%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG029-3 : TPTP v8.1.0. Bugfixed v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 20:35:49 EDT 2022
% Result : Unsatisfiable 8.18s 8.37s
% Output : CNFRefutation 8.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 84
% Syntax : Number of clauses : 336 ( 177 unt; 0 nHn; 159 RR)
% Number of literals : 563 ( 562 equ; 229 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 970 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_additive_identity,axiom,
add(additive_identity,X) = X ).
cnf(add_inverse,axiom,
add(additive_inverse(X),X) = additive_identity ).
cnf(sum_of_inverses,axiom,
additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X)) = X ).
cnf(multiply_over_add1,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).
cnf(inverse_product2,axiom,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ).
cnf(inverse_additive_identity,axiom,
additive_inverse(additive_identity) = additive_identity ).
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(right_moufang,hypothesis,
multiply(Z,multiply(X,multiply(Y,X))) = multiply(multiply(multiply(Z,X),Y),X) ).
cnf(left_moufang,hypothesis,
multiply(multiply(X,multiply(Y,X)),Z) = multiply(X,multiply(Y,multiply(X,Z))) ).
cnf(associator,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ).
cnf(associator_skew_symmetry1,axiom,
associator(Y,X,Z) = additive_inverse(associator(X,Y,Z)) ).
cnf(associator_skew_symmetry2,axiom,
associator(Z,Y,X) = additive_inverse(associator(X,Y,Z)) ).
cnf(prove_middle_law,negated_conjecture,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)) ).
cnf(refute_0_0,plain,
add(X_34,add(additive_inverse(X_34),X_36)) = add(add(X_34,additive_inverse(X_34)),X_36),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_34)),bind(Y,$fot(additive_inverse(X_34))),bind(Z,$fot(X_36))]]) ).
cnf(refute_0_1,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_2,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_3,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_5,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_for_addition,refute_0_4]) ).
cnf(refute_0_6,plain,
add(additive_inverse(X),X) = add(X,additive_inverse(X)),
inference(subst,[],[refute_0_5:[bind(Y,$fot(additive_inverse(X)))]]) ).
cnf(refute_0_7,plain,
( add(additive_inverse(X),X) != add(X,additive_inverse(X))
| add(additive_inverse(X),X) != additive_identity
| add(X,additive_inverse(X)) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X),X),additive_identity) ),[0],$fot(add(X,additive_inverse(X)))]]) ).
cnf(refute_0_8,plain,
( add(additive_inverse(X),X) != additive_identity
| add(X,additive_inverse(X)) = additive_identity ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X),X),add(X,additive_inverse(X))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
add(X,additive_inverse(X)) = additive_identity,
inference(resolve,[$cnf( $equal(add(additive_inverse(X),X),additive_identity) )],[add_inverse,refute_0_8]) ).
cnf(refute_0_10,plain,
add(X_34,additive_inverse(X_34)) = additive_identity,
inference(subst,[],[refute_0_9:[bind(X,$fot(X_34))]]) ).
cnf(refute_0_11,plain,
( add(X_34,add(additive_inverse(X_34),X_36)) != add(add(X_34,additive_inverse(X_34)),X_36)
| add(X_34,additive_inverse(X_34)) != additive_identity
| add(X_34,add(additive_inverse(X_34),X_36)) = add(additive_identity,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_34,add(additive_inverse(X_34),X_36)),add(add(X_34,additive_inverse(X_34)),X_36)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_12,plain,
( add(X_34,add(additive_inverse(X_34),X_36)) != add(add(X_34,additive_inverse(X_34)),X_36)
| add(X_34,add(additive_inverse(X_34),X_36)) = add(additive_identity,X_36) ),
inference(resolve,[$cnf( $equal(add(X_34,additive_inverse(X_34)),additive_identity) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
add(X_34,add(additive_inverse(X_34),X_36)) = add(additive_identity,X_36),
inference(resolve,[$cnf( $equal(add(X_34,add(additive_inverse(X_34),X_36)),add(add(X_34,additive_inverse(X_34)),X_36)) )],[refute_0_0,refute_0_12]) ).
cnf(refute_0_14,plain,
add(additive_identity,X_36) = X_36,
inference(subst,[],[left_additive_identity:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_15,plain,
( add(X_34,add(additive_inverse(X_34),X_36)) != add(additive_identity,X_36)
| add(additive_identity,X_36) != X_36
| add(X_34,add(additive_inverse(X_34),X_36)) = X_36 ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_34,add(additive_inverse(X_34),X_36)),X_36) ),[0],$fot(add(additive_identity,X_36))]]) ).
cnf(refute_0_16,plain,
( add(X_34,add(additive_inverse(X_34),X_36)) != add(additive_identity,X_36)
| add(X_34,add(additive_inverse(X_34),X_36)) = X_36 ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_36),X_36) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
add(X_34,add(additive_inverse(X_34),X_36)) = X_36,
inference(resolve,[$cnf( $equal(add(X_34,add(additive_inverse(X_34),X_36)),add(additive_identity,X_36)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
add(X_37,add(additive_inverse(X_37),X_38)) = X_38,
inference(subst,[],[refute_0_17:[bind(X_34,$fot(X_37)),bind(X_36,$fot(X_38))]]) ).
cnf(refute_0_19,plain,
add(X_38,additive_inverse(X_37)) = add(additive_inverse(X_37),X_38),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_38)),bind(Y,$fot(additive_inverse(X_37)))]]) ).
cnf(refute_0_20,plain,
( add(X_38,additive_inverse(X_37)) != add(additive_inverse(X_37),X_38)
| add(additive_inverse(X_37),X_38) = add(X_38,additive_inverse(X_37)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(add(X_38,additive_inverse(X_37)))),bind(Y0,$fot(add(additive_inverse(X_37),X_38)))]]) ).
cnf(refute_0_21,plain,
add(additive_inverse(X_37),X_38) = add(X_38,additive_inverse(X_37)),
inference(resolve,[$cnf( $equal(add(X_38,additive_inverse(X_37)),add(additive_inverse(X_37),X_38)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( add(X_37,add(additive_inverse(X_37),X_38)) != X_38
| add(additive_inverse(X_37),X_38) != add(X_38,additive_inverse(X_37))
| add(X_37,add(X_38,additive_inverse(X_37))) = X_38 ),
introduced(tautology,[equality,[$cnf( $equal(add(X_37,add(additive_inverse(X_37),X_38)),X_38) ),[0,1],$fot(add(X_38,additive_inverse(X_37)))]]) ).
cnf(refute_0_23,plain,
( add(X_37,add(additive_inverse(X_37),X_38)) != X_38
| add(X_37,add(X_38,additive_inverse(X_37))) = X_38 ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_37),X_38),add(X_38,additive_inverse(X_37))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
add(X_37,add(X_38,additive_inverse(X_37))) = X_38,
inference(resolve,[$cnf( $equal(add(X_37,add(additive_inverse(X_37),X_38)),X_38) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
add(multiply(X_70,multiply(X_71,X_72)),add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72))))) = multiply(multiply(X_70,X_71),X_72),
inference(subst,[],[refute_0_24:[bind(X_37,$fot(multiply(X_70,multiply(X_71,X_72)))),bind(X_38,$fot(multiply(multiply(X_70,X_71),X_72)))]]) ).
cnf(refute_0_26,plain,
associator(X_70,X_71,X_72) = add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))),
inference(subst,[],[associator:[bind(X,$fot(X_70)),bind(Y,$fot(X_71)),bind(Z,$fot(X_72))]]) ).
cnf(refute_0_27,plain,
( associator(X_70,X_71,X_72) != add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72))))
| add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))) = associator(X_70,X_71,X_72) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(associator(X_70,X_71,X_72))),bind(Y0,$fot(add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72))))))]]) ).
cnf(refute_0_28,plain,
add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))) = associator(X_70,X_71,X_72),
inference(resolve,[$cnf( $equal(associator(X_70,X_71,X_72),add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( add(multiply(X_70,multiply(X_71,X_72)),add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72))))) != multiply(multiply(X_70,X_71),X_72)
| add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))) != associator(X_70,X_71,X_72)
| add(multiply(X_70,multiply(X_71,X_72)),associator(X_70,X_71,X_72)) = multiply(multiply(X_70,X_71),X_72) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_70,multiply(X_71,X_72)),add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72))))),multiply(multiply(X_70,X_71),X_72)) ),[0,1],$fot(associator(X_70,X_71,X_72))]]) ).
cnf(refute_0_30,plain,
( add(multiply(X_70,multiply(X_71,X_72)),add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72))))) != multiply(multiply(X_70,X_71),X_72)
| add(multiply(X_70,multiply(X_71,X_72)),associator(X_70,X_71,X_72)) = multiply(multiply(X_70,X_71),X_72) ),
inference(resolve,[$cnf( $equal(add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))),associator(X_70,X_71,X_72)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
add(multiply(X_70,multiply(X_71,X_72)),associator(X_70,X_71,X_72)) = multiply(multiply(X_70,X_71),X_72),
inference(resolve,[$cnf( $equal(add(multiply(X_70,multiply(X_71,X_72)),add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72))))),multiply(multiply(X_70,X_71),X_72)) )],[refute_0_25,refute_0_30]) ).
cnf(refute_0_32,plain,
add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) = add(add(associator(X_60,X_61,X_62),associator(X_60,X_62,X_61)),Z),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(associator(X_60,X_61,X_62))),bind(Y,$fot(associator(X_60,X_62,X_61)))]]) ).
cnf(refute_0_33,plain,
add(associator(X_27,X_28,X_29),additive_inverse(associator(X_27,X_28,X_29))) = additive_identity,
inference(subst,[],[refute_0_9:[bind(X,$fot(associator(X_27,X_28,X_29)))]]) ).
cnf(refute_0_34,plain,
associator(X_28,X_27,X_29) = additive_inverse(associator(X_27,X_28,X_29)),
inference(subst,[],[associator_skew_symmetry1:[bind(X,$fot(X_27)),bind(Y,$fot(X_28)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_35,plain,
( associator(X_28,X_27,X_29) != additive_inverse(associator(X_27,X_28,X_29))
| additive_inverse(associator(X_27,X_28,X_29)) = associator(X_28,X_27,X_29) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(associator(X_28,X_27,X_29))),bind(Y0,$fot(additive_inverse(associator(X_27,X_28,X_29))))]]) ).
cnf(refute_0_36,plain,
additive_inverse(associator(X_27,X_28,X_29)) = associator(X_28,X_27,X_29),
inference(resolve,[$cnf( $equal(associator(X_28,X_27,X_29),additive_inverse(associator(X_27,X_28,X_29))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( add(associator(X_27,X_28,X_29),additive_inverse(associator(X_27,X_28,X_29))) != additive_identity
| additive_inverse(associator(X_27,X_28,X_29)) != associator(X_28,X_27,X_29)
| add(associator(X_27,X_28,X_29),associator(X_28,X_27,X_29)) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_27,X_28,X_29),additive_inverse(associator(X_27,X_28,X_29))),additive_identity) ),[0,1],$fot(associator(X_28,X_27,X_29))]]) ).
cnf(refute_0_38,plain,
( add(associator(X_27,X_28,X_29),additive_inverse(associator(X_27,X_28,X_29))) != additive_identity
| add(associator(X_27,X_28,X_29),associator(X_28,X_27,X_29)) = additive_identity ),
inference(resolve,[$cnf( $equal(additive_inverse(associator(X_27,X_28,X_29)),associator(X_28,X_27,X_29)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
add(associator(X_27,X_28,X_29),associator(X_28,X_27,X_29)) = additive_identity,
inference(resolve,[$cnf( $equal(add(associator(X_27,X_28,X_29),additive_inverse(associator(X_27,X_28,X_29))),additive_identity) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
add(associator(X_57,X_58,X_59),associator(X_58,X_57,X_59)) = additive_identity,
inference(subst,[],[refute_0_39:[bind(X_27,$fot(X_57)),bind(X_28,$fot(X_58)),bind(X_29,$fot(X_59))]]) ).
cnf(refute_0_41,plain,
( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z))
| additive_inverse(associator(X,Y,Z)) = associator(Y,X,Z) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(associator(Y,X,Z))),bind(Y0,$fot(additive_inverse(associator(X,Y,Z))))]]) ).
cnf(refute_0_42,plain,
additive_inverse(associator(X,Y,Z)) = associator(Y,X,Z),
inference(resolve,[$cnf( $equal(associator(Y,X,Z),additive_inverse(associator(X,Y,Z))) )],[associator_skew_symmetry1,refute_0_41]) ).
cnf(refute_0_43,plain,
( additive_inverse(associator(X,Y,Z)) != associator(Y,X,Z)
| associator(Z,Y,X) != additive_inverse(associator(X,Y,Z))
| associator(Z,Y,X) = associator(Y,X,Z) ),
introduced(tautology,[equality,[$cnf( $equal(associator(Z,Y,X),additive_inverse(associator(X,Y,Z))) ),[1],$fot(associator(Y,X,Z))]]) ).
cnf(refute_0_44,plain,
( associator(Z,Y,X) != additive_inverse(associator(X,Y,Z))
| associator(Z,Y,X) = associator(Y,X,Z) ),
inference(resolve,[$cnf( $equal(additive_inverse(associator(X,Y,Z)),associator(Y,X,Z)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
associator(Z,Y,X) = associator(Y,X,Z),
inference(resolve,[$cnf( $equal(associator(Z,Y,X),additive_inverse(associator(X,Y,Z))) )],[associator_skew_symmetry2,refute_0_44]) ).
cnf(refute_0_46,plain,
associator(X_58,X_57,X_59) = associator(X_57,X_59,X_58),
inference(subst,[],[refute_0_45:[bind(X,$fot(X_59)),bind(Y,$fot(X_57)),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_47,plain,
( add(associator(X_57,X_58,X_59),associator(X_58,X_57,X_59)) != additive_identity
| associator(X_58,X_57,X_59) != associator(X_57,X_59,X_58)
| add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58)) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_57,X_58,X_59),associator(X_58,X_57,X_59)),additive_identity) ),[0,1],$fot(associator(X_57,X_59,X_58))]]) ).
cnf(refute_0_48,plain,
( add(associator(X_57,X_58,X_59),associator(X_58,X_57,X_59)) != additive_identity
| add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58)) = additive_identity ),
inference(resolve,[$cnf( $equal(associator(X_58,X_57,X_59),associator(X_57,X_59,X_58)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58)) = additive_identity,
inference(resolve,[$cnf( $equal(add(associator(X_57,X_58,X_59),associator(X_58,X_57,X_59)),additive_identity) )],[refute_0_40,refute_0_48]) ).
cnf(refute_0_50,plain,
add(associator(X_60,X_61,X_62),associator(X_60,X_62,X_61)) = additive_identity,
inference(subst,[],[refute_0_49:[bind(X_57,$fot(X_60)),bind(X_58,$fot(X_61)),bind(X_59,$fot(X_62))]]) ).
cnf(refute_0_51,plain,
( add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) != add(add(associator(X_60,X_61,X_62),associator(X_60,X_62,X_61)),Z)
| add(associator(X_60,X_61,X_62),associator(X_60,X_62,X_61)) != additive_identity
| add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) = add(additive_identity,Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)),add(add(associator(X_60,X_61,X_62),associator(X_60,X_62,X_61)),Z)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_52,plain,
( add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) != add(add(associator(X_60,X_61,X_62),associator(X_60,X_62,X_61)),Z)
| add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) = add(additive_identity,Z) ),
inference(resolve,[$cnf( $equal(add(associator(X_60,X_61,X_62),associator(X_60,X_62,X_61)),additive_identity) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) = add(additive_identity,Z),
inference(resolve,[$cnf( $equal(add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)),add(add(associator(X_60,X_61,X_62),associator(X_60,X_62,X_61)),Z)) )],[refute_0_32,refute_0_52]) ).
cnf(refute_0_54,plain,
add(additive_identity,Z) = Z,
inference(subst,[],[left_additive_identity:[bind(X,$fot(Z))]]) ).
cnf(refute_0_55,plain,
( add(additive_identity,Z) != Z
| add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) != add(additive_identity,Z)
| add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) = Z ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)),add(additive_identity,Z)) ),[1],$fot(Z)]]) ).
cnf(refute_0_56,plain,
( add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) != add(additive_identity,Z)
| add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) = Z ),
inference(resolve,[$cnf( $equal(add(additive_identity,Z),Z) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)) = Z,
inference(resolve,[$cnf( $equal(add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),Z)),add(additive_identity,Z)) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
add(associator(X_64,X_65,X_66),add(associator(X_64,X_66,X_65),add(X_38,additive_inverse(associator(X_64,X_66,X_65))))) = add(X_38,additive_inverse(associator(X_64,X_66,X_65))),
inference(subst,[],[refute_0_57:[bind(Z,$fot(add(X_38,additive_inverse(associator(X_64,X_66,X_65))))),bind(X_60,$fot(X_64)),bind(X_61,$fot(X_65)),bind(X_62,$fot(X_66))]]) ).
cnf(refute_0_59,plain,
add(associator(X_64,X_66,X_65),add(X_38,additive_inverse(associator(X_64,X_66,X_65)))) = X_38,
inference(subst,[],[refute_0_24:[bind(X_37,$fot(associator(X_64,X_66,X_65)))]]) ).
cnf(refute_0_60,plain,
( add(associator(X_64,X_65,X_66),add(associator(X_64,X_66,X_65),add(X_38,additive_inverse(associator(X_64,X_66,X_65))))) != add(X_38,additive_inverse(associator(X_64,X_66,X_65)))
| add(associator(X_64,X_66,X_65),add(X_38,additive_inverse(associator(X_64,X_66,X_65)))) != X_38
| add(associator(X_64,X_65,X_66),X_38) = add(X_38,additive_inverse(associator(X_64,X_66,X_65))) ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_64,X_65,X_66),add(associator(X_64,X_66,X_65),add(X_38,additive_inverse(associator(X_64,X_66,X_65))))),add(X_38,additive_inverse(associator(X_64,X_66,X_65)))) ),[0,1],$fot(X_38)]]) ).
cnf(refute_0_61,plain,
( add(associator(X_64,X_65,X_66),add(associator(X_64,X_66,X_65),add(X_38,additive_inverse(associator(X_64,X_66,X_65))))) != add(X_38,additive_inverse(associator(X_64,X_66,X_65)))
| add(associator(X_64,X_65,X_66),X_38) = add(X_38,additive_inverse(associator(X_64,X_66,X_65))) ),
inference(resolve,[$cnf( $equal(add(associator(X_64,X_66,X_65),add(X_38,additive_inverse(associator(X_64,X_66,X_65)))),X_38) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
add(associator(X_64,X_65,X_66),X_38) = add(X_38,additive_inverse(associator(X_64,X_66,X_65))),
inference(resolve,[$cnf( $equal(add(associator(X_64,X_65,X_66),add(associator(X_64,X_66,X_65),add(X_38,additive_inverse(associator(X_64,X_66,X_65))))),add(X_38,additive_inverse(associator(X_64,X_66,X_65)))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
additive_inverse(associator(X_64,X_66,X_65)) = associator(X_66,X_64,X_65),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_64)),bind(Y,$fot(X_66)),bind(Z,$fot(X_65))]]) ).
cnf(refute_0_64,plain,
add(X_38,additive_inverse(associator(X_64,X_66,X_65))) = add(X_38,additive_inverse(associator(X_64,X_66,X_65))),
introduced(tautology,[refl,[$fot(add(X_38,additive_inverse(associator(X_64,X_66,X_65))))]]) ).
cnf(refute_0_65,plain,
( add(X_38,additive_inverse(associator(X_64,X_66,X_65))) != add(X_38,additive_inverse(associator(X_64,X_66,X_65)))
| additive_inverse(associator(X_64,X_66,X_65)) != associator(X_66,X_64,X_65)
| add(X_38,additive_inverse(associator(X_64,X_66,X_65))) = add(X_38,associator(X_66,X_64,X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_38,additive_inverse(associator(X_64,X_66,X_65))),add(X_38,additive_inverse(associator(X_64,X_66,X_65)))) ),[1,1],$fot(associator(X_66,X_64,X_65))]]) ).
cnf(refute_0_66,plain,
( additive_inverse(associator(X_64,X_66,X_65)) != associator(X_66,X_64,X_65)
| add(X_38,additive_inverse(associator(X_64,X_66,X_65))) = add(X_38,associator(X_66,X_64,X_65)) ),
inference(resolve,[$cnf( $equal(add(X_38,additive_inverse(associator(X_64,X_66,X_65))),add(X_38,additive_inverse(associator(X_64,X_66,X_65)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
add(X_38,additive_inverse(associator(X_64,X_66,X_65))) = add(X_38,associator(X_66,X_64,X_65)),
inference(resolve,[$cnf( $equal(additive_inverse(associator(X_64,X_66,X_65)),associator(X_66,X_64,X_65)) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( add(X_38,additive_inverse(associator(X_64,X_66,X_65))) != add(X_38,associator(X_66,X_64,X_65))
| add(associator(X_64,X_65,X_66),X_38) != add(X_38,additive_inverse(associator(X_64,X_66,X_65)))
| add(associator(X_64,X_65,X_66),X_38) = add(X_38,associator(X_66,X_64,X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_64,X_65,X_66),X_38),add(X_38,additive_inverse(associator(X_64,X_66,X_65)))) ),[1],$fot(add(X_38,associator(X_66,X_64,X_65)))]]) ).
cnf(refute_0_69,plain,
( add(associator(X_64,X_65,X_66),X_38) != add(X_38,additive_inverse(associator(X_64,X_66,X_65)))
| add(associator(X_64,X_65,X_66),X_38) = add(X_38,associator(X_66,X_64,X_65)) ),
inference(resolve,[$cnf( $equal(add(X_38,additive_inverse(associator(X_64,X_66,X_65))),add(X_38,associator(X_66,X_64,X_65))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
add(associator(X_64,X_65,X_66),X_38) = add(X_38,associator(X_66,X_64,X_65)),
inference(resolve,[$cnf( $equal(add(associator(X_64,X_65,X_66),X_38),add(X_38,additive_inverse(associator(X_64,X_66,X_65)))) )],[refute_0_62,refute_0_69]) ).
cnf(refute_0_71,plain,
( add(associator(X_64,X_65,X_66),X_38) != add(X_38,associator(X_66,X_64,X_65))
| add(X_38,associator(X_66,X_64,X_65)) = add(associator(X_64,X_65,X_66),X_38) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(add(associator(X_64,X_65,X_66),X_38))),bind(Y0,$fot(add(X_38,associator(X_66,X_64,X_65))))]]) ).
cnf(refute_0_72,plain,
add(X_38,associator(X_66,X_64,X_65)) = add(associator(X_64,X_65,X_66),X_38),
inference(resolve,[$cnf( $equal(add(associator(X_64,X_65,X_66),X_38),add(X_38,associator(X_66,X_64,X_65))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
add(multiply(X_70,multiply(X_71,X_72)),associator(X_70,X_71,X_72)) = add(associator(X_71,X_72,X_70),multiply(X_70,multiply(X_71,X_72))),
inference(subst,[],[refute_0_72:[bind(X_38,$fot(multiply(X_70,multiply(X_71,X_72)))),bind(X_64,$fot(X_71)),bind(X_65,$fot(X_72)),bind(X_66,$fot(X_70))]]) ).
cnf(refute_0_74,plain,
( add(multiply(X_70,multiply(X_71,X_72)),associator(X_70,X_71,X_72)) != multiply(multiply(X_70,X_71),X_72)
| add(multiply(X_70,multiply(X_71,X_72)),associator(X_70,X_71,X_72)) != add(associator(X_71,X_72,X_70),multiply(X_70,multiply(X_71,X_72)))
| add(associator(X_71,X_72,X_70),multiply(X_70,multiply(X_71,X_72))) = multiply(multiply(X_70,X_71),X_72) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_70,multiply(X_71,X_72)),associator(X_70,X_71,X_72)),multiply(multiply(X_70,X_71),X_72)) ),[0],$fot(add(associator(X_71,X_72,X_70),multiply(X_70,multiply(X_71,X_72))))]]) ).
cnf(refute_0_75,plain,
( add(multiply(X_70,multiply(X_71,X_72)),associator(X_70,X_71,X_72)) != multiply(multiply(X_70,X_71),X_72)
| add(associator(X_71,X_72,X_70),multiply(X_70,multiply(X_71,X_72))) = multiply(multiply(X_70,X_71),X_72) ),
inference(resolve,[$cnf( $equal(add(multiply(X_70,multiply(X_71,X_72)),associator(X_70,X_71,X_72)),add(associator(X_71,X_72,X_70),multiply(X_70,multiply(X_71,X_72)))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
add(associator(X_71,X_72,X_70),multiply(X_70,multiply(X_71,X_72))) = multiply(multiply(X_70,X_71),X_72),
inference(resolve,[$cnf( $equal(add(multiply(X_70,multiply(X_71,X_72)),associator(X_70,X_71,X_72)),multiply(multiply(X_70,X_71),X_72)) )],[refute_0_31,refute_0_75]) ).
cnf(refute_0_77,plain,
add(associator(X_343,multiply(X_151,X_342),X_342),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) = multiply(multiply(X_342,X_343),multiply(X_151,X_342)),
inference(subst,[],[refute_0_76:[bind(X_70,$fot(X_342)),bind(X_71,$fot(X_343)),bind(X_72,$fot(multiply(X_151,X_342)))]]) ).
cnf(refute_0_78,plain,
associator(Z,Y,multiply(X_151,Z)) = associator(Y,multiply(X_151,Z),Z),
inference(subst,[],[refute_0_45:[bind(X,$fot(multiply(X_151,Z)))]]) ).
cnf(refute_0_79,plain,
associator(X,multiply(X_130,X),Z) = add(multiply(multiply(X,multiply(X_130,X)),Z),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))),
inference(subst,[],[associator:[bind(Y,$fot(multiply(X_130,X)))]]) ).
cnf(refute_0_80,plain,
multiply(multiply(X,multiply(X_130,X)),Z) = multiply(X,multiply(X_130,multiply(X,Z))),
inference(subst,[],[left_moufang:[bind(Y,$fot(X_130))]]) ).
cnf(refute_0_81,plain,
( multiply(multiply(X,multiply(X_130,X)),Z) != multiply(X,multiply(X_130,multiply(X,Z)))
| associator(X,multiply(X_130,X),Z) != add(multiply(multiply(X,multiply(X_130,X)),Z),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))
| associator(X,multiply(X_130,X),Z) = add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))) ),
introduced(tautology,[equality,[$cnf( $equal(associator(X,multiply(X_130,X),Z),add(multiply(multiply(X,multiply(X_130,X)),Z),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))) ),[1,0],$fot(multiply(X,multiply(X_130,multiply(X,Z))))]]) ).
cnf(refute_0_82,plain,
( associator(X,multiply(X_130,X),Z) != add(multiply(multiply(X,multiply(X_130,X)),Z),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))
| associator(X,multiply(X_130,X),Z) = add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,multiply(X_130,X)),Z),multiply(X,multiply(X_130,multiply(X,Z)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
associator(X,multiply(X_130,X),Z) = add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))),
inference(resolve,[$cnf( $equal(associator(X,multiply(X_130,X),Z),add(multiply(multiply(X,multiply(X_130,X)),Z),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
associator(multiply(X_115,Z),Y,Z) = add(multiply(multiply(multiply(X_115,Z),Y),Z),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z)))),
inference(subst,[],[associator:[bind(X,$fot(multiply(X_115,Z)))]]) ).
cnf(refute_0_85,plain,
multiply(X_115,multiply(Z,multiply(Y,Z))) = multiply(multiply(multiply(X_115,Z),Y),Z),
inference(subst,[],[right_moufang:[bind(X,$fot(Z)),bind(Z,$fot(X_115))]]) ).
cnf(refute_0_86,plain,
( multiply(X_115,multiply(Z,multiply(Y,Z))) != multiply(multiply(multiply(X_115,Z),Y),Z)
| multiply(multiply(multiply(X_115,Z),Y),Z) = multiply(X_115,multiply(Z,multiply(Y,Z))) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(X_115,multiply(Z,multiply(Y,Z))))),bind(Y0,$fot(multiply(multiply(multiply(X_115,Z),Y),Z)))]]) ).
cnf(refute_0_87,plain,
multiply(multiply(multiply(X_115,Z),Y),Z) = multiply(X_115,multiply(Z,multiply(Y,Z))),
inference(resolve,[$cnf( $equal(multiply(X_115,multiply(Z,multiply(Y,Z))),multiply(multiply(multiply(X_115,Z),Y),Z)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( multiply(multiply(multiply(X_115,Z),Y),Z) != multiply(X_115,multiply(Z,multiply(Y,Z)))
| associator(multiply(X_115,Z),Y,Z) != add(multiply(multiply(multiply(X_115,Z),Y),Z),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))
| associator(multiply(X_115,Z),Y,Z) = add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z)))) ),
introduced(tautology,[equality,[$cnf( $equal(associator(multiply(X_115,Z),Y,Z),add(multiply(multiply(multiply(X_115,Z),Y),Z),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))) ),[1,0],$fot(multiply(X_115,multiply(Z,multiply(Y,Z))))]]) ).
cnf(refute_0_89,plain,
( associator(multiply(X_115,Z),Y,Z) != add(multiply(multiply(multiply(X_115,Z),Y),Z),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))
| associator(multiply(X_115,Z),Y,Z) = add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_115,Z),Y),Z),multiply(X_115,multiply(Z,multiply(Y,Z)))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
associator(multiply(X_115,Z),Y,Z) = add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z)))),
inference(resolve,[$cnf( $equal(associator(multiply(X_115,Z),Y,Z),add(multiply(multiply(multiply(X_115,Z),Y),Z),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))) )],[refute_0_84,refute_0_89]) ).
cnf(refute_0_91,plain,
( associator(Z,Y,X) != associator(Y,X,Z)
| associator(Y,X,Z) = associator(Z,Y,X) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(associator(Z,Y,X))),bind(Y0,$fot(associator(Y,X,Z)))]]) ).
cnf(refute_0_92,plain,
associator(Y,X,Z) = associator(Z,Y,X),
inference(resolve,[$cnf( $equal(associator(Z,Y,X),associator(Y,X,Z)) )],[refute_0_45,refute_0_91]) ).
cnf(refute_0_93,plain,
associator(multiply(X_115,Z),Y,Z) = associator(Z,multiply(X_115,Z),Y),
inference(subst,[],[refute_0_92:[bind(X,$fot(Y)),bind(Y,$fot(multiply(X_115,Z)))]]) ).
cnf(refute_0_94,plain,
( associator(multiply(X_115,Z),Y,Z) != add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))
| associator(multiply(X_115,Z),Y,Z) != associator(Z,multiply(X_115,Z),Y)
| associator(Z,multiply(X_115,Z),Y) = add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z)))) ),
introduced(tautology,[equality,[$cnf( $equal(associator(multiply(X_115,Z),Y,Z),add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))) ),[0],$fot(associator(Z,multiply(X_115,Z),Y))]]) ).
cnf(refute_0_95,plain,
( associator(multiply(X_115,Z),Y,Z) != add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))
| associator(Z,multiply(X_115,Z),Y) = add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z)))) ),
inference(resolve,[$cnf( $equal(associator(multiply(X_115,Z),Y,Z),associator(Z,multiply(X_115,Z),Y)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
add(additive_inverse(X_9),additive_inverse(X_8)) = add(additive_inverse(X_8),additive_inverse(X_9)),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(additive_inverse(X_9))),bind(Y,$fot(additive_inverse(X_8)))]]) ).
cnf(refute_0_97,plain,
additive_inverse(add(X_8,X_9)) = add(additive_inverse(X_8),additive_inverse(X_9)),
inference(subst,[],[sum_of_inverses:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_98,plain,
( additive_inverse(add(X_8,X_9)) != add(additive_inverse(X_8),additive_inverse(X_9))
| add(additive_inverse(X_8),additive_inverse(X_9)) = additive_inverse(add(X_8,X_9)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(additive_inverse(add(X_8,X_9)))),bind(Y0,$fot(add(additive_inverse(X_8),additive_inverse(X_9))))]]) ).
cnf(refute_0_99,plain,
add(additive_inverse(X_8),additive_inverse(X_9)) = additive_inverse(add(X_8,X_9)),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_8,X_9)),add(additive_inverse(X_8),additive_inverse(X_9))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( add(additive_inverse(X_8),additive_inverse(X_9)) != additive_inverse(add(X_8,X_9))
| add(additive_inverse(X_9),additive_inverse(X_8)) != add(additive_inverse(X_8),additive_inverse(X_9))
| add(additive_inverse(X_9),additive_inverse(X_8)) = additive_inverse(add(X_8,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X_9),additive_inverse(X_8)),add(additive_inverse(X_8),additive_inverse(X_9))) ),[1],$fot(additive_inverse(add(X_8,X_9)))]]) ).
cnf(refute_0_101,plain,
( add(additive_inverse(X_9),additive_inverse(X_8)) != add(additive_inverse(X_8),additive_inverse(X_9))
| add(additive_inverse(X_9),additive_inverse(X_8)) = additive_inverse(add(X_8,X_9)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_8),additive_inverse(X_9)),additive_inverse(add(X_8,X_9))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
add(additive_inverse(X_9),additive_inverse(X_8)) = additive_inverse(add(X_8,X_9)),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_9),additive_inverse(X_8)),add(additive_inverse(X_8),additive_inverse(X_9))) )],[refute_0_96,refute_0_101]) ).
cnf(refute_0_103,plain,
( additive_inverse(add(X,Y)) != add(additive_inverse(X),additive_inverse(Y))
| add(additive_inverse(X),additive_inverse(Y)) = additive_inverse(add(X,Y)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(additive_inverse(add(X,Y)))),bind(Y0,$fot(add(additive_inverse(X),additive_inverse(Y))))]]) ).
cnf(refute_0_104,plain,
add(additive_inverse(X),additive_inverse(Y)) = additive_inverse(add(X,Y)),
inference(resolve,[$cnf( $equal(additive_inverse(add(X,Y)),add(additive_inverse(X),additive_inverse(Y))) )],[sum_of_inverses,refute_0_103]) ).
cnf(refute_0_105,plain,
add(additive_inverse(X_9),additive_inverse(X_8)) = additive_inverse(add(X_9,X_8)),
inference(subst,[],[refute_0_104:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_106,plain,
( add(additive_inverse(X_9),additive_inverse(X_8)) != additive_inverse(add(X_8,X_9))
| add(additive_inverse(X_9),additive_inverse(X_8)) != additive_inverse(add(X_9,X_8))
| additive_inverse(add(X_9,X_8)) = additive_inverse(add(X_8,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X_9),additive_inverse(X_8)),additive_inverse(add(X_8,X_9))) ),[0],$fot(additive_inverse(add(X_9,X_8)))]]) ).
cnf(refute_0_107,plain,
( add(additive_inverse(X_9),additive_inverse(X_8)) != additive_inverse(add(X_8,X_9))
| additive_inverse(add(X_9,X_8)) = additive_inverse(add(X_8,X_9)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_9),additive_inverse(X_8)),additive_inverse(add(X_9,X_8))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
additive_inverse(add(X_9,X_8)) = additive_inverse(add(X_8,X_9)),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_9),additive_inverse(X_8)),additive_inverse(add(X_8,X_9))) )],[refute_0_102,refute_0_107]) ).
cnf(refute_0_109,plain,
additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) = additive_inverse(add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72))))),
inference(subst,[],[refute_0_108:[bind(X_8,$fot(multiply(multiply(X_70,X_71),X_72))),bind(X_9,$fot(additive_inverse(multiply(X_70,multiply(X_71,X_72)))))]]) ).
cnf(refute_0_110,plain,
( add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))) != associator(X_70,X_71,X_72)
| additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) != additive_inverse(add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))))
| additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) = additive_inverse(associator(X_70,X_71,X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))),additive_inverse(add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))))) ),[1,0],$fot(associator(X_70,X_71,X_72))]]) ).
cnf(refute_0_111,plain,
( additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) != additive_inverse(add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))))
| additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) = additive_inverse(associator(X_70,X_71,X_72)) ),
inference(resolve,[$cnf( $equal(add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))),associator(X_70,X_71,X_72)) )],[refute_0_28,refute_0_110]) ).
cnf(refute_0_112,plain,
additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) = additive_inverse(associator(X_70,X_71,X_72)),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))),additive_inverse(add(multiply(multiply(X_70,X_71),X_72),additive_inverse(multiply(X_70,multiply(X_71,X_72)))))) )],[refute_0_109,refute_0_111]) ).
cnf(refute_0_113,plain,
additive_inverse(add(additive_inverse(X),X_9)) = add(additive_inverse(additive_inverse(X)),additive_inverse(X_9)),
inference(subst,[],[sum_of_inverses:[bind(X,$fot(additive_inverse(X))),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_114,plain,
( additive_inverse(add(additive_inverse(X),X_9)) != add(additive_inverse(additive_inverse(X)),additive_inverse(X_9))
| additive_inverse(additive_inverse(X)) != X
| additive_inverse(add(additive_inverse(X),X_9)) = add(X,additive_inverse(X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(additive_inverse(X),X_9)),add(additive_inverse(additive_inverse(X)),additive_inverse(X_9))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_115,plain,
( additive_inverse(add(additive_inverse(X),X_9)) != add(additive_inverse(additive_inverse(X)),additive_inverse(X_9))
| additive_inverse(add(additive_inverse(X),X_9)) = add(X,additive_inverse(X_9)) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_114]) ).
cnf(refute_0_116,plain,
additive_inverse(add(additive_inverse(X),X_9)) = add(X,additive_inverse(X_9)),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(X),X_9)),add(additive_inverse(additive_inverse(X)),additive_inverse(X_9))) )],[refute_0_113,refute_0_115]) ).
cnf(refute_0_117,plain,
additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) = add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))),
inference(subst,[],[refute_0_116:[bind(X,$fot(multiply(X_70,multiply(X_71,X_72)))),bind(X_9,$fot(multiply(multiply(X_70,X_71),X_72)))]]) ).
cnf(refute_0_118,plain,
( additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) != add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72)))
| additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) != additive_inverse(associator(X_70,X_71,X_72))
| add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))) = additive_inverse(associator(X_70,X_71,X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))),additive_inverse(associator(X_70,X_71,X_72))) ),[0],$fot(add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))))]]) ).
cnf(refute_0_119,plain,
( additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) != additive_inverse(associator(X_70,X_71,X_72))
| add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))) = additive_inverse(associator(X_70,X_71,X_72)) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))),add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72)))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
additive_inverse(associator(X_70,X_71,X_72)) = associator(X_71,X_70,X_72),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_70)),bind(Y,$fot(X_71)),bind(Z,$fot(X_72))]]) ).
cnf(refute_0_121,plain,
( add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))) != additive_inverse(associator(X_70,X_71,X_72))
| additive_inverse(associator(X_70,X_71,X_72)) != associator(X_71,X_70,X_72)
| add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))) = associator(X_71,X_70,X_72) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))),associator(X_71,X_70,X_72)) ),[0],$fot(additive_inverse(associator(X_70,X_71,X_72)))]]) ).
cnf(refute_0_122,plain,
( add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))) != additive_inverse(associator(X_70,X_71,X_72))
| add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))) = associator(X_71,X_70,X_72) ),
inference(resolve,[$cnf( $equal(additive_inverse(associator(X_70,X_71,X_72)),associator(X_71,X_70,X_72)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))) != additive_inverse(associator(X_70,X_71,X_72))
| add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))) = associator(X_71,X_70,X_72) ),
inference(resolve,[$cnf( $equal(add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))),additive_inverse(associator(X_70,X_71,X_72))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
add(multiply(X_70,multiply(X_71,X_72)),additive_inverse(multiply(multiply(X_70,X_71),X_72))) = associator(X_71,X_70,X_72),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(multiply(X_70,multiply(X_71,X_72))),multiply(multiply(X_70,X_71),X_72))),additive_inverse(associator(X_70,X_71,X_72))) )],[refute_0_112,refute_0_123]) ).
cnf(refute_0_125,plain,
add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z)))) = associator(Z,X_115,multiply(Y,Z)),
inference(subst,[],[refute_0_124:[bind(X_70,$fot(X_115)),bind(X_71,$fot(Z)),bind(X_72,$fot(multiply(Y,Z)))]]) ).
cnf(refute_0_126,plain,
( add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z)))) != associator(Z,X_115,multiply(Y,Z))
| associator(Z,multiply(X_115,Z),Y) != add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))
| associator(Z,multiply(X_115,Z),Y) = associator(Z,X_115,multiply(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(associator(Z,multiply(X_115,Z),Y),add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))) ),[1],$fot(associator(Z,X_115,multiply(Y,Z)))]]) ).
cnf(refute_0_127,plain,
( associator(Z,multiply(X_115,Z),Y) != add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))
| associator(Z,multiply(X_115,Z),Y) = associator(Z,X_115,multiply(Y,Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z)))),associator(Z,X_115,multiply(Y,Z))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
( associator(multiply(X_115,Z),Y,Z) != add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))
| associator(Z,multiply(X_115,Z),Y) = associator(Z,X_115,multiply(Y,Z)) ),
inference(resolve,[$cnf( $equal(associator(Z,multiply(X_115,Z),Y),add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))) )],[refute_0_95,refute_0_127]) ).
cnf(refute_0_129,plain,
associator(Z,multiply(X_115,Z),Y) = associator(Z,X_115,multiply(Y,Z)),
inference(resolve,[$cnf( $equal(associator(multiply(X_115,Z),Y,Z),add(multiply(X_115,multiply(Z,multiply(Y,Z))),additive_inverse(multiply(multiply(X_115,Z),multiply(Y,Z))))) )],[refute_0_90,refute_0_128]) ).
cnf(refute_0_130,plain,
associator(X,multiply(X_130,X),Z) = associator(X,X_130,multiply(Z,X)),
inference(subst,[],[refute_0_129:[bind(Y,$fot(Z)),bind(Z,$fot(X)),bind(X_115,$fot(X_130))]]) ).
cnf(refute_0_131,plain,
( associator(X,multiply(X_130,X),Z) != add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))
| associator(X,multiply(X_130,X),Z) != associator(X,X_130,multiply(Z,X))
| associator(X,X_130,multiply(Z,X)) = add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))) ),
introduced(tautology,[equality,[$cnf( $equal(associator(X,multiply(X_130,X),Z),add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))) ),[0],$fot(associator(X,X_130,multiply(Z,X)))]]) ).
cnf(refute_0_132,plain,
( associator(X,multiply(X_130,X),Z) != add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))
| associator(X,X_130,multiply(Z,X)) = add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))) ),
inference(resolve,[$cnf( $equal(associator(X,multiply(X_130,X),Z),associator(X,X_130,multiply(Z,X))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z))) = associator(X,X_130,Z),
inference(subst,[],[refute_0_124:[bind(X_70,$fot(X_130)),bind(X_71,$fot(X)),bind(X_72,$fot(Z))]]) ).
cnf(refute_0_134,plain,
multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))) = multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))),
introduced(tautology,[refl,[$fot(multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))))]]) ).
cnf(refute_0_135,plain,
( multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))) != multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z))))
| add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z))) != associator(X,X_130,Z)
| multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))) = multiply(X,associator(X,X_130,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))),multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z))))) ),[1,1],$fot(associator(X,X_130,Z))]]) ).
cnf(refute_0_136,plain,
( add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z))) != associator(X,X_130,Z)
| multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))) = multiply(X,associator(X,X_130,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))),multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z))))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))) = multiply(X,associator(X,X_130,Z)),
inference(resolve,[$cnf( $equal(add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z))),associator(X,X_130,Z)) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(X_41,add(X_42,additive_inverse(Y))) = add(multiply(X_41,X_42),multiply(X_41,additive_inverse(Y))),
inference(subst,[],[multiply_over_add1:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(additive_inverse(Y)))]]) ).
cnf(refute_0_139,plain,
multiply(X_41,additive_inverse(Y)) = additive_inverse(multiply(X_41,Y)),
inference(subst,[],[inverse_product2:[bind(X,$fot(X_41))]]) ).
cnf(refute_0_140,plain,
( multiply(X_41,add(X_42,additive_inverse(Y))) != add(multiply(X_41,X_42),multiply(X_41,additive_inverse(Y)))
| multiply(X_41,additive_inverse(Y)) != additive_inverse(multiply(X_41,Y))
| multiply(X_41,add(X_42,additive_inverse(Y))) = add(multiply(X_41,X_42),additive_inverse(multiply(X_41,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_41,add(X_42,additive_inverse(Y))),add(multiply(X_41,X_42),multiply(X_41,additive_inverse(Y)))) ),[1,1],$fot(additive_inverse(multiply(X_41,Y)))]]) ).
cnf(refute_0_141,plain,
( multiply(X_41,add(X_42,additive_inverse(Y))) != add(multiply(X_41,X_42),multiply(X_41,additive_inverse(Y)))
| multiply(X_41,add(X_42,additive_inverse(Y))) = add(multiply(X_41,X_42),additive_inverse(multiply(X_41,Y))) ),
inference(resolve,[$cnf( $equal(multiply(X_41,additive_inverse(Y)),additive_inverse(multiply(X_41,Y))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(X_41,add(X_42,additive_inverse(Y))) = add(multiply(X_41,X_42),additive_inverse(multiply(X_41,Y))),
inference(resolve,[$cnf( $equal(multiply(X_41,add(X_42,additive_inverse(Y))),add(multiply(X_41,X_42),multiply(X_41,additive_inverse(Y)))) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
( multiply(X_41,add(X_42,additive_inverse(Y))) != add(multiply(X_41,X_42),additive_inverse(multiply(X_41,Y)))
| add(multiply(X_41,X_42),additive_inverse(multiply(X_41,Y))) = multiply(X_41,add(X_42,additive_inverse(Y))) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(X_41,add(X_42,additive_inverse(Y))))),bind(Y0,$fot(add(multiply(X_41,X_42),additive_inverse(multiply(X_41,Y)))))]]) ).
cnf(refute_0_144,plain,
add(multiply(X_41,X_42),additive_inverse(multiply(X_41,Y))) = multiply(X_41,add(X_42,additive_inverse(Y))),
inference(resolve,[$cnf( $equal(multiply(X_41,add(X_42,additive_inverse(Y))),add(multiply(X_41,X_42),additive_inverse(multiply(X_41,Y)))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))) = multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))),
inference(subst,[],[refute_0_144:[bind(Y,$fot(multiply(multiply(X_130,X),Z))),bind(X_41,$fot(X)),bind(X_42,$fot(multiply(X_130,multiply(X,Z))))]]) ).
cnf(refute_0_146,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_147,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_3,refute_0_146]) ).
cnf(refute_0_148,plain,
( multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))) != multiply(X,associator(X,X_130,Z))
| add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))) != multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z))))
| add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))) = multiply(X,associator(X,X_130,Z)) ),
inference(subst,[],[refute_0_147:[bind(X0,$fot(add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))))),bind(Y0,$fot(multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))))),bind(Z0,$fot(multiply(X,associator(X,X_130,Z))))]]) ).
cnf(refute_0_149,plain,
( multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))) != multiply(X,associator(X,X_130,Z))
| add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))) = multiply(X,associator(X,X_130,Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))),multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z))))) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))) = multiply(X,associator(X,X_130,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(multiply(X_130,multiply(X,Z)),additive_inverse(multiply(multiply(X_130,X),Z)))),multiply(X,associator(X,X_130,Z))) )],[refute_0_137,refute_0_149]) ).
cnf(refute_0_151,plain,
( add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))) != multiply(X,associator(X,X_130,Z))
| associator(X,X_130,multiply(Z,X)) != add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))
| associator(X,X_130,multiply(Z,X)) = multiply(X,associator(X,X_130,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(associator(X,X_130,multiply(Z,X)),add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))) ),[1],$fot(multiply(X,associator(X,X_130,Z)))]]) ).
cnf(refute_0_152,plain,
( associator(X,X_130,multiply(Z,X)) != add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))
| associator(X,X_130,multiply(Z,X)) = multiply(X,associator(X,X_130,Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z)))),multiply(X,associator(X,X_130,Z))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
( associator(X,multiply(X_130,X),Z) != add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))
| associator(X,X_130,multiply(Z,X)) = multiply(X,associator(X,X_130,Z)) ),
inference(resolve,[$cnf( $equal(associator(X,X_130,multiply(Z,X)),add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))) )],[refute_0_132,refute_0_152]) ).
cnf(refute_0_154,plain,
associator(X,X_130,multiply(Z,X)) = multiply(X,associator(X,X_130,Z)),
inference(resolve,[$cnf( $equal(associator(X,multiply(X_130,X),Z),add(multiply(X,multiply(X_130,multiply(X,Z))),additive_inverse(multiply(X,multiply(multiply(X_130,X),Z))))) )],[refute_0_83,refute_0_153]) ).
cnf(refute_0_155,plain,
associator(Z,Y,multiply(X_151,Z)) = multiply(Z,associator(Z,Y,X_151)),
inference(subst,[],[refute_0_154:[bind(X,$fot(Z)),bind(Z,$fot(X_151)),bind(X_130,$fot(Y))]]) ).
cnf(refute_0_156,plain,
( associator(Z,Y,multiply(X_151,Z)) != multiply(Z,associator(Z,Y,X_151))
| associator(Z,Y,multiply(X_151,Z)) != associator(Y,multiply(X_151,Z),Z)
| multiply(Z,associator(Z,Y,X_151)) = associator(Y,multiply(X_151,Z),Z) ),
introduced(tautology,[equality,[$cnf( $equal(associator(Z,Y,multiply(X_151,Z)),associator(Y,multiply(X_151,Z),Z)) ),[0],$fot(multiply(Z,associator(Z,Y,X_151)))]]) ).
cnf(refute_0_157,plain,
( associator(Z,Y,multiply(X_151,Z)) != associator(Y,multiply(X_151,Z),Z)
| multiply(Z,associator(Z,Y,X_151)) = associator(Y,multiply(X_151,Z),Z) ),
inference(resolve,[$cnf( $equal(associator(Z,Y,multiply(X_151,Z)),multiply(Z,associator(Z,Y,X_151))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
multiply(Z,associator(Z,Y,X_151)) = associator(Y,multiply(X_151,Z),Z),
inference(resolve,[$cnf( $equal(associator(Z,Y,multiply(X_151,Z)),associator(Y,multiply(X_151,Z),Z)) )],[refute_0_78,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(X_342,associator(X_342,X_343,X_151)) = associator(X_343,multiply(X_151,X_342),X_342),
inference(subst,[],[refute_0_158:[bind(Y,$fot(X_343)),bind(Z,$fot(X_342))]]) ).
cnf(refute_0_160,plain,
( multiply(X_342,associator(X_342,X_343,X_151)) != associator(X_343,multiply(X_151,X_342),X_342)
| associator(X_343,multiply(X_151,X_342),X_342) = multiply(X_342,associator(X_342,X_343,X_151)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(X_342,associator(X_342,X_343,X_151)))),bind(Y0,$fot(associator(X_343,multiply(X_151,X_342),X_342)))]]) ).
cnf(refute_0_161,plain,
associator(X_343,multiply(X_151,X_342),X_342) = multiply(X_342,associator(X_342,X_343,X_151)),
inference(resolve,[$cnf( $equal(multiply(X_342,associator(X_342,X_343,X_151)),associator(X_343,multiply(X_151,X_342),X_342)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( add(associator(X_343,multiply(X_151,X_342),X_342),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) != multiply(multiply(X_342,X_343),multiply(X_151,X_342))
| associator(X_343,multiply(X_151,X_342),X_342) != multiply(X_342,associator(X_342,X_343,X_151))
| add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) = multiply(multiply(X_342,X_343),multiply(X_151,X_342)) ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_343,multiply(X_151,X_342),X_342),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))),multiply(multiply(X_342,X_343),multiply(X_151,X_342))) ),[0,0],$fot(multiply(X_342,associator(X_342,X_343,X_151)))]]) ).
cnf(refute_0_163,plain,
( add(associator(X_343,multiply(X_151,X_342),X_342),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) != multiply(multiply(X_342,X_343),multiply(X_151,X_342))
| add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) = multiply(multiply(X_342,X_343),multiply(X_151,X_342)) ),
inference(resolve,[$cnf( $equal(associator(X_343,multiply(X_151,X_342),X_342),multiply(X_342,associator(X_342,X_343,X_151))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) = multiply(multiply(X_342,X_343),multiply(X_151,X_342)),
inference(resolve,[$cnf( $equal(add(associator(X_343,multiply(X_151,X_342),X_342),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))),multiply(multiply(X_342,X_343),multiply(X_151,X_342))) )],[refute_0_77,refute_0_163]) ).
cnf(refute_0_165,plain,
add(associator(X_64,X_65,X_66),multiply(X_66,multiply(X_64,X_65))) = add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65)),
inference(subst,[],[refute_0_70:[bind(X_38,$fot(multiply(X_66,multiply(X_64,X_65))))]]) ).
cnf(refute_0_166,plain,
add(associator(X_64,X_65,X_66),multiply(X_66,multiply(X_64,X_65))) = multiply(multiply(X_66,X_64),X_65),
inference(subst,[],[refute_0_76:[bind(X_70,$fot(X_66)),bind(X_71,$fot(X_64)),bind(X_72,$fot(X_65))]]) ).
cnf(refute_0_167,plain,
( add(associator(X_64,X_65,X_66),multiply(X_66,multiply(X_64,X_65))) != multiply(multiply(X_66,X_64),X_65)
| add(associator(X_64,X_65,X_66),multiply(X_66,multiply(X_64,X_65))) != add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65))
| multiply(multiply(X_66,X_64),X_65) = add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_64,X_65,X_66),multiply(X_66,multiply(X_64,X_65))),add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65))) ),[0],$fot(multiply(multiply(X_66,X_64),X_65))]]) ).
cnf(refute_0_168,plain,
( add(associator(X_64,X_65,X_66),multiply(X_66,multiply(X_64,X_65))) != add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65))
| multiply(multiply(X_66,X_64),X_65) = add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65)) ),
inference(resolve,[$cnf( $equal(add(associator(X_64,X_65,X_66),multiply(X_66,multiply(X_64,X_65))),multiply(multiply(X_66,X_64),X_65)) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(multiply(X_66,X_64),X_65) = add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65)),
inference(resolve,[$cnf( $equal(add(associator(X_64,X_65,X_66),multiply(X_66,multiply(X_64,X_65))),add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65))) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),add(X_262,associator(X_61,X_62,X_60)))) = add(X_262,associator(X_61,X_62,X_60)),
inference(subst,[],[refute_0_57:[bind(Z,$fot(add(X_262,associator(X_61,X_62,X_60))))]]) ).
cnf(refute_0_171,plain,
additive_inverse(add(X_8,additive_inverse(X))) = add(additive_inverse(X_8),additive_inverse(additive_inverse(X))),
inference(subst,[],[sum_of_inverses:[bind(X,$fot(X_8)),bind(Y,$fot(additive_inverse(X)))]]) ).
cnf(refute_0_172,plain,
( additive_inverse(add(X_8,additive_inverse(X))) != add(additive_inverse(X_8),additive_inverse(additive_inverse(X)))
| additive_inverse(additive_inverse(X)) != X
| additive_inverse(add(X_8,additive_inverse(X))) = add(additive_inverse(X_8),X) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(X_8,additive_inverse(X))),add(additive_inverse(X_8),additive_inverse(additive_inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_173,plain,
( additive_inverse(add(X_8,additive_inverse(X))) != add(additive_inverse(X_8),additive_inverse(additive_inverse(X)))
| additive_inverse(add(X_8,additive_inverse(X))) = add(additive_inverse(X_8),X) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_172]) ).
cnf(refute_0_174,plain,
additive_inverse(add(X_8,additive_inverse(X))) = add(additive_inverse(X_8),X),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_8,additive_inverse(X))),add(additive_inverse(X_8),additive_inverse(additive_inverse(X)))) )],[refute_0_171,refute_0_173]) ).
cnf(refute_0_175,plain,
additive_inverse(add(add(X_34,X_35),additive_inverse(X))) = add(additive_inverse(add(X_34,X_35)),X),
inference(subst,[],[refute_0_174:[bind(X_8,$fot(add(X_34,X_35)))]]) ).
cnf(refute_0_176,plain,
add(X_34,add(X_35,additive_inverse(X))) = add(add(X_34,X_35),additive_inverse(X)),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_34)),bind(Y,$fot(X_35)),bind(Z,$fot(additive_inverse(X)))]]) ).
cnf(refute_0_177,plain,
( add(X_34,add(X_35,additive_inverse(X))) != add(add(X_34,X_35),additive_inverse(X))
| add(add(X_34,X_35),additive_inverse(X)) = add(X_34,add(X_35,additive_inverse(X))) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(add(X_34,add(X_35,additive_inverse(X))))),bind(Y0,$fot(add(add(X_34,X_35),additive_inverse(X))))]]) ).
cnf(refute_0_178,plain,
add(add(X_34,X_35),additive_inverse(X)) = add(X_34,add(X_35,additive_inverse(X))),
inference(resolve,[$cnf( $equal(add(X_34,add(X_35,additive_inverse(X))),add(add(X_34,X_35),additive_inverse(X))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( add(add(X_34,X_35),additive_inverse(X)) != add(X_34,add(X_35,additive_inverse(X)))
| additive_inverse(add(add(X_34,X_35),additive_inverse(X))) != add(additive_inverse(add(X_34,X_35)),X)
| additive_inverse(add(X_34,add(X_35,additive_inverse(X)))) = add(additive_inverse(add(X_34,X_35)),X) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(add(X_34,X_35),additive_inverse(X))),add(additive_inverse(add(X_34,X_35)),X)) ),[0,0],$fot(add(X_34,add(X_35,additive_inverse(X))))]]) ).
cnf(refute_0_180,plain,
( additive_inverse(add(add(X_34,X_35),additive_inverse(X))) != add(additive_inverse(add(X_34,X_35)),X)
| additive_inverse(add(X_34,add(X_35,additive_inverse(X)))) = add(additive_inverse(add(X_34,X_35)),X) ),
inference(resolve,[$cnf( $equal(add(add(X_34,X_35),additive_inverse(X)),add(X_34,add(X_35,additive_inverse(X)))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
additive_inverse(add(X_34,add(X_35,additive_inverse(X)))) = add(additive_inverse(add(X_34,X_35)),X),
inference(resolve,[$cnf( $equal(additive_inverse(add(add(X_34,X_35),additive_inverse(X))),add(additive_inverse(add(X_34,X_35)),X)) )],[refute_0_175,refute_0_180]) ).
cnf(refute_0_182,plain,
additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) = add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158),
inference(subst,[],[refute_0_181:[bind(X,$fot(X_158)),bind(X_34,$fot(associator(X_57,X_58,X_59))),bind(X_35,$fot(associator(X_57,X_59,X_58)))]]) ).
cnf(refute_0_183,plain,
( add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58)) != additive_identity
| additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) != add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158)
| additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) = add(additive_inverse(additive_identity),X_158) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))),add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158)) ),[1,0,0],$fot(additive_identity)]]) ).
cnf(refute_0_184,plain,
( additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) != add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158)
| additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) = add(additive_inverse(additive_identity),X_158) ),
inference(resolve,[$cnf( $equal(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58)),additive_identity) )],[refute_0_49,refute_0_183]) ).
cnf(refute_0_185,plain,
additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) = add(additive_inverse(additive_identity),X_158),
inference(resolve,[$cnf( $equal(additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))),add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158)) )],[refute_0_182,refute_0_184]) ).
cnf(refute_0_186,plain,
additive_inverse(associator(X_57,X_58,X_59)) = associator(X_58,X_57,X_59),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_57)),bind(Y,$fot(X_58)),bind(Z,$fot(X_59))]]) ).
cnf(refute_0_187,plain,
add(X_158,additive_inverse(associator(X_57,X_58,X_59))) = add(X_158,additive_inverse(associator(X_57,X_58,X_59))),
introduced(tautology,[refl,[$fot(add(X_158,additive_inverse(associator(X_57,X_58,X_59))))]]) ).
cnf(refute_0_188,plain,
( add(X_158,additive_inverse(associator(X_57,X_58,X_59))) != add(X_158,additive_inverse(associator(X_57,X_58,X_59)))
| additive_inverse(associator(X_57,X_58,X_59)) != associator(X_58,X_57,X_59)
| add(X_158,additive_inverse(associator(X_57,X_58,X_59))) = add(X_158,associator(X_58,X_57,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_158,additive_inverse(associator(X_57,X_58,X_59))),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) ),[1,1],$fot(associator(X_58,X_57,X_59))]]) ).
cnf(refute_0_189,plain,
( additive_inverse(associator(X_57,X_58,X_59)) != associator(X_58,X_57,X_59)
| add(X_158,additive_inverse(associator(X_57,X_58,X_59))) = add(X_158,associator(X_58,X_57,X_59)) ),
inference(resolve,[$cnf( $equal(add(X_158,additive_inverse(associator(X_57,X_58,X_59))),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
add(X_158,additive_inverse(associator(X_57,X_58,X_59))) = add(X_158,associator(X_58,X_57,X_59)),
inference(resolve,[$cnf( $equal(additive_inverse(associator(X_57,X_58,X_59)),associator(X_58,X_57,X_59)) )],[refute_0_186,refute_0_189]) ).
cnf(refute_0_191,plain,
add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) = add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))),
introduced(tautology,[refl,[$fot(add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))))]]) ).
cnf(refute_0_192,plain,
( add(X_158,additive_inverse(associator(X_57,X_58,X_59))) != add(X_158,associator(X_58,X_57,X_59))
| add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) != add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))
| add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) = add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))),add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))) ),[1,1],$fot(add(X_158,associator(X_58,X_57,X_59)))]]) ).
cnf(refute_0_193,plain,
( add(X_158,additive_inverse(associator(X_57,X_58,X_59))) != add(X_158,associator(X_58,X_57,X_59))
| add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) = add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) ),
inference(resolve,[$cnf( $equal(add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))),add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) = add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))),
inference(resolve,[$cnf( $equal(add(X_158,additive_inverse(associator(X_57,X_58,X_59))),add(X_158,associator(X_58,X_57,X_59))) )],[refute_0_190,refute_0_193]) ).
cnf(refute_0_195,plain,
additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) = add(additive_inverse(add(additive_inverse(X),additive_inverse(Y))),X_158),
inference(subst,[],[refute_0_181:[bind(X,$fot(X_158)),bind(X_34,$fot(additive_inverse(X))),bind(X_35,$fot(additive_inverse(Y)))]]) ).
cnf(refute_0_196,plain,
( add(additive_inverse(X),additive_inverse(Y)) != additive_inverse(add(X,Y))
| additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) != add(additive_inverse(add(additive_inverse(X),additive_inverse(Y))),X_158)
| additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) = add(additive_inverse(additive_inverse(add(X,Y))),X_158) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))),add(additive_inverse(add(additive_inverse(X),additive_inverse(Y))),X_158)) ),[1,0,0],$fot(additive_inverse(add(X,Y)))]]) ).
cnf(refute_0_197,plain,
( additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) != add(additive_inverse(add(additive_inverse(X),additive_inverse(Y))),X_158)
| additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) = add(additive_inverse(additive_inverse(add(X,Y))),X_158) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X),additive_inverse(Y)),additive_inverse(add(X,Y))) )],[refute_0_104,refute_0_196]) ).
cnf(refute_0_198,plain,
additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) = add(additive_inverse(additive_inverse(add(X,Y))),X_158),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))),add(additive_inverse(add(additive_inverse(X),additive_inverse(Y))),X_158)) )],[refute_0_195,refute_0_197]) ).
cnf(refute_0_199,plain,
( add(X,add(Y,Z)) != add(add(X,Y),Z)
| add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(add(X,add(Y,Z)))),bind(Y0,$fot(add(add(X,Y),Z)))]]) ).
cnf(refute_0_200,plain,
add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(X,add(Y,Z)),add(add(X,Y),Z)) )],[associativity_for_addition,refute_0_199]) ).
cnf(refute_0_201,plain,
add(add(X_158,X),Y) = add(X_158,add(X,Y)),
inference(subst,[],[refute_0_200:[bind(X,$fot(X_158)),bind(Y,$fot(X)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_202,plain,
add(X_158,additive_inverse(additive_inverse(X))) = add(X_158,additive_inverse(additive_inverse(X))),
introduced(tautology,[refl,[$fot(add(X_158,additive_inverse(additive_inverse(X))))]]) ).
cnf(refute_0_203,plain,
( add(X_158,additive_inverse(additive_inverse(X))) != add(X_158,additive_inverse(additive_inverse(X)))
| additive_inverse(additive_inverse(X)) != X
| add(X_158,additive_inverse(additive_inverse(X))) = add(X_158,X) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_158,additive_inverse(additive_inverse(X))),add(X_158,additive_inverse(additive_inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_204,plain,
( additive_inverse(additive_inverse(X)) != X
| add(X_158,additive_inverse(additive_inverse(X))) = add(X_158,X) ),
inference(resolve,[$cnf( $equal(add(X_158,additive_inverse(additive_inverse(X))),add(X_158,additive_inverse(additive_inverse(X)))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
add(X_158,additive_inverse(additive_inverse(X))) = add(X_158,X),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_204]) ).
cnf(refute_0_206,plain,
additive_inverse(add(additive_inverse(X_158),additive_inverse(X))) = add(X_158,additive_inverse(additive_inverse(X))),
inference(subst,[],[refute_0_116:[bind(X,$fot(X_158)),bind(X_9,$fot(additive_inverse(X)))]]) ).
cnf(refute_0_207,plain,
( add(X_158,additive_inverse(additive_inverse(X))) != add(X_158,X)
| additive_inverse(add(additive_inverse(X_158),additive_inverse(X))) != add(X_158,additive_inverse(additive_inverse(X)))
| additive_inverse(add(additive_inverse(X_158),additive_inverse(X))) = add(X_158,X) ),
inference(subst,[],[refute_0_147:[bind(X0,$fot(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))))),bind(Y0,$fot(add(X_158,additive_inverse(additive_inverse(X))))),bind(Z0,$fot(add(X_158,X)))]]) ).
cnf(refute_0_208,plain,
( add(X_158,additive_inverse(additive_inverse(X))) != add(X_158,X)
| additive_inverse(add(additive_inverse(X_158),additive_inverse(X))) = add(X_158,X) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),add(X_158,additive_inverse(additive_inverse(X)))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
additive_inverse(add(additive_inverse(X_158),additive_inverse(X))) = add(X_158,X),
inference(resolve,[$cnf( $equal(add(X_158,additive_inverse(additive_inverse(X))),add(X_158,X)) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) = add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y),
introduced(tautology,[refl,[$fot(add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y))]]) ).
cnf(refute_0_211,plain,
( add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) != add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y)
| additive_inverse(add(additive_inverse(X_158),additive_inverse(X))) != add(X_158,X)
| add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) = add(add(X_158,X),Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y),add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y)) ),[1,0],$fot(add(X_158,X))]]) ).
cnf(refute_0_212,plain,
( additive_inverse(add(additive_inverse(X_158),additive_inverse(X))) != add(X_158,X)
| add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) = add(add(X_158,X),Y) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y),add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y)) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) = add(add(X_158,X),Y),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),add(X_158,X)) )],[refute_0_209,refute_0_212]) ).
cnf(refute_0_214,plain,
( add(add(X_158,X),Y) != add(X_158,add(X,Y))
| add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) != add(add(X_158,X),Y)
| add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) = add(X_158,add(X,Y)) ),
inference(subst,[],[refute_0_147:[bind(X0,$fot(add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y))),bind(Y0,$fot(add(add(X_158,X),Y))),bind(Z0,$fot(add(X_158,add(X,Y))))]]) ).
cnf(refute_0_215,plain,
( add(add(X_158,X),Y) != add(X_158,add(X,Y))
| add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) = add(X_158,add(X,Y)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y),add(add(X_158,X),Y)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) = add(X_158,add(X,Y)),
inference(resolve,[$cnf( $equal(add(add(X_158,X),Y),add(X_158,add(X,Y))) )],[refute_0_201,refute_0_215]) ).
cnf(refute_0_217,plain,
additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) = additive_inverse(add(X_8,add(X_160,additive_inverse(X_158)))),
inference(subst,[],[refute_0_108:[bind(X_9,$fot(add(X_160,additive_inverse(X_158))))]]) ).
cnf(refute_0_218,plain,
additive_inverse(add(X_8,add(X_160,additive_inverse(X_158)))) = add(additive_inverse(add(X_8,X_160)),X_158),
inference(subst,[],[refute_0_181:[bind(X,$fot(X_158)),bind(X_34,$fot(X_8)),bind(X_35,$fot(X_160))]]) ).
cnf(refute_0_219,plain,
( additive_inverse(add(X_8,add(X_160,additive_inverse(X_158)))) != add(additive_inverse(add(X_8,X_160)),X_158)
| additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) != additive_inverse(add(X_8,add(X_160,additive_inverse(X_158))))
| additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) = add(additive_inverse(add(X_8,X_160)),X_158) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)),additive_inverse(add(X_8,add(X_160,additive_inverse(X_158))))) ),[1],$fot(add(additive_inverse(add(X_8,X_160)),X_158))]]) ).
cnf(refute_0_220,plain,
( additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) != additive_inverse(add(X_8,add(X_160,additive_inverse(X_158))))
| additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) = add(additive_inverse(add(X_8,X_160)),X_158) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_8,add(X_160,additive_inverse(X_158)))),add(additive_inverse(add(X_8,X_160)),X_158)) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) = add(additive_inverse(add(X_8,X_160)),X_158),
inference(resolve,[$cnf( $equal(additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)),additive_inverse(add(X_8,add(X_160,additive_inverse(X_158))))) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
add(add(X_160,additive_inverse(X_158)),X_8) = add(X_160,add(additive_inverse(X_158),X_8)),
inference(subst,[],[refute_0_200:[bind(X,$fot(X_160)),bind(Y,$fot(additive_inverse(X_158))),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_223,plain,
additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) = additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)),
introduced(tautology,[refl,[$fot(additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)))]]) ).
cnf(refute_0_224,plain,
( add(add(X_160,additive_inverse(X_158)),X_8) != add(X_160,add(additive_inverse(X_158),X_8))
| additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) != additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8))
| additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) = additive_inverse(add(X_160,add(additive_inverse(X_158),X_8))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)),additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8))) ),[1,0],$fot(add(X_160,add(additive_inverse(X_158),X_8)))]]) ).
cnf(refute_0_225,plain,
( add(add(X_160,additive_inverse(X_158)),X_8) != add(X_160,add(additive_inverse(X_158),X_8))
| additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) = additive_inverse(add(X_160,add(additive_inverse(X_158),X_8))) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)),additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) = additive_inverse(add(X_160,add(additive_inverse(X_158),X_8))),
inference(resolve,[$cnf( $equal(add(add(X_160,additive_inverse(X_158)),X_8),add(X_160,add(additive_inverse(X_158),X_8))) )],[refute_0_222,refute_0_225]) ).
cnf(refute_0_227,plain,
( additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) != add(additive_inverse(add(X_8,X_160)),X_158)
| additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) != additive_inverse(add(X_160,add(additive_inverse(X_158),X_8)))
| additive_inverse(add(X_160,add(additive_inverse(X_158),X_8))) = add(additive_inverse(add(X_8,X_160)),X_158) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)),add(additive_inverse(add(X_8,X_160)),X_158)) ),[0],$fot(additive_inverse(add(X_160,add(additive_inverse(X_158),X_8))))]]) ).
cnf(refute_0_228,plain,
( additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)) != add(additive_inverse(add(X_8,X_160)),X_158)
| additive_inverse(add(X_160,add(additive_inverse(X_158),X_8))) = add(additive_inverse(add(X_8,X_160)),X_158) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)),additive_inverse(add(X_160,add(additive_inverse(X_158),X_8)))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
additive_inverse(add(X_160,add(additive_inverse(X_158),X_8))) = add(additive_inverse(add(X_8,X_160)),X_158),
inference(resolve,[$cnf( $equal(additive_inverse(add(add(X_160,additive_inverse(X_158)),X_8)),add(additive_inverse(add(X_8,X_160)),X_158)) )],[refute_0_221,refute_0_228]) ).
cnf(refute_0_230,plain,
additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) = add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y),
inference(subst,[],[refute_0_229:[bind(X_158,$fot(Y)),bind(X_160,$fot(additive_inverse(X))),bind(X_8,$fot(additive_inverse(X_158)))]]) ).
cnf(refute_0_231,plain,
( add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) != add(X_158,add(X,Y))
| additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) != add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y)
| additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) = add(X_158,add(X,Y)) ),
inference(subst,[],[refute_0_147:[bind(X0,$fot(additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))))),bind(Y0,$fot(add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y))),bind(Z0,$fot(add(X_158,add(X,Y))))]]) ).
cnf(refute_0_232,plain,
( add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y) != add(X_158,add(X,Y))
| additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) = add(X_158,add(X,Y)) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))),add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y)) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) = add(X_158,add(X,Y)),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(additive_inverse(X_158),additive_inverse(X))),Y),add(X_158,add(X,Y))) )],[refute_0_216,refute_0_232]) ).
cnf(refute_0_234,plain,
( additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) != add(X_158,add(X,Y))
| additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) != add(additive_inverse(additive_inverse(add(X,Y))),X_158)
| add(X_158,add(X,Y)) = add(additive_inverse(additive_inverse(add(X,Y))),X_158) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))),add(additive_inverse(additive_inverse(add(X,Y))),X_158)) ),[0],$fot(add(X_158,add(X,Y)))]]) ).
cnf(refute_0_235,plain,
( additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) != add(additive_inverse(additive_inverse(add(X,Y))),X_158)
| add(X_158,add(X,Y)) = add(additive_inverse(additive_inverse(add(X,Y))),X_158) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))),add(X_158,add(X,Y))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
add(add(X,Y),X_158) = add(X,add(Y,X_158)),
inference(subst,[],[refute_0_200:[bind(Z,$fot(X_158))]]) ).
cnf(refute_0_237,plain,
additive_inverse(additive_inverse(add(X,Y))) = add(X,Y),
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(add(X,Y)))]]) ).
cnf(refute_0_238,plain,
add(additive_inverse(additive_inverse(add(X,Y))),X_158) = add(additive_inverse(additive_inverse(add(X,Y))),X_158),
introduced(tautology,[refl,[$fot(add(additive_inverse(additive_inverse(add(X,Y))),X_158))]]) ).
cnf(refute_0_239,plain,
( add(additive_inverse(additive_inverse(add(X,Y))),X_158) != add(additive_inverse(additive_inverse(add(X,Y))),X_158)
| additive_inverse(additive_inverse(add(X,Y))) != add(X,Y)
| add(additive_inverse(additive_inverse(add(X,Y))),X_158) = add(add(X,Y),X_158) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(additive_inverse(add(X,Y))),X_158),add(additive_inverse(additive_inverse(add(X,Y))),X_158)) ),[1,0],$fot(add(X,Y))]]) ).
cnf(refute_0_240,plain,
( additive_inverse(additive_inverse(add(X,Y))) != add(X,Y)
| add(additive_inverse(additive_inverse(add(X,Y))),X_158) = add(add(X,Y),X_158) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(add(X,Y))),X_158),add(additive_inverse(additive_inverse(add(X,Y))),X_158)) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
add(additive_inverse(additive_inverse(add(X,Y))),X_158) = add(add(X,Y),X_158),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(add(X,Y))),add(X,Y)) )],[refute_0_237,refute_0_240]) ).
cnf(refute_0_242,plain,
( add(add(X,Y),X_158) != add(X,add(Y,X_158))
| add(additive_inverse(additive_inverse(add(X,Y))),X_158) != add(add(X,Y),X_158)
| add(additive_inverse(additive_inverse(add(X,Y))),X_158) = add(X,add(Y,X_158)) ),
inference(subst,[],[refute_0_147:[bind(X0,$fot(add(additive_inverse(additive_inverse(add(X,Y))),X_158))),bind(Y0,$fot(add(add(X,Y),X_158))),bind(Z0,$fot(add(X,add(Y,X_158))))]]) ).
cnf(refute_0_243,plain,
( add(add(X,Y),X_158) != add(X,add(Y,X_158))
| add(additive_inverse(additive_inverse(add(X,Y))),X_158) = add(X,add(Y,X_158)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(add(X,Y))),X_158),add(add(X,Y),X_158)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
add(additive_inverse(additive_inverse(add(X,Y))),X_158) = add(X,add(Y,X_158)),
inference(resolve,[$cnf( $equal(add(add(X,Y),X_158),add(X,add(Y,X_158))) )],[refute_0_236,refute_0_243]) ).
cnf(refute_0_245,plain,
( add(X_158,add(X,Y)) != add(additive_inverse(additive_inverse(add(X,Y))),X_158)
| add(additive_inverse(additive_inverse(add(X,Y))),X_158) != add(X,add(Y,X_158))
| add(X_158,add(X,Y)) = add(X,add(Y,X_158)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_158,add(X,Y)),add(X,add(Y,X_158))) ),[0],$fot(add(additive_inverse(additive_inverse(add(X,Y))),X_158))]]) ).
cnf(refute_0_246,plain,
( add(X_158,add(X,Y)) != add(additive_inverse(additive_inverse(add(X,Y))),X_158)
| add(X_158,add(X,Y)) = add(X,add(Y,X_158)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(add(X,Y))),X_158),add(X,add(Y,X_158))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
( additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))) != add(additive_inverse(additive_inverse(add(X,Y))),X_158)
| add(X_158,add(X,Y)) = add(X,add(Y,X_158)) ),
inference(resolve,[$cnf( $equal(add(X_158,add(X,Y)),add(additive_inverse(additive_inverse(add(X,Y))),X_158)) )],[refute_0_235,refute_0_246]) ).
cnf(refute_0_248,plain,
add(X_158,add(X,Y)) = add(X,add(Y,X_158)),
inference(resolve,[$cnf( $equal(additive_inverse(add(additive_inverse(X),add(additive_inverse(Y),additive_inverse(X_158)))),add(additive_inverse(additive_inverse(add(X,Y))),X_158)) )],[refute_0_198,refute_0_247]) ).
cnf(refute_0_249,plain,
add(additive_inverse(associator(X_57,X_58,X_59)),add(associator(X_59,X_57,X_58),X_158)) = add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))),
inference(subst,[],[refute_0_248:[bind(X,$fot(associator(X_59,X_57,X_58))),bind(Y,$fot(X_158)),bind(X_158,$fot(additive_inverse(associator(X_57,X_58,X_59))))]]) ).
cnf(refute_0_250,plain,
add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)) = add(add(additive_inverse(X_56),associator(X_53,X_54,X_55)),Z),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(additive_inverse(X_56))),bind(Y,$fot(associator(X_53,X_54,X_55)))]]) ).
cnf(refute_0_251,plain,
additive_inverse(add(X_8,additive_inverse(associator(X_27,X_28,X_29)))) = add(additive_inverse(X_8),associator(X_27,X_28,X_29)),
inference(subst,[],[refute_0_174:[bind(X,$fot(associator(X_27,X_28,X_29)))]]) ).
cnf(refute_0_252,plain,
( additive_inverse(add(X_8,additive_inverse(associator(X_27,X_28,X_29)))) != add(additive_inverse(X_8),associator(X_27,X_28,X_29))
| additive_inverse(associator(X_27,X_28,X_29)) != associator(X_28,X_27,X_29)
| additive_inverse(add(X_8,associator(X_28,X_27,X_29))) = add(additive_inverse(X_8),associator(X_27,X_28,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(X_8,additive_inverse(associator(X_27,X_28,X_29)))),add(additive_inverse(X_8),associator(X_27,X_28,X_29))) ),[0,0,1],$fot(associator(X_28,X_27,X_29))]]) ).
cnf(refute_0_253,plain,
( additive_inverse(add(X_8,additive_inverse(associator(X_27,X_28,X_29)))) != add(additive_inverse(X_8),associator(X_27,X_28,X_29))
| additive_inverse(add(X_8,associator(X_28,X_27,X_29))) = add(additive_inverse(X_8),associator(X_27,X_28,X_29)) ),
inference(resolve,[$cnf( $equal(additive_inverse(associator(X_27,X_28,X_29)),associator(X_28,X_27,X_29)) )],[refute_0_36,refute_0_252]) ).
cnf(refute_0_254,plain,
additive_inverse(add(X_8,associator(X_28,X_27,X_29))) = add(additive_inverse(X_8),associator(X_27,X_28,X_29)),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_8,additive_inverse(associator(X_27,X_28,X_29)))),add(additive_inverse(X_8),associator(X_27,X_28,X_29))) )],[refute_0_251,refute_0_253]) ).
cnf(refute_0_255,plain,
additive_inverse(add(X_56,associator(X_54,X_53,X_55))) = add(additive_inverse(X_56),associator(X_53,X_54,X_55)),
inference(subst,[],[refute_0_254:[bind(X_27,$fot(X_53)),bind(X_28,$fot(X_54)),bind(X_29,$fot(X_55)),bind(X_8,$fot(X_56))]]) ).
cnf(refute_0_256,plain,
( additive_inverse(add(X_56,associator(X_54,X_53,X_55))) != add(additive_inverse(X_56),associator(X_53,X_54,X_55))
| add(additive_inverse(X_56),associator(X_53,X_54,X_55)) = additive_inverse(add(X_56,associator(X_54,X_53,X_55))) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(additive_inverse(add(X_56,associator(X_54,X_53,X_55))))),bind(Y0,$fot(add(additive_inverse(X_56),associator(X_53,X_54,X_55))))]]) ).
cnf(refute_0_257,plain,
add(additive_inverse(X_56),associator(X_53,X_54,X_55)) = additive_inverse(add(X_56,associator(X_54,X_53,X_55))),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_56,associator(X_54,X_53,X_55))),add(additive_inverse(X_56),associator(X_53,X_54,X_55))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
( add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)) != add(add(additive_inverse(X_56),associator(X_53,X_54,X_55)),Z)
| add(additive_inverse(X_56),associator(X_53,X_54,X_55)) != additive_inverse(add(X_56,associator(X_54,X_53,X_55)))
| add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)) = add(additive_inverse(add(X_56,associator(X_54,X_53,X_55))),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)),add(add(additive_inverse(X_56),associator(X_53,X_54,X_55)),Z)) ),[1,0],$fot(additive_inverse(add(X_56,associator(X_54,X_53,X_55))))]]) ).
cnf(refute_0_259,plain,
( add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)) != add(add(additive_inverse(X_56),associator(X_53,X_54,X_55)),Z)
| add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)) = add(additive_inverse(add(X_56,associator(X_54,X_53,X_55))),Z) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_56),associator(X_53,X_54,X_55)),additive_inverse(add(X_56,associator(X_54,X_53,X_55)))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)) = add(additive_inverse(add(X_56,associator(X_54,X_53,X_55))),Z),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)),add(add(additive_inverse(X_56),associator(X_53,X_54,X_55)),Z)) )],[refute_0_250,refute_0_259]) ).
cnf(refute_0_261,plain,
( add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)) != add(additive_inverse(add(X_56,associator(X_54,X_53,X_55))),Z)
| add(additive_inverse(add(X_56,associator(X_54,X_53,X_55))),Z) = add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)))),bind(Y0,$fot(add(additive_inverse(add(X_56,associator(X_54,X_53,X_55))),Z)))]]) ).
cnf(refute_0_262,plain,
add(additive_inverse(add(X_56,associator(X_54,X_53,X_55))),Z) = add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_56),add(associator(X_53,X_54,X_55),Z)),add(additive_inverse(add(X_56,associator(X_54,X_53,X_55))),Z)) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158) = add(additive_inverse(associator(X_57,X_58,X_59)),add(associator(X_59,X_57,X_58),X_158)),
inference(subst,[],[refute_0_262:[bind(Z,$fot(X_158)),bind(X_53,$fot(X_59)),bind(X_54,$fot(X_57)),bind(X_55,$fot(X_58)),bind(X_56,$fot(associator(X_57,X_58,X_59)))]]) ).
cnf(refute_0_264,plain,
( add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158) != add(additive_inverse(associator(X_57,X_58,X_59)),add(associator(X_59,X_57,X_58),X_158))
| add(additive_inverse(associator(X_57,X_58,X_59)),add(associator(X_59,X_57,X_58),X_158)) != add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))
| add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158) = add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) ),
inference(subst,[],[refute_0_147:[bind(X0,$fot(add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158))),bind(Y0,$fot(add(additive_inverse(associator(X_57,X_58,X_59)),add(associator(X_59,X_57,X_58),X_158)))),bind(Z0,$fot(add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))))]]) ).
cnf(refute_0_265,plain,
( add(additive_inverse(associator(X_57,X_58,X_59)),add(associator(X_59,X_57,X_58),X_158)) != add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))
| add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158) = add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158),add(additive_inverse(associator(X_57,X_58,X_59)),add(associator(X_59,X_57,X_58),X_158))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158) = add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))),
inference(resolve,[$cnf( $equal(add(additive_inverse(associator(X_57,X_58,X_59)),add(associator(X_59,X_57,X_58),X_158)),add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))) )],[refute_0_249,refute_0_265]) ).
cnf(refute_0_267,plain,
( add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158) != add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))
| additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) != add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158)
| additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) = add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) ),
inference(subst,[],[refute_0_147:[bind(X0,$fot(additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))))),bind(Y0,$fot(add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158))),bind(Z0,$fot(add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))))]]) ).
cnf(refute_0_268,plain,
( add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158) != add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))
| additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) = add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))),add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158)) )],[refute_0_182,refute_0_267]) ).
cnf(refute_0_269,plain,
additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) = add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(associator(X_57,X_58,X_59),associator(X_57,X_59,X_58))),X_158),add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))) )],[refute_0_266,refute_0_268]) ).
cnf(refute_0_270,plain,
( add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) != add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59)))
| additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) != add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))
| additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) = add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) ),
inference(subst,[],[refute_0_147:[bind(X0,$fot(additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))))),bind(Y0,$fot(add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))))),bind(Z0,$fot(add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59)))))]]) ).
cnf(refute_0_271,plain,
( add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))) != add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59)))
| additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) = add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))),add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59))))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) = add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))),
inference(resolve,[$cnf( $equal(add(associator(X_59,X_57,X_58),add(X_158,additive_inverse(associator(X_57,X_58,X_59)))),add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59)))) )],[refute_0_194,refute_0_271]) ).
cnf(refute_0_273,plain,
( additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) != add(additive_inverse(additive_identity),X_158)
| additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) != add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59)))
| add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) = add(additive_inverse(additive_identity),X_158) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))),add(additive_inverse(additive_identity),X_158)) ),[0],$fot(add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))))]]) ).
cnf(refute_0_274,plain,
( additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) != add(additive_inverse(additive_identity),X_158)
| add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) = add(additive_inverse(additive_identity),X_158) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))),add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59)))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
add(additive_identity,X_158) = X_158,
inference(subst,[],[left_additive_identity:[bind(X,$fot(X_158))]]) ).
cnf(refute_0_276,plain,
add(additive_inverse(additive_identity),X_158) = add(additive_inverse(additive_identity),X_158),
introduced(tautology,[refl,[$fot(add(additive_inverse(additive_identity),X_158))]]) ).
cnf(refute_0_277,plain,
( add(additive_inverse(additive_identity),X_158) != add(additive_inverse(additive_identity),X_158)
| additive_inverse(additive_identity) != additive_identity
| add(additive_inverse(additive_identity),X_158) = add(additive_identity,X_158) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(additive_identity),X_158),add(additive_inverse(additive_identity),X_158)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_278,plain,
( additive_inverse(additive_identity) != additive_identity
| add(additive_inverse(additive_identity),X_158) = add(additive_identity,X_158) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_identity),X_158),add(additive_inverse(additive_identity),X_158)) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
add(additive_inverse(additive_identity),X_158) = add(additive_identity,X_158),
inference(resolve,[$cnf( $equal(additive_inverse(additive_identity),additive_identity) )],[inverse_additive_identity,refute_0_278]) ).
cnf(refute_0_280,plain,
( add(additive_identity,X_158) != X_158
| add(additive_inverse(additive_identity),X_158) != add(additive_identity,X_158)
| add(additive_inverse(additive_identity),X_158) = X_158 ),
inference(subst,[],[refute_0_147:[bind(X0,$fot(add(additive_inverse(additive_identity),X_158))),bind(Y0,$fot(add(additive_identity,X_158))),bind(Z0,$fot(X_158))]]) ).
cnf(refute_0_281,plain,
( add(additive_identity,X_158) != X_158
| add(additive_inverse(additive_identity),X_158) = X_158 ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_identity),X_158),add(additive_identity,X_158)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
add(additive_inverse(additive_identity),X_158) = X_158,
inference(resolve,[$cnf( $equal(add(additive_identity,X_158),X_158) )],[refute_0_275,refute_0_281]) ).
cnf(refute_0_283,plain,
( add(additive_inverse(additive_identity),X_158) != X_158
| add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) != add(additive_inverse(additive_identity),X_158)
| add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) = X_158 ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))),add(additive_inverse(additive_identity),X_158)) ),[1],$fot(X_158)]]) ).
cnf(refute_0_284,plain,
( add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) != add(additive_inverse(additive_identity),X_158)
| add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) = X_158 ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_identity),X_158),X_158) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
( additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))) != add(additive_inverse(additive_identity),X_158)
| add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) = X_158 ),
inference(resolve,[$cnf( $equal(add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))),add(additive_inverse(additive_identity),X_158)) )],[refute_0_274,refute_0_284]) ).
cnf(refute_0_286,plain,
add(associator(X_59,X_57,X_58),add(X_158,associator(X_58,X_57,X_59))) = X_158,
inference(resolve,[$cnf( $equal(additive_inverse(add(associator(X_57,X_58,X_59),add(associator(X_57,X_59,X_58),additive_inverse(X_158)))),add(additive_inverse(additive_identity),X_158)) )],[refute_0_185,refute_0_285]) ).
cnf(refute_0_287,plain,
add(associator(X_60,X_62,X_61),add(X_262,associator(X_61,X_62,X_60))) = X_262,
inference(subst,[],[refute_0_286:[bind(X_158,$fot(X_262)),bind(X_57,$fot(X_62)),bind(X_58,$fot(X_61)),bind(X_59,$fot(X_60))]]) ).
cnf(refute_0_288,plain,
( add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),add(X_262,associator(X_61,X_62,X_60)))) != add(X_262,associator(X_61,X_62,X_60))
| add(associator(X_60,X_62,X_61),add(X_262,associator(X_61,X_62,X_60))) != X_262
| add(associator(X_60,X_61,X_62),X_262) = add(X_262,associator(X_61,X_62,X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),add(X_262,associator(X_61,X_62,X_60)))),add(X_262,associator(X_61,X_62,X_60))) ),[0,1],$fot(X_262)]]) ).
cnf(refute_0_289,plain,
( add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),add(X_262,associator(X_61,X_62,X_60)))) != add(X_262,associator(X_61,X_62,X_60))
| add(associator(X_60,X_61,X_62),X_262) = add(X_262,associator(X_61,X_62,X_60)) ),
inference(resolve,[$cnf( $equal(add(associator(X_60,X_62,X_61),add(X_262,associator(X_61,X_62,X_60))),X_262) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
add(associator(X_60,X_61,X_62),X_262) = add(X_262,associator(X_61,X_62,X_60)),
inference(resolve,[$cnf( $equal(add(associator(X_60,X_61,X_62),add(associator(X_60,X_62,X_61),add(X_262,associator(X_61,X_62,X_60)))),add(X_262,associator(X_61,X_62,X_60))) )],[refute_0_170,refute_0_289]) ).
cnf(refute_0_291,plain,
( add(associator(X_60,X_61,X_62),X_262) != add(X_262,associator(X_61,X_62,X_60))
| add(X_262,associator(X_61,X_62,X_60)) = add(associator(X_60,X_61,X_62),X_262) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(add(associator(X_60,X_61,X_62),X_262))),bind(Y0,$fot(add(X_262,associator(X_61,X_62,X_60))))]]) ).
cnf(refute_0_292,plain,
add(X_262,associator(X_61,X_62,X_60)) = add(associator(X_60,X_61,X_62),X_262),
inference(resolve,[$cnf( $equal(add(associator(X_60,X_61,X_62),X_262),add(X_262,associator(X_61,X_62,X_60))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65)) = add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65))),
inference(subst,[],[refute_0_292:[bind(X_262,$fot(multiply(X_66,multiply(X_64,X_65)))),bind(X_60,$fot(X_65)),bind(X_61,$fot(X_66)),bind(X_62,$fot(X_64))]]) ).
cnf(refute_0_294,plain,
( multiply(multiply(X_66,X_64),X_65) != add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65))
| add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65)) != add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65)))
| multiply(multiply(X_66,X_64),X_65) = add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_66,X_64),X_65),add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65)))) ),[0],$fot(add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65)))]]) ).
cnf(refute_0_295,plain,
( multiply(multiply(X_66,X_64),X_65) != add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65))
| multiply(multiply(X_66,X_64),X_65) = add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65)),add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65)))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
multiply(multiply(X_66,X_64),X_65) = add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_66,X_64),X_65),add(multiply(X_66,multiply(X_64,X_65)),associator(X_66,X_64,X_65))) )],[refute_0_169,refute_0_295]) ).
cnf(refute_0_297,plain,
( multiply(multiply(X_66,X_64),X_65) != add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65)))
| add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65))) = multiply(multiply(X_66,X_64),X_65) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(multiply(X_66,X_64),X_65))),bind(Y0,$fot(add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65)))))]]) ).
cnf(refute_0_298,plain,
add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65))) = multiply(multiply(X_66,X_64),X_65),
inference(resolve,[$cnf( $equal(multiply(multiply(X_66,X_64),X_65),add(associator(X_65,X_66,X_64),multiply(X_66,multiply(X_64,X_65)))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342))) = multiply(multiply(X_343,X_151),X_342),
inference(subst,[],[refute_0_298:[bind(X_64,$fot(X_151)),bind(X_65,$fot(X_342)),bind(X_66,$fot(X_343))]]) ).
cnf(refute_0_300,plain,
multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))) = multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))),
introduced(tautology,[refl,[$fot(multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))))]]) ).
cnf(refute_0_301,plain,
( multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))) != multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342))))
| add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342))) != multiply(multiply(X_343,X_151),X_342)
| multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))) = multiply(X_342,multiply(multiply(X_343,X_151),X_342)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))),multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342))))) ),[1,1],$fot(multiply(multiply(X_343,X_151),X_342))]]) ).
cnf(refute_0_302,plain,
( add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342))) != multiply(multiply(X_343,X_151),X_342)
| multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))) = multiply(X_342,multiply(multiply(X_343,X_151),X_342)) ),
inference(resolve,[$cnf( $equal(multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))),multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342))))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))) = multiply(X_342,multiply(multiply(X_343,X_151),X_342)),
inference(resolve,[$cnf( $equal(add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342))),multiply(multiply(X_343,X_151),X_342)) )],[refute_0_299,refute_0_302]) ).
cnf(refute_0_304,plain,
( multiply(X,add(Y,Z)) != add(multiply(X,Y),multiply(X,Z))
| add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_305,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[multiply_over_add1,refute_0_304]) ).
cnf(refute_0_306,plain,
add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) = multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))),
inference(subst,[],[refute_0_305:[bind(X,$fot(X_342)),bind(Y,$fot(associator(X_342,X_343,X_151))),bind(Z,$fot(multiply(X_343,multiply(X_151,X_342))))]]) ).
cnf(refute_0_307,plain,
( multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))) != multiply(X_342,multiply(multiply(X_343,X_151),X_342))
| add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) != multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342))))
| add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) = multiply(X_342,multiply(multiply(X_343,X_151),X_342)) ),
inference(subst,[],[refute_0_147:[bind(X0,$fot(add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))))),bind(Y0,$fot(multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))))),bind(Z0,$fot(multiply(X_342,multiply(multiply(X_343,X_151),X_342))))]]) ).
cnf(refute_0_308,plain,
( multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))) != multiply(X_342,multiply(multiply(X_343,X_151),X_342))
| add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) = multiply(X_342,multiply(multiply(X_343,X_151),X_342)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))),multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342))))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) = multiply(X_342,multiply(multiply(X_343,X_151),X_342)),
inference(resolve,[$cnf( $equal(multiply(X_342,add(associator(X_342,X_343,X_151),multiply(X_343,multiply(X_151,X_342)))),multiply(X_342,multiply(multiply(X_343,X_151),X_342))) )],[refute_0_303,refute_0_308]) ).
cnf(refute_0_310,plain,
( add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) != multiply(X_342,multiply(multiply(X_343,X_151),X_342))
| add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) != multiply(multiply(X_342,X_343),multiply(X_151,X_342))
| multiply(X_342,multiply(multiply(X_343,X_151),X_342)) = multiply(multiply(X_342,X_343),multiply(X_151,X_342)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))),multiply(multiply(X_342,X_343),multiply(X_151,X_342))) ),[0],$fot(multiply(X_342,multiply(multiply(X_343,X_151),X_342)))]]) ).
cnf(refute_0_311,plain,
( add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))) != multiply(multiply(X_342,X_343),multiply(X_151,X_342))
| multiply(X_342,multiply(multiply(X_343,X_151),X_342)) = multiply(multiply(X_342,X_343),multiply(X_151,X_342)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))),multiply(X_342,multiply(multiply(X_343,X_151),X_342))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
multiply(X_342,multiply(multiply(X_343,X_151),X_342)) = multiply(multiply(X_342,X_343),multiply(X_151,X_342)),
inference(resolve,[$cnf( $equal(add(multiply(X_342,associator(X_342,X_343,X_151)),multiply(X_342,multiply(X_343,multiply(X_151,X_342)))),multiply(multiply(X_342,X_343),multiply(X_151,X_342))) )],[refute_0_164,refute_0_311]) ).
cnf(refute_0_313,plain,
( multiply(X_342,multiply(multiply(X_343,X_151),X_342)) != multiply(multiply(X_342,X_343),multiply(X_151,X_342))
| multiply(multiply(X_342,X_343),multiply(X_151,X_342)) = multiply(X_342,multiply(multiply(X_343,X_151),X_342)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(multiply(X_342,multiply(multiply(X_343,X_151),X_342)))),bind(Y0,$fot(multiply(multiply(X_342,X_343),multiply(X_151,X_342))))]]) ).
cnf(refute_0_314,plain,
multiply(multiply(X_342,X_343),multiply(X_151,X_342)) = multiply(X_342,multiply(multiply(X_343,X_151),X_342)),
inference(resolve,[$cnf( $equal(multiply(X_342,multiply(multiply(X_343,X_151),X_342)),multiply(multiply(X_342,X_343),multiply(X_151,X_342))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
multiply(multiply(cx,cy),multiply(cz,cx)) = multiply(cx,multiply(multiply(cy,cz),cx)),
inference(subst,[],[refute_0_314:[bind(X_151,$fot(cz)),bind(X_342,$fot(cx)),bind(X_343,$fot(cy))]]) ).
cnf(refute_0_316,plain,
( multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx))
| multiply(cx,multiply(multiply(cy,cz),cx)) != multiply(cx,multiply(multiply(cy,cz),cx))
| multiply(multiply(cx,cy),multiply(cz,cx)) = multiply(cx,multiply(multiply(cy,cz),cx)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(cx,cy),multiply(cz,cx)),multiply(cx,multiply(multiply(cy,cz),cx))) ),[0],$fot(multiply(cx,multiply(multiply(cy,cz),cx)))]]) ).
cnf(refute_0_317,plain,
( multiply(cx,multiply(multiply(cy,cz),cx)) != multiply(cx,multiply(multiply(cy,cz),cx))
| multiply(multiply(cx,cy),multiply(cz,cx)) = multiply(cx,multiply(multiply(cy,cz),cx)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(cx,cy),multiply(cz,cx)),multiply(cx,multiply(multiply(cy,cz),cx))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
multiply(cx,multiply(multiply(cy,cz),cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(resolve,[$cnf( $equal(multiply(multiply(cx,cy),multiply(cz,cx)),multiply(cx,multiply(multiply(cy,cz),cx))) )],[refute_0_317,prove_middle_law]) ).
cnf(refute_0_319,plain,
multiply(cx,multiply(multiply(cy,cz),cx)) = multiply(cx,multiply(multiply(cy,cz),cx)),
introduced(tautology,[refl,[$fot(multiply(cx,multiply(multiply(cy,cz),cx)))]]) ).
cnf(refute_0_320,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(cx,multiply(multiply(cy,cz),cx)),multiply(cx,multiply(multiply(cy,cz),cx))) )],[refute_0_319,refute_0_318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG029-3 : TPTP v8.1.0. Bugfixed v2.4.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 19:13:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.18/8.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.18/8.37
% 8.18/8.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.18/8.41
%------------------------------------------------------------------------------