plain,
( multiply(a,X_11) != multiply(X_11,inverse(b))
| multiply(X_11,inverse(b)) = multiply(a,X_11) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(a,X_11))),bind(Y0,$fot(multiply(X_11,inverse(b))))]]) ).
cnf(refute_0_484,plain,
multiply(X_11,inverse(b)) = multiply(a,X_11),
inference(resolve,[$cnf( $equal(multiply(a,X_11),multiply(X_11,inverse(b))) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
multiply(a,inverse(b)) = multiply(a,a),
inference(subst,[],[refute_0_484:[bind(X_11,$fot(a))]]) ).
cnf(refute_0_486,plain,
( multiply(a,a) != a
| multiply(a,inverse(b)) != multiply(a,a)
| multiply(a,inverse(b)) = a ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(multiply(a,inverse(b)))),bind(Y0,$fot(multiply(a,a))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_487,plain,
( multiply(a,a) != a
| multiply(a,inverse(b)) = a ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),multiply(a,a)) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
multiply(a,inverse(b)) = a,
inference(resolve,[$cnf( $equal(multiply(a,a),a) )],[refute_0_428,refute_0_487]) ).
cnf(refute_0_489,plain,
( multiply(a,add(b,inverse(b))) != multiply(a,inverse(b))
| multiply(a,inverse(b)) != a
| multiply(a,add(b,inverse(b))) = a ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(multiply(a,add(b,inverse(b))))),bind(Y0,$fot(multiply(a,inverse(b)))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_490,plain,
( multiply(a,inverse(b)) != a
| multiply(a,add(b,inverse(b))) = a ),
inference(resolve,[$cnf( $equal(multiply(a,add(b,inverse(b))),multiply(a,inverse(b))) )],[refute_0_334,refute_0_489]) ).
cnf(refute_0_491,plain,
multiply(a,add(b,inverse(b))) = a,
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),a) )],[refute_0_488,refute_0_490]) ).
cnf(refute_0_492,plain,
( multiply(a,add(b,inverse(b))) != a
| multiply(a,add(b,inverse(b))) != inverse(b)
| a = inverse(b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,add(b,inverse(b))),inverse(b)) ),[0],$fot(a)]]) ).
cnf(refute_0_493,plain,
( multiply(a,add(b,inverse(b))) != inverse(b)
| a = inverse(b) ),
inference(resolve,[$cnf( $equal(multiply(a,add(b,inverse(b))),a) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
a = inverse(b),
inference(resolve,[$cnf( $equal(multiply(a,add(b,inverse(b))),inverse(b)) )],[refute_0_378,refute_0_493]) ).
cnf(refute_0_495,plain,
( a != inverse(b)
| inverse(b) = a ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(a)),bind(Y0,$fot(inverse(b)))]]) ).
cnf(refute_0_496,plain,
inverse(b) = a,
inference(resolve,[$cnf( $equal(a,inverse(b)) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
( b != inverse(inverse(b))
| inverse(b) != a
| b = inverse(a) ),
introduced(tautology,[equality,[$cnf( $equal(b,inverse(inverse(b))) ),[1,0],$fot(a)]]) ).
cnf(refute_0_498,plain,
( b != inverse(inverse(b))
| b = inverse(a) ),
inference(resolve,[$cnf( $equal(inverse(b),a) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
b = inverse(a),
inference(resolve,[$cnf( $equal(b,inverse(inverse(b))) )],[refute_0_325,refute_0_498]) ).
cnf(refute_0_500,plain,
$false,
inference(resolve,[$cnf( $equal(b,inverse(a)) )],[refute_0_499,prove_a_inverse_is_b]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 1 16:02:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.62/0.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.84
% 0.62/0.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.71/0.88
%------------------------------------------------------------------------------