TSTP Solution File: RNG012-6 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG012-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 : Mon Jul 18 20:35:45 EDT 2022
% Result : Unsatisfiable 133.03s 133.21s
% Output : CNFRefutation 133.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 150
% Syntax : Number of clauses : 704 ( 366 unt; 0 nHn; 338 RR)
% Number of literals : 1186 (1185 equ; 485 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 1909 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_additive_identity,axiom,
add(additive_identity,X) = X ).
cnf(right_additive_identity,axiom,
add(X,additive_identity) = X ).
cnf(left_multiplicative_zero,axiom,
multiply(additive_identity,X) = additive_identity ).
cnf(right_additive_inverse,axiom,
add(X,additive_inverse(X)) = additive_identity ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X)) = X ).
cnf(distribute1,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).
cnf(distribute2,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ).
cnf(commutativity_for_addition,axiom,
add(X,Y) = add(Y,X) ).
cnf(associativity_for_addition,axiom,
add(X,add(Y,Z)) = add(add(X,Y),Z) ).
cnf(commutator,axiom,
commutator(X,Y) = add(multiply(Y,X),additive_inverse(multiply(X,Y))) ).
cnf(prove_equation,negated_conjecture,
multiply(additive_inverse(a),additive_inverse(b)) != multiply(a,b) ).
cnf(refute_0_0,plain,
add(X_42,add(additive_inverse(X_42),X_44)) = add(add(X_42,additive_inverse(X_42)),X_44),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_42)),bind(Y,$fot(additive_inverse(X_42))),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_1,plain,
add(X_42,additive_inverse(X_42)) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_2,plain,
( add(X_42,add(additive_inverse(X_42),X_44)) != add(add(X_42,additive_inverse(X_42)),X_44)
| add(X_42,additive_inverse(X_42)) != additive_identity
| add(X_42,add(additive_inverse(X_42),X_44)) = add(additive_identity,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),X_44)),add(add(X_42,additive_inverse(X_42)),X_44)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_3,plain,
( add(X_42,add(additive_inverse(X_42),X_44)) != add(add(X_42,additive_inverse(X_42)),X_44)
| add(X_42,add(additive_inverse(X_42),X_44)) = add(additive_identity,X_44) ),
inference(resolve,[$cnf( $equal(add(X_42,additive_inverse(X_42)),additive_identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
add(X_42,add(additive_inverse(X_42),X_44)) = add(additive_identity,X_44),
inference(resolve,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),X_44)),add(add(X_42,additive_inverse(X_42)),X_44)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
add(additive_identity,X_44) = X_44,
inference(subst,[],[left_additive_identity:[bind(X,$fot(X_44))]]) ).
cnf(refute_0_6,plain,
( add(X_42,add(additive_inverse(X_42),X_44)) != add(additive_identity,X_44)
| add(additive_identity,X_44) != X_44
| add(X_42,add(additive_inverse(X_42),X_44)) = X_44 ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_42,add(additive_inverse(X_42),X_44)),X_44) ),[0],$fot(add(additive_identity,X_44))]]) ).
cnf(refute_0_7,plain,
( add(X_42,add(additive_inverse(X_42),X_44)) != add(additive_identity,X_44)
| add(X_42,add(additive_inverse(X_42),X_44)) = X_44 ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_44),X_44) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
add(X_42,add(additive_inverse(X_42),X_44)) = X_44,
inference(resolve,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),X_44)),add(additive_identity,X_44)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
add(X_42,add(additive_inverse(X_42),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))))) = add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))),
inference(subst,[],[refute_0_8:[bind(X_44,$fot(add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))))]]) ).
cnf(refute_0_10,plain,
add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(add(X_42,X_43)))]]) ).
cnf(refute_0_11,plain,
add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) = add(add(X_42,X_43),additive_inverse(add(X_42,X_43))),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(additive_inverse(add(X_42,X_43))))]]) ).
cnf(refute_0_12,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_14,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) != add(add(X_42,X_43),additive_inverse(add(X_42,X_43)))
| add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) = add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))))),bind(Y0,$fot(add(add(X_42,X_43),additive_inverse(add(X_42,X_43)))))]]) ).
cnf(refute_0_16,plain,
add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) = add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))),add(add(X_42,X_43),additive_inverse(add(X_42,X_43)))) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) != add(X_42,add(X_43,additive_inverse(add(X_42,X_43))))
| add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) != additive_identity
| add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_42,X_43),additive_inverse(add(X_42,X_43))),additive_identity) ),[0],$fot(add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))))]]) ).
cnf(refute_0_18,plain,
( add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) != additive_identity
| add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) = additive_identity ),
inference(resolve,[$cnf( $equal(add(add(X_42,X_43),additive_inverse(add(X_42,X_43))),add(X_42,add(X_43,additive_inverse(add(X_42,X_43))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) = additive_identity,
inference(resolve,[$cnf( $equal(add(add(X_42,X_43),additive_inverse(add(X_42,X_43))),additive_identity) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
add(additive_inverse(X_42),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))) = additive_identity,
inference(subst,[],[refute_0_19:[bind(X_42,$fot(additive_inverse(X_42))),bind(X_43,$fot(X_58))]]) ).
cnf(refute_0_21,plain,
( add(X_42,add(additive_inverse(X_42),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))))) != add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))
| add(additive_inverse(X_42),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))) != additive_identity
| add(X_42,additive_identity) = add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))))),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_22,plain,
( add(X_42,add(additive_inverse(X_42),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))))) != add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))
| add(X_42,additive_identity) = add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_42),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))),additive_identity) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
add(X_42,additive_identity) = add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))),
inference(resolve,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))))),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))) )],[refute_0_9,refute_0_22]) ).
cnf(refute_0_24,plain,
add(X_42,additive_identity) = X_42,
inference(subst,[],[right_additive_identity:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_25,plain,
( add(X_42,additive_identity) != X_42
| add(X_42,additive_identity) != add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))
| X_42 = add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,additive_identity),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))) ),[0],$fot(X_42)]]) ).
cnf(refute_0_26,plain,
( add(X_42,additive_identity) != add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))
| X_42 = add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))) ),
inference(resolve,[$cnf( $equal(add(X_42,additive_identity),X_42) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
X_42 = add(X_58,additive_inverse(add(additive_inverse(X_42),X_58))),
inference(resolve,[$cnf( $equal(add(X_42,additive_identity),add(X_58,additive_inverse(add(additive_inverse(X_42),X_58)))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
additive_inverse(X) = add(X_64,additive_inverse(add(additive_inverse(additive_inverse(X)),X_64))),
inference(subst,[],[refute_0_27:[bind(X_42,$fot(additive_inverse(X))),bind(X_58,$fot(X_64))]]) ).
cnf(refute_0_29,plain,
( additive_inverse(X) != add(X_64,additive_inverse(add(additive_inverse(additive_inverse(X)),X_64)))
| additive_inverse(additive_inverse(X)) != X
| additive_inverse(X) = add(X_64,additive_inverse(add(X,X_64))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(X),add(X_64,additive_inverse(add(additive_inverse(additive_inverse(X)),X_64)))) ),[1,1,0,0],$fot(X)]]) ).
cnf(refute_0_30,plain,
( additive_inverse(X) != add(X_64,additive_inverse(add(additive_inverse(additive_inverse(X)),X_64)))
| additive_inverse(X) = add(X_64,additive_inverse(add(X,X_64))) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_29]) ).
cnf(refute_0_31,plain,
additive_inverse(X) = add(X_64,additive_inverse(add(X,X_64))),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(X_64,additive_inverse(add(additive_inverse(additive_inverse(X)),X_64)))) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
additive_inverse(multiply(X_704,X_703)) = add(multiply(additive_inverse(X_703),X_704),additive_inverse(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704)))),
inference(subst,[],[refute_0_31:[bind(X,$fot(multiply(X_704,X_703))),bind(X_64,$fot(multiply(additive_inverse(X_703),X_704)))]]) ).
cnf(refute_0_33,plain,
commutator(X,add(X_79,X_78)) = add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_79,X_78)))),
inference(subst,[],[commutator:[bind(Y,$fot(add(X_79,X_78)))]]) ).
cnf(refute_0_34,plain,
add(multiply(X_47,X_49),multiply(X_47,X_48)) = add(multiply(X_47,X_48),multiply(X_47,X_49)),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(multiply(X_47,X_49))),bind(Y,$fot(multiply(X_47,X_48)))]]) ).
cnf(refute_0_35,plain,
multiply(X_47,add(X_48,X_49)) = add(multiply(X_47,X_48),multiply(X_47,X_49)),
inference(subst,[],[distribute1:[bind(X,$fot(X_47)),bind(Y,$fot(X_48)),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_36,plain,
( multiply(X_47,add(X_48,X_49)) != add(multiply(X_47,X_48),multiply(X_47,X_49))
| add(multiply(X_47,X_48),multiply(X_47,X_49)) = multiply(X_47,add(X_48,X_49)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(multiply(X_47,add(X_48,X_49)))),bind(Y0,$fot(add(multiply(X_47,X_48),multiply(X_47,X_49))))]]) ).
cnf(refute_0_37,plain,
add(multiply(X_47,X_48),multiply(X_47,X_49)) = multiply(X_47,add(X_48,X_49)),
inference(resolve,[$cnf( $equal(multiply(X_47,add(X_48,X_49)),add(multiply(X_47,X_48),multiply(X_47,X_49))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( add(multiply(X_47,X_48),multiply(X_47,X_49)) != multiply(X_47,add(X_48,X_49))
| add(multiply(X_47,X_49),multiply(X_47,X_48)) != add(multiply(X_47,X_48),multiply(X_47,X_49))
| add(multiply(X_47,X_49),multiply(X_47,X_48)) = multiply(X_47,add(X_48,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_47,X_49),multiply(X_47,X_48)),add(multiply(X_47,X_48),multiply(X_47,X_49))) ),[1],$fot(multiply(X_47,add(X_48,X_49)))]]) ).
cnf(refute_0_39,plain,
( add(multiply(X_47,X_49),multiply(X_47,X_48)) != add(multiply(X_47,X_48),multiply(X_47,X_49))
| add(multiply(X_47,X_49),multiply(X_47,X_48)) = multiply(X_47,add(X_48,X_49)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_47,X_48),multiply(X_47,X_49)),multiply(X_47,add(X_48,X_49))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
add(multiply(X_47,X_49),multiply(X_47,X_48)) = multiply(X_47,add(X_48,X_49)),
inference(resolve,[$cnf( $equal(add(multiply(X_47,X_49),multiply(X_47,X_48)),add(multiply(X_47,X_48),multiply(X_47,X_49))) )],[refute_0_34,refute_0_39]) ).
cnf(refute_0_41,plain,
( multiply(X,add(Y,Z)) != add(multiply(X,Y),multiply(X,Z))
| add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_42,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[distribute1,refute_0_41]) ).
cnf(refute_0_43,plain,
add(multiply(X_47,X_49),multiply(X_47,X_48)) = multiply(X_47,add(X_49,X_48)),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_47)),bind(Y,$fot(X_49)),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_44,plain,
( add(multiply(X_47,X_49),multiply(X_47,X_48)) != multiply(X_47,add(X_48,X_49))
| add(multiply(X_47,X_49),multiply(X_47,X_48)) != multiply(X_47,add(X_49,X_48))
| multiply(X_47,add(X_49,X_48)) = multiply(X_47,add(X_48,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_47,X_49),multiply(X_47,X_48)),multiply(X_47,add(X_48,X_49))) ),[0],$fot(multiply(X_47,add(X_49,X_48)))]]) ).
cnf(refute_0_45,plain,
( add(multiply(X_47,X_49),multiply(X_47,X_48)) != multiply(X_47,add(X_48,X_49))
| multiply(X_47,add(X_49,X_48)) = multiply(X_47,add(X_48,X_49)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_47,X_49),multiply(X_47,X_48)),multiply(X_47,add(X_49,X_48))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(X_47,add(X_49,X_48)) = multiply(X_47,add(X_48,X_49)),
inference(resolve,[$cnf( $equal(add(multiply(X_47,X_49),multiply(X_47,X_48)),multiply(X_47,add(X_48,X_49))) )],[refute_0_40,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(X,add(X_79,X_78)) = multiply(X,add(X_78,X_79)),
inference(subst,[],[refute_0_46:[bind(X_47,$fot(X)),bind(X_48,$fot(X_78)),bind(X_49,$fot(X_79))]]) ).
cnf(refute_0_48,plain,
( multiply(X,add(X_79,X_78)) != multiply(X,add(X_78,X_79))
| commutator(X,add(X_79,X_78)) != add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_79,X_78))))
| commutator(X,add(X_79,X_78)) = add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_78,X_79)))) ),
introduced(tautology,[equality,[$cnf( $equal(commutator(X,add(X_79,X_78)),add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_79,X_78))))) ),[1,1,0],$fot(multiply(X,add(X_78,X_79)))]]) ).
cnf(refute_0_49,plain,
( commutator(X,add(X_79,X_78)) != add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_79,X_78))))
| commutator(X,add(X_79,X_78)) = add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_78,X_79)))) ),
inference(resolve,[$cnf( $equal(multiply(X,add(X_79,X_78)),multiply(X,add(X_78,X_79))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
commutator(X,add(X_79,X_78)) = add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_78,X_79)))),
inference(resolve,[$cnf( $equal(commutator(X,add(X_79,X_78)),add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_79,X_78))))) )],[refute_0_33,refute_0_49]) ).
cnf(refute_0_51,plain,
commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) = add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,add(X_639,additive_inverse(add(X_639,X)))))),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_638)),bind(X_78,$fot(X_639)),bind(X_79,$fot(additive_inverse(add(X_639,X))))]]) ).
cnf(refute_0_52,plain,
additive_inverse(X) = add(additive_inverse(add(X_65,X)),additive_inverse(add(X,additive_inverse(add(X_65,X))))),
inference(subst,[],[refute_0_31:[bind(X_64,$fot(additive_inverse(add(X_65,X))))]]) ).
cnf(refute_0_53,plain,
additive_inverse(X_65) = add(X,additive_inverse(add(X_65,X))),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_65)),bind(X_64,$fot(X))]]) ).
cnf(refute_0_54,plain,
( additive_inverse(X_65) != add(X,additive_inverse(add(X_65,X)))
| add(X,additive_inverse(add(X_65,X))) = additive_inverse(X_65) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(X_65))),bind(Y0,$fot(add(X,additive_inverse(add(X_65,X)))))]]) ).
cnf(refute_0_55,plain,
add(X,additive_inverse(add(X_65,X))) = additive_inverse(X_65),
inference(resolve,[$cnf( $equal(additive_inverse(X_65),add(X,additive_inverse(add(X_65,X)))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( add(X,additive_inverse(add(X_65,X))) != additive_inverse(X_65)
| additive_inverse(X) != add(additive_inverse(add(X_65,X)),additive_inverse(add(X,additive_inverse(add(X_65,X)))))
| additive_inverse(X) = add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(X),add(additive_inverse(add(X_65,X)),additive_inverse(add(X,additive_inverse(add(X_65,X)))))) ),[1,1,0],$fot(additive_inverse(X_65))]]) ).
cnf(refute_0_57,plain,
( additive_inverse(X) != add(additive_inverse(add(X_65,X)),additive_inverse(add(X,additive_inverse(add(X_65,X)))))
| additive_inverse(X) = add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))) ),
inference(resolve,[$cnf( $equal(add(X,additive_inverse(add(X_65,X))),additive_inverse(X_65)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
additive_inverse(X) = add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(additive_inverse(add(X_65,X)),additive_inverse(add(X,additive_inverse(add(X_65,X)))))) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
additive_inverse(additive_inverse(X_65)) = X_65,
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(X_65))]]) ).
cnf(refute_0_60,plain,
add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))) = add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))),
introduced(tautology,[refl,[$fot(add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))))]]) ).
cnf(refute_0_61,plain,
( add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))) != add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X)))
| additive_inverse(additive_inverse(X_65)) != X_65
| add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))) = add(X_65,additive_inverse(add(X_65,X))) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))),add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X)))) ),[1,0],$fot(X_65)]]) ).
cnf(refute_0_62,plain,
( additive_inverse(additive_inverse(X_65)) != X_65
| add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))) = add(X_65,additive_inverse(add(X_65,X))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))),add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X)))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))) = add(X_65,additive_inverse(add(X_65,X))),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X_65)),X_65) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_65,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_for_addition,refute_0_64]) ).
cnf(refute_0_66,plain,
add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))) = add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))),
inference(subst,[],[refute_0_65:[bind(X,$fot(additive_inverse(additive_inverse(X_65)))),bind(Y,$fot(additive_inverse(add(X_65,X))))]]) ).
cnf(refute_0_67,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_68,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_14,refute_0_67]) ).
cnf(refute_0_69,plain,
( add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))) != add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X)))
| add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))) != add(X_65,additive_inverse(add(X_65,X)))
| add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))) = add(X_65,additive_inverse(add(X_65,X))) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))))),bind(Y0,$fot(add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))))),bind(Z0,$fot(add(X_65,additive_inverse(add(X_65,X)))))]]) ).
cnf(refute_0_70,plain,
( add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))) != add(X_65,additive_inverse(add(X_65,X)))
| add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))) = add(X_65,additive_inverse(add(X_65,X))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))),add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X)))) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))) = add(X_65,additive_inverse(add(X_65,X))),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(X_65)),additive_inverse(add(X_65,X))),add(X_65,additive_inverse(add(X_65,X)))) )],[refute_0_63,refute_0_70]) ).
cnf(refute_0_72,plain,
( add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))) != add(X_65,additive_inverse(add(X_65,X)))
| additive_inverse(X) != add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65)))
| additive_inverse(X) = add(X_65,additive_inverse(add(X_65,X))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(X),add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65)))) ),[1],$fot(add(X_65,additive_inverse(add(X_65,X))))]]) ).
cnf(refute_0_73,plain,
( additive_inverse(X) != add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65)))
| additive_inverse(X) = add(X_65,additive_inverse(add(X_65,X))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65))),add(X_65,additive_inverse(add(X_65,X)))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
additive_inverse(X) = add(X_65,additive_inverse(add(X_65,X))),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(additive_inverse(add(X_65,X)),additive_inverse(additive_inverse(X_65)))) )],[refute_0_58,refute_0_73]) ).
cnf(refute_0_75,plain,
additive_inverse(X) = add(X_639,additive_inverse(add(X_639,X))),
inference(subst,[],[refute_0_74:[bind(X_65,$fot(X_639))]]) ).
cnf(refute_0_76,plain,
( additive_inverse(X) != add(X_639,additive_inverse(add(X_639,X)))
| add(X_639,additive_inverse(add(X_639,X))) = additive_inverse(X) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(X))),bind(Y0,$fot(add(X_639,additive_inverse(add(X_639,X)))))]]) ).
cnf(refute_0_77,plain,
add(X_639,additive_inverse(add(X_639,X))) = additive_inverse(X),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(X_639,additive_inverse(add(X_639,X)))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( add(X_639,additive_inverse(add(X_639,X))) != additive_inverse(X)
| commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) != add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,add(X_639,additive_inverse(add(X_639,X))))))
| commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) = add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)),add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,add(X_639,additive_inverse(add(X_639,X))))))) ),[1,1,0,1],$fot(additive_inverse(X))]]) ).
cnf(refute_0_79,plain,
( commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) != add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,add(X_639,additive_inverse(add(X_639,X))))))
| commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) = add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) ),
inference(resolve,[$cnf( $equal(add(X_639,additive_inverse(add(X_639,X))),additive_inverse(X)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) = add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))),
inference(resolve,[$cnf( $equal(commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)),add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,add(X_639,additive_inverse(add(X_639,X))))))) )],[refute_0_51,refute_0_79]) ).
cnf(refute_0_81,plain,
commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))) = commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))),
introduced(tautology,[refl,[$fot(commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))))]]) ).
cnf(refute_0_82,plain,
( add(X_639,additive_inverse(add(X_639,X))) != additive_inverse(X)
| commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))) != commutator(X_638,add(X_639,additive_inverse(add(X_639,X))))
| commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))) = commutator(X_638,additive_inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))),commutator(X_638,add(X_639,additive_inverse(add(X_639,X))))) ),[1,1],$fot(additive_inverse(X))]]) ).
cnf(refute_0_83,plain,
( add(X_639,additive_inverse(add(X_639,X))) != additive_inverse(X)
| commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))) = commutator(X_638,additive_inverse(X)) ),
inference(resolve,[$cnf( $equal(commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))),commutator(X_638,add(X_639,additive_inverse(add(X_639,X))))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))) = commutator(X_638,additive_inverse(X)),
inference(resolve,[$cnf( $equal(add(X_639,additive_inverse(add(X_639,X))),additive_inverse(X)) )],[refute_0_77,refute_0_83]) ).
cnf(refute_0_85,plain,
commutator(X_638,add(X_640,X_639)) = add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640)))),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_638)),bind(X_78,$fot(X_639)),bind(X_79,$fot(X_640))]]) ).
cnf(refute_0_86,plain,
add(X_639,X_640) = add(X_640,X_639),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_639)),bind(Y,$fot(X_640))]]) ).
cnf(refute_0_87,plain,
( add(X_639,X_640) != add(X_640,X_639)
| add(X_640,X_639) = add(X_639,X_640) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_639,X_640))),bind(Y0,$fot(add(X_640,X_639)))]]) ).
cnf(refute_0_88,plain,
add(X_640,X_639) = add(X_639,X_640),
inference(resolve,[$cnf( $equal(add(X_639,X_640),add(X_640,X_639)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( add(X_640,X_639) != add(X_639,X_640)
| commutator(X_638,add(X_640,X_639)) != add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640))))
| commutator(X_638,add(X_639,X_640)) = add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640)))) ),
introduced(tautology,[equality,[$cnf( $equal(commutator(X_638,add(X_640,X_639)),add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640))))) ),[0,1],$fot(add(X_639,X_640))]]) ).
cnf(refute_0_90,plain,
( commutator(X_638,add(X_640,X_639)) != add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640))))
| commutator(X_638,add(X_639,X_640)) = add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640)))) ),
inference(resolve,[$cnf( $equal(add(X_640,X_639),add(X_639,X_640)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
commutator(X_638,add(X_639,X_640)) = add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640)))),
inference(resolve,[$cnf( $equal(commutator(X_638,add(X_640,X_639)),add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640))))) )],[refute_0_85,refute_0_90]) ).
cnf(refute_0_92,plain,
( commutator(X,add(X_79,X_78)) != add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_78,X_79))))
| add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_78,X_79)))) = commutator(X,add(X_79,X_78)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(commutator(X,add(X_79,X_78)))),bind(Y0,$fot(add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_78,X_79))))))]]) ).
cnf(refute_0_93,plain,
add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_78,X_79)))) = commutator(X,add(X_79,X_78)),
inference(resolve,[$cnf( $equal(commutator(X,add(X_79,X_78)),add(multiply(add(X_79,X_78),X),additive_inverse(multiply(X,add(X_78,X_79))))) )],[refute_0_50,refute_0_92]) ).
cnf(refute_0_94,plain,
add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640)))) = commutator(X_638,add(X_640,X_639)),
inference(subst,[],[refute_0_93:[bind(X,$fot(X_638)),bind(X_78,$fot(X_639)),bind(X_79,$fot(X_640))]]) ).
cnf(refute_0_95,plain,
( add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640)))) != commutator(X_638,add(X_640,X_639))
| commutator(X_638,add(X_639,X_640)) != add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640))))
| commutator(X_638,add(X_639,X_640)) = commutator(X_638,add(X_640,X_639)) ),
introduced(tautology,[equality,[$cnf( $equal(commutator(X_638,add(X_639,X_640)),add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640))))) ),[1],$fot(commutator(X_638,add(X_640,X_639)))]]) ).
cnf(refute_0_96,plain,
( commutator(X_638,add(X_639,X_640)) != add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640))))
| commutator(X_638,add(X_639,X_640)) = commutator(X_638,add(X_640,X_639)) ),
inference(resolve,[$cnf( $equal(add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640)))),commutator(X_638,add(X_640,X_639))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
commutator(X_638,add(X_639,X_640)) = commutator(X_638,add(X_640,X_639)),
inference(resolve,[$cnf( $equal(commutator(X_638,add(X_639,X_640)),add(multiply(add(X_640,X_639),X_638),additive_inverse(multiply(X_638,add(X_639,X_640))))) )],[refute_0_91,refute_0_96]) ).
cnf(refute_0_98,plain,
( commutator(X_638,add(X_639,X_640)) != commutator(X_638,add(X_640,X_639))
| commutator(X_638,add(X_640,X_639)) = commutator(X_638,add(X_639,X_640)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(commutator(X_638,add(X_639,X_640)))),bind(Y0,$fot(commutator(X_638,add(X_640,X_639))))]]) ).
cnf(refute_0_99,plain,
commutator(X_638,add(X_640,X_639)) = commutator(X_638,add(X_639,X_640)),
inference(resolve,[$cnf( $equal(commutator(X_638,add(X_639,X_640)),commutator(X_638,add(X_640,X_639))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) = commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))),
inference(subst,[],[refute_0_99:[bind(X_640,$fot(additive_inverse(add(X_639,X))))]]) ).
cnf(refute_0_101,plain,
( commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))) != commutator(X_638,additive_inverse(X))
| commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) != commutator(X_638,add(X_639,additive_inverse(add(X_639,X))))
| commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) = commutator(X_638,additive_inverse(X)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)))),bind(Y0,$fot(commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))))),bind(Z0,$fot(commutator(X_638,additive_inverse(X))))]]) ).
cnf(refute_0_102,plain,
( commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))) != commutator(X_638,additive_inverse(X))
| commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) = commutator(X_638,additive_inverse(X)) ),
inference(resolve,[$cnf( $equal(commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)),commutator(X_638,add(X_639,additive_inverse(add(X_639,X))))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) = commutator(X_638,additive_inverse(X)),
inference(resolve,[$cnf( $equal(commutator(X_638,add(X_639,additive_inverse(add(X_639,X)))),commutator(X_638,additive_inverse(X))) )],[refute_0_84,refute_0_102]) ).
cnf(refute_0_104,plain,
( commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) != add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X))))
| commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) != commutator(X_638,additive_inverse(X))
| commutator(X_638,additive_inverse(X)) = add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)),add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X))))) ),[0],$fot(commutator(X_638,additive_inverse(X)))]]) ).
cnf(refute_0_105,plain,
( commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) != add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X))))
| commutator(X_638,additive_inverse(X)) = add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) ),
inference(resolve,[$cnf( $equal(commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)),commutator(X_638,additive_inverse(X))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(add(X_639,additive_inverse(add(X_639,X))),X_638) = multiply(add(X_639,additive_inverse(add(X_639,X))),X_638),
introduced(tautology,[refl,[$fot(multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))]]) ).
cnf(refute_0_107,plain,
( multiply(add(X_639,additive_inverse(add(X_639,X))),X_638) != multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)
| add(X_639,additive_inverse(add(X_639,X))) != additive_inverse(X)
| multiply(add(X_639,additive_inverse(add(X_639,X))),X_638) = multiply(additive_inverse(X),X_638) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_639,additive_inverse(add(X_639,X))),X_638),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) ),[1,0],$fot(additive_inverse(X))]]) ).
cnf(refute_0_108,plain,
( add(X_639,additive_inverse(add(X_639,X))) != additive_inverse(X)
| multiply(add(X_639,additive_inverse(add(X_639,X))),X_638) = multiply(additive_inverse(X),X_638) ),
inference(resolve,[$cnf( $equal(multiply(add(X_639,additive_inverse(add(X_639,X))),X_638),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
multiply(add(X_639,additive_inverse(add(X_639,X))),X_638) = multiply(additive_inverse(X),X_638),
inference(resolve,[$cnf( $equal(add(X_639,additive_inverse(add(X_639,X))),additive_inverse(X)) )],[refute_0_77,refute_0_108]) ).
cnf(refute_0_110,plain,
add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),
introduced(tautology,[refl,[$fot(add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)))]]) ).
cnf(refute_0_111,plain,
( multiply(add(X_639,additive_inverse(add(X_639,X))),X_638) != multiply(additive_inverse(X),X_638)
| add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) != add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))
| add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))) ),[1,1],$fot(multiply(additive_inverse(X),X_638))]]) ).
cnf(refute_0_112,plain,
( multiply(add(X_639,additive_inverse(add(X_639,X))),X_638) != multiply(additive_inverse(X),X_638)
| add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)),
inference(resolve,[$cnf( $equal(multiply(add(X_639,additive_inverse(add(X_639,X))),X_638),multiply(additive_inverse(X),X_638)) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) = add(add(multiply(X_47,X_48),multiply(X_47,X_49)),Z),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(multiply(X_47,X_48))),bind(Y,$fot(multiply(X_47,X_49)))]]) ).
cnf(refute_0_115,plain,
( add(multiply(X_47,X_48),multiply(X_47,X_49)) != multiply(X_47,add(X_48,X_49))
| add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) != add(add(multiply(X_47,X_48),multiply(X_47,X_49)),Z)
| add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) = add(multiply(X_47,add(X_48,X_49)),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)),add(add(multiply(X_47,X_48),multiply(X_47,X_49)),Z)) ),[1,0],$fot(multiply(X_47,add(X_48,X_49)))]]) ).
cnf(refute_0_116,plain,
( add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) != add(add(multiply(X_47,X_48),multiply(X_47,X_49)),Z)
| add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) = add(multiply(X_47,add(X_48,X_49)),Z) ),
inference(resolve,[$cnf( $equal(add(multiply(X_47,X_48),multiply(X_47,X_49)),multiply(X_47,add(X_48,X_49))) )],[refute_0_37,refute_0_115]) ).
cnf(refute_0_117,plain,
add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) = add(multiply(X_47,add(X_48,X_49)),Z),
inference(resolve,[$cnf( $equal(add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)),add(add(multiply(X_47,X_48),multiply(X_47,X_49)),Z)) )],[refute_0_114,refute_0_116]) ).
cnf(refute_0_118,plain,
add(multiply(X_574,X_575),add(multiply(X_574,X_576),additive_inverse(multiply(X_574,X_575)))) = add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575))),
inference(subst,[],[refute_0_117:[bind(Z,$fot(additive_inverse(multiply(X_574,X_575)))),bind(X_47,$fot(X_574)),bind(X_48,$fot(X_575)),bind(X_49,$fot(X_576))]]) ).
cnf(refute_0_119,plain,
add(X_45,add(additive_inverse(X_45),X_46)) = X_46,
inference(subst,[],[refute_0_8:[bind(X_42,$fot(X_45)),bind(X_44,$fot(X_46))]]) ).
cnf(refute_0_120,plain,
add(X_46,additive_inverse(X_45)) = add(additive_inverse(X_45),X_46),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_46)),bind(Y,$fot(additive_inverse(X_45)))]]) ).
cnf(refute_0_121,plain,
( add(X_46,additive_inverse(X_45)) != add(additive_inverse(X_45),X_46)
| add(additive_inverse(X_45),X_46) = add(X_46,additive_inverse(X_45)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_46,additive_inverse(X_45)))),bind(Y0,$fot(add(additive_inverse(X_45),X_46)))]]) ).
cnf(refute_0_122,plain,
add(additive_inverse(X_45),X_46) = add(X_46,additive_inverse(X_45)),
inference(resolve,[$cnf( $equal(add(X_46,additive_inverse(X_45)),add(additive_inverse(X_45),X_46)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( add(X_45,add(additive_inverse(X_45),X_46)) != X_46
| add(additive_inverse(X_45),X_46) != add(X_46,additive_inverse(X_45))
| add(X_45,add(X_46,additive_inverse(X_45))) = X_46 ),
introduced(tautology,[equality,[$cnf( $equal(add(X_45,add(additive_inverse(X_45),X_46)),X_46) ),[0,1],$fot(add(X_46,additive_inverse(X_45)))]]) ).
cnf(refute_0_124,plain,
( add(X_45,add(additive_inverse(X_45),X_46)) != X_46
| add(X_45,add(X_46,additive_inverse(X_45))) = X_46 ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_45),X_46),add(X_46,additive_inverse(X_45))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
add(X_45,add(X_46,additive_inverse(X_45))) = X_46,
inference(resolve,[$cnf( $equal(add(X_45,add(additive_inverse(X_45),X_46)),X_46) )],[refute_0_119,refute_0_124]) ).
cnf(refute_0_126,plain,
add(multiply(X_574,X_575),add(multiply(X_574,X_576),additive_inverse(multiply(X_574,X_575)))) = multiply(X_574,X_576),
inference(subst,[],[refute_0_125:[bind(X_45,$fot(multiply(X_574,X_575))),bind(X_46,$fot(multiply(X_574,X_576)))]]) ).
cnf(refute_0_127,plain,
( add(multiply(X_574,X_575),add(multiply(X_574,X_576),additive_inverse(multiply(X_574,X_575)))) != multiply(X_574,X_576)
| add(multiply(X_574,X_575),add(multiply(X_574,X_576),additive_inverse(multiply(X_574,X_575)))) != add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575)))
| multiply(X_574,X_576) = add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_574,X_575),add(multiply(X_574,X_576),additive_inverse(multiply(X_574,X_575)))),add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575)))) ),[0],$fot(multiply(X_574,X_576))]]) ).
cnf(refute_0_128,plain,
( add(multiply(X_574,X_575),add(multiply(X_574,X_576),additive_inverse(multiply(X_574,X_575)))) != add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575)))
| multiply(X_574,X_576) = add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_574,X_575),add(multiply(X_574,X_576),additive_inverse(multiply(X_574,X_575)))),multiply(X_574,X_576)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
multiply(X_574,X_576) = add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575))),
inference(resolve,[$cnf( $equal(add(multiply(X_574,X_575),add(multiply(X_574,X_576),additive_inverse(multiply(X_574,X_575)))),add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575)))) )],[refute_0_118,refute_0_128]) ).
cnf(refute_0_130,plain,
add(X_42,add(X_43,X_44)) = add(add(X_42,X_43),X_44),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_131,plain,
add(X_44,X_43) = add(X_43,X_44),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_44)),bind(Y,$fot(X_43))]]) ).
cnf(refute_0_132,plain,
( add(X_44,X_43) != add(X_43,X_44)
| add(X_43,X_44) = add(X_44,X_43) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_44,X_43))),bind(Y0,$fot(add(X_43,X_44)))]]) ).
cnf(refute_0_133,plain,
add(X_43,X_44) = add(X_44,X_43),
inference(resolve,[$cnf( $equal(add(X_44,X_43),add(X_43,X_44)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
( add(X_42,add(X_43,X_44)) != add(add(X_42,X_43),X_44)
| add(X_43,X_44) != add(X_44,X_43)
| add(X_42,add(X_44,X_43)) = add(add(X_42,X_43),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(add(X_42,X_43),X_44)) ),[0,1],$fot(add(X_44,X_43))]]) ).
cnf(refute_0_135,plain,
( add(X_42,add(X_43,X_44)) != add(add(X_42,X_43),X_44)
| add(X_42,add(X_44,X_43)) = add(add(X_42,X_43),X_44) ),
inference(resolve,[$cnf( $equal(add(X_43,X_44),add(X_44,X_43)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
add(X_42,add(X_44,X_43)) = add(add(X_42,X_43),X_44),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(add(X_42,X_43),X_44)) )],[refute_0_130,refute_0_135]) ).
cnf(refute_0_137,plain,
( add(X,add(Y,Z)) != add(add(X,Y),Z)
| add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X,add(Y,Z)))),bind(Y0,$fot(add(add(X,Y),Z)))]]) ).
cnf(refute_0_138,plain,
add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(X,add(Y,Z)),add(add(X,Y),Z)) )],[associativity_for_addition,refute_0_137]) ).
cnf(refute_0_139,plain,
add(add(X_42,X_43),X_44) = add(X_42,add(X_43,X_44)),
inference(subst,[],[refute_0_138:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_140,plain,
( add(X_42,add(X_44,X_43)) != add(add(X_42,X_43),X_44)
| add(add(X_42,X_43),X_44) != add(X_42,add(X_43,X_44))
| add(X_42,add(X_44,X_43)) = add(X_42,add(X_43,X_44)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_42,add(X_44,X_43)),add(X_42,add(X_43,X_44))) ),[0],$fot(add(add(X_42,X_43),X_44))]]) ).
cnf(refute_0_141,plain,
( add(X_42,add(X_44,X_43)) != add(add(X_42,X_43),X_44)
| add(X_42,add(X_44,X_43)) = add(X_42,add(X_43,X_44)) ),
inference(resolve,[$cnf( $equal(add(add(X_42,X_43),X_44),add(X_42,add(X_43,X_44))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
add(X_42,add(X_44,X_43)) = add(X_42,add(X_43,X_44)),
inference(resolve,[$cnf( $equal(add(X_42,add(X_44,X_43)),add(add(X_42,X_43),X_44)) )],[refute_0_136,refute_0_141]) ).
cnf(refute_0_143,plain,
add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))) = add(multiply(X_574,X_575),add(multiply(X_574,X_576),X_44)),
inference(subst,[],[refute_0_142:[bind(X_42,$fot(multiply(X_574,X_575))),bind(X_43,$fot(multiply(X_574,X_576)))]]) ).
cnf(refute_0_144,plain,
add(multiply(X_574,X_575),add(multiply(X_574,X_576),X_44)) = add(multiply(X_574,add(X_575,X_576)),X_44),
inference(subst,[],[refute_0_117:[bind(Z,$fot(X_44)),bind(X_47,$fot(X_574)),bind(X_48,$fot(X_575)),bind(X_49,$fot(X_576))]]) ).
cnf(refute_0_145,plain,
( add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))) != add(multiply(X_574,X_575),add(multiply(X_574,X_576),X_44))
| add(multiply(X_574,X_575),add(multiply(X_574,X_576),X_44)) != add(multiply(X_574,add(X_575,X_576)),X_44)
| add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))) = add(multiply(X_574,add(X_575,X_576)),X_44) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))),add(multiply(X_574,add(X_575,X_576)),X_44)) ),[0],$fot(add(multiply(X_574,X_575),add(multiply(X_574,X_576),X_44)))]]) ).
cnf(refute_0_146,plain,
( add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))) != add(multiply(X_574,X_575),add(multiply(X_574,X_576),X_44))
| add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))) = add(multiply(X_574,add(X_575,X_576)),X_44) ),
inference(resolve,[$cnf( $equal(add(multiply(X_574,X_575),add(multiply(X_574,X_576),X_44)),add(multiply(X_574,add(X_575,X_576)),X_44)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))) = add(multiply(X_574,add(X_575,X_576)),X_44),
inference(resolve,[$cnf( $equal(add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))),add(multiply(X_574,X_575),add(multiply(X_574,X_576),X_44))) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
add(X,add(X_42,X_43)) = add(add(X_42,X_43),X),
inference(subst,[],[commutativity_for_addition:[bind(Y,$fot(add(X_42,X_43)))]]) ).
cnf(refute_0_149,plain,
add(X_42,add(X_43,X)) = add(add(X_42,X_43),X),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(X))]]) ).
cnf(refute_0_150,plain,
( add(X_42,add(X_43,X)) != add(add(X_42,X_43),X)
| add(add(X_42,X_43),X) = add(X_42,add(X_43,X)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_42,add(X_43,X)))),bind(Y0,$fot(add(add(X_42,X_43),X)))]]) ).
cnf(refute_0_151,plain,
add(add(X_42,X_43),X) = add(X_42,add(X_43,X)),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X)),add(add(X_42,X_43),X)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( add(X,add(X_42,X_43)) != add(add(X_42,X_43),X)
| add(add(X_42,X_43),X) != add(X_42,add(X_43,X))
| add(X,add(X_42,X_43)) = add(X_42,add(X_43,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,add(X_42,X_43)),add(X_42,add(X_43,X))) ),[0],$fot(add(add(X_42,X_43),X))]]) ).
cnf(refute_0_153,plain,
( add(X,add(X_42,X_43)) != add(add(X_42,X_43),X)
| add(X,add(X_42,X_43)) = add(X_42,add(X_43,X)) ),
inference(resolve,[$cnf( $equal(add(add(X_42,X_43),X),add(X_42,add(X_43,X))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
add(X,add(X_42,X_43)) = add(X_42,add(X_43,X)),
inference(resolve,[$cnf( $equal(add(X,add(X_42,X_43)),add(add(X_42,X_43),X)) )],[refute_0_148,refute_0_153]) ).
cnf(refute_0_155,plain,
add(multiply(X,Z),add(X_122,multiply(X,Y))) = add(X_122,add(multiply(X,Y),multiply(X,Z))),
inference(subst,[],[refute_0_154:[bind(X,$fot(multiply(X,Z))),bind(X_42,$fot(X_122)),bind(X_43,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_156,plain,
( add(multiply(X,Y),multiply(X,Z)) != multiply(X,add(Y,Z))
| add(multiply(X,Z),add(X_122,multiply(X,Y))) != add(X_122,add(multiply(X,Y),multiply(X,Z)))
| add(multiply(X,Z),add(X_122,multiply(X,Y))) = add(X_122,multiply(X,add(Y,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,Z),add(X_122,multiply(X,Y))),add(X_122,add(multiply(X,Y),multiply(X,Z)))) ),[1,1],$fot(multiply(X,add(Y,Z)))]]) ).
cnf(refute_0_157,plain,
( add(multiply(X,Z),add(X_122,multiply(X,Y))) != add(X_122,add(multiply(X,Y),multiply(X,Z)))
| add(multiply(X,Z),add(X_122,multiply(X,Y))) = add(X_122,multiply(X,add(Y,Z))) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),multiply(X,Z)),multiply(X,add(Y,Z))) )],[refute_0_42,refute_0_156]) ).
cnf(refute_0_158,plain,
add(multiply(X,Z),add(X_122,multiply(X,Y))) = add(X_122,multiply(X,add(Y,Z))),
inference(resolve,[$cnf( $equal(add(multiply(X,Z),add(X_122,multiply(X,Y))),add(X_122,add(multiply(X,Y),multiply(X,Z)))) )],[refute_0_155,refute_0_157]) ).
cnf(refute_0_159,plain,
add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))) = add(X_44,multiply(X_574,add(X_576,X_575))),
inference(subst,[],[refute_0_158:[bind(X,$fot(X_574)),bind(Y,$fot(X_576)),bind(Z,$fot(X_575)),bind(X_122,$fot(X_44))]]) ).
cnf(refute_0_160,plain,
( add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))) != add(X_44,multiply(X_574,add(X_576,X_575)))
| add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))) != add(multiply(X_574,add(X_575,X_576)),X_44)
| add(X_44,multiply(X_574,add(X_576,X_575))) = add(multiply(X_574,add(X_575,X_576)),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))),add(multiply(X_574,add(X_575,X_576)),X_44)) ),[0],$fot(add(X_44,multiply(X_574,add(X_576,X_575))))]]) ).
cnf(refute_0_161,plain,
( add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))) != add(multiply(X_574,add(X_575,X_576)),X_44)
| add(X_44,multiply(X_574,add(X_576,X_575))) = add(multiply(X_574,add(X_575,X_576)),X_44) ),
inference(resolve,[$cnf( $equal(add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))),add(X_44,multiply(X_574,add(X_576,X_575)))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
add(X_44,multiply(X_574,add(X_576,X_575))) = add(multiply(X_574,add(X_575,X_576)),X_44),
inference(resolve,[$cnf( $equal(add(multiply(X_574,X_575),add(X_44,multiply(X_574,X_576))),add(multiply(X_574,add(X_575,X_576)),X_44)) )],[refute_0_147,refute_0_161]) ).
cnf(refute_0_163,plain,
( add(X_44,multiply(X_574,add(X_576,X_575))) != add(multiply(X_574,add(X_575,X_576)),X_44)
| add(multiply(X_574,add(X_575,X_576)),X_44) = add(X_44,multiply(X_574,add(X_576,X_575))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_44,multiply(X_574,add(X_576,X_575))))),bind(Y0,$fot(add(multiply(X_574,add(X_575,X_576)),X_44)))]]) ).
cnf(refute_0_164,plain,
add(multiply(X_574,add(X_575,X_576)),X_44) = add(X_44,multiply(X_574,add(X_576,X_575))),
inference(resolve,[$cnf( $equal(add(X_44,multiply(X_574,add(X_576,X_575))),add(multiply(X_574,add(X_575,X_576)),X_44)) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575))) = add(additive_inverse(multiply(X_574,X_575)),multiply(X_574,add(X_576,X_575))),
inference(subst,[],[refute_0_164:[bind(X_44,$fot(additive_inverse(multiply(X_574,X_575))))]]) ).
cnf(refute_0_166,plain,
( multiply(X_574,X_576) != add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575)))
| add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575))) != add(additive_inverse(multiply(X_574,X_575)),multiply(X_574,add(X_576,X_575)))
| multiply(X_574,X_576) = add(additive_inverse(multiply(X_574,X_575)),multiply(X_574,add(X_576,X_575))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_574,X_576),add(additive_inverse(multiply(X_574,X_575)),multiply(X_574,add(X_576,X_575)))) ),[0],$fot(add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575))))]]) ).
cnf(refute_0_167,plain,
( multiply(X_574,X_576) != add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575)))
| multiply(X_574,X_576) = add(additive_inverse(multiply(X_574,X_575)),multiply(X_574,add(X_576,X_575))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575))),add(additive_inverse(multiply(X_574,X_575)),multiply(X_574,add(X_576,X_575)))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
multiply(X_574,X_576) = add(additive_inverse(multiply(X_574,X_575)),multiply(X_574,add(X_576,X_575))),
inference(resolve,[$cnf( $equal(multiply(X_574,X_576),add(multiply(X_574,add(X_575,X_576)),additive_inverse(multiply(X_574,X_575)))) )],[refute_0_129,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(X_577,X_579) = add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,add(X_579,add(additive_inverse(X_579),X_44)))),
inference(subst,[],[refute_0_168:[bind(X_574,$fot(X_577)),bind(X_575,$fot(add(additive_inverse(X_579),X_44))),bind(X_576,$fot(X_579))]]) ).
cnf(refute_0_170,plain,
add(X_579,add(additive_inverse(X_579),X_44)) = X_44,
inference(subst,[],[refute_0_8:[bind(X_42,$fot(X_579))]]) ).
cnf(refute_0_171,plain,
( multiply(X_577,X_579) != add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,add(X_579,add(additive_inverse(X_579),X_44))))
| add(X_579,add(additive_inverse(X_579),X_44)) != X_44
| multiply(X_577,X_579) = add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_577,X_579),add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,add(X_579,add(additive_inverse(X_579),X_44))))) ),[1,1,1],$fot(X_44)]]) ).
cnf(refute_0_172,plain,
( multiply(X_577,X_579) != add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,add(X_579,add(additive_inverse(X_579),X_44))))
| multiply(X_577,X_579) = add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)) ),
inference(resolve,[$cnf( $equal(add(X_579,add(additive_inverse(X_579),X_44)),X_44) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(X_577,X_579) = add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)),
inference(resolve,[$cnf( $equal(multiply(X_577,X_579),add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,add(X_579,add(additive_inverse(X_579),X_44))))) )],[refute_0_169,refute_0_172]) ).
cnf(refute_0_174,plain,
additive_inverse(multiply(X,Z)) = add(multiply(X,Y),additive_inverse(add(multiply(X,Y),multiply(X,Z)))),
inference(subst,[],[refute_0_74:[bind(X,$fot(multiply(X,Z))),bind(X_65,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_175,plain,
( add(multiply(X,Y),multiply(X,Z)) != multiply(X,add(Y,Z))
| additive_inverse(multiply(X,Z)) != add(multiply(X,Y),additive_inverse(add(multiply(X,Y),multiply(X,Z))))
| additive_inverse(multiply(X,Z)) = add(multiply(X,Y),additive_inverse(multiply(X,add(Y,Z)))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X,Z)),add(multiply(X,Y),additive_inverse(add(multiply(X,Y),multiply(X,Z))))) ),[1,1,0],$fot(multiply(X,add(Y,Z)))]]) ).
cnf(refute_0_176,plain,
( additive_inverse(multiply(X,Z)) != add(multiply(X,Y),additive_inverse(add(multiply(X,Y),multiply(X,Z))))
| additive_inverse(multiply(X,Z)) = add(multiply(X,Y),additive_inverse(multiply(X,add(Y,Z)))) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),multiply(X,Z)),multiply(X,add(Y,Z))) )],[refute_0_42,refute_0_175]) ).
cnf(refute_0_177,plain,
additive_inverse(multiply(X,Z)) = add(multiply(X,Y),additive_inverse(multiply(X,add(Y,Z)))),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X,Z)),add(multiply(X,Y),additive_inverse(add(multiply(X,Y),multiply(X,Z))))) )],[refute_0_174,refute_0_176]) ).
cnf(refute_0_178,plain,
( additive_inverse(multiply(X,Z)) != add(multiply(X,Y),additive_inverse(multiply(X,add(Y,Z))))
| add(multiply(X,Y),additive_inverse(multiply(X,add(Y,Z)))) = additive_inverse(multiply(X,Z)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(multiply(X,Z)))),bind(Y0,$fot(add(multiply(X,Y),additive_inverse(multiply(X,add(Y,Z))))))]]) ).
cnf(refute_0_179,plain,
add(multiply(X,Y),additive_inverse(multiply(X,add(Y,Z)))) = additive_inverse(multiply(X,Z)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X,Z)),add(multiply(X,Y),additive_inverse(multiply(X,add(Y,Z))))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
add(multiply(X_577,X_44),additive_inverse(multiply(X_577,add(X_44,additive_inverse(X_579))))) = additive_inverse(multiply(X_577,additive_inverse(X_579))),
inference(subst,[],[refute_0_179:[bind(X,$fot(X_577)),bind(Y,$fot(X_44)),bind(Z,$fot(additive_inverse(X_579)))]]) ).
cnf(refute_0_181,plain,
add(X,add(additive_inverse(add(X_65,X)),Z)) = add(add(X,additive_inverse(add(X_65,X))),Z),
inference(subst,[],[associativity_for_addition:[bind(Y,$fot(additive_inverse(add(X_65,X))))]]) ).
cnf(refute_0_182,plain,
( add(X,add(additive_inverse(add(X_65,X)),Z)) != add(add(X,additive_inverse(add(X_65,X))),Z)
| add(X,additive_inverse(add(X_65,X))) != additive_inverse(X_65)
| add(X,add(additive_inverse(add(X_65,X)),Z)) = add(additive_inverse(X_65),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(additive_inverse(add(X_65,X)),Z)),add(add(X,additive_inverse(add(X_65,X))),Z)) ),[1,0],$fot(additive_inverse(X_65))]]) ).
cnf(refute_0_183,plain,
( add(X,add(additive_inverse(add(X_65,X)),Z)) != add(add(X,additive_inverse(add(X_65,X))),Z)
| add(X,add(additive_inverse(add(X_65,X)),Z)) = add(additive_inverse(X_65),Z) ),
inference(resolve,[$cnf( $equal(add(X,additive_inverse(add(X_65,X))),additive_inverse(X_65)) )],[refute_0_55,refute_0_182]) ).
cnf(refute_0_184,plain,
add(X,add(additive_inverse(add(X_65,X)),Z)) = add(additive_inverse(X_65),Z),
inference(resolve,[$cnf( $equal(add(X,add(additive_inverse(add(X_65,X)),Z)),add(add(X,additive_inverse(add(X_65,X))),Z)) )],[refute_0_181,refute_0_183]) ).
cnf(refute_0_185,plain,
add(commutator(X,add(X_79,X_78)),add(additive_inverse(add(multiply(X,add(X_78,X_79)),commutator(X,add(X_79,X_78)))),X_522)) = add(additive_inverse(multiply(X,add(X_78,X_79))),X_522),
inference(subst,[],[refute_0_184:[bind(X,$fot(commutator(X,add(X_79,X_78)))),bind(Z,$fot(X_522)),bind(X_65,$fot(multiply(X,add(X_78,X_79))))]]) ).
cnf(refute_0_186,plain,
add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) = multiply(Y,X),
inference(subst,[],[refute_0_125:[bind(X_45,$fot(multiply(X,Y))),bind(X_46,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_187,plain,
( commutator(X,Y) != add(multiply(Y,X),additive_inverse(multiply(X,Y)))
| add(multiply(Y,X),additive_inverse(multiply(X,Y))) = commutator(X,Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(commutator(X,Y))),bind(Y0,$fot(add(multiply(Y,X),additive_inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_188,plain,
add(multiply(Y,X),additive_inverse(multiply(X,Y))) = commutator(X,Y),
inference(resolve,[$cnf( $equal(commutator(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) )],[commutator,refute_0_187]) ).
cnf(refute_0_189,plain,
( add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) != multiply(Y,X)
| add(multiply(Y,X),additive_inverse(multiply(X,Y))) != commutator(X,Y)
| add(multiply(X,Y),commutator(X,Y)) = multiply(Y,X) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))),multiply(Y,X)) ),[0,1],$fot(commutator(X,Y))]]) ).
cnf(refute_0_190,plain,
( add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) != multiply(Y,X)
| add(multiply(X,Y),commutator(X,Y)) = multiply(Y,X) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,X),additive_inverse(multiply(X,Y))),commutator(X,Y)) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
add(multiply(X,Y),commutator(X,Y)) = multiply(Y,X),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))),multiply(Y,X)) )],[refute_0_186,refute_0_190]) ).
cnf(refute_0_192,plain,
add(multiply(X,add(X_79,X_78)),commutator(X,add(X_79,X_78))) = multiply(add(X_79,X_78),X),
inference(subst,[],[refute_0_191:[bind(Y,$fot(add(X_79,X_78)))]]) ).
cnf(refute_0_193,plain,
( multiply(X,add(X_79,X_78)) != multiply(X,add(X_78,X_79))
| add(multiply(X,add(X_79,X_78)),commutator(X,add(X_79,X_78))) != multiply(add(X_79,X_78),X)
| add(multiply(X,add(X_78,X_79)),commutator(X,add(X_79,X_78))) = multiply(add(X_79,X_78),X) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,add(X_79,X_78)),commutator(X,add(X_79,X_78))),multiply(add(X_79,X_78),X)) ),[0,0],$fot(multiply(X,add(X_78,X_79)))]]) ).
cnf(refute_0_194,plain,
( add(multiply(X,add(X_79,X_78)),commutator(X,add(X_79,X_78))) != multiply(add(X_79,X_78),X)
| add(multiply(X,add(X_78,X_79)),commutator(X,add(X_79,X_78))) = multiply(add(X_79,X_78),X) ),
inference(resolve,[$cnf( $equal(multiply(X,add(X_79,X_78)),multiply(X,add(X_78,X_79))) )],[refute_0_47,refute_0_193]) ).
cnf(refute_0_195,plain,
add(multiply(X,add(X_78,X_79)),commutator(X,add(X_79,X_78))) = multiply(add(X_79,X_78),X),
inference(resolve,[$cnf( $equal(add(multiply(X,add(X_79,X_78)),commutator(X,add(X_79,X_78))),multiply(add(X_79,X_78),X)) )],[refute_0_192,refute_0_194]) ).
cnf(refute_0_196,plain,
( add(multiply(X,add(X_78,X_79)),commutator(X,add(X_79,X_78))) != multiply(add(X_79,X_78),X)
| add(commutator(X,add(X_79,X_78)),add(additive_inverse(add(multiply(X,add(X_78,X_79)),commutator(X,add(X_79,X_78)))),X_522)) != add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)
| add(commutator(X,add(X_79,X_78)),add(additive_inverse(multiply(add(X_79,X_78),X)),X_522)) = add(additive_inverse(multiply(X,add(X_78,X_79))),X_522) ),
introduced(tautology,[equality,[$cnf( $equal(add(commutator(X,add(X_79,X_78)),add(additive_inverse(add(multiply(X,add(X_78,X_79)),commutator(X,add(X_79,X_78)))),X_522)),add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)) ),[0,1,0,0],$fot(multiply(add(X_79,X_78),X))]]) ).
cnf(refute_0_197,plain,
( add(commutator(X,add(X_79,X_78)),add(additive_inverse(add(multiply(X,add(X_78,X_79)),commutator(X,add(X_79,X_78)))),X_522)) != add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)
| add(commutator(X,add(X_79,X_78)),add(additive_inverse(multiply(add(X_79,X_78),X)),X_522)) = add(additive_inverse(multiply(X,add(X_78,X_79))),X_522) ),
inference(resolve,[$cnf( $equal(add(multiply(X,add(X_78,X_79)),commutator(X,add(X_79,X_78))),multiply(add(X_79,X_78),X)) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
add(commutator(X,add(X_79,X_78)),add(additive_inverse(multiply(add(X_79,X_78),X)),X_522)) = add(additive_inverse(multiply(X,add(X_78,X_79))),X_522),
inference(resolve,[$cnf( $equal(add(commutator(X,add(X_79,X_78)),add(additive_inverse(add(multiply(X,add(X_78,X_79)),commutator(X,add(X_79,X_78)))),X_522)),add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)) )],[refute_0_185,refute_0_197]) ).
cnf(refute_0_199,plain,
add(X_42,add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42))))) = additive_inverse(add(X_65,additive_inverse(X_42))),
inference(subst,[],[refute_0_8:[bind(X_44,$fot(additive_inverse(add(X_65,additive_inverse(X_42)))))]]) ).
cnf(refute_0_200,plain,
additive_inverse(X_65) = add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42)))),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_65)),bind(X_64,$fot(additive_inverse(X_42)))]]) ).
cnf(refute_0_201,plain,
( additive_inverse(X_65) != add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42))))
| add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42)))) = additive_inverse(X_65) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(X_65))),bind(Y0,$fot(add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42))))))]]) ).
cnf(refute_0_202,plain,
add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42)))) = additive_inverse(X_65),
inference(resolve,[$cnf( $equal(additive_inverse(X_65),add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42))))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
( add(X_42,add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42))))) != additive_inverse(add(X_65,additive_inverse(X_42)))
| add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42)))) != additive_inverse(X_65)
| add(X_42,additive_inverse(X_65)) = additive_inverse(add(X_65,additive_inverse(X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42))))),additive_inverse(add(X_65,additive_inverse(X_42)))) ),[0,1],$fot(additive_inverse(X_65))]]) ).
cnf(refute_0_204,plain,
( add(X_42,add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42))))) != additive_inverse(add(X_65,additive_inverse(X_42)))
| add(X_42,additive_inverse(X_65)) = additive_inverse(add(X_65,additive_inverse(X_42))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42)))),additive_inverse(X_65)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
add(X_42,additive_inverse(X_65)) = additive_inverse(add(X_65,additive_inverse(X_42))),
inference(resolve,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),additive_inverse(add(X_65,additive_inverse(X_42))))),additive_inverse(add(X_65,additive_inverse(X_42)))) )],[refute_0_199,refute_0_204]) ).
cnf(refute_0_206,plain,
add(additive_inverse(X),additive_inverse(X_174)) = additive_inverse(add(X_174,additive_inverse(additive_inverse(X)))),
inference(subst,[],[refute_0_205:[bind(X_42,$fot(additive_inverse(X))),bind(X_65,$fot(X_174))]]) ).
cnf(refute_0_207,plain,
( add(additive_inverse(X),additive_inverse(X_174)) != additive_inverse(add(X_174,additive_inverse(additive_inverse(X))))
| additive_inverse(additive_inverse(X)) != X
| add(additive_inverse(X),additive_inverse(X_174)) = additive_inverse(add(X_174,X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X),additive_inverse(X_174)),additive_inverse(add(X_174,additive_inverse(additive_inverse(X))))) ),[1,0,1],$fot(X)]]) ).
cnf(refute_0_208,plain,
( add(additive_inverse(X),additive_inverse(X_174)) != additive_inverse(add(X_174,additive_inverse(additive_inverse(X))))
| add(additive_inverse(X),additive_inverse(X_174)) = additive_inverse(add(X_174,X)) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_207]) ).
cnf(refute_0_209,plain,
add(additive_inverse(X),additive_inverse(X_174)) = additive_inverse(add(X_174,X)),
inference(resolve,[$cnf( $equal(add(additive_inverse(X),additive_inverse(X_174)),additive_inverse(add(X_174,additive_inverse(additive_inverse(X))))) )],[refute_0_206,refute_0_208]) ).
cnf(refute_0_210,plain,
add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) = additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))),
inference(subst,[],[refute_0_209:[bind(X,$fot(additive_inverse(add(commutator(X_515,X_516),X_517)))),bind(X_174,$fot(multiply(X_516,X_515)))]]) ).
cnf(refute_0_211,plain,
additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)) = add(multiply(X_279,X_278),additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)))),
inference(subst,[],[refute_0_74:[bind(X,$fot(add(additive_inverse(multiply(X_278,X_279)),X_280))),bind(X_65,$fot(multiply(X_279,X_278)))]]) ).
cnf(refute_0_212,plain,
add(multiply(Y,X),add(additive_inverse(multiply(X,Y)),X_44)) = add(add(multiply(Y,X),additive_inverse(multiply(X,Y))),X_44),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(multiply(Y,X))),bind(Y,$fot(additive_inverse(multiply(X,Y)))),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_213,plain,
( add(multiply(Y,X),add(additive_inverse(multiply(X,Y)),X_44)) != add(add(multiply(Y,X),additive_inverse(multiply(X,Y))),X_44)
| add(multiply(Y,X),additive_inverse(multiply(X,Y))) != commutator(X,Y)
| add(multiply(Y,X),add(additive_inverse(multiply(X,Y)),X_44)) = add(commutator(X,Y),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,X),add(additive_inverse(multiply(X,Y)),X_44)),add(add(multiply(Y,X),additive_inverse(multiply(X,Y))),X_44)) ),[1,0],$fot(commutator(X,Y))]]) ).
cnf(refute_0_214,plain,
( add(multiply(Y,X),add(additive_inverse(multiply(X,Y)),X_44)) != add(add(multiply(Y,X),additive_inverse(multiply(X,Y))),X_44)
| add(multiply(Y,X),add(additive_inverse(multiply(X,Y)),X_44)) = add(commutator(X,Y),X_44) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,X),additive_inverse(multiply(X,Y))),commutator(X,Y)) )],[refute_0_188,refute_0_213]) ).
cnf(refute_0_215,plain,
add(multiply(Y,X),add(additive_inverse(multiply(X,Y)),X_44)) = add(commutator(X,Y),X_44),
inference(resolve,[$cnf( $equal(add(multiply(Y,X),add(additive_inverse(multiply(X,Y)),X_44)),add(add(multiply(Y,X),additive_inverse(multiply(X,Y))),X_44)) )],[refute_0_212,refute_0_214]) ).
cnf(refute_0_216,plain,
add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)) = add(commutator(X_278,X_279),X_280),
inference(subst,[],[refute_0_215:[bind(X,$fot(X_278)),bind(Y,$fot(X_279)),bind(X_44,$fot(X_280))]]) ).
cnf(refute_0_217,plain,
( add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)) != add(commutator(X_278,X_279),X_280)
| additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)) != add(multiply(X_279,X_278),additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280))))
| additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)) = add(multiply(X_279,X_278),additive_inverse(add(commutator(X_278,X_279),X_280))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),add(multiply(X_279,X_278),additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280))))) ),[1,1,0],$fot(add(commutator(X_278,X_279),X_280))]]) ).
cnf(refute_0_218,plain,
( additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)) != add(multiply(X_279,X_278),additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280))))
| additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)) = add(multiply(X_279,X_278),additive_inverse(add(commutator(X_278,X_279),X_280))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)),add(commutator(X_278,X_279),X_280)) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)) = add(multiply(X_279,X_278),additive_inverse(add(commutator(X_278,X_279),X_280))),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),add(multiply(X_279,X_278),additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280))))) )],[refute_0_211,refute_0_218]) ).
cnf(refute_0_220,plain,
add(X_42,add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67)))) = additive_inverse(add(additive_inverse(X_42),X_67)),
inference(subst,[],[refute_0_8:[bind(X_44,$fot(additive_inverse(add(additive_inverse(X_42),X_67))))]]) ).
cnf(refute_0_221,plain,
additive_inverse(X_67) = add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67))),
inference(subst,[],[refute_0_74:[bind(X,$fot(X_67)),bind(X_65,$fot(additive_inverse(X_42)))]]) ).
cnf(refute_0_222,plain,
( additive_inverse(X_67) != add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67)))
| add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67))) = additive_inverse(X_67) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(X_67))),bind(Y0,$fot(add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67)))))]]) ).
cnf(refute_0_223,plain,
add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67))) = additive_inverse(X_67),
inference(resolve,[$cnf( $equal(additive_inverse(X_67),add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67)))) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
( add(X_42,add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67)))) != additive_inverse(add(additive_inverse(X_42),X_67))
| add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67))) != additive_inverse(X_67)
| add(X_42,additive_inverse(X_67)) = additive_inverse(add(additive_inverse(X_42),X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67)))),additive_inverse(add(additive_inverse(X_42),X_67))) ),[0,1],$fot(additive_inverse(X_67))]]) ).
cnf(refute_0_225,plain,
( add(X_42,add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67)))) != additive_inverse(add(additive_inverse(X_42),X_67))
| add(X_42,additive_inverse(X_67)) = additive_inverse(add(additive_inverse(X_42),X_67)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67))),additive_inverse(X_67)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
add(X_42,additive_inverse(X_67)) = additive_inverse(add(additive_inverse(X_42),X_67)),
inference(resolve,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),additive_inverse(add(additive_inverse(X_42),X_67)))),additive_inverse(add(additive_inverse(X_42),X_67))) )],[refute_0_220,refute_0_225]) ).
cnf(refute_0_227,plain,
( add(X_42,additive_inverse(X_67)) != additive_inverse(add(additive_inverse(X_42),X_67))
| additive_inverse(add(additive_inverse(X_42),X_67)) = add(X_42,additive_inverse(X_67)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_42,additive_inverse(X_67)))),bind(Y0,$fot(additive_inverse(add(additive_inverse(X_42),X_67))))]]) ).
cnf(refute_0_228,plain,
additive_inverse(add(additive_inverse(X_42),X_67)) = add(X_42,additive_inverse(X_67)),
inference(resolve,[$cnf( $equal(add(X_42,additive_inverse(X_67)),additive_inverse(add(additive_inverse(X_42),X_67))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)) = add(multiply(X_278,X_279),additive_inverse(X_280)),
inference(subst,[],[refute_0_228:[bind(X_42,$fot(multiply(X_278,X_279))),bind(X_67,$fot(X_280))]]) ).
cnf(refute_0_230,plain,
( additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)) != add(multiply(X_278,X_279),additive_inverse(X_280))
| additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)) != add(multiply(X_279,X_278),additive_inverse(add(commutator(X_278,X_279),X_280)))
| add(multiply(X_278,X_279),additive_inverse(X_280)) = add(multiply(X_279,X_278),additive_inverse(add(commutator(X_278,X_279),X_280))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),add(multiply(X_279,X_278),additive_inverse(add(commutator(X_278,X_279),X_280)))) ),[0],$fot(add(multiply(X_278,X_279),additive_inverse(X_280)))]]) ).
cnf(refute_0_231,plain,
( additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)) != add(multiply(X_279,X_278),additive_inverse(add(commutator(X_278,X_279),X_280)))
| add(multiply(X_278,X_279),additive_inverse(X_280)) = add(multiply(X_279,X_278),additive_inverse(add(commutator(X_278,X_279),X_280))) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),add(multiply(X_278,X_279),additive_inverse(X_280))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
add(multiply(X_278,X_279),additive_inverse(X_280)) = add(multiply(X_279,X_278),additive_inverse(add(commutator(X_278,X_279),X_280))),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),add(multiply(X_279,X_278),additive_inverse(add(commutator(X_278,X_279),X_280)))) )],[refute_0_219,refute_0_231]) ).
cnf(refute_0_233,plain,
add(multiply(X_515,X_516),additive_inverse(X_517)) = add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))),
inference(subst,[],[refute_0_232:[bind(X_278,$fot(X_515)),bind(X_279,$fot(X_516)),bind(X_280,$fot(X_517))]]) ).
cnf(refute_0_234,plain,
( add(multiply(X_515,X_516),additive_inverse(X_517)) != add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))
| add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))) = add(multiply(X_515,X_516),additive_inverse(X_517)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(multiply(X_515,X_516),additive_inverse(X_517)))),bind(Y0,$fot(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))))]]) ).
cnf(refute_0_235,plain,
add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))) = add(multiply(X_515,X_516),additive_inverse(X_517)),
inference(resolve,[$cnf( $equal(add(multiply(X_515,X_516),additive_inverse(X_517)),add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
( add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))) != add(multiply(X_515,X_516),additive_inverse(X_517))
| add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) != additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))))
| add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) = additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517))) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))),additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))))) ),[1,0],$fot(add(multiply(X_515,X_516),additive_inverse(X_517)))]]) ).
cnf(refute_0_237,plain,
( add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) != additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))))
| add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) = additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))),add(multiply(X_515,X_516),additive_inverse(X_517))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) = additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517))),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))),additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))))) )],[refute_0_210,refute_0_237]) ).
cnf(refute_0_239,plain,
add(X_42,add(X_43,X)) = add(X_42,add(X,X_43)),
inference(subst,[],[refute_0_142:[bind(X_43,$fot(X)),bind(X_44,$fot(X_43))]]) ).
cnf(refute_0_240,plain,
( add(X,add(X_42,X_43)) != add(X_42,add(X_43,X))
| add(X_42,add(X_43,X)) != add(X_42,add(X,X_43))
| add(X,add(X_42,X_43)) = add(X_42,add(X,X_43)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,add(X_42,X_43)),add(X_42,add(X,X_43))) ),[0],$fot(add(X_42,add(X_43,X)))]]) ).
cnf(refute_0_241,plain,
( add(X,add(X_42,X_43)) != add(X_42,add(X_43,X))
| add(X,add(X_42,X_43)) = add(X_42,add(X,X_43)) ),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X)),add(X_42,add(X,X_43))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
add(X,add(X_42,X_43)) = add(X_42,add(X,X_43)),
inference(resolve,[$cnf( $equal(add(X,add(X_42,X_43)),add(X_42,add(X_43,X))) )],[refute_0_154,refute_0_241]) ).
cnf(refute_0_243,plain,
( add(X,add(X_42,X_43)) != add(X_42,add(X,X_43))
| add(X_42,add(X,X_43)) = add(X,add(X_42,X_43)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X,add(X_42,X_43)))),bind(Y0,$fot(add(X_42,add(X,X_43))))]]) ).
cnf(refute_0_244,plain,
add(X_42,add(X,X_43)) = add(X,add(X_42,X_43)),
inference(resolve,[$cnf( $equal(add(X,add(X_42,X_43)),add(X_42,add(X,X_43))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
add(additive_inverse(multiply(X_516,X_515)),add(commutator(X_515,X_516),X_517)) = add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)),
inference(subst,[],[refute_0_244:[bind(X,$fot(commutator(X_515,X_516))),bind(X_42,$fot(additive_inverse(multiply(X_516,X_515)))),bind(X_43,$fot(X_517))]]) ).
cnf(refute_0_246,plain,
add(X,add(Y,add(additive_inverse(Y),X_46))) = add(add(X,Y),add(additive_inverse(Y),X_46)),
inference(subst,[],[associativity_for_addition:[bind(Z,$fot(add(additive_inverse(Y),X_46)))]]) ).
cnf(refute_0_247,plain,
add(Y,add(additive_inverse(Y),X_46)) = X_46,
inference(subst,[],[refute_0_8:[bind(X_42,$fot(Y)),bind(X_44,$fot(X_46))]]) ).
cnf(refute_0_248,plain,
( add(X,add(Y,add(additive_inverse(Y),X_46))) != add(add(X,Y),add(additive_inverse(Y),X_46))
| add(Y,add(additive_inverse(Y),X_46)) != X_46
| add(X,X_46) = add(add(X,Y),add(additive_inverse(Y),X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(Y,add(additive_inverse(Y),X_46))),add(add(X,Y),add(additive_inverse(Y),X_46))) ),[0,1],$fot(X_46)]]) ).
cnf(refute_0_249,plain,
( add(X,add(Y,add(additive_inverse(Y),X_46))) != add(add(X,Y),add(additive_inverse(Y),X_46))
| add(X,X_46) = add(add(X,Y),add(additive_inverse(Y),X_46)) ),
inference(resolve,[$cnf( $equal(add(Y,add(additive_inverse(Y),X_46)),X_46) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
add(X,X_46) = add(add(X,Y),add(additive_inverse(Y),X_46)),
inference(resolve,[$cnf( $equal(add(X,add(Y,add(additive_inverse(Y),X_46))),add(add(X,Y),add(additive_inverse(Y),X_46))) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
add(add(X,Y),X_46) = add(X,add(Y,X_46)),
inference(subst,[],[refute_0_138:[bind(Z,$fot(X_46))]]) ).
cnf(refute_0_252,plain,
add(additive_inverse(Y),add(add(X,Y),X_46)) = add(additive_inverse(Y),add(add(X,Y),X_46)),
introduced(tautology,[refl,[$fot(add(additive_inverse(Y),add(add(X,Y),X_46)))]]) ).
cnf(refute_0_253,plain,
( add(add(X,Y),X_46) != add(X,add(Y,X_46))
| add(additive_inverse(Y),add(add(X,Y),X_46)) != add(additive_inverse(Y),add(add(X,Y),X_46))
| add(additive_inverse(Y),add(add(X,Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(Y),add(add(X,Y),X_46)),add(additive_inverse(Y),add(add(X,Y),X_46))) ),[1,1],$fot(add(X,add(Y,X_46)))]]) ).
cnf(refute_0_254,plain,
( add(add(X,Y),X_46) != add(X,add(Y,X_46))
| add(additive_inverse(Y),add(add(X,Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(add(X,Y),X_46)),add(additive_inverse(Y),add(add(X,Y),X_46))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
add(additive_inverse(Y),add(add(X,Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))),
inference(resolve,[$cnf( $equal(add(add(X,Y),X_46),add(X,add(Y,X_46))) )],[refute_0_251,refute_0_254]) ).
cnf(refute_0_256,plain,
add(X_43,X_42) = add(X_42,X_43),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_43)),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_257,plain,
( add(X_43,X_42) != add(X_42,X_43)
| add(X_42,X_43) = add(X_43,X_42) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_43,X_42))),bind(Y0,$fot(add(X_42,X_43)))]]) ).
cnf(refute_0_258,plain,
add(X_42,X_43) = add(X_43,X_42),
inference(resolve,[$cnf( $equal(add(X_43,X_42),add(X_42,X_43)) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
( add(X_42,X_43) != add(X_43,X_42)
| add(X_42,add(X_43,X_44)) != add(add(X_42,X_43),X_44)
| add(X_42,add(X_43,X_44)) = add(add(X_43,X_42),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(add(X_42,X_43),X_44)) ),[1,0],$fot(add(X_43,X_42))]]) ).
cnf(refute_0_260,plain,
( add(X_42,add(X_43,X_44)) != add(add(X_42,X_43),X_44)
| add(X_42,add(X_43,X_44)) = add(add(X_43,X_42),X_44) ),
inference(resolve,[$cnf( $equal(add(X_42,X_43),add(X_43,X_42)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
add(X_42,add(X_43,X_44)) = add(add(X_43,X_42),X_44),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(add(X_42,X_43),X_44)) )],[refute_0_130,refute_0_260]) ).
cnf(refute_0_262,plain,
add(add(X_43,X_42),X_44) = add(X_43,add(X_42,X_44)),
inference(subst,[],[refute_0_138:[bind(X,$fot(X_43)),bind(Y,$fot(X_42)),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_263,plain,
( add(X_42,add(X_43,X_44)) != add(add(X_43,X_42),X_44)
| add(add(X_43,X_42),X_44) != add(X_43,add(X_42,X_44))
| add(X_42,add(X_43,X_44)) = add(X_43,add(X_42,X_44)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_42,add(X_43,X_44)),add(X_43,add(X_42,X_44))) ),[0],$fot(add(add(X_43,X_42),X_44))]]) ).
cnf(refute_0_264,plain,
( add(X_42,add(X_43,X_44)) != add(add(X_43,X_42),X_44)
| add(X_42,add(X_43,X_44)) = add(X_43,add(X_42,X_44)) ),
inference(resolve,[$cnf( $equal(add(add(X_43,X_42),X_44),add(X_43,add(X_42,X_44))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
add(X_42,add(X_43,X_44)) = add(X_43,add(X_42,X_44)),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(add(X_43,X_42),X_44)) )],[refute_0_261,refute_0_264]) ).
cnf(refute_0_266,plain,
( add(X_42,add(X_43,X_44)) != add(X_43,add(X_42,X_44))
| add(X_43,add(X_42,X_44)) = add(X_42,add(X_43,X_44)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_42,add(X_43,X_44)))),bind(Y0,$fot(add(X_43,add(X_42,X_44))))]]) ).
cnf(refute_0_267,plain,
add(X_43,add(X_42,X_44)) = add(X_42,add(X_43,X_44)),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(X_43,add(X_42,X_44))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
add(add(X,Y),add(additive_inverse(Y),X_46)) = add(additive_inverse(Y),add(add(X,Y),X_46)),
inference(subst,[],[refute_0_267:[bind(X_42,$fot(additive_inverse(Y))),bind(X_43,$fot(add(X,Y))),bind(X_44,$fot(X_46))]]) ).
cnf(refute_0_269,plain,
( add(add(X,Y),add(additive_inverse(Y),X_46)) != add(additive_inverse(Y),add(add(X,Y),X_46))
| add(additive_inverse(Y),add(add(X,Y),X_46)) != add(additive_inverse(Y),add(X,add(Y,X_46)))
| add(add(X,Y),add(additive_inverse(Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(add(X,Y),add(additive_inverse(Y),X_46)))),bind(Y0,$fot(add(additive_inverse(Y),add(add(X,Y),X_46)))),bind(Z0,$fot(add(additive_inverse(Y),add(X,add(Y,X_46)))))]]) ).
cnf(refute_0_270,plain,
( add(additive_inverse(Y),add(add(X,Y),X_46)) != add(additive_inverse(Y),add(X,add(Y,X_46)))
| add(add(X,Y),add(additive_inverse(Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),add(additive_inverse(Y),X_46)),add(additive_inverse(Y),add(add(X,Y),X_46))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
add(add(X,Y),add(additive_inverse(Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(add(X,Y),X_46)),add(additive_inverse(Y),add(X,add(Y,X_46)))) )],[refute_0_255,refute_0_270]) ).
cnf(refute_0_272,plain,
( add(X,X_46) != add(add(X,Y),add(additive_inverse(Y),X_46))
| add(add(X,Y),add(additive_inverse(Y),X_46)) != add(additive_inverse(Y),add(X,add(Y,X_46)))
| add(X,X_46) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,X_46),add(additive_inverse(Y),add(X,add(Y,X_46)))) ),[0],$fot(add(add(X,Y),add(additive_inverse(Y),X_46)))]]) ).
cnf(refute_0_273,plain,
( add(X,X_46) != add(add(X,Y),add(additive_inverse(Y),X_46))
| add(X,X_46) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),add(additive_inverse(Y),X_46)),add(additive_inverse(Y),add(X,add(Y,X_46)))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
add(X,X_46) = add(additive_inverse(Y),add(X,add(Y,X_46))),
inference(resolve,[$cnf( $equal(add(X,X_46),add(add(X,Y),add(additive_inverse(Y),X_46))) )],[refute_0_250,refute_0_273]) ).
cnf(refute_0_275,plain,
add(X_53,add(add(X,Y),additive_inverse(X_53))) = add(X,Y),
inference(subst,[],[refute_0_125:[bind(X_45,$fot(X_53)),bind(X_46,$fot(add(X,Y)))]]) ).
cnf(refute_0_276,plain,
add(X,add(Y,additive_inverse(X_53))) = add(add(X,Y),additive_inverse(X_53)),
inference(subst,[],[associativity_for_addition:[bind(Z,$fot(additive_inverse(X_53)))]]) ).
cnf(refute_0_277,plain,
( add(X,add(Y,additive_inverse(X_53))) != add(add(X,Y),additive_inverse(X_53))
| add(add(X,Y),additive_inverse(X_53)) = add(X,add(Y,additive_inverse(X_53))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X,add(Y,additive_inverse(X_53))))),bind(Y0,$fot(add(add(X,Y),additive_inverse(X_53))))]]) ).
cnf(refute_0_278,plain,
add(add(X,Y),additive_inverse(X_53)) = add(X,add(Y,additive_inverse(X_53))),
inference(resolve,[$cnf( $equal(add(X,add(Y,additive_inverse(X_53))),add(add(X,Y),additive_inverse(X_53))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
( add(X_53,add(add(X,Y),additive_inverse(X_53))) != add(X,Y)
| add(add(X,Y),additive_inverse(X_53)) != add(X,add(Y,additive_inverse(X_53)))
| add(X_53,add(X,add(Y,additive_inverse(X_53)))) = add(X,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_53,add(add(X,Y),additive_inverse(X_53))),add(X,Y)) ),[0,1],$fot(add(X,add(Y,additive_inverse(X_53))))]]) ).
cnf(refute_0_280,plain,
( add(X_53,add(add(X,Y),additive_inverse(X_53))) != add(X,Y)
| add(X_53,add(X,add(Y,additive_inverse(X_53)))) = add(X,Y) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),additive_inverse(X_53)),add(X,add(Y,additive_inverse(X_53)))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
add(X_53,add(X,add(Y,additive_inverse(X_53)))) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X_53,add(add(X,Y),additive_inverse(X_53))),add(X,Y)) )],[refute_0_275,refute_0_280]) ).
cnf(refute_0_282,plain,
add(Y,add(X_46,add(X,additive_inverse(Y)))) = add(X_46,X),
inference(subst,[],[refute_0_281:[bind(X,$fot(X_46)),bind(Y,$fot(X)),bind(X_53,$fot(Y))]]) ).
cnf(refute_0_283,plain,
add(X,add(X_42,add(X_123,X_121))) = add(X_42,add(add(X_123,X_121),X)),
inference(subst,[],[refute_0_154:[bind(X_43,$fot(add(X_123,X_121)))]]) ).
cnf(refute_0_284,plain,
add(X_121,add(X_42,X_123)) = add(X_42,add(X_123,X_121)),
inference(subst,[],[refute_0_154:[bind(X,$fot(X_121)),bind(X_43,$fot(X_123))]]) ).
cnf(refute_0_285,plain,
( add(X_121,add(X_42,X_123)) != add(X_42,add(X_123,X_121))
| add(X_42,add(X_123,X_121)) = add(X_121,add(X_42,X_123)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_121,add(X_42,X_123)))),bind(Y0,$fot(add(X_42,add(X_123,X_121))))]]) ).
cnf(refute_0_286,plain,
add(X_42,add(X_123,X_121)) = add(X_121,add(X_42,X_123)),
inference(resolve,[$cnf( $equal(add(X_121,add(X_42,X_123)),add(X_42,add(X_123,X_121))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
( add(X,add(X_42,add(X_123,X_121))) != add(X_42,add(add(X_123,X_121),X))
| add(X_42,add(X_123,X_121)) != add(X_121,add(X_42,X_123))
| add(X,add(X_121,add(X_42,X_123))) = add(X_42,add(add(X_123,X_121),X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(X_42,add(X_123,X_121))),add(X_42,add(add(X_123,X_121),X))) ),[0,1],$fot(add(X_121,add(X_42,X_123)))]]) ).
cnf(refute_0_288,plain,
( add(X,add(X_42,add(X_123,X_121))) != add(X_42,add(add(X_123,X_121),X))
| add(X,add(X_121,add(X_42,X_123))) = add(X_42,add(add(X_123,X_121),X)) ),
inference(resolve,[$cnf( $equal(add(X_42,add(X_123,X_121)),add(X_121,add(X_42,X_123))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
add(X,add(X_121,add(X_42,X_123))) = add(X_42,add(add(X_123,X_121),X)),
inference(resolve,[$cnf( $equal(add(X,add(X_42,add(X_123,X_121))),add(X_42,add(add(X_123,X_121),X))) )],[refute_0_283,refute_0_288]) ).
cnf(refute_0_290,plain,
add(add(X_123,X_121),X) = add(X_123,add(X_121,X)),
inference(subst,[],[refute_0_138:[bind(X,$fot(X_123)),bind(Y,$fot(X_121)),bind(Z,$fot(X))]]) ).
cnf(refute_0_291,plain,
add(X_42,add(add(X_123,X_121),X)) = add(X_42,add(add(X_123,X_121),X)),
introduced(tautology,[refl,[$fot(add(X_42,add(add(X_123,X_121),X)))]]) ).
cnf(refute_0_292,plain,
( add(X_42,add(add(X_123,X_121),X)) != add(X_42,add(add(X_123,X_121),X))
| add(add(X_123,X_121),X) != add(X_123,add(X_121,X))
| add(X_42,add(add(X_123,X_121),X)) = add(X_42,add(X_123,add(X_121,X))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(add(X_123,X_121),X)),add(X_42,add(add(X_123,X_121),X))) ),[1,1],$fot(add(X_123,add(X_121,X)))]]) ).
cnf(refute_0_293,plain,
( add(add(X_123,X_121),X) != add(X_123,add(X_121,X))
| add(X_42,add(add(X_123,X_121),X)) = add(X_42,add(X_123,add(X_121,X))) ),
inference(resolve,[$cnf( $equal(add(X_42,add(add(X_123,X_121),X)),add(X_42,add(add(X_123,X_121),X))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
add(X_42,add(add(X_123,X_121),X)) = add(X_42,add(X_123,add(X_121,X))),
inference(resolve,[$cnf( $equal(add(add(X_123,X_121),X),add(X_123,add(X_121,X))) )],[refute_0_290,refute_0_293]) ).
cnf(refute_0_295,plain,
( add(X,add(X_121,add(X_42,X_123))) != add(X_42,add(add(X_123,X_121),X))
| add(X_42,add(add(X_123,X_121),X)) != add(X_42,add(X_123,add(X_121,X)))
| add(X,add(X_121,add(X_42,X_123))) = add(X_42,add(X_123,add(X_121,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,add(X_121,add(X_42,X_123))),add(X_42,add(X_123,add(X_121,X)))) ),[0],$fot(add(X_42,add(add(X_123,X_121),X)))]]) ).
cnf(refute_0_296,plain,
( add(X,add(X_121,add(X_42,X_123))) != add(X_42,add(add(X_123,X_121),X))
| add(X,add(X_121,add(X_42,X_123))) = add(X_42,add(X_123,add(X_121,X))) ),
inference(resolve,[$cnf( $equal(add(X_42,add(add(X_123,X_121),X)),add(X_42,add(X_123,add(X_121,X)))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
add(X,add(X_121,add(X_42,X_123))) = add(X_42,add(X_123,add(X_121,X))),
inference(resolve,[$cnf( $equal(add(X,add(X_121,add(X_42,X_123))),add(X_42,add(add(X_123,X_121),X))) )],[refute_0_289,refute_0_296]) ).
cnf(refute_0_298,plain,
add(additive_inverse(Y),add(X,add(Y,X_46))) = add(Y,add(X_46,add(X,additive_inverse(Y)))),
inference(subst,[],[refute_0_297:[bind(X,$fot(additive_inverse(Y))),bind(X_121,$fot(X)),bind(X_123,$fot(X_46)),bind(X_42,$fot(Y))]]) ).
cnf(refute_0_299,plain,
( add(Y,add(X_46,add(X,additive_inverse(Y)))) != add(X_46,X)
| add(additive_inverse(Y),add(X,add(Y,X_46))) != add(Y,add(X_46,add(X,additive_inverse(Y))))
| add(additive_inverse(Y),add(X,add(Y,X_46))) = add(X_46,X) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(additive_inverse(Y),add(X,add(Y,X_46))))),bind(Y0,$fot(add(Y,add(X_46,add(X,additive_inverse(Y)))))),bind(Z0,$fot(add(X_46,X)))]]) ).
cnf(refute_0_300,plain,
( add(Y,add(X_46,add(X,additive_inverse(Y)))) != add(X_46,X)
| add(additive_inverse(Y),add(X,add(Y,X_46))) = add(X_46,X) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(X,add(Y,X_46))),add(Y,add(X_46,add(X,additive_inverse(Y))))) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
add(additive_inverse(Y),add(X,add(Y,X_46))) = add(X_46,X),
inference(resolve,[$cnf( $equal(add(Y,add(X_46,add(X,additive_inverse(Y)))),add(X_46,X)) )],[refute_0_282,refute_0_300]) ).
cnf(refute_0_302,plain,
( add(X,X_46) != add(additive_inverse(Y),add(X,add(Y,X_46)))
| add(additive_inverse(Y),add(X,add(Y,X_46))) != add(X_46,X)
| add(X,X_46) = add(X_46,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,X_46),add(X_46,X)) ),[0],$fot(add(additive_inverse(Y),add(X,add(Y,X_46))))]]) ).
cnf(refute_0_303,plain,
( add(X,X_46) != add(additive_inverse(Y),add(X,add(Y,X_46)))
| add(X,X_46) = add(X_46,X) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(X,add(Y,X_46))),add(X_46,X)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
add(X,X_46) = add(X_46,X),
inference(resolve,[$cnf( $equal(add(X,X_46),add(additive_inverse(Y),add(X,add(Y,X_46)))) )],[refute_0_274,refute_0_303]) ).
cnf(refute_0_305,plain,
( add(X,X_46) != add(X_46,X)
| add(X_46,X) = add(X,X_46) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X,X_46))),bind(Y0,$fot(add(X_46,X)))]]) ).
cnf(refute_0_306,plain,
add(X_46,X) = add(X,X_46),
inference(resolve,[$cnf( $equal(add(X,X_46),add(X_46,X)) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))) = add(additive_inverse(multiply(X_516,X_515)),add(commutator(X_515,X_516),X_517)),
inference(subst,[],[refute_0_306:[bind(X,$fot(additive_inverse(multiply(X_516,X_515)))),bind(X_46,$fot(add(commutator(X_515,X_516),X_517)))]]) ).
cnf(refute_0_308,plain,
( add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))) != add(additive_inverse(multiply(X_516,X_515)),add(commutator(X_515,X_516),X_517))
| add(additive_inverse(multiply(X_516,X_515)),add(commutator(X_515,X_516),X_517)) != add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))
| add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))) = add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))))),bind(Y0,$fot(add(additive_inverse(multiply(X_516,X_515)),add(commutator(X_515,X_516),X_517)))),bind(Z0,$fot(add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))))]]) ).
cnf(refute_0_309,plain,
( add(additive_inverse(multiply(X_516,X_515)),add(commutator(X_515,X_516),X_517)) != add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))
| add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))) = add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) ),
inference(resolve,[$cnf( $equal(add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))),add(additive_inverse(multiply(X_516,X_515)),add(commutator(X_515,X_516),X_517))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))) = add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_516,X_515)),add(commutator(X_515,X_516),X_517)),add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))) )],[refute_0_245,refute_0_309]) ).
cnf(refute_0_311,plain,
( add(X_42,additive_inverse(X_65)) != additive_inverse(add(X_65,additive_inverse(X_42)))
| additive_inverse(add(X_65,additive_inverse(X_42))) = add(X_42,additive_inverse(X_65)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_42,additive_inverse(X_65)))),bind(Y0,$fot(additive_inverse(add(X_65,additive_inverse(X_42)))))]]) ).
cnf(refute_0_312,plain,
additive_inverse(add(X_65,additive_inverse(X_42))) = add(X_42,additive_inverse(X_65)),
inference(resolve,[$cnf( $equal(add(X_42,additive_inverse(X_65)),additive_inverse(add(X_65,additive_inverse(X_42)))) )],[refute_0_205,refute_0_311]) ).
cnf(refute_0_313,plain,
additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))) = add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))),
inference(subst,[],[refute_0_312:[bind(X_42,$fot(add(commutator(X_515,X_516),X_517))),bind(X_65,$fot(multiply(X_516,X_515)))]]) ).
cnf(refute_0_314,plain,
( add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))) != add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))
| additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))) != add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515)))
| additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))) = add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))))),bind(Y0,$fot(add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))))),bind(Z0,$fot(add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))))]]) ).
cnf(refute_0_315,plain,
( add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))) != add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))
| additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))) = add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))),add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515)))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))) = add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)),
inference(resolve,[$cnf( $equal(add(add(commutator(X_515,X_516),X_517),additive_inverse(multiply(X_516,X_515))),add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))) )],[refute_0_310,refute_0_315]) ).
cnf(refute_0_317,plain,
( add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) != additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))))
| additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))) != add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))
| add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) = add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))))),bind(Y0,$fot(additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))))),bind(Z0,$fot(add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))))]]) ).
cnf(refute_0_318,plain,
( additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))) != add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))
| add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) = add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))),additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517))))) )],[refute_0_210,refute_0_317]) ).
cnf(refute_0_319,plain,
add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) = add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(X_516,X_515),additive_inverse(add(commutator(X_515,X_516),X_517)))),add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))) )],[refute_0_316,refute_0_318]) ).
cnf(refute_0_320,plain,
( add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) != add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))
| add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) != additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517)))
| add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) = additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517))) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))),additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517)))) ),[0],$fot(add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)))]]) ).
cnf(refute_0_321,plain,
( add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) != additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517)))
| add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) = additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))),add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517))) = add(X_517,additive_inverse(multiply(X_515,X_516))),
inference(subst,[],[refute_0_312:[bind(X_42,$fot(X_517)),bind(X_65,$fot(multiply(X_515,X_516)))]]) ).
cnf(refute_0_323,plain,
( add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) != additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517)))
| additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517))) != add(X_517,additive_inverse(multiply(X_515,X_516)))
| add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) = add(X_517,additive_inverse(multiply(X_515,X_516))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)),add(X_517,additive_inverse(multiply(X_515,X_516)))) ),[0],$fot(additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517))))]]) ).
cnf(refute_0_324,plain,
( add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) != additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517)))
| add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) = add(X_517,additive_inverse(multiply(X_515,X_516))) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517))),add(X_517,additive_inverse(multiply(X_515,X_516)))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
( add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))) != additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517)))
| add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) = add(X_517,additive_inverse(multiply(X_515,X_516))) ),
inference(resolve,[$cnf( $equal(add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)),additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517)))) )],[refute_0_321,refute_0_324]) ).
cnf(refute_0_326,plain,
add(commutator(X_515,X_516),add(additive_inverse(multiply(X_516,X_515)),X_517)) = add(X_517,additive_inverse(multiply(X_515,X_516))),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(add(commutator(X_515,X_516),X_517))),additive_inverse(multiply(X_516,X_515))),additive_inverse(add(multiply(X_515,X_516),additive_inverse(X_517)))) )],[refute_0_238,refute_0_325]) ).
cnf(refute_0_327,plain,
add(commutator(X,add(X_79,X_78)),add(additive_inverse(multiply(add(X_79,X_78),X)),X_522)) = add(X_522,additive_inverse(multiply(X,add(X_79,X_78)))),
inference(subst,[],[refute_0_326:[bind(X_515,$fot(X)),bind(X_516,$fot(add(X_79,X_78))),bind(X_517,$fot(X_522))]]) ).
cnf(refute_0_328,plain,
( add(commutator(X,add(X_79,X_78)),add(additive_inverse(multiply(add(X_79,X_78),X)),X_522)) != add(X_522,additive_inverse(multiply(X,add(X_79,X_78))))
| add(commutator(X,add(X_79,X_78)),add(additive_inverse(multiply(add(X_79,X_78),X)),X_522)) != add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)
| add(X_522,additive_inverse(multiply(X,add(X_79,X_78)))) = add(additive_inverse(multiply(X,add(X_78,X_79))),X_522) ),
introduced(tautology,[equality,[$cnf( $equal(add(commutator(X,add(X_79,X_78)),add(additive_inverse(multiply(add(X_79,X_78),X)),X_522)),add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)) ),[0],$fot(add(X_522,additive_inverse(multiply(X,add(X_79,X_78)))))]]) ).
cnf(refute_0_329,plain,
( add(commutator(X,add(X_79,X_78)),add(additive_inverse(multiply(add(X_79,X_78),X)),X_522)) != add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)
| add(X_522,additive_inverse(multiply(X,add(X_79,X_78)))) = add(additive_inverse(multiply(X,add(X_78,X_79))),X_522) ),
inference(resolve,[$cnf( $equal(add(commutator(X,add(X_79,X_78)),add(additive_inverse(multiply(add(X_79,X_78),X)),X_522)),add(X_522,additive_inverse(multiply(X,add(X_79,X_78))))) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
add(X_522,additive_inverse(multiply(X,add(X_79,X_78)))) = add(additive_inverse(multiply(X,add(X_78,X_79))),X_522),
inference(resolve,[$cnf( $equal(add(commutator(X,add(X_79,X_78)),add(additive_inverse(multiply(add(X_79,X_78),X)),X_522)),add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)) )],[refute_0_198,refute_0_329]) ).
cnf(refute_0_331,plain,
( add(X_522,additive_inverse(multiply(X,add(X_79,X_78)))) != add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)
| add(additive_inverse(multiply(X,add(X_78,X_79))),X_522) = add(X_522,additive_inverse(multiply(X,add(X_79,X_78)))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_522,additive_inverse(multiply(X,add(X_79,X_78)))))),bind(Y0,$fot(add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)))]]) ).
cnf(refute_0_332,plain,
add(additive_inverse(multiply(X,add(X_78,X_79))),X_522) = add(X_522,additive_inverse(multiply(X,add(X_79,X_78)))),
inference(resolve,[$cnf( $equal(add(X_522,additive_inverse(multiply(X,add(X_79,X_78)))),add(additive_inverse(multiply(X,add(X_78,X_79))),X_522)) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)) = add(multiply(X_577,X_44),additive_inverse(multiply(X_577,add(X_44,additive_inverse(X_579))))),
inference(subst,[],[refute_0_332:[bind(X,$fot(X_577)),bind(X_522,$fot(multiply(X_577,X_44))),bind(X_78,$fot(additive_inverse(X_579))),bind(X_79,$fot(X_44))]]) ).
cnf(refute_0_334,plain,
( add(multiply(X_577,X_44),additive_inverse(multiply(X_577,add(X_44,additive_inverse(X_579))))) != additive_inverse(multiply(X_577,additive_inverse(X_579)))
| add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)) != add(multiply(X_577,X_44),additive_inverse(multiply(X_577,add(X_44,additive_inverse(X_579)))))
| add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)) = additive_inverse(multiply(X_577,additive_inverse(X_579))) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)))),bind(Y0,$fot(add(multiply(X_577,X_44),additive_inverse(multiply(X_577,add(X_44,additive_inverse(X_579))))))),bind(Z0,$fot(additive_inverse(multiply(X_577,additive_inverse(X_579)))))]]) ).
cnf(refute_0_335,plain,
( add(multiply(X_577,X_44),additive_inverse(multiply(X_577,add(X_44,additive_inverse(X_579))))) != additive_inverse(multiply(X_577,additive_inverse(X_579)))
| add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)) = additive_inverse(multiply(X_577,additive_inverse(X_579))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)),add(multiply(X_577,X_44),additive_inverse(multiply(X_577,add(X_44,additive_inverse(X_579)))))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)) = additive_inverse(multiply(X_577,additive_inverse(X_579))),
inference(resolve,[$cnf( $equal(add(multiply(X_577,X_44),additive_inverse(multiply(X_577,add(X_44,additive_inverse(X_579))))),additive_inverse(multiply(X_577,additive_inverse(X_579)))) )],[refute_0_180,refute_0_335]) ).
cnf(refute_0_337,plain,
( multiply(X_577,X_579) != add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44))
| add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)) != additive_inverse(multiply(X_577,additive_inverse(X_579)))
| multiply(X_577,X_579) = additive_inverse(multiply(X_577,additive_inverse(X_579))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_577,X_579),additive_inverse(multiply(X_577,additive_inverse(X_579)))) ),[0],$fot(add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)))]]) ).
cnf(refute_0_338,plain,
( multiply(X_577,X_579) != add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44))
| multiply(X_577,X_579) = additive_inverse(multiply(X_577,additive_inverse(X_579))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44)),additive_inverse(multiply(X_577,additive_inverse(X_579)))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
multiply(X_577,X_579) = additive_inverse(multiply(X_577,additive_inverse(X_579))),
inference(resolve,[$cnf( $equal(multiply(X_577,X_579),add(additive_inverse(multiply(X_577,add(additive_inverse(X_579),X_44))),multiply(X_577,X_44))) )],[refute_0_173,refute_0_338]) ).
cnf(refute_0_340,plain,
( multiply(X_577,X_579) != additive_inverse(multiply(X_577,additive_inverse(X_579)))
| additive_inverse(multiply(X_577,additive_inverse(X_579))) = multiply(X_577,X_579) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(multiply(X_577,X_579))),bind(Y0,$fot(additive_inverse(multiply(X_577,additive_inverse(X_579)))))]]) ).
cnf(refute_0_341,plain,
additive_inverse(multiply(X_577,additive_inverse(X_579))) = multiply(X_577,X_579),
inference(resolve,[$cnf( $equal(multiply(X_577,X_579),additive_inverse(multiply(X_577,additive_inverse(X_579)))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
additive_inverse(multiply(X_638,additive_inverse(X))) = multiply(X_638,X),
inference(subst,[],[refute_0_341:[bind(X_577,$fot(X_638)),bind(X_579,$fot(X))]]) ).
cnf(refute_0_343,plain,
add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),
introduced(tautology,[refl,[$fot(add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)))]]) ).
cnf(refute_0_344,plain,
( add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) != add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))
| additive_inverse(multiply(X_638,additive_inverse(X))) != multiply(X_638,X)
| add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))) ),[1,0],$fot(multiply(X_638,X))]]) ).
cnf(refute_0_345,plain,
( additive_inverse(multiply(X_638,additive_inverse(X))) != multiply(X_638,X)
| add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(X_638,X)) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
( add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) != add(multiply(X_638,X),multiply(additive_inverse(X),X_638))
| add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) != add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))
| add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)))),bind(Y0,$fot(add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)))),bind(Z0,$fot(add(multiply(X_638,X),multiply(additive_inverse(X),X_638))))]]) ).
cnf(refute_0_348,plain,
( add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) != add(multiply(X_638,X),multiply(additive_inverse(X),X_638))
| add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)),
inference(resolve,[$cnf( $equal(add(multiply(X_638,X),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),add(multiply(X_638,X),multiply(additive_inverse(X),X_638))) )],[refute_0_113,refute_0_348]) ).
cnf(refute_0_350,plain,
add(X_130,add(multiply(X,Z),multiply(Y,Z))) = add(multiply(X,Z),add(X_130,multiply(Y,Z))),
inference(subst,[],[refute_0_265:[bind(X_42,$fot(X_130)),bind(X_43,$fot(multiply(X,Z))),bind(X_44,$fot(multiply(Y,Z)))]]) ).
cnf(refute_0_351,plain,
( multiply(add(X,Y),Z) != add(multiply(X,Z),multiply(Y,Z))
| add(multiply(X,Z),multiply(Y,Z)) = multiply(add(X,Y),Z) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(multiply(add(X,Y),Z))),bind(Y0,$fot(add(multiply(X,Z),multiply(Y,Z))))]]) ).
cnf(refute_0_352,plain,
add(multiply(X,Z),multiply(Y,Z)) = multiply(add(X,Y),Z),
inference(resolve,[$cnf( $equal(multiply(add(X,Y),Z),add(multiply(X,Z),multiply(Y,Z))) )],[distribute2,refute_0_351]) ).
cnf(refute_0_353,plain,
( add(X_130,add(multiply(X,Z),multiply(Y,Z))) != add(multiply(X,Z),add(X_130,multiply(Y,Z)))
| add(multiply(X,Z),multiply(Y,Z)) != multiply(add(X,Y),Z)
| add(X_130,multiply(add(X,Y),Z)) = add(multiply(X,Z),add(X_130,multiply(Y,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_130,add(multiply(X,Z),multiply(Y,Z))),add(multiply(X,Z),add(X_130,multiply(Y,Z)))) ),[0,1],$fot(multiply(add(X,Y),Z))]]) ).
cnf(refute_0_354,plain,
( add(X_130,add(multiply(X,Z),multiply(Y,Z))) != add(multiply(X,Z),add(X_130,multiply(Y,Z)))
| add(X_130,multiply(add(X,Y),Z)) = add(multiply(X,Z),add(X_130,multiply(Y,Z))) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Z),multiply(Y,Z)),multiply(add(X,Y),Z)) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
add(X_130,multiply(add(X,Y),Z)) = add(multiply(X,Z),add(X_130,multiply(Y,Z))),
inference(resolve,[$cnf( $equal(add(X_130,add(multiply(X,Z),multiply(Y,Z))),add(multiply(X,Z),add(X_130,multiply(Y,Z)))) )],[refute_0_350,refute_0_354]) ).
cnf(refute_0_356,plain,
add(multiply(Y,Z),add(X_122,multiply(X,Z))) = add(X_122,add(multiply(X,Z),multiply(Y,Z))),
inference(subst,[],[refute_0_154:[bind(X,$fot(multiply(Y,Z))),bind(X_42,$fot(X_122)),bind(X_43,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_357,plain,
( add(multiply(X,Z),multiply(Y,Z)) != multiply(add(X,Y),Z)
| add(multiply(Y,Z),add(X_122,multiply(X,Z))) != add(X_122,add(multiply(X,Z),multiply(Y,Z)))
| add(multiply(Y,Z),add(X_122,multiply(X,Z))) = add(X_122,multiply(add(X,Y),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Z),add(X_122,multiply(X,Z))),add(X_122,add(multiply(X,Z),multiply(Y,Z)))) ),[1,1],$fot(multiply(add(X,Y),Z))]]) ).
cnf(refute_0_358,plain,
( add(multiply(Y,Z),add(X_122,multiply(X,Z))) != add(X_122,add(multiply(X,Z),multiply(Y,Z)))
| add(multiply(Y,Z),add(X_122,multiply(X,Z))) = add(X_122,multiply(add(X,Y),Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Z),multiply(Y,Z)),multiply(add(X,Y),Z)) )],[refute_0_352,refute_0_357]) ).
cnf(refute_0_359,plain,
add(multiply(Y,Z),add(X_122,multiply(X,Z))) = add(X_122,multiply(add(X,Y),Z)),
inference(resolve,[$cnf( $equal(add(multiply(Y,Z),add(X_122,multiply(X,Z))),add(X_122,add(multiply(X,Z),multiply(Y,Z)))) )],[refute_0_356,refute_0_358]) ).
cnf(refute_0_360,plain,
add(multiply(X,Z),add(X_130,multiply(Y,Z))) = add(X_130,multiply(add(Y,X),Z)),
inference(subst,[],[refute_0_359:[bind(X,$fot(Y)),bind(Y,$fot(X)),bind(X_122,$fot(X_130))]]) ).
cnf(refute_0_361,plain,
( add(X_130,multiply(add(X,Y),Z)) != add(multiply(X,Z),add(X_130,multiply(Y,Z)))
| add(multiply(X,Z),add(X_130,multiply(Y,Z))) != add(X_130,multiply(add(Y,X),Z))
| add(X_130,multiply(add(X,Y),Z)) = add(X_130,multiply(add(Y,X),Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_130,multiply(add(X,Y),Z)),add(X_130,multiply(add(Y,X),Z))) ),[0],$fot(add(multiply(X,Z),add(X_130,multiply(Y,Z))))]]) ).
cnf(refute_0_362,plain,
( add(X_130,multiply(add(X,Y),Z)) != add(multiply(X,Z),add(X_130,multiply(Y,Z)))
| add(X_130,multiply(add(X,Y),Z)) = add(X_130,multiply(add(Y,X),Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Z),add(X_130,multiply(Y,Z))),add(X_130,multiply(add(Y,X),Z))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
add(X_130,multiply(add(X,Y),Z)) = add(X_130,multiply(add(Y,X),Z)),
inference(resolve,[$cnf( $equal(add(X_130,multiply(add(X,Y),Z)),add(multiply(X,Z),add(X_130,multiply(Y,Z)))) )],[refute_0_355,refute_0_362]) ).
cnf(refute_0_364,plain,
( add(X_130,multiply(add(X,Y),Z)) != add(X_130,multiply(add(Y,X),Z))
| add(X_130,multiply(add(Y,X),Z)) = add(X_130,multiply(add(X,Y),Z)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_130,multiply(add(X,Y),Z)))),bind(Y0,$fot(add(X_130,multiply(add(Y,X),Z))))]]) ).
cnf(refute_0_365,plain,
add(X_130,multiply(add(Y,X),Z)) = add(X_130,multiply(add(X,Y),Z)),
inference(resolve,[$cnf( $equal(add(X_130,multiply(add(X,Y),Z)),add(X_130,multiply(add(Y,X),Z))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(additive_inverse(add(X_639,X)),X_639),X_638)) = add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),
inference(subst,[],[refute_0_365:[bind(X,$fot(X_639)),bind(Y,$fot(additive_inverse(add(X_639,X)))),bind(Z,$fot(X_638)),bind(X_130,$fot(additive_inverse(multiply(X_638,additive_inverse(X)))))]]) ).
cnf(refute_0_367,plain,
add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_43,X_44))),X_522)) = add(additive_inverse(X_523),X_522),
inference(subst,[],[refute_0_184:[bind(X,$fot(add(X_43,X_44))),bind(Z,$fot(X_522)),bind(X_65,$fot(X_523))]]) ).
cnf(refute_0_368,plain,
add(X_523,add(X_44,X_43)) = add(X_523,add(X_43,X_44)),
inference(subst,[],[refute_0_142:[bind(X_42,$fot(X_523))]]) ).
cnf(refute_0_369,plain,
( add(X_523,add(X_44,X_43)) != add(X_523,add(X_43,X_44))
| add(X_523,add(X_43,X_44)) = add(X_523,add(X_44,X_43)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_523,add(X_44,X_43)))),bind(Y0,$fot(add(X_523,add(X_43,X_44))))]]) ).
cnf(refute_0_370,plain,
add(X_523,add(X_43,X_44)) = add(X_523,add(X_44,X_43)),
inference(resolve,[$cnf( $equal(add(X_523,add(X_44,X_43)),add(X_523,add(X_43,X_44))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
( add(X_523,add(X_43,X_44)) != add(X_523,add(X_44,X_43))
| add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_43,X_44))),X_522)) != add(additive_inverse(X_523),X_522)
| add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)) = add(additive_inverse(X_523),X_522) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_43,X_44))),X_522)),add(additive_inverse(X_523),X_522)) ),[0,1,0,0],$fot(add(X_523,add(X_44,X_43)))]]) ).
cnf(refute_0_372,plain,
( add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_43,X_44))),X_522)) != add(additive_inverse(X_523),X_522)
| add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)) = add(additive_inverse(X_523),X_522) ),
inference(resolve,[$cnf( $equal(add(X_523,add(X_43,X_44)),add(X_523,add(X_44,X_43))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)) = add(additive_inverse(X_523),X_522),
inference(resolve,[$cnf( $equal(add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_43,X_44))),X_522)),add(additive_inverse(X_523),X_522)) )],[refute_0_367,refute_0_372]) ).
cnf(refute_0_374,plain,
add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)) = add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))),
inference(subst,[],[refute_0_138:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)))]]) ).
cnf(refute_0_375,plain,
( add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)) != add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)))
| add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)) != add(additive_inverse(X_523),X_522)
| add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) = add(additive_inverse(X_523),X_522) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)),add(additive_inverse(X_523),X_522)) ),[0],$fot(add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))))]]) ).
cnf(refute_0_376,plain,
( add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)) != add(additive_inverse(X_523),X_522)
| add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) = add(additive_inverse(X_523),X_522) ),
inference(resolve,[$cnf( $equal(add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)),add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) = add(additive_inverse(X_523),X_522),
inference(resolve,[$cnf( $equal(add(add(X_43,X_44),add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)),add(additive_inverse(X_523),X_522)) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
add(additive_inverse(add(X_123,X)),add(X_122,X_123)) = add(X_122,add(X_123,additive_inverse(add(X_123,X)))),
inference(subst,[],[refute_0_154:[bind(X,$fot(additive_inverse(add(X_123,X)))),bind(X_42,$fot(X_122)),bind(X_43,$fot(X_123))]]) ).
cnf(refute_0_379,plain,
additive_inverse(X) = add(X_123,additive_inverse(add(X_123,X))),
inference(subst,[],[refute_0_74:[bind(X_65,$fot(X_123))]]) ).
cnf(refute_0_380,plain,
( additive_inverse(X) != add(X_123,additive_inverse(add(X_123,X)))
| add(X_123,additive_inverse(add(X_123,X))) = additive_inverse(X) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(X))),bind(Y0,$fot(add(X_123,additive_inverse(add(X_123,X)))))]]) ).
cnf(refute_0_381,plain,
add(X_123,additive_inverse(add(X_123,X))) = additive_inverse(X),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(X_123,additive_inverse(add(X_123,X)))) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
( add(X_123,additive_inverse(add(X_123,X))) != additive_inverse(X)
| add(additive_inverse(add(X_123,X)),add(X_122,X_123)) != add(X_122,add(X_123,additive_inverse(add(X_123,X))))
| add(additive_inverse(add(X_123,X)),add(X_122,X_123)) = add(X_122,additive_inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(add(X_123,X)),add(X_122,X_123)),add(X_122,add(X_123,additive_inverse(add(X_123,X))))) ),[1,1],$fot(additive_inverse(X))]]) ).
cnf(refute_0_383,plain,
( add(additive_inverse(add(X_123,X)),add(X_122,X_123)) != add(X_122,add(X_123,additive_inverse(add(X_123,X))))
| add(additive_inverse(add(X_123,X)),add(X_122,X_123)) = add(X_122,additive_inverse(X)) ),
inference(resolve,[$cnf( $equal(add(X_123,additive_inverse(add(X_123,X))),additive_inverse(X)) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
add(additive_inverse(add(X_123,X)),add(X_122,X_123)) = add(X_122,additive_inverse(X)),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(X_123,X)),add(X_122,X_123)),add(X_122,add(X_123,additive_inverse(add(X_123,X))))) )],[refute_0_378,refute_0_383]) ).
cnf(refute_0_385,plain,
add(X_121,add(X_122,X_123)) = add(X_122,add(X_123,X_121)),
inference(subst,[],[refute_0_154:[bind(X,$fot(X_121)),bind(X_42,$fot(X_122)),bind(X_43,$fot(X_123))]]) ).
cnf(refute_0_386,plain,
add(X_123,X_122) = add(X_122,X_123),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_123)),bind(Y,$fot(X_122))]]) ).
cnf(refute_0_387,plain,
( add(X_123,X_122) != add(X_122,X_123)
| add(X_122,X_123) = add(X_123,X_122) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_123,X_122))),bind(Y0,$fot(add(X_122,X_123)))]]) ).
cnf(refute_0_388,plain,
add(X_122,X_123) = add(X_123,X_122),
inference(resolve,[$cnf( $equal(add(X_123,X_122),add(X_122,X_123)) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
( add(X_121,add(X_122,X_123)) != add(X_122,add(X_123,X_121))
| add(X_122,X_123) != add(X_123,X_122)
| add(X_121,add(X_123,X_122)) = add(X_122,add(X_123,X_121)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_121,add(X_122,X_123)),add(X_122,add(X_123,X_121))) ),[0,1],$fot(add(X_123,X_122))]]) ).
cnf(refute_0_390,plain,
( add(X_121,add(X_122,X_123)) != add(X_122,add(X_123,X_121))
| add(X_121,add(X_123,X_122)) = add(X_122,add(X_123,X_121)) ),
inference(resolve,[$cnf( $equal(add(X_122,X_123),add(X_123,X_122)) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
add(X_121,add(X_123,X_122)) = add(X_122,add(X_123,X_121)),
inference(resolve,[$cnf( $equal(add(X_121,add(X_122,X_123)),add(X_122,add(X_123,X_121))) )],[refute_0_385,refute_0_390]) ).
cnf(refute_0_392,plain,
( add(X_121,add(X_123,X_122)) != add(X_122,add(X_123,X_121))
| add(X_122,add(X_123,X_121)) = add(X_121,add(X_123,X_122)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_121,add(X_123,X_122)))),bind(Y0,$fot(add(X_122,add(X_123,X_121))))]]) ).
cnf(refute_0_393,plain,
add(X_122,add(X_123,X_121)) = add(X_121,add(X_123,X_122)),
inference(resolve,[$cnf( $equal(add(X_121,add(X_123,X_122)),add(X_122,add(X_123,X_121))) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
add(additive_inverse(add(X_123,X)),add(X_122,X_123)) = add(X_123,add(X_122,additive_inverse(add(X_123,X)))),
inference(subst,[],[refute_0_393:[bind(X_121,$fot(X_123)),bind(X_122,$fot(additive_inverse(add(X_123,X)))),bind(X_123,$fot(X_122))]]) ).
cnf(refute_0_395,plain,
( add(additive_inverse(add(X_123,X)),add(X_122,X_123)) != add(X_122,additive_inverse(X))
| add(additive_inverse(add(X_123,X)),add(X_122,X_123)) != add(X_123,add(X_122,additive_inverse(add(X_123,X))))
| add(X_123,add(X_122,additive_inverse(add(X_123,X)))) = add(X_122,additive_inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(add(X_123,X)),add(X_122,X_123)),add(X_122,additive_inverse(X))) ),[0],$fot(add(X_123,add(X_122,additive_inverse(add(X_123,X)))))]]) ).
cnf(refute_0_396,plain,
( add(additive_inverse(add(X_123,X)),add(X_122,X_123)) != add(X_122,additive_inverse(X))
| add(X_123,add(X_122,additive_inverse(add(X_123,X)))) = add(X_122,additive_inverse(X)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(X_123,X)),add(X_122,X_123)),add(X_123,add(X_122,additive_inverse(add(X_123,X))))) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
add(X_123,add(X_122,additive_inverse(add(X_123,X)))) = add(X_122,additive_inverse(X)),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(X_123,X)),add(X_122,X_123)),add(X_122,additive_inverse(X))) )],[refute_0_384,refute_0_396]) ).
cnf(refute_0_398,plain,
add(X_43,add(X_522,additive_inverse(add(X_43,X_523)))) = add(X_522,additive_inverse(X_523)),
inference(subst,[],[refute_0_397:[bind(X,$fot(X_523)),bind(X_122,$fot(X_522)),bind(X_123,$fot(X_43))]]) ).
cnf(refute_0_399,plain,
add(X,add(X_42,additive_inverse(add(X_607,add(X_42,X_608))))) = add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X)),
inference(subst,[],[refute_0_154:[bind(X_43,$fot(additive_inverse(add(X_607,add(X_42,X_608)))))]]) ).
cnf(refute_0_400,plain,
additive_inverse(add(X_123,X_121)) = add(X_65,additive_inverse(add(X_65,add(X_123,X_121)))),
inference(subst,[],[refute_0_74:[bind(X,$fot(add(X_123,X_121)))]]) ).
cnf(refute_0_401,plain,
add(X_121,add(X_65,X_123)) = add(X_65,add(X_123,X_121)),
inference(subst,[],[refute_0_154:[bind(X,$fot(X_121)),bind(X_42,$fot(X_65)),bind(X_43,$fot(X_123))]]) ).
cnf(refute_0_402,plain,
( add(X_121,add(X_65,X_123)) != add(X_65,add(X_123,X_121))
| add(X_65,add(X_123,X_121)) = add(X_121,add(X_65,X_123)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_121,add(X_65,X_123)))),bind(Y0,$fot(add(X_65,add(X_123,X_121))))]]) ).
cnf(refute_0_403,plain,
add(X_65,add(X_123,X_121)) = add(X_121,add(X_65,X_123)),
inference(resolve,[$cnf( $equal(add(X_121,add(X_65,X_123)),add(X_65,add(X_123,X_121))) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
( add(X_65,add(X_123,X_121)) != add(X_121,add(X_65,X_123))
| additive_inverse(add(X_123,X_121)) != add(X_65,additive_inverse(add(X_65,add(X_123,X_121))))
| additive_inverse(add(X_123,X_121)) = add(X_65,additive_inverse(add(X_121,add(X_65,X_123)))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(X_123,X_121)),add(X_65,additive_inverse(add(X_65,add(X_123,X_121))))) ),[1,1,0],$fot(add(X_121,add(X_65,X_123)))]]) ).
cnf(refute_0_405,plain,
( additive_inverse(add(X_123,X_121)) != add(X_65,additive_inverse(add(X_65,add(X_123,X_121))))
| additive_inverse(add(X_123,X_121)) = add(X_65,additive_inverse(add(X_121,add(X_65,X_123)))) ),
inference(resolve,[$cnf( $equal(add(X_65,add(X_123,X_121)),add(X_121,add(X_65,X_123))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
additive_inverse(add(X_123,X_121)) = add(X_65,additive_inverse(add(X_121,add(X_65,X_123)))),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_123,X_121)),add(X_65,additive_inverse(add(X_65,add(X_123,X_121))))) )],[refute_0_400,refute_0_405]) ).
cnf(refute_0_407,plain,
additive_inverse(add(X_608,X_607)) = add(X_42,additive_inverse(add(X_607,add(X_42,X_608)))),
inference(subst,[],[refute_0_406:[bind(X_121,$fot(X_607)),bind(X_123,$fot(X_608)),bind(X_65,$fot(X_42))]]) ).
cnf(refute_0_408,plain,
( additive_inverse(add(X_608,X_607)) != add(X_42,additive_inverse(add(X_607,add(X_42,X_608))))
| add(X_42,additive_inverse(add(X_607,add(X_42,X_608)))) = additive_inverse(add(X_608,X_607)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(add(X_608,X_607)))),bind(Y0,$fot(add(X_42,additive_inverse(add(X_607,add(X_42,X_608))))))]]) ).
cnf(refute_0_409,plain,
add(X_42,additive_inverse(add(X_607,add(X_42,X_608)))) = additive_inverse(add(X_608,X_607)),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_608,X_607)),add(X_42,additive_inverse(add(X_607,add(X_42,X_608))))) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
( add(X,add(X_42,additive_inverse(add(X_607,add(X_42,X_608))))) != add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X))
| add(X_42,additive_inverse(add(X_607,add(X_42,X_608)))) != additive_inverse(add(X_608,X_607))
| add(X,additive_inverse(add(X_608,X_607))) = add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(X_42,additive_inverse(add(X_607,add(X_42,X_608))))),add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X))) ),[0,1],$fot(additive_inverse(add(X_608,X_607)))]]) ).
cnf(refute_0_411,plain,
( add(X,add(X_42,additive_inverse(add(X_607,add(X_42,X_608))))) != add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X))
| add(X,additive_inverse(add(X_608,X_607))) = add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X)) ),
inference(resolve,[$cnf( $equal(add(X_42,additive_inverse(add(X_607,add(X_42,X_608)))),additive_inverse(add(X_608,X_607))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
add(X,additive_inverse(add(X_608,X_607))) = add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X)),
inference(resolve,[$cnf( $equal(add(X,add(X_42,additive_inverse(add(X_607,add(X_42,X_608))))),add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X))) )],[refute_0_399,refute_0_411]) ).
cnf(refute_0_413,plain,
( add(X,additive_inverse(add(X_608,X_607))) != add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X))
| add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X)) = add(X,additive_inverse(add(X_608,X_607))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X,additive_inverse(add(X_608,X_607))))),bind(Y0,$fot(add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X))))]]) ).
cnf(refute_0_414,plain,
add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X)) = add(X,additive_inverse(add(X_608,X_607))),
inference(resolve,[$cnf( $equal(add(X,additive_inverse(add(X_608,X_607))),add(X_42,add(additive_inverse(add(X_607,add(X_42,X_608))),X))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)) = add(X_522,additive_inverse(add(X_43,X_523))),
inference(subst,[],[refute_0_414:[bind(X,$fot(X_522)),bind(X_42,$fot(X_44)),bind(X_607,$fot(X_523)),bind(X_608,$fot(X_43))]]) ).
cnf(refute_0_416,plain,
add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) = add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))),
introduced(tautology,[refl,[$fot(add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))))]]) ).
cnf(refute_0_417,plain,
( add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) != add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)))
| add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)) != add(X_522,additive_inverse(add(X_43,X_523)))
| add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) = add(X_43,add(X_522,additive_inverse(add(X_43,X_523)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))),add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)))) ),[1,1],$fot(add(X_522,additive_inverse(add(X_43,X_523))))]]) ).
cnf(refute_0_418,plain,
( add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)) != add(X_522,additive_inverse(add(X_43,X_523)))
| add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) = add(X_43,add(X_522,additive_inverse(add(X_43,X_523)))) ),
inference(resolve,[$cnf( $equal(add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))),add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) = add(X_43,add(X_522,additive_inverse(add(X_43,X_523)))),
inference(resolve,[$cnf( $equal(add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522)),add(X_522,additive_inverse(add(X_43,X_523)))) )],[refute_0_415,refute_0_418]) ).
cnf(refute_0_420,plain,
( add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) != add(X_43,add(X_522,additive_inverse(add(X_43,X_523))))
| add(X_43,add(X_522,additive_inverse(add(X_43,X_523)))) != add(X_522,additive_inverse(X_523))
| add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) = add(X_522,additive_inverse(X_523)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))))),bind(Y0,$fot(add(X_43,add(X_522,additive_inverse(add(X_43,X_523)))))),bind(Z0,$fot(add(X_522,additive_inverse(X_523))))]]) ).
cnf(refute_0_421,plain,
( add(X_43,add(X_522,additive_inverse(add(X_43,X_523)))) != add(X_522,additive_inverse(X_523))
| add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) = add(X_522,additive_inverse(X_523)) ),
inference(resolve,[$cnf( $equal(add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))),add(X_43,add(X_522,additive_inverse(add(X_43,X_523))))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) = add(X_522,additive_inverse(X_523)),
inference(resolve,[$cnf( $equal(add(X_43,add(X_522,additive_inverse(add(X_43,X_523)))),add(X_522,additive_inverse(X_523))) )],[refute_0_398,refute_0_421]) ).
cnf(refute_0_423,plain,
( add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) != add(X_522,additive_inverse(X_523))
| add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) != add(additive_inverse(X_523),X_522)
| add(X_522,additive_inverse(X_523)) = add(additive_inverse(X_523),X_522) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))),add(additive_inverse(X_523),X_522)) ),[0],$fot(add(X_522,additive_inverse(X_523)))]]) ).
cnf(refute_0_424,plain,
( add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))) != add(additive_inverse(X_523),X_522)
| add(X_522,additive_inverse(X_523)) = add(additive_inverse(X_523),X_522) ),
inference(resolve,[$cnf( $equal(add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))),add(X_522,additive_inverse(X_523))) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
add(X_522,additive_inverse(X_523)) = add(additive_inverse(X_523),X_522),
inference(resolve,[$cnf( $equal(add(X_43,add(X_44,add(additive_inverse(add(X_523,add(X_44,X_43))),X_522))),add(additive_inverse(X_523),X_522)) )],[refute_0_377,refute_0_424]) ).
cnf(refute_0_426,plain,
add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) = add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(additive_inverse(add(X_639,X)),X_639),X_638)),
inference(subst,[],[refute_0_425:[bind(X_522,$fot(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638))),bind(X_523,$fot(multiply(X_638,additive_inverse(X))))]]) ).
cnf(refute_0_427,plain,
( add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) != add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(additive_inverse(add(X_639,X)),X_639),X_638))
| add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(additive_inverse(add(X_639,X)),X_639),X_638)) != add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))
| add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) = add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))))),bind(Y0,$fot(add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(additive_inverse(add(X_639,X)),X_639),X_638)))),bind(Z0,$fot(add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))))]]) ).
cnf(refute_0_428,plain,
( add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(additive_inverse(add(X_639,X)),X_639),X_638)) != add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))
| add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) = add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) ),
inference(resolve,[$cnf( $equal(add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))),add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(additive_inverse(add(X_639,X)),X_639),X_638))) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) = add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(additive_inverse(add(X_639,X)),X_639),X_638)),add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))) )],[refute_0_366,refute_0_428]) ).
cnf(refute_0_430,plain,
( add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) != add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))
| add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) != add(multiply(X_638,X),multiply(additive_inverse(X),X_638))
| add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))))),bind(Y0,$fot(add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)))),bind(Z0,$fot(add(multiply(X_638,X),multiply(additive_inverse(X),X_638))))]]) ).
cnf(refute_0_431,plain,
( add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)) != add(multiply(X_638,X),multiply(additive_inverse(X),X_638))
| add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)) ),
inference(resolve,[$cnf( $equal(add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))),add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638))) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_638,additive_inverse(X))),multiply(add(X_639,additive_inverse(add(X_639,X))),X_638)),add(multiply(X_638,X),multiply(additive_inverse(X),X_638))) )],[refute_0_349,refute_0_431]) ).
cnf(refute_0_433,plain,
( add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))) != add(multiply(X_638,X),multiply(additive_inverse(X),X_638))
| commutator(X_638,additive_inverse(X)) != add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X))))
| commutator(X_638,additive_inverse(X)) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)) ),
introduced(tautology,[equality,[$cnf( $equal(commutator(X_638,additive_inverse(X)),add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X))))) ),[1],$fot(add(multiply(X_638,X),multiply(additive_inverse(X),X_638)))]]) ).
cnf(refute_0_434,plain,
( commutator(X_638,additive_inverse(X)) != add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X))))
| commutator(X_638,additive_inverse(X)) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)) ),
inference(resolve,[$cnf( $equal(add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X)))),add(multiply(X_638,X),multiply(additive_inverse(X),X_638))) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
( commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)) != add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X))))
| commutator(X_638,additive_inverse(X)) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)) ),
inference(resolve,[$cnf( $equal(commutator(X_638,additive_inverse(X)),add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X))))) )],[refute_0_105,refute_0_434]) ).
cnf(refute_0_436,plain,
commutator(X_638,additive_inverse(X)) = add(multiply(X_638,X),multiply(additive_inverse(X),X_638)),
inference(resolve,[$cnf( $equal(commutator(X_638,add(additive_inverse(add(X_639,X)),X_639)),add(multiply(add(additive_inverse(add(X_639,X)),X_639),X_638),additive_inverse(multiply(X_638,additive_inverse(X))))) )],[refute_0_80,refute_0_435]) ).
cnf(refute_0_437,plain,
commutator(X_704,additive_inverse(X_703)) = add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704)),
inference(subst,[],[refute_0_436:[bind(X,$fot(X_703)),bind(X_638,$fot(X_704))]]) ).
cnf(refute_0_438,plain,
( commutator(X_704,additive_inverse(X_703)) != add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))
| add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704)) = commutator(X_704,additive_inverse(X_703)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(commutator(X_704,additive_inverse(X_703)))),bind(Y0,$fot(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))))]]) ).
cnf(refute_0_439,plain,
add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704)) = commutator(X_704,additive_inverse(X_703)),
inference(resolve,[$cnf( $equal(commutator(X_704,additive_inverse(X_703)),add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
( add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704)) != commutator(X_704,additive_inverse(X_703))
| additive_inverse(multiply(X_704,X_703)) != add(multiply(additive_inverse(X_703),X_704),additive_inverse(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))))
| additive_inverse(multiply(X_704,X_703)) = add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X_704,X_703)),add(multiply(additive_inverse(X_703),X_704),additive_inverse(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))))) ),[1,1,0],$fot(commutator(X_704,additive_inverse(X_703)))]]) ).
cnf(refute_0_441,plain,
( additive_inverse(multiply(X_704,X_703)) != add(multiply(additive_inverse(X_703),X_704),additive_inverse(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))))
| additive_inverse(multiply(X_704,X_703)) = add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704)),commutator(X_704,additive_inverse(X_703))) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
additive_inverse(multiply(X_704,X_703)) = add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_704,X_703)),add(multiply(additive_inverse(X_703),X_704),additive_inverse(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))))) )],[refute_0_32,refute_0_441]) ).
cnf(refute_0_443,plain,
add(multiply(additive_inverse(X_703),X_704),commutator(additive_inverse(X_703),X_704)) = multiply(X_704,additive_inverse(X_703)),
inference(subst,[],[refute_0_191:[bind(X,$fot(additive_inverse(X_703))),bind(Y,$fot(X_704))]]) ).
cnf(refute_0_444,plain,
additive_inverse(commutator(X,Y)) = add(multiply(X,Y),additive_inverse(add(multiply(X,Y),commutator(X,Y)))),
inference(subst,[],[refute_0_74:[bind(X,$fot(commutator(X,Y))),bind(X_65,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_445,plain,
( add(multiply(X,Y),commutator(X,Y)) != multiply(Y,X)
| additive_inverse(commutator(X,Y)) != add(multiply(X,Y),additive_inverse(add(multiply(X,Y),commutator(X,Y))))
| additive_inverse(commutator(X,Y)) = add(multiply(X,Y),additive_inverse(multiply(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(commutator(X,Y)),add(multiply(X,Y),additive_inverse(add(multiply(X,Y),commutator(X,Y))))) ),[1,1,0],$fot(multiply(Y,X))]]) ).
cnf(refute_0_446,plain,
( additive_inverse(commutator(X,Y)) != add(multiply(X,Y),additive_inverse(add(multiply(X,Y),commutator(X,Y))))
| additive_inverse(commutator(X,Y)) = add(multiply(X,Y),additive_inverse(multiply(Y,X))) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),commutator(X,Y)),multiply(Y,X)) )],[refute_0_191,refute_0_445]) ).
cnf(refute_0_447,plain,
additive_inverse(commutator(X,Y)) = add(multiply(X,Y),additive_inverse(multiply(Y,X))),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(X,Y)),add(multiply(X,Y),additive_inverse(add(multiply(X,Y),commutator(X,Y))))) )],[refute_0_444,refute_0_446]) ).
cnf(refute_0_448,plain,
add(multiply(X,Y),additive_inverse(multiply(Y,X))) = commutator(Y,X),
inference(subst,[],[refute_0_188:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_449,plain,
( add(multiply(X,Y),additive_inverse(multiply(Y,X))) != commutator(Y,X)
| additive_inverse(commutator(X,Y)) != add(multiply(X,Y),additive_inverse(multiply(Y,X)))
| additive_inverse(commutator(X,Y)) = commutator(Y,X) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(commutator(X,Y)),add(multiply(X,Y),additive_inverse(multiply(Y,X)))) ),[1],$fot(commutator(Y,X))]]) ).
cnf(refute_0_450,plain,
( additive_inverse(commutator(X,Y)) != add(multiply(X,Y),additive_inverse(multiply(Y,X)))
| additive_inverse(commutator(X,Y)) = commutator(Y,X) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),additive_inverse(multiply(Y,X))),commutator(Y,X)) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
additive_inverse(commutator(X,Y)) = commutator(Y,X),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(X,Y)),add(multiply(X,Y),additive_inverse(multiply(Y,X)))) )],[refute_0_447,refute_0_450]) ).
cnf(refute_0_452,plain,
additive_inverse(commutator(X_704,additive_inverse(X_703))) = commutator(additive_inverse(X_703),X_704),
inference(subst,[],[refute_0_451:[bind(X,$fot(X_704)),bind(Y,$fot(additive_inverse(X_703)))]]) ).
cnf(refute_0_453,plain,
add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))),
introduced(tautology,[refl,[$fot(add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))))]]) ).
cnf(refute_0_454,plain,
( add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) != add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703))))
| additive_inverse(commutator(X_704,additive_inverse(X_703))) != commutator(additive_inverse(X_703),X_704)
| add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = add(multiply(additive_inverse(X_703),X_704),commutator(additive_inverse(X_703),X_704)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))),add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703))))) ),[1,1],$fot(commutator(additive_inverse(X_703),X_704))]]) ).
cnf(refute_0_455,plain,
( additive_inverse(commutator(X_704,additive_inverse(X_703))) != commutator(additive_inverse(X_703),X_704)
| add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = add(multiply(additive_inverse(X_703),X_704),commutator(additive_inverse(X_703),X_704)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))),add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703))))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = add(multiply(additive_inverse(X_703),X_704),commutator(additive_inverse(X_703),X_704)),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(X_704,additive_inverse(X_703))),commutator(additive_inverse(X_703),X_704)) )],[refute_0_452,refute_0_455]) ).
cnf(refute_0_457,plain,
( add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) != add(multiply(additive_inverse(X_703),X_704),commutator(additive_inverse(X_703),X_704))
| add(multiply(additive_inverse(X_703),X_704),commutator(additive_inverse(X_703),X_704)) != multiply(X_704,additive_inverse(X_703))
| add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = multiply(X_704,additive_inverse(X_703)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))))),bind(Y0,$fot(add(multiply(additive_inverse(X_703),X_704),commutator(additive_inverse(X_703),X_704)))),bind(Z0,$fot(multiply(X_704,additive_inverse(X_703))))]]) ).
cnf(refute_0_458,plain,
( add(multiply(additive_inverse(X_703),X_704),commutator(additive_inverse(X_703),X_704)) != multiply(X_704,additive_inverse(X_703))
| add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = multiply(X_704,additive_inverse(X_703)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))),add(multiply(additive_inverse(X_703),X_704),commutator(additive_inverse(X_703),X_704))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = multiply(X_704,additive_inverse(X_703)),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X_703),X_704),commutator(additive_inverse(X_703),X_704)),multiply(X_704,additive_inverse(X_703))) )],[refute_0_443,refute_0_458]) ).
cnf(refute_0_460,plain,
( add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))) != multiply(X_704,additive_inverse(X_703))
| additive_inverse(multiply(X_704,X_703)) != add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703))))
| additive_inverse(multiply(X_704,X_703)) = multiply(X_704,additive_inverse(X_703)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X_704,X_703)),add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703))))) ),[1],$fot(multiply(X_704,additive_inverse(X_703)))]]) ).
cnf(refute_0_461,plain,
( additive_inverse(multiply(X_704,X_703)) != add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703))))
| additive_inverse(multiply(X_704,X_703)) = multiply(X_704,additive_inverse(X_703)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703)))),multiply(X_704,additive_inverse(X_703))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
additive_inverse(multiply(X_704,X_703)) = multiply(X_704,additive_inverse(X_703)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_704,X_703)),add(multiply(additive_inverse(X_703),X_704),additive_inverse(commutator(X_704,additive_inverse(X_703))))) )],[refute_0_442,refute_0_461]) ).
cnf(refute_0_463,plain,
( additive_inverse(multiply(X_704,X_703)) != multiply(X_704,additive_inverse(X_703))
| multiply(X_704,additive_inverse(X_703)) = additive_inverse(multiply(X_704,X_703)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(multiply(X_704,X_703)))),bind(Y0,$fot(multiply(X_704,additive_inverse(X_703))))]]) ).
cnf(refute_0_464,plain,
multiply(X_704,additive_inverse(X_703)) = additive_inverse(multiply(X_704,X_703)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_704,X_703)),multiply(X_704,additive_inverse(X_703))) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
multiply(additive_inverse(a),additive_inverse(b)) = additive_inverse(multiply(additive_inverse(a),b)),
inference(subst,[],[refute_0_464:[bind(X_703,$fot(b)),bind(X_704,$fot(additive_inverse(a)))]]) ).
cnf(refute_0_466,plain,
( multiply(additive_inverse(a),additive_inverse(b)) != additive_inverse(multiply(additive_inverse(a),b))
| additive_inverse(multiply(additive_inverse(a),b)) != multiply(a,b)
| multiply(additive_inverse(a),additive_inverse(b)) = multiply(a,b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(additive_inverse(a),additive_inverse(b)),multiply(a,b)) ),[0],$fot(additive_inverse(multiply(additive_inverse(a),b)))]]) ).
cnf(refute_0_467,plain,
( additive_inverse(multiply(additive_inverse(a),b)) != multiply(a,b)
| multiply(additive_inverse(a),additive_inverse(b)) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(a),additive_inverse(b)),additive_inverse(multiply(additive_inverse(a),b))) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
additive_inverse(multiply(additive_inverse(a),b)) != multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(a),additive_inverse(b)),multiply(a,b)) )],[refute_0_467,prove_equation]) ).
cnf(refute_0_469,plain,
additive_inverse(additive_inverse(multiply(a,b))) = multiply(a,b),
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(multiply(a,b)))]]) ).
cnf(refute_0_470,plain,
add(multiply(X,additive_inverse(X_769)),commutator(X,additive_inverse(X_769))) = multiply(additive_inverse(X_769),X),
inference(subst,[],[refute_0_191:[bind(Y,$fot(additive_inverse(X_769)))]]) ).
cnf(refute_0_471,plain,
additive_inverse(commutator(additive_inverse(X_767),X_768)) = add(commutator(X_767,X_768),additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)))),
inference(subst,[],[refute_0_74:[bind(X,$fot(commutator(additive_inverse(X_767),X_768))),bind(X_65,$fot(commutator(X_767,X_768)))]]) ).
cnf(refute_0_472,plain,
add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) = additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280))),
inference(subst,[],[refute_0_209:[bind(X,$fot(add(additive_inverse(multiply(X_278,X_279)),X_280))),bind(X_174,$fot(multiply(X_279,X_278)))]]) ).
cnf(refute_0_473,plain,
( add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)) != add(commutator(X_278,X_279),X_280)
| add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) != additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)))
| add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) = additive_inverse(add(commutator(X_278,X_279),X_280)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))),additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)))) ),[1,0],$fot(add(commutator(X_278,X_279),X_280))]]) ).
cnf(refute_0_474,plain,
( add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) != additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)))
| add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) = additive_inverse(add(commutator(X_278,X_279),X_280)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)),add(commutator(X_278,X_279),X_280)) )],[refute_0_216,refute_0_473]) ).
cnf(refute_0_475,plain,
add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) = additive_inverse(add(commutator(X_278,X_279),X_280)),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))),additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)))) )],[refute_0_472,refute_0_474]) ).
cnf(refute_0_476,plain,
add(additive_inverse(X_175),additive_inverse(add(X_65,additive_inverse(X_42)))) = additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)),
inference(subst,[],[refute_0_209:[bind(X,$fot(X_175)),bind(X_174,$fot(add(X_65,additive_inverse(X_42))))]]) ).
cnf(refute_0_477,plain,
( add(additive_inverse(X_175),additive_inverse(add(X_65,additive_inverse(X_42)))) != additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))
| additive_inverse(add(X_65,additive_inverse(X_42))) != add(X_42,additive_inverse(X_65))
| add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))) = additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X_175),additive_inverse(add(X_65,additive_inverse(X_42)))),additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))) ),[0,1],$fot(add(X_42,additive_inverse(X_65)))]]) ).
cnf(refute_0_478,plain,
( add(additive_inverse(X_175),additive_inverse(add(X_65,additive_inverse(X_42)))) != additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))
| add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))) = additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_65,additive_inverse(X_42))),add(X_42,additive_inverse(X_65))) )],[refute_0_312,refute_0_477]) ).
cnf(refute_0_479,plain,
add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))) = additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_175),additive_inverse(add(X_65,additive_inverse(X_42)))),additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))) )],[refute_0_476,refute_0_478]) ).
cnf(refute_0_480,plain,
add(additive_inverse(X_175),add(X_43,additive_inverse(X_176))) = add(X_43,add(additive_inverse(X_175),additive_inverse(X_176))),
inference(subst,[],[refute_0_265:[bind(X_42,$fot(additive_inverse(X_175))),bind(X_44,$fot(additive_inverse(X_176)))]]) ).
cnf(refute_0_481,plain,
add(additive_inverse(X_175),additive_inverse(X_176)) = additive_inverse(add(X_176,X_175)),
inference(subst,[],[refute_0_209:[bind(X,$fot(X_175)),bind(X_174,$fot(X_176))]]) ).
cnf(refute_0_482,plain,
( add(additive_inverse(X_175),add(X_43,additive_inverse(X_176))) != add(X_43,add(additive_inverse(X_175),additive_inverse(X_176)))
| add(additive_inverse(X_175),additive_inverse(X_176)) != additive_inverse(add(X_176,X_175))
| add(additive_inverse(X_175),add(X_43,additive_inverse(X_176))) = add(X_43,additive_inverse(add(X_176,X_175))) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X_175),add(X_43,additive_inverse(X_176))),add(X_43,add(additive_inverse(X_175),additive_inverse(X_176)))) ),[1,1],$fot(additive_inverse(add(X_176,X_175)))]]) ).
cnf(refute_0_483,plain,
( add(additive_inverse(X_175),add(X_43,additive_inverse(X_176))) != add(X_43,add(additive_inverse(X_175),additive_inverse(X_176)))
| add(additive_inverse(X_175),add(X_43,additive_inverse(X_176))) = add(X_43,additive_inverse(add(X_176,X_175))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_175),additive_inverse(X_176)),additive_inverse(add(X_176,X_175))) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
add(additive_inverse(X_175),add(X_43,additive_inverse(X_176))) = add(X_43,additive_inverse(add(X_176,X_175))),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_175),add(X_43,additive_inverse(X_176))),add(X_43,add(additive_inverse(X_175),additive_inverse(X_176)))) )],[refute_0_480,refute_0_483]) ).
cnf(refute_0_485,plain,
add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))) = add(X_42,additive_inverse(add(X_65,X_175))),
inference(subst,[],[refute_0_484:[bind(X_176,$fot(X_65)),bind(X_43,$fot(X_42))]]) ).
cnf(refute_0_486,plain,
( add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))) != add(X_42,additive_inverse(add(X_65,X_175)))
| add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))) != additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))
| add(X_42,additive_inverse(add(X_65,X_175))) = additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))),additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))) ),[0],$fot(add(X_42,additive_inverse(add(X_65,X_175))))]]) ).
cnf(refute_0_487,plain,
( add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))) != additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))
| add(X_42,additive_inverse(add(X_65,X_175))) = additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))),add(X_42,additive_inverse(add(X_65,X_175)))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
add(add(X_65,additive_inverse(X_42)),X_175) = add(X_65,add(additive_inverse(X_42),X_175)),
inference(subst,[],[refute_0_138:[bind(X,$fot(X_65)),bind(Y,$fot(additive_inverse(X_42))),bind(Z,$fot(X_175))]]) ).
cnf(refute_0_489,plain,
additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)) = additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)),
introduced(tautology,[refl,[$fot(additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)))]]) ).
cnf(refute_0_490,plain,
( add(add(X_65,additive_inverse(X_42)),X_175) != add(X_65,add(additive_inverse(X_42),X_175))
| additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)) != additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))
| additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)) = additive_inverse(add(X_65,add(additive_inverse(X_42),X_175))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)),additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))) ),[1,0],$fot(add(X_65,add(additive_inverse(X_42),X_175)))]]) ).
cnf(refute_0_491,plain,
( add(add(X_65,additive_inverse(X_42)),X_175) != add(X_65,add(additive_inverse(X_42),X_175))
| additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)) = additive_inverse(add(X_65,add(additive_inverse(X_42),X_175))) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)),additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)) = additive_inverse(add(X_65,add(additive_inverse(X_42),X_175))),
inference(resolve,[$cnf( $equal(add(add(X_65,additive_inverse(X_42)),X_175),add(X_65,add(additive_inverse(X_42),X_175))) )],[refute_0_488,refute_0_491]) ).
cnf(refute_0_493,plain,
( add(X_42,additive_inverse(add(X_65,X_175))) != additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))
| additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)) != additive_inverse(add(X_65,add(additive_inverse(X_42),X_175)))
| add(X_42,additive_inverse(add(X_65,X_175))) = additive_inverse(add(X_65,add(additive_inverse(X_42),X_175))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_42,additive_inverse(add(X_65,X_175))),additive_inverse(add(X_65,add(additive_inverse(X_42),X_175)))) ),[0],$fot(additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)))]]) ).
cnf(refute_0_494,plain,
( add(X_42,additive_inverse(add(X_65,X_175))) != additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))
| add(X_42,additive_inverse(add(X_65,X_175))) = additive_inverse(add(X_65,add(additive_inverse(X_42),X_175))) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175)),additive_inverse(add(X_65,add(additive_inverse(X_42),X_175)))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
( add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))) != additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))
| add(X_42,additive_inverse(add(X_65,X_175))) = additive_inverse(add(X_65,add(additive_inverse(X_42),X_175))) ),
inference(resolve,[$cnf( $equal(add(X_42,additive_inverse(add(X_65,X_175))),additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))) )],[refute_0_487,refute_0_494]) ).
cnf(refute_0_496,plain,
add(X_42,additive_inverse(add(X_65,X_175))) = additive_inverse(add(X_65,add(additive_inverse(X_42),X_175))),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_175),add(X_42,additive_inverse(X_65))),additive_inverse(add(add(X_65,additive_inverse(X_42)),X_175))) )],[refute_0_479,refute_0_495]) ).
cnf(refute_0_497,plain,
( add(X_42,additive_inverse(add(X_65,X_175))) != additive_inverse(add(X_65,add(additive_inverse(X_42),X_175)))
| additive_inverse(add(X_65,add(additive_inverse(X_42),X_175))) = add(X_42,additive_inverse(add(X_65,X_175))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_42,additive_inverse(add(X_65,X_175))))),bind(Y0,$fot(additive_inverse(add(X_65,add(additive_inverse(X_42),X_175)))))]]) ).
cnf(refute_0_498,plain,
additive_inverse(add(X_65,add(additive_inverse(X_42),X_175))) = add(X_42,additive_inverse(add(X_65,X_175))),
inference(resolve,[$cnf( $equal(add(X_42,additive_inverse(add(X_65,X_175))),additive_inverse(add(X_65,add(additive_inverse(X_42),X_175)))) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280))) = add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280))),
inference(subst,[],[refute_0_498:[bind(X_175,$fot(X_280)),bind(X_42,$fot(multiply(X_278,X_279))),bind(X_65,$fot(multiply(X_279,X_278)))]]) ).
cnf(refute_0_500,plain,
( add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) != additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)))
| additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280))) != add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280)))
| add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) = add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280))) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))))),bind(Y0,$fot(additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280))))),bind(Z0,$fot(add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280)))))]]) ).
cnf(refute_0_501,plain,
( additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280))) != add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280)))
| add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) = add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))),additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280)))) )],[refute_0_472,refute_0_500]) ).
cnf(refute_0_502,plain,
add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) = add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280))),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(X_279,X_278),add(additive_inverse(multiply(X_278,X_279)),X_280))),add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280)))) )],[refute_0_499,refute_0_501]) ).
cnf(refute_0_503,plain,
( add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) != add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280)))
| add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) != additive_inverse(add(commutator(X_278,X_279),X_280))
| add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280))) = additive_inverse(add(commutator(X_278,X_279),X_280)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))),additive_inverse(add(commutator(X_278,X_279),X_280))) ),[0],$fot(add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280))))]]) ).
cnf(refute_0_504,plain,
( add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))) != additive_inverse(add(commutator(X_278,X_279),X_280))
| add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280))) = additive_inverse(add(commutator(X_278,X_279),X_280)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))),add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280)))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),X_280))) = additive_inverse(add(commutator(X_278,X_279),X_280)),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(additive_inverse(multiply(X_278,X_279)),X_280)),additive_inverse(multiply(X_279,X_278))),additive_inverse(add(commutator(X_278,X_279),X_280))) )],[refute_0_475,refute_0_504]) ).
cnf(refute_0_506,plain,
add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279)))) = additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279))),
inference(subst,[],[refute_0_505:[bind(X_280,$fot(commutator(additive_inverse(X_278),X_279)))]]) ).
cnf(refute_0_507,plain,
additive_inverse(multiply(additive_inverse(X_703),X_704)) = add(multiply(X_704,X_703),additive_inverse(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704)))),
inference(subst,[],[refute_0_74:[bind(X,$fot(multiply(additive_inverse(X_703),X_704))),bind(X_65,$fot(multiply(X_704,X_703)))]]) ).
cnf(refute_0_508,plain,
( add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704)) != commutator(X_704,additive_inverse(X_703))
| additive_inverse(multiply(additive_inverse(X_703),X_704)) != add(multiply(X_704,X_703),additive_inverse(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))))
| additive_inverse(multiply(additive_inverse(X_703),X_704)) = add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_703),X_704)),add(multiply(X_704,X_703),additive_inverse(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))))) ),[1,1,0],$fot(commutator(X_704,additive_inverse(X_703)))]]) ).
cnf(refute_0_509,plain,
( additive_inverse(multiply(additive_inverse(X_703),X_704)) != add(multiply(X_704,X_703),additive_inverse(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))))
| additive_inverse(multiply(additive_inverse(X_703),X_704)) = add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704)),commutator(X_704,additive_inverse(X_703))) )],[refute_0_439,refute_0_508]) ).
cnf(refute_0_510,plain,
additive_inverse(multiply(additive_inverse(X_703),X_704)) = add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_703),X_704)),add(multiply(X_704,X_703),additive_inverse(add(multiply(X_704,X_703),multiply(additive_inverse(X_703),X_704))))) )],[refute_0_507,refute_0_509]) ).
cnf(refute_0_511,plain,
add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))),
introduced(tautology,[refl,[$fot(add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))))]]) ).
cnf(refute_0_512,plain,
( add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))) != add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703))))
| additive_inverse(commutator(X_704,additive_inverse(X_703))) != commutator(additive_inverse(X_703),X_704)
| add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = add(multiply(X_704,X_703),commutator(additive_inverse(X_703),X_704)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))),add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703))))) ),[1,1],$fot(commutator(additive_inverse(X_703),X_704))]]) ).
cnf(refute_0_513,plain,
( additive_inverse(commutator(X_704,additive_inverse(X_703))) != commutator(additive_inverse(X_703),X_704)
| add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = add(multiply(X_704,X_703),commutator(additive_inverse(X_703),X_704)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))),add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703))))) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))) = add(multiply(X_704,X_703),commutator(additive_inverse(X_703),X_704)),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(X_704,additive_inverse(X_703))),commutator(additive_inverse(X_703),X_704)) )],[refute_0_452,refute_0_513]) ).
cnf(refute_0_515,plain,
( add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))) != add(multiply(X_704,X_703),commutator(additive_inverse(X_703),X_704))
| additive_inverse(multiply(additive_inverse(X_703),X_704)) != add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703))))
| additive_inverse(multiply(additive_inverse(X_703),X_704)) = add(multiply(X_704,X_703),commutator(additive_inverse(X_703),X_704)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_703),X_704)),add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703))))) ),[1],$fot(add(multiply(X_704,X_703),commutator(additive_inverse(X_703),X_704)))]]) ).
cnf(refute_0_516,plain,
( additive_inverse(multiply(additive_inverse(X_703),X_704)) != add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703))))
| additive_inverse(multiply(additive_inverse(X_703),X_704)) = add(multiply(X_704,X_703),commutator(additive_inverse(X_703),X_704)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703)))),add(multiply(X_704,X_703),commutator(additive_inverse(X_703),X_704))) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
additive_inverse(multiply(additive_inverse(X_703),X_704)) = add(multiply(X_704,X_703),commutator(additive_inverse(X_703),X_704)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_703),X_704)),add(multiply(X_704,X_703),additive_inverse(commutator(X_704,additive_inverse(X_703))))) )],[refute_0_510,refute_0_516]) ).
cnf(refute_0_518,plain,
additive_inverse(multiply(additive_inverse(X_278),X_279)) = add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279)),
inference(subst,[],[refute_0_517:[bind(X_703,$fot(X_278)),bind(X_704,$fot(X_279))]]) ).
cnf(refute_0_519,plain,
( additive_inverse(multiply(additive_inverse(X_278),X_279)) != add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279))
| add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279)) = additive_inverse(multiply(additive_inverse(X_278),X_279)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(multiply(additive_inverse(X_278),X_279)))),bind(Y0,$fot(add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279))))]]) ).
cnf(refute_0_520,plain,
add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279)) = additive_inverse(multiply(additive_inverse(X_278),X_279)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_278),X_279)),add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279))) )],[refute_0_518,refute_0_519]) ).
cnf(refute_0_521,plain,
( add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279)))) != additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279)))
| add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279)) != additive_inverse(multiply(additive_inverse(X_278),X_279))
| add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) = additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279)))),additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279)))) ),[0,1,0],$fot(additive_inverse(multiply(additive_inverse(X_278),X_279)))]]) ).
cnf(refute_0_522,plain,
( add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279)))) != additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279)))
| add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) = additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279)),additive_inverse(multiply(additive_inverse(X_278),X_279))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) = additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279))),
inference(resolve,[$cnf( $equal(add(multiply(X_278,X_279),additive_inverse(add(multiply(X_279,X_278),commutator(additive_inverse(X_278),X_279)))),additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279)))) )],[refute_0_506,refute_0_522]) ).
cnf(refute_0_524,plain,
multiply(additive_identity,X_279) = additive_identity,
inference(subst,[],[left_multiplicative_zero:[bind(X,$fot(X_279))]]) ).
cnf(refute_0_525,plain,
add(X_278,additive_inverse(X_278)) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(X_278))]]) ).
cnf(refute_0_526,plain,
multiply(add(X_278,additive_inverse(X_278)),X_279) = multiply(add(X_278,additive_inverse(X_278)),X_279),
introduced(tautology,[refl,[$fot(multiply(add(X_278,additive_inverse(X_278)),X_279))]]) ).
cnf(refute_0_527,plain,
( multiply(add(X_278,additive_inverse(X_278)),X_279) != multiply(add(X_278,additive_inverse(X_278)),X_279)
| add(X_278,additive_inverse(X_278)) != additive_identity
| multiply(add(X_278,additive_inverse(X_278)),X_279) = multiply(additive_identity,X_279) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_278,additive_inverse(X_278)),X_279),multiply(add(X_278,additive_inverse(X_278)),X_279)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_528,plain,
( add(X_278,additive_inverse(X_278)) != additive_identity
| multiply(add(X_278,additive_inverse(X_278)),X_279) = multiply(additive_identity,X_279) ),
inference(resolve,[$cnf( $equal(multiply(add(X_278,additive_inverse(X_278)),X_279),multiply(add(X_278,additive_inverse(X_278)),X_279)) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
multiply(add(X_278,additive_inverse(X_278)),X_279) = multiply(additive_identity,X_279),
inference(resolve,[$cnf( $equal(add(X_278,additive_inverse(X_278)),additive_identity) )],[refute_0_525,refute_0_528]) ).
cnf(refute_0_530,plain,
( multiply(add(X_278,additive_inverse(X_278)),X_279) != multiply(additive_identity,X_279)
| multiply(additive_identity,X_279) != additive_identity
| multiply(add(X_278,additive_inverse(X_278)),X_279) = additive_identity ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(multiply(add(X_278,additive_inverse(X_278)),X_279))),bind(Y0,$fot(multiply(additive_identity,X_279))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_531,plain,
( multiply(additive_identity,X_279) != additive_identity
| multiply(add(X_278,additive_inverse(X_278)),X_279) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(add(X_278,additive_inverse(X_278)),X_279),multiply(additive_identity,X_279)) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
multiply(add(X_278,additive_inverse(X_278)),X_279) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_279),additive_identity) )],[refute_0_524,refute_0_531]) ).
cnf(refute_0_533,plain,
add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)) = multiply(add(X_278,additive_inverse(X_278)),X_279),
inference(subst,[],[refute_0_352:[bind(X,$fot(X_278)),bind(Y,$fot(additive_inverse(X_278))),bind(Z,$fot(X_279))]]) ).
cnf(refute_0_534,plain,
( multiply(add(X_278,additive_inverse(X_278)),X_279) != additive_identity
| add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)) != multiply(add(X_278,additive_inverse(X_278)),X_279)
| add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)) = additive_identity ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)))),bind(Y0,$fot(multiply(add(X_278,additive_inverse(X_278)),X_279))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_535,plain,
( multiply(add(X_278,additive_inverse(X_278)),X_279) != additive_identity
| add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)) = additive_identity ),
inference(resolve,[$cnf( $equal(add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)),multiply(add(X_278,additive_inverse(X_278)),X_279)) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(add(X_278,additive_inverse(X_278)),X_279),additive_identity) )],[refute_0_532,refute_0_535]) ).
cnf(refute_0_537,plain,
additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279))) = multiply(additive_inverse(X_278),X_279),
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(multiply(additive_inverse(X_278),X_279)))]]) ).
cnf(refute_0_538,plain,
add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) = add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))),
introduced(tautology,[refl,[$fot(add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))))]]) ).
cnf(refute_0_539,plain,
( add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) != add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279))))
| additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279))) != multiply(additive_inverse(X_278),X_279)
| add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) = add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))),add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279))))) ),[1,1],$fot(multiply(additive_inverse(X_278),X_279))]]) ).
cnf(refute_0_540,plain,
( additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279))) != multiply(additive_inverse(X_278),X_279)
| add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) = add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))),add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279))))) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) = add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279))),multiply(additive_inverse(X_278),X_279)) )],[refute_0_537,refute_0_540]) ).
cnf(refute_0_542,plain,
( add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)) != additive_identity
| add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) != add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279))
| add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) = additive_identity ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))))),bind(Y0,$fot(add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_543,plain,
( add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)) != additive_identity
| add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) = additive_identity ),
inference(resolve,[$cnf( $equal(add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))),add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279))) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) = additive_identity,
inference(resolve,[$cnf( $equal(add(multiply(X_278,X_279),multiply(additive_inverse(X_278),X_279)),additive_identity) )],[refute_0_536,refute_0_543]) ).
cnf(refute_0_545,plain,
( add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) != additive_identity
| add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) != additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279)))
| additive_identity = additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))),additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279)))) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_546,plain,
( add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))) != additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279)))
| additive_identity = additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))),additive_identity) )],[refute_0_544,refute_0_545]) ).
cnf(refute_0_547,plain,
additive_identity = additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279))),
inference(resolve,[$cnf( $equal(add(multiply(X_278,X_279),additive_inverse(additive_inverse(multiply(additive_inverse(X_278),X_279)))),additive_inverse(add(commutator(X_278,X_279),commutator(additive_inverse(X_278),X_279)))) )],[refute_0_523,refute_0_546]) ).
cnf(refute_0_548,plain,
additive_identity = additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),
inference(subst,[],[refute_0_547:[bind(X_278,$fot(X_767)),bind(X_279,$fot(X_768))]]) ).
cnf(refute_0_549,plain,
( additive_identity != additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)))
| additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))) = additive_identity ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)))))]]) ).
cnf(refute_0_550,plain,
additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
( additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))) != additive_identity
| additive_inverse(commutator(additive_inverse(X_767),X_768)) != add(commutator(X_767,X_768),additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))))
| additive_inverse(commutator(additive_inverse(X_767),X_768)) = add(commutator(X_767,X_768),additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(commutator(additive_inverse(X_767),X_768)),add(commutator(X_767,X_768),additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_552,plain,
( additive_inverse(commutator(additive_inverse(X_767),X_768)) != add(commutator(X_767,X_768),additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))))
| additive_inverse(commutator(additive_inverse(X_767),X_768)) = add(commutator(X_767,X_768),additive_identity) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),additive_identity) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
additive_inverse(commutator(additive_inverse(X_767),X_768)) = add(commutator(X_767,X_768),additive_identity),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(additive_inverse(X_767),X_768)),add(commutator(X_767,X_768),additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))))) )],[refute_0_471,refute_0_552]) ).
cnf(refute_0_554,plain,
additive_inverse(commutator(additive_inverse(X_767),X_768)) = commutator(X_768,additive_inverse(X_767)),
inference(subst,[],[refute_0_451:[bind(X,$fot(additive_inverse(X_767))),bind(Y,$fot(X_768))]]) ).
cnf(refute_0_555,plain,
( additive_inverse(commutator(additive_inverse(X_767),X_768)) != add(commutator(X_767,X_768),additive_identity)
| additive_inverse(commutator(additive_inverse(X_767),X_768)) != commutator(X_768,additive_inverse(X_767))
| commutator(X_768,additive_inverse(X_767)) = add(commutator(X_767,X_768),additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(commutator(additive_inverse(X_767),X_768)),add(commutator(X_767,X_768),additive_identity)) ),[0],$fot(commutator(X_768,additive_inverse(X_767)))]]) ).
cnf(refute_0_556,plain,
( additive_inverse(commutator(additive_inverse(X_767),X_768)) != add(commutator(X_767,X_768),additive_identity)
| commutator(X_768,additive_inverse(X_767)) = add(commutator(X_767,X_768),additive_identity) ),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(additive_inverse(X_767),X_768)),commutator(X_768,additive_inverse(X_767))) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
add(additive_identity,commutator(X_767,X_768)) = commutator(X_767,X_768),
inference(subst,[],[left_additive_identity:[bind(X,$fot(commutator(X_767,X_768)))]]) ).
cnf(refute_0_558,plain,
add(commutator(X_767,X_768),additive_identity) = add(additive_identity,commutator(X_767,X_768)),
inference(subst,[],[refute_0_306:[bind(X,$fot(additive_identity)),bind(X_46,$fot(commutator(X_767,X_768)))]]) ).
cnf(refute_0_559,plain,
( add(additive_identity,commutator(X_767,X_768)) != commutator(X_767,X_768)
| add(commutator(X_767,X_768),additive_identity) != add(additive_identity,commutator(X_767,X_768))
| add(commutator(X_767,X_768),additive_identity) = commutator(X_767,X_768) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(commutator(X_767,X_768),additive_identity))),bind(Y0,$fot(add(additive_identity,commutator(X_767,X_768)))),bind(Z0,$fot(commutator(X_767,X_768)))]]) ).
cnf(refute_0_560,plain,
( add(additive_identity,commutator(X_767,X_768)) != commutator(X_767,X_768)
| add(commutator(X_767,X_768),additive_identity) = commutator(X_767,X_768) ),
inference(resolve,[$cnf( $equal(add(commutator(X_767,X_768),additive_identity),add(additive_identity,commutator(X_767,X_768))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
add(commutator(X_767,X_768),additive_identity) = commutator(X_767,X_768),
inference(resolve,[$cnf( $equal(add(additive_identity,commutator(X_767,X_768)),commutator(X_767,X_768)) )],[refute_0_557,refute_0_560]) ).
cnf(refute_0_562,plain,
( add(commutator(X_767,X_768),additive_identity) != commutator(X_767,X_768)
| commutator(X_768,additive_inverse(X_767)) != add(commutator(X_767,X_768),additive_identity)
| commutator(X_768,additive_inverse(X_767)) = commutator(X_767,X_768) ),
introduced(tautology,[equality,[$cnf( $equal(commutator(X_768,additive_inverse(X_767)),add(commutator(X_767,X_768),additive_identity)) ),[1],$fot(commutator(X_767,X_768))]]) ).
cnf(refute_0_563,plain,
( commutator(X_768,additive_inverse(X_767)) != add(commutator(X_767,X_768),additive_identity)
| commutator(X_768,additive_inverse(X_767)) = commutator(X_767,X_768) ),
inference(resolve,[$cnf( $equal(add(commutator(X_767,X_768),additive_identity),commutator(X_767,X_768)) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
( additive_inverse(commutator(additive_inverse(X_767),X_768)) != add(commutator(X_767,X_768),additive_identity)
| commutator(X_768,additive_inverse(X_767)) = commutator(X_767,X_768) ),
inference(resolve,[$cnf( $equal(commutator(X_768,additive_inverse(X_767)),add(commutator(X_767,X_768),additive_identity)) )],[refute_0_556,refute_0_563]) ).
cnf(refute_0_565,plain,
commutator(X_768,additive_inverse(X_767)) = commutator(X_767,X_768),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(additive_inverse(X_767),X_768)),add(commutator(X_767,X_768),additive_identity)) )],[refute_0_553,refute_0_564]) ).
cnf(refute_0_566,plain,
commutator(X,additive_inverse(X_769)) = commutator(X_769,X),
inference(subst,[],[refute_0_565:[bind(X_767,$fot(X_769)),bind(X_768,$fot(X))]]) ).
cnf(refute_0_567,plain,
( add(multiply(X,additive_inverse(X_769)),commutator(X,additive_inverse(X_769))) != multiply(additive_inverse(X_769),X)
| commutator(X,additive_inverse(X_769)) != commutator(X_769,X)
| add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) = multiply(additive_inverse(X_769),X) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,additive_inverse(X_769)),commutator(X,additive_inverse(X_769))),multiply(additive_inverse(X_769),X)) ),[0,1],$fot(commutator(X_769,X))]]) ).
cnf(refute_0_568,plain,
( add(multiply(X,additive_inverse(X_769)),commutator(X,additive_inverse(X_769))) != multiply(additive_inverse(X_769),X)
| add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) = multiply(additive_inverse(X_769),X) ),
inference(resolve,[$cnf( $equal(commutator(X,additive_inverse(X_769)),commutator(X_769,X)) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) = multiply(additive_inverse(X_769),X),
inference(resolve,[$cnf( $equal(add(multiply(X,additive_inverse(X_769)),commutator(X,additive_inverse(X_769))),multiply(additive_inverse(X_769),X)) )],[refute_0_470,refute_0_568]) ).
cnf(refute_0_570,plain,
add(multiply(X,X_769),commutator(X,X_769)) = multiply(X_769,X),
inference(subst,[],[refute_0_191:[bind(Y,$fot(X_769))]]) ).
cnf(refute_0_571,plain,
additive_inverse(add(multiply(X,X_769),commutator(X,X_769))) = additive_inverse(add(multiply(X,X_769),commutator(X,X_769))),
introduced(tautology,[refl,[$fot(additive_inverse(add(multiply(X,X_769),commutator(X,X_769))))]]) ).
cnf(refute_0_572,plain,
( add(multiply(X,X_769),commutator(X,X_769)) != multiply(X_769,X)
| additive_inverse(add(multiply(X,X_769),commutator(X,X_769))) != additive_inverse(add(multiply(X,X_769),commutator(X,X_769)))
| additive_inverse(add(multiply(X,X_769),commutator(X,X_769))) = additive_inverse(multiply(X_769,X)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(multiply(X,X_769),commutator(X,X_769))),additive_inverse(add(multiply(X,X_769),commutator(X,X_769)))) ),[1,0],$fot(multiply(X_769,X))]]) ).
cnf(refute_0_573,plain,
( add(multiply(X,X_769),commutator(X,X_769)) != multiply(X_769,X)
| additive_inverse(add(multiply(X,X_769),commutator(X,X_769))) = additive_inverse(multiply(X_769,X)) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(X,X_769),commutator(X,X_769))),additive_inverse(add(multiply(X,X_769),commutator(X,X_769)))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
additive_inverse(add(multiply(X,X_769),commutator(X,X_769))) = additive_inverse(multiply(X_769,X)),
inference(resolve,[$cnf( $equal(add(multiply(X,X_769),commutator(X,X_769)),multiply(X_769,X)) )],[refute_0_570,refute_0_573]) ).
cnf(refute_0_575,plain,
add(commutator(X,Y),additive_inverse(X_174)) = additive_inverse(add(X_174,additive_inverse(commutator(X,Y)))),
inference(subst,[],[refute_0_205:[bind(X_42,$fot(commutator(X,Y))),bind(X_65,$fot(X_174))]]) ).
cnf(refute_0_576,plain,
( add(commutator(X,Y),additive_inverse(X_174)) != additive_inverse(add(X_174,additive_inverse(commutator(X,Y))))
| additive_inverse(commutator(X,Y)) != commutator(Y,X)
| add(commutator(X,Y),additive_inverse(X_174)) = additive_inverse(add(X_174,commutator(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(add(commutator(X,Y),additive_inverse(X_174)),additive_inverse(add(X_174,additive_inverse(commutator(X,Y))))) ),[1,0,1],$fot(commutator(Y,X))]]) ).
cnf(refute_0_577,plain,
( add(commutator(X,Y),additive_inverse(X_174)) != additive_inverse(add(X_174,additive_inverse(commutator(X,Y))))
| add(commutator(X,Y),additive_inverse(X_174)) = additive_inverse(add(X_174,commutator(Y,X))) ),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(X,Y)),commutator(Y,X)) )],[refute_0_451,refute_0_576]) ).
cnf(refute_0_578,plain,
add(commutator(X,Y),additive_inverse(X_174)) = additive_inverse(add(X_174,commutator(Y,X))),
inference(resolve,[$cnf( $equal(add(commutator(X,Y),additive_inverse(X_174)),additive_inverse(add(X_174,additive_inverse(commutator(X,Y))))) )],[refute_0_575,refute_0_577]) ).
cnf(refute_0_579,plain,
add(commutator(X_769,X),additive_inverse(multiply(X,X_769))) = additive_inverse(add(multiply(X,X_769),commutator(X,X_769))),
inference(subst,[],[refute_0_578:[bind(X,$fot(X_769)),bind(Y,$fot(X)),bind(X_174,$fot(multiply(X,X_769)))]]) ).
cnf(refute_0_580,plain,
( add(commutator(X_769,X),additive_inverse(multiply(X,X_769))) != additive_inverse(add(multiply(X,X_769),commutator(X,X_769)))
| additive_inverse(add(multiply(X,X_769),commutator(X,X_769))) != additive_inverse(multiply(X_769,X))
| add(commutator(X_769,X),additive_inverse(multiply(X,X_769))) = additive_inverse(multiply(X_769,X)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(commutator(X_769,X),additive_inverse(multiply(X,X_769))))),bind(Y0,$fot(additive_inverse(add(multiply(X,X_769),commutator(X,X_769))))),bind(Z0,$fot(additive_inverse(multiply(X_769,X))))]]) ).
cnf(refute_0_581,plain,
( additive_inverse(add(multiply(X,X_769),commutator(X,X_769))) != additive_inverse(multiply(X_769,X))
| add(commutator(X_769,X),additive_inverse(multiply(X,X_769))) = additive_inverse(multiply(X_769,X)) ),
inference(resolve,[$cnf( $equal(add(commutator(X_769,X),additive_inverse(multiply(X,X_769))),additive_inverse(add(multiply(X,X_769),commutator(X,X_769)))) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
add(commutator(X_769,X),additive_inverse(multiply(X,X_769))) = additive_inverse(multiply(X_769,X)),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(X,X_769),commutator(X,X_769))),additive_inverse(multiply(X_769,X))) )],[refute_0_574,refute_0_581]) ).
cnf(refute_0_583,plain,
multiply(X,additive_inverse(X_769)) = additive_inverse(multiply(X,X_769)),
inference(subst,[],[refute_0_464:[bind(X_703,$fot(X_769)),bind(X_704,$fot(X))]]) ).
cnf(refute_0_584,plain,
add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) = add(commutator(X_769,X),multiply(X,additive_inverse(X_769))),
introduced(tautology,[refl,[$fot(add(commutator(X_769,X),multiply(X,additive_inverse(X_769))))]]) ).
cnf(refute_0_585,plain,
( multiply(X,additive_inverse(X_769)) != additive_inverse(multiply(X,X_769))
| add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) != add(commutator(X_769,X),multiply(X,additive_inverse(X_769)))
| add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) = add(commutator(X_769,X),additive_inverse(multiply(X,X_769))) ),
introduced(tautology,[equality,[$cnf( $equal(add(commutator(X_769,X),multiply(X,additive_inverse(X_769))),add(commutator(X_769,X),multiply(X,additive_inverse(X_769)))) ),[1,1],$fot(additive_inverse(multiply(X,X_769)))]]) ).
cnf(refute_0_586,plain,
( multiply(X,additive_inverse(X_769)) != additive_inverse(multiply(X,X_769))
| add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) = add(commutator(X_769,X),additive_inverse(multiply(X,X_769))) ),
inference(resolve,[$cnf( $equal(add(commutator(X_769,X),multiply(X,additive_inverse(X_769))),add(commutator(X_769,X),multiply(X,additive_inverse(X_769)))) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) = add(commutator(X_769,X),additive_inverse(multiply(X,X_769))),
inference(resolve,[$cnf( $equal(multiply(X,additive_inverse(X_769)),additive_inverse(multiply(X,X_769))) )],[refute_0_583,refute_0_586]) ).
cnf(refute_0_588,plain,
( add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) != add(commutator(X_769,X),additive_inverse(multiply(X,X_769)))
| add(commutator(X_769,X),additive_inverse(multiply(X,X_769))) != additive_inverse(multiply(X_769,X))
| add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) = additive_inverse(multiply(X_769,X)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(commutator(X_769,X),multiply(X,additive_inverse(X_769))))),bind(Y0,$fot(add(commutator(X_769,X),additive_inverse(multiply(X,X_769))))),bind(Z0,$fot(additive_inverse(multiply(X_769,X))))]]) ).
cnf(refute_0_589,plain,
( add(commutator(X_769,X),additive_inverse(multiply(X,X_769))) != additive_inverse(multiply(X_769,X))
| add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) = additive_inverse(multiply(X_769,X)) ),
inference(resolve,[$cnf( $equal(add(commutator(X_769,X),multiply(X,additive_inverse(X_769))),add(commutator(X_769,X),additive_inverse(multiply(X,X_769)))) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) = additive_inverse(multiply(X_769,X)),
inference(resolve,[$cnf( $equal(add(commutator(X_769,X),additive_inverse(multiply(X,X_769))),additive_inverse(multiply(X_769,X))) )],[refute_0_582,refute_0_589]) ).
cnf(refute_0_591,plain,
add(X,add(add(X_54,additive_inverse(X)),Z)) = add(add(X,add(X_54,additive_inverse(X))),Z),
inference(subst,[],[associativity_for_addition:[bind(Y,$fot(add(X_54,additive_inverse(X))))]]) ).
cnf(refute_0_592,plain,
add(X,add(X_54,additive_inverse(X))) = X_54,
inference(subst,[],[refute_0_125:[bind(X_45,$fot(X)),bind(X_46,$fot(X_54))]]) ).
cnf(refute_0_593,plain,
( add(X,add(X_54,additive_inverse(X))) != X_54
| add(X,add(add(X_54,additive_inverse(X)),Z)) != add(add(X,add(X_54,additive_inverse(X))),Z)
| add(X,add(add(X_54,additive_inverse(X)),Z)) = add(X_54,Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(add(X_54,additive_inverse(X)),Z)),add(add(X,add(X_54,additive_inverse(X))),Z)) ),[1,0],$fot(X_54)]]) ).
cnf(refute_0_594,plain,
( add(X,add(add(X_54,additive_inverse(X)),Z)) != add(add(X,add(X_54,additive_inverse(X))),Z)
| add(X,add(add(X_54,additive_inverse(X)),Z)) = add(X_54,Z) ),
inference(resolve,[$cnf( $equal(add(X,add(X_54,additive_inverse(X))),X_54) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
add(X,add(add(X_54,additive_inverse(X)),Z)) = add(X_54,Z),
inference(resolve,[$cnf( $equal(add(X,add(add(X_54,additive_inverse(X)),Z)),add(add(X,add(X_54,additive_inverse(X))),Z)) )],[refute_0_591,refute_0_594]) ).
cnf(refute_0_596,plain,
add(add(X_54,additive_inverse(X)),Z) = add(X_54,add(additive_inverse(X),Z)),
inference(subst,[],[refute_0_138:[bind(X,$fot(X_54)),bind(Y,$fot(additive_inverse(X)))]]) ).
cnf(refute_0_597,plain,
add(X,add(add(X_54,additive_inverse(X)),Z)) = add(X,add(add(X_54,additive_inverse(X)),Z)),
introduced(tautology,[refl,[$fot(add(X,add(add(X_54,additive_inverse(X)),Z)))]]) ).
cnf(refute_0_598,plain,
( add(X,add(add(X_54,additive_inverse(X)),Z)) != add(X,add(add(X_54,additive_inverse(X)),Z))
| add(add(X_54,additive_inverse(X)),Z) != add(X_54,add(additive_inverse(X),Z))
| add(X,add(add(X_54,additive_inverse(X)),Z)) = add(X,add(X_54,add(additive_inverse(X),Z))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(add(X_54,additive_inverse(X)),Z)),add(X,add(add(X_54,additive_inverse(X)),Z))) ),[1,1],$fot(add(X_54,add(additive_inverse(X),Z)))]]) ).
cnf(refute_0_599,plain,
( add(add(X_54,additive_inverse(X)),Z) != add(X_54,add(additive_inverse(X),Z))
| add(X,add(add(X_54,additive_inverse(X)),Z)) = add(X,add(X_54,add(additive_inverse(X),Z))) ),
inference(resolve,[$cnf( $equal(add(X,add(add(X_54,additive_inverse(X)),Z)),add(X,add(add(X_54,additive_inverse(X)),Z))) )],[refute_0_597,refute_0_598]) ).
cnf(refute_0_600,plain,
add(X,add(add(X_54,additive_inverse(X)),Z)) = add(X,add(X_54,add(additive_inverse(X),Z))),
inference(resolve,[$cnf( $equal(add(add(X_54,additive_inverse(X)),Z),add(X_54,add(additive_inverse(X),Z))) )],[refute_0_596,refute_0_599]) ).
cnf(refute_0_601,plain,
( add(X,add(add(X_54,additive_inverse(X)),Z)) != add(X,add(X_54,add(additive_inverse(X),Z)))
| add(X,add(add(X_54,additive_inverse(X)),Z)) != add(X_54,Z)
| add(X,add(X_54,add(additive_inverse(X),Z))) = add(X_54,Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(add(X_54,additive_inverse(X)),Z)),add(X_54,Z)) ),[0],$fot(add(X,add(X_54,add(additive_inverse(X),Z))))]]) ).
cnf(refute_0_602,plain,
( add(X,add(add(X_54,additive_inverse(X)),Z)) != add(X_54,Z)
| add(X,add(X_54,add(additive_inverse(X),Z))) = add(X_54,Z) ),
inference(resolve,[$cnf( $equal(add(X,add(add(X_54,additive_inverse(X)),Z)),add(X,add(X_54,add(additive_inverse(X),Z)))) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
add(X,add(X_54,add(additive_inverse(X),Z))) = add(X_54,Z),
inference(resolve,[$cnf( $equal(add(X,add(add(X_54,additive_inverse(X)),Z)),add(X_54,Z)) )],[refute_0_595,refute_0_602]) ).
cnf(refute_0_604,plain,
add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),Z))) = add(X_54,Z),
inference(subst,[],[refute_0_603:[bind(X,$fot(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))))]]) ).
cnf(refute_0_605,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),Z))) != add(X_54,Z)
| additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))) != additive_identity
| add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) = add(X_54,Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),Z))),add(X_54,Z)) ),[0,1,1,0],$fot(additive_identity)]]) ).
cnf(refute_0_606,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),Z))) != add(X_54,Z)
| add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) = add(X_54,Z) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),additive_identity) )],[refute_0_550,refute_0_605]) ).
cnf(refute_0_607,plain,
add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) = add(X_54,Z),
inference(resolve,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),Z))),add(X_54,Z)) )],[refute_0_604,refute_0_606]) ).
cnf(refute_0_608,plain,
add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54)) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))),
inference(subst,[],[refute_0_138:[bind(X,$fot(commutator(X_767,X_768))),bind(Y,$fot(commutator(additive_inverse(X_767),X_768))),bind(Z,$fot(add(Z,X_54)))]]) ).
cnf(refute_0_609,plain,
add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))) = add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54)),
inference(subst,[],[left_additive_identity:[bind(X,$fot(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))))]]) ).
cnf(refute_0_610,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54)) != add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54)))
| add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))) != add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))
| add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))))),bind(Y0,$fot(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54)))),bind(Z0,$fot(add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54)))))]]) ).
cnf(refute_0_611,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54)) != add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54)))
| add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) ),
inference(resolve,[$cnf( $equal(add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))),add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))),
inference(resolve,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54)),add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54)))) )],[refute_0_608,refute_0_611]) ).
cnf(refute_0_613,plain,
add(X_123,add(X_122,additive_inverse(add(X_123,additive_inverse(add(X_607,add(X_123,X_608))))))) = add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))),
inference(subst,[],[refute_0_397:[bind(X,$fot(additive_inverse(add(X_607,add(X_123,X_608)))))]]) ).
cnf(refute_0_614,plain,
additive_inverse(add(X_608,X_607)) = add(X_123,additive_inverse(add(X_607,add(X_123,X_608)))),
inference(subst,[],[refute_0_406:[bind(X_121,$fot(X_607)),bind(X_123,$fot(X_608)),bind(X_65,$fot(X_123))]]) ).
cnf(refute_0_615,plain,
( additive_inverse(add(X_608,X_607)) != add(X_123,additive_inverse(add(X_607,add(X_123,X_608))))
| add(X_123,additive_inverse(add(X_607,add(X_123,X_608)))) = additive_inverse(add(X_608,X_607)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(add(X_608,X_607)))),bind(Y0,$fot(add(X_123,additive_inverse(add(X_607,add(X_123,X_608))))))]]) ).
cnf(refute_0_616,plain,
add(X_123,additive_inverse(add(X_607,add(X_123,X_608)))) = additive_inverse(add(X_608,X_607)),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_608,X_607)),add(X_123,additive_inverse(add(X_607,add(X_123,X_608))))) )],[refute_0_614,refute_0_615]) ).
cnf(refute_0_617,plain,
( add(X_123,add(X_122,additive_inverse(add(X_123,additive_inverse(add(X_607,add(X_123,X_608))))))) != add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))
| add(X_123,additive_inverse(add(X_607,add(X_123,X_608)))) != additive_inverse(add(X_608,X_607))
| add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) = add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_123,add(X_122,additive_inverse(add(X_123,additive_inverse(add(X_607,add(X_123,X_608))))))),add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))) ),[0,1,1,0],$fot(additive_inverse(add(X_608,X_607)))]]) ).
cnf(refute_0_618,plain,
( add(X_123,add(X_122,additive_inverse(add(X_123,additive_inverse(add(X_607,add(X_123,X_608))))))) != add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))
| add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) = add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))) ),
inference(resolve,[$cnf( $equal(add(X_123,additive_inverse(add(X_607,add(X_123,X_608)))),additive_inverse(add(X_608,X_607))) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) = add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))),
inference(resolve,[$cnf( $equal(add(X_123,add(X_122,additive_inverse(add(X_123,additive_inverse(add(X_607,add(X_123,X_608))))))),add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))) )],[refute_0_613,refute_0_618]) ).
cnf(refute_0_620,plain,
additive_inverse(additive_inverse(add(X_608,X_607))) = add(X_608,X_607),
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(add(X_608,X_607)))]]) ).
cnf(refute_0_621,plain,
add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))) = add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))),
introduced(tautology,[refl,[$fot(add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))))]]) ).
cnf(refute_0_622,plain,
( add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))) != add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))
| additive_inverse(additive_inverse(add(X_608,X_607))) != add(X_608,X_607)
| add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))) = add(X_122,add(X_608,X_607)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))),add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) ),[1,1],$fot(add(X_608,X_607))]]) ).
cnf(refute_0_623,plain,
( additive_inverse(additive_inverse(add(X_608,X_607))) != add(X_608,X_607)
| add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))) = add(X_122,add(X_608,X_607)) ),
inference(resolve,[$cnf( $equal(add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))),add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))) = add(X_122,add(X_608,X_607)),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(add(X_608,X_607))),add(X_608,X_607)) )],[refute_0_620,refute_0_623]) ).
cnf(refute_0_625,plain,
add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) = add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))),
introduced(tautology,[refl,[$fot(add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))))]]) ).
cnf(refute_0_626,plain,
( add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))) != add(X_122,add(X_608,X_607))
| add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) != add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))))
| add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) = add(X_123,add(X_122,add(X_608,X_607))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))),add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))))) ),[1,1],$fot(add(X_122,add(X_608,X_607)))]]) ).
cnf(refute_0_627,plain,
( add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))) != add(X_122,add(X_608,X_607))
| add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) = add(X_123,add(X_122,add(X_608,X_607))) ),
inference(resolve,[$cnf( $equal(add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))),add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))))) )],[refute_0_625,refute_0_626]) ).
cnf(refute_0_628,plain,
add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) = add(X_123,add(X_122,add(X_608,X_607))),
inference(resolve,[$cnf( $equal(add(X_122,additive_inverse(additive_inverse(add(X_608,X_607)))),add(X_122,add(X_608,X_607))) )],[refute_0_624,refute_0_627]) ).
cnf(refute_0_629,plain,
( add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) != add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))
| add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) != add(X_123,add(X_122,add(X_608,X_607)))
| add(X_123,add(X_122,add(X_608,X_607))) = add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))),add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))) ),[0],$fot(add(X_123,add(X_122,add(X_608,X_607))))]]) ).
cnf(refute_0_630,plain,
( add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) != add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))
| add(X_123,add(X_122,add(X_608,X_607))) = add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))) ),
inference(resolve,[$cnf( $equal(add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))),add(X_123,add(X_122,add(X_608,X_607)))) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))) = add(X_607,add(X_123,X_608)),
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(add(X_607,add(X_123,X_608))))]]) ).
cnf(refute_0_632,plain,
add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))) = add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))),
introduced(tautology,[refl,[$fot(add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))))]]) ).
cnf(refute_0_633,plain,
( add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))) != add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))
| additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))) != add(X_607,add(X_123,X_608))
| add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))) = add(X_122,add(X_607,add(X_123,X_608))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))),add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))) ),[1,1],$fot(add(X_607,add(X_123,X_608)))]]) ).
cnf(refute_0_634,plain,
( additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))) != add(X_607,add(X_123,X_608))
| add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))) = add(X_122,add(X_607,add(X_123,X_608))) ),
inference(resolve,[$cnf( $equal(add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))),add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))) = add(X_122,add(X_607,add(X_123,X_608))),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))),add(X_607,add(X_123,X_608))) )],[refute_0_631,refute_0_634]) ).
cnf(refute_0_636,plain,
( add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))) != add(X_122,add(X_607,add(X_123,X_608)))
| add(X_123,add(X_122,add(X_608,X_607))) != add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))
| add(X_123,add(X_122,add(X_608,X_607))) = add(X_122,add(X_607,add(X_123,X_608))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_123,add(X_122,add(X_608,X_607))),add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))) ),[1],$fot(add(X_122,add(X_607,add(X_123,X_608))))]]) ).
cnf(refute_0_637,plain,
( add(X_123,add(X_122,add(X_608,X_607))) != add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))
| add(X_123,add(X_122,add(X_608,X_607))) = add(X_122,add(X_607,add(X_123,X_608))) ),
inference(resolve,[$cnf( $equal(add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608))))),add(X_122,add(X_607,add(X_123,X_608)))) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
( add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))) != add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))
| add(X_123,add(X_122,add(X_608,X_607))) = add(X_122,add(X_607,add(X_123,X_608))) ),
inference(resolve,[$cnf( $equal(add(X_123,add(X_122,add(X_608,X_607))),add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))) )],[refute_0_630,refute_0_637]) ).
cnf(refute_0_639,plain,
add(X_123,add(X_122,add(X_608,X_607))) = add(X_122,add(X_607,add(X_123,X_608))),
inference(resolve,[$cnf( $equal(add(X_123,add(X_122,additive_inverse(additive_inverse(add(X_608,X_607))))),add(X_122,additive_inverse(additive_inverse(add(X_607,add(X_123,X_608)))))) )],[refute_0_619,refute_0_638]) ).
cnf(refute_0_640,plain,
( add(X_123,add(X_122,add(X_608,X_607))) != add(X_122,add(X_607,add(X_123,X_608)))
| add(X_122,add(X_607,add(X_123,X_608))) = add(X_123,add(X_122,add(X_608,X_607))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_123,add(X_122,add(X_608,X_607))))),bind(Y0,$fot(add(X_122,add(X_607,add(X_123,X_608)))))]]) ).
cnf(refute_0_641,plain,
add(X_122,add(X_607,add(X_123,X_608))) = add(X_123,add(X_122,add(X_608,X_607))),
inference(resolve,[$cnf( $equal(add(X_123,add(X_122,add(X_608,X_607))),add(X_122,add(X_607,add(X_123,X_608)))) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) = add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))),
inference(subst,[],[refute_0_641:[bind(X_122,$fot(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)))),bind(X_123,$fot(additive_identity)),bind(X_607,$fot(X_54)),bind(X_608,$fot(Z))]]) ).
cnf(refute_0_643,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) != add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54)))
| add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))) != add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54)))
| add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))))),bind(Y0,$fot(add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))))),bind(Z0,$fot(add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54)))))]]) ).
cnf(refute_0_644,plain,
( add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))) != add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54)))
| add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) ),
inference(resolve,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))),add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54)))) )],[refute_0_642,refute_0_643]) ).
cnf(refute_0_645,plain,
add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))),
inference(resolve,[$cnf( $equal(add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(Z,X_54))),add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54)))) )],[refute_0_612,refute_0_644]) ).
cnf(refute_0_646,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) != add(X_54,Z)
| add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) != add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54)))
| add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) = add(X_54,Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))),add(X_54,Z)) ),[0],$fot(add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))))]]) ).
cnf(refute_0_647,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))) != add(X_54,Z)
| add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) = add(X_54,Z) ),
inference(resolve,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))),add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54)))) )],[refute_0_645,refute_0_646]) ).
cnf(refute_0_648,plain,
add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) = add(X_54,Z),
inference(resolve,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(X_54,add(additive_identity,Z))),add(X_54,Z)) )],[refute_0_607,refute_0_647]) ).
cnf(refute_0_649,plain,
add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),X_44)) = X_44,
inference(subst,[],[refute_0_8:[bind(X_42,$fot(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))))]]) ).
cnf(refute_0_650,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),X_44)) != X_44
| additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))) != additive_identity
| add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) = X_44 ),
introduced(tautology,[equality,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),X_44)),X_44) ),[0,1,0],$fot(additive_identity)]]) ).
cnf(refute_0_651,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),X_44)) != X_44
| add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) = X_44 ),
inference(resolve,[$cnf( $equal(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),additive_identity) )],[refute_0_550,refute_0_650]) ).
cnf(refute_0_652,plain,
add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) = X_44,
inference(resolve,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_inverse(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768))),X_44)),X_44) )],[refute_0_649,refute_0_651]) ).
cnf(refute_0_653,plain,
add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)),
inference(subst,[],[refute_0_138:[bind(X,$fot(commutator(X_767,X_768))),bind(Y,$fot(commutator(additive_inverse(X_767),X_768))),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_654,plain,
add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)) = add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44),
inference(subst,[],[left_additive_identity:[bind(X,$fot(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)))]]) ).
cnf(refute_0_655,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44) != add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44))
| add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)) != add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)
| add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)))),bind(Y0,$fot(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44))),bind(Z0,$fot(add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44))))]]) ).
cnf(refute_0_656,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44) != add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44))
| add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)) ),
inference(resolve,[$cnf( $equal(add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)),add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)),
inference(resolve,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44),add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44))) )],[refute_0_653,refute_0_656]) ).
cnf(refute_0_658,plain,
add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) = add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)),
inference(subst,[],[refute_0_244:[bind(X,$fot(additive_identity)),bind(X_42,$fot(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)))),bind(X_43,$fot(X_44))]]) ).
cnf(refute_0_659,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) != add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44))
| add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)) != add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44))
| add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)))),bind(Y0,$fot(add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)))),bind(Z0,$fot(add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44))))]]) ).
cnf(refute_0_660,plain,
( add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)) != add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44))
| add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)) ),
inference(resolve,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)),add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) = add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)),
inference(resolve,[$cnf( $equal(add(additive_identity,add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),X_44)),add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44))) )],[refute_0_657,refute_0_660]) ).
cnf(refute_0_662,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) != X_44
| add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) != add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44))
| add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)) = X_44 ),
introduced(tautology,[equality,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)),X_44) ),[0],$fot(add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)))]]) ).
cnf(refute_0_663,plain,
( add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)) != X_44
| add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)) = X_44 ),
inference(resolve,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)),add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44))) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),X_44)) = X_44,
inference(resolve,[$cnf( $equal(add(add(commutator(X_767,X_768),commutator(additive_inverse(X_767),X_768)),add(additive_identity,X_44)),X_44) )],[refute_0_652,refute_0_663]) ).
cnf(refute_0_665,plain,
add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) = add(Z,X_54),
inference(subst,[],[refute_0_664:[bind(X_44,$fot(add(Z,X_54)))]]) ).
cnf(refute_0_666,plain,
( add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) != add(Z,X_54)
| add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) != add(X_54,Z)
| add(Z,X_54) = add(X_54,Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))),add(X_54,Z)) ),[0],$fot(add(Z,X_54))]]) ).
cnf(refute_0_667,plain,
( add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))) != add(X_54,Z)
| add(Z,X_54) = add(X_54,Z) ),
inference(resolve,[$cnf( $equal(add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))),add(Z,X_54)) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
add(Z,X_54) = add(X_54,Z),
inference(resolve,[$cnf( $equal(add(commutator(X_767,X_768),add(commutator(additive_inverse(X_767),X_768),add(Z,X_54))),add(X_54,Z)) )],[refute_0_648,refute_0_667]) ).
cnf(refute_0_669,plain,
( add(Z,X_54) != add(X_54,Z)
| add(X_54,Z) = add(Z,X_54) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(Z,X_54))),bind(Y0,$fot(add(X_54,Z)))]]) ).
cnf(refute_0_670,plain,
add(X_54,Z) = add(Z,X_54),
inference(resolve,[$cnf( $equal(add(Z,X_54),add(X_54,Z)) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) = add(commutator(X_769,X),multiply(X,additive_inverse(X_769))),
inference(subst,[],[refute_0_670:[bind(Z,$fot(commutator(X_769,X))),bind(X_54,$fot(multiply(X,additive_inverse(X_769))))]]) ).
cnf(refute_0_672,plain,
( add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) != add(commutator(X_769,X),multiply(X,additive_inverse(X_769)))
| add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) != additive_inverse(multiply(X_769,X))
| add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) = additive_inverse(multiply(X_769,X)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)))),bind(Y0,$fot(add(commutator(X_769,X),multiply(X,additive_inverse(X_769))))),bind(Z0,$fot(additive_inverse(multiply(X_769,X))))]]) ).
cnf(refute_0_673,plain,
( add(commutator(X_769,X),multiply(X,additive_inverse(X_769))) != additive_inverse(multiply(X_769,X))
| add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) = additive_inverse(multiply(X_769,X)) ),
inference(resolve,[$cnf( $equal(add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)),add(commutator(X_769,X),multiply(X,additive_inverse(X_769)))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) = additive_inverse(multiply(X_769,X)),
inference(resolve,[$cnf( $equal(add(commutator(X_769,X),multiply(X,additive_inverse(X_769))),additive_inverse(multiply(X_769,X))) )],[refute_0_590,refute_0_673]) ).
cnf(refute_0_675,plain,
( add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) != multiply(additive_inverse(X_769),X)
| add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) != additive_inverse(multiply(X_769,X))
| additive_inverse(multiply(X_769,X)) = multiply(additive_inverse(X_769),X) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)),multiply(additive_inverse(X_769),X)) ),[0],$fot(additive_inverse(multiply(X_769,X)))]]) ).
cnf(refute_0_676,plain,
( add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)) != multiply(additive_inverse(X_769),X)
| additive_inverse(multiply(X_769,X)) = multiply(additive_inverse(X_769),X) ),
inference(resolve,[$cnf( $equal(add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)),additive_inverse(multiply(X_769,X))) )],[refute_0_674,refute_0_675]) ).
cnf(refute_0_677,plain,
additive_inverse(multiply(X_769,X)) = multiply(additive_inverse(X_769),X),
inference(resolve,[$cnf( $equal(add(multiply(X,additive_inverse(X_769)),commutator(X_769,X)),multiply(additive_inverse(X_769),X)) )],[refute_0_569,refute_0_676]) ).
cnf(refute_0_678,plain,
( additive_inverse(multiply(X_769,X)) != multiply(additive_inverse(X_769),X)
| multiply(additive_inverse(X_769),X) = additive_inverse(multiply(X_769,X)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(multiply(X_769,X)))),bind(Y0,$fot(multiply(additive_inverse(X_769),X)))]]) ).
cnf(refute_0_679,plain,
multiply(additive_inverse(X_769),X) = additive_inverse(multiply(X_769,X)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_769,X)),multiply(additive_inverse(X_769),X)) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
multiply(additive_inverse(a),b) = additive_inverse(multiply(a,b)),
inference(subst,[],[refute_0_679:[bind(X,$fot(b)),bind(X_769,$fot(a))]]) ).
cnf(refute_0_681,plain,
additive_inverse(multiply(additive_inverse(a),b)) = additive_inverse(multiply(additive_inverse(a),b)),
introduced(tautology,[refl,[$fot(additive_inverse(multiply(additive_inverse(a),b)))]]) ).
cnf(refute_0_682,plain,
( multiply(additive_inverse(a),b) != additive_inverse(multiply(a,b))
| additive_inverse(multiply(additive_inverse(a),b)) != additive_inverse(multiply(additive_inverse(a),b))
| additive_inverse(multiply(additive_inverse(a),b)) = additive_inverse(additive_inverse(multiply(a,b))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(additive_inverse(a),b)),additive_inverse(multiply(additive_inverse(a),b))) ),[1,0],$fot(additive_inverse(multiply(a,b)))]]) ).
cnf(refute_0_683,plain,
( multiply(additive_inverse(a),b) != additive_inverse(multiply(a,b))
| additive_inverse(multiply(additive_inverse(a),b)) = additive_inverse(additive_inverse(multiply(a,b))) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(a),b)),additive_inverse(multiply(additive_inverse(a),b))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
additive_inverse(multiply(additive_inverse(a),b)) = additive_inverse(additive_inverse(multiply(a,b))),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(a),b),additive_inverse(multiply(a,b))) )],[refute_0_680,refute_0_683]) ).
cnf(refute_0_685,plain,
( additive_inverse(multiply(additive_inverse(a),b)) != additive_inverse(additive_inverse(multiply(a,b)))
| additive_inverse(additive_inverse(multiply(a,b))) != multiply(a,b)
| additive_inverse(multiply(additive_inverse(a),b)) = multiply(a,b) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(additive_inverse(multiply(additive_inverse(a),b)))),bind(Y0,$fot(additive_inverse(additive_inverse(multiply(a,b))))),bind(Z0,$fot(multiply(a,b)))]]) ).
cnf(refute_0_686,plain,
( additive_inverse(additive_inverse(multiply(a,b))) != multiply(a,b)
| additive_inverse(multiply(additive_inverse(a),b)) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(a),b)),additive_inverse(additive_inverse(multiply(a,b)))) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
additive_inverse(multiply(additive_inverse(a),b)) = multiply(a,b),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(multiply(a,b))),multiply(a,b)) )],[refute_0_469,refute_0_686]) ).
cnf(refute_0_688,plain,
( multiply(a,b) != multiply(a,b)
| additive_inverse(multiply(additive_inverse(a),b)) != multiply(a,b)
| additive_inverse(multiply(additive_inverse(a),b)) = multiply(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(additive_inverse(a),b)),multiply(a,b)) ),[1],$fot(multiply(a,b))]]) ).
cnf(refute_0_689,plain,
( multiply(a,b) != multiply(a,b)
| additive_inverse(multiply(additive_inverse(a),b)) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(a),b)),multiply(a,b)) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
multiply(a,b) != multiply(a,b),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(a),b)),multiply(a,b)) )],[refute_0_689,refute_0_468]) ).
cnf(refute_0_691,plain,
multiply(a,b) = multiply(a,b),
introduced(tautology,[refl,[$fot(multiply(a,b))]]) ).
cnf(refute_0_692,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(a,b)) )],[refute_0_691,refute_0_690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : RNG012-6 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.10 % Command : metis --show proof --show saturation %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Mon May 30 05:36:57 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.10/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 133.03/133.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 133.03/133.21
% 133.03/133.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 133.09/133.27
%------------------------------------------------------------------------------