TSTP Solution File: BOO017-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO017-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 23:44:41 EDT 2022
% Result : Unsatisfiable 1.00s 1.16s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 78
% Number of leaves : 144
% Syntax : Number of clauses : 650 ( 327 unt; 0 nHn; 330 RR)
% Number of literals : 1109 (1108 equ; 461 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; 5 con; 0-2 aty)
% Number of variables : 1017 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X) ).
cnf(commutativity_of_multiply,axiom,
multiply(X,Y) = multiply(Y,X) ).
cnf(distributivity1,axiom,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ).
cnf(distributivity2,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ).
cnf(distributivity3,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ).
cnf(distributivity4,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X) = X ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X ).
cnf(additive_id2,axiom,
add(additive_identity,X) = X ).
cnf(x_times_y,hypothesis,
add(x,y) = z ).
cnf(prove_sum,negated_conjecture,
multiply(x,z) != x ).
cnf(refute_0_0,plain,
add(x,multiply(X_21,y)) = multiply(add(x,X_21),add(x,y)),
inference(subst,[],[distributivity2:[bind(X,$fot(x)),bind(Y,$fot(X_21)),bind(Z,$fot(y))]]) ).
cnf(refute_0_1,plain,
( add(x,multiply(X_21,y)) != multiply(add(x,X_21),add(x,y))
| add(x,y) != z
| add(x,multiply(X_21,y)) = multiply(add(x,X_21),z) ),
introduced(tautology,[equality,[$cnf( $equal(add(x,multiply(X_21,y)),multiply(add(x,X_21),add(x,y))) ),[1,1],$fot(z)]]) ).
cnf(refute_0_2,plain,
( add(x,multiply(X_21,y)) != multiply(add(x,X_21),add(x,y))
| add(x,multiply(X_21,y)) = multiply(add(x,X_21),z) ),
inference(resolve,[$cnf( $equal(add(x,y),z) )],[x_times_y,refute_0_1]) ).
cnf(refute_0_3,plain,
add(x,multiply(X_21,y)) = multiply(add(x,X_21),z),
inference(resolve,[$cnf( $equal(add(x,multiply(X_21,y)),multiply(add(x,X_21),add(x,y))) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( multiply(X,Y) != multiply(Y,X)
| multiply(Y,X) = multiply(X,Y) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_8,plain,
multiply(Y,X) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(Y,X)) )],[commutativity_of_multiply,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(add(x,X_21),z) = multiply(z,add(x,X_21)),
inference(subst,[],[refute_0_8:[bind(X,$fot(z)),bind(Y,$fot(add(x,X_21)))]]) ).
cnf(refute_0_10,plain,
( multiply(add(x,X_21),z) != multiply(z,add(x,X_21))
| add(x,multiply(X_21,y)) != multiply(add(x,X_21),z)
| add(x,multiply(X_21,y)) = multiply(z,add(x,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(add(x,multiply(X_21,y)),multiply(add(x,X_21),z)) ),[1],$fot(multiply(z,add(x,X_21)))]]) ).
cnf(refute_0_11,plain,
( add(x,multiply(X_21,y)) != multiply(add(x,X_21),z)
| add(x,multiply(X_21,y)) = multiply(z,add(x,X_21)) ),
inference(resolve,[$cnf( $equal(multiply(add(x,X_21),z),multiply(z,add(x,X_21))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
add(x,multiply(X_21,y)) = multiply(z,add(x,X_21)),
inference(resolve,[$cnf( $equal(add(x,multiply(X_21,y)),multiply(add(x,X_21),z)) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
add(x,multiply(additive_identity,y)) = multiply(z,add(x,additive_identity)),
inference(subst,[],[refute_0_12:[bind(X_21,$fot(additive_identity))]]) ).
cnf(refute_0_14,plain,
multiply(add(additive_identity,X_59),additive_identity) = add(multiply(additive_identity,additive_identity),multiply(X_59,additive_identity)),
inference(subst,[],[distributivity3:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_59)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_15,plain,
add(multiply(additive_identity,X_11),X_12) = multiply(add(additive_identity,X_12),add(X_11,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_16,plain,
add(additive_identity,X_12) = X_12,
inference(subst,[],[additive_id2:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_17,plain,
( add(multiply(additive_identity,X_11),X_12) != multiply(add(additive_identity,X_12),add(X_11,X_12))
| add(additive_identity,X_12) != X_12
| add(multiply(additive_identity,X_11),X_12) = multiply(X_12,add(X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_11),X_12),multiply(add(additive_identity,X_12),add(X_11,X_12))) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_18,plain,
( add(multiply(additive_identity,X_11),X_12) != multiply(add(additive_identity,X_12),add(X_11,X_12))
| add(multiply(additive_identity,X_11),X_12) = multiply(X_12,add(X_11,X_12)) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_12),X_12) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
add(multiply(additive_identity,X_11),X_12) = multiply(X_12,add(X_11,X_12)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_11),X_12),multiply(add(additive_identity,X_12),add(X_11,X_12))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
add(multiply(additive_identity,additive_identity),X_16) = multiply(X_16,add(additive_identity,X_16)),
inference(subst,[],[refute_0_19:[bind(X_11,$fot(additive_identity)),bind(X_12,$fot(X_16))]]) ).
cnf(refute_0_21,plain,
add(additive_identity,X_16) = X_16,
inference(subst,[],[additive_id2:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_22,plain,
( add(multiply(additive_identity,additive_identity),X_16) != multiply(X_16,add(additive_identity,X_16))
| add(additive_identity,X_16) != X_16
| add(multiply(additive_identity,additive_identity),X_16) = multiply(X_16,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_16),multiply(X_16,add(additive_identity,X_16))) ),[1,1],$fot(X_16)]]) ).
cnf(refute_0_23,plain,
( add(multiply(additive_identity,additive_identity),X_16) != multiply(X_16,add(additive_identity,X_16))
| add(multiply(additive_identity,additive_identity),X_16) = multiply(X_16,X_16) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_16),X_16) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
add(multiply(additive_identity,additive_identity),X_16) = multiply(X_16,X_16),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_16),multiply(X_16,add(additive_identity,X_16))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
add(multiply(additive_identity,additive_identity),multiply(X_59,additive_identity)) = multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity)),
inference(subst,[],[refute_0_24:[bind(X_16,$fot(multiply(X_59,additive_identity)))]]) ).
cnf(refute_0_26,plain,
( multiply(add(additive_identity,X_59),additive_identity) != add(multiply(additive_identity,additive_identity),multiply(X_59,additive_identity))
| add(multiply(additive_identity,additive_identity),multiply(X_59,additive_identity)) != multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))
| multiply(add(additive_identity,X_59),additive_identity) = multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(additive_identity,X_59),additive_identity),multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))) ),[0],$fot(add(multiply(additive_identity,additive_identity),multiply(X_59,additive_identity)))]]) ).
cnf(refute_0_27,plain,
( multiply(add(additive_identity,X_59),additive_identity) != add(multiply(additive_identity,additive_identity),multiply(X_59,additive_identity))
| multiply(add(additive_identity,X_59),additive_identity) = multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_59,additive_identity)),multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(add(additive_identity,X_59),additive_identity) = multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity)),
inference(resolve,[$cnf( $equal(multiply(add(additive_identity,X_59),additive_identity),add(multiply(additive_identity,additive_identity),multiply(X_59,additive_identity))) )],[refute_0_14,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(add(X_58,multiplicative_identity),X_60) = add(multiply(X_58,X_60),multiply(multiplicative_identity,X_60)),
inference(subst,[],[distributivity3:[bind(X,$fot(X_58)),bind(Y,$fot(multiplicative_identity)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_30,plain,
multiply(multiplicative_identity,X_60) = X_60,
inference(subst,[],[multiplicative_id2:[bind(X,$fot(X_60))]]) ).
cnf(refute_0_31,plain,
( multiply(add(X_58,multiplicative_identity),X_60) != add(multiply(X_58,X_60),multiply(multiplicative_identity,X_60))
| multiply(multiplicative_identity,X_60) != X_60
| multiply(add(X_58,multiplicative_identity),X_60) = add(multiply(X_58,X_60),X_60) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_58,multiplicative_identity),X_60),add(multiply(X_58,X_60),multiply(multiplicative_identity,X_60))) ),[1,1],$fot(X_60)]]) ).
cnf(refute_0_32,plain,
( multiply(add(X_58,multiplicative_identity),X_60) != add(multiply(X_58,X_60),multiply(multiplicative_identity,X_60))
| multiply(add(X_58,multiplicative_identity),X_60) = add(multiply(X_58,X_60),X_60) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,X_60),X_60) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(add(X_58,multiplicative_identity),X_60) = add(multiply(X_58,X_60),X_60),
inference(resolve,[$cnf( $equal(multiply(add(X_58,multiplicative_identity),X_60),add(multiply(X_58,X_60),multiply(multiplicative_identity,X_60))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
add(X_20,multiply(X_21,inverse(X_20))) = multiply(add(X_20,X_21),add(X_20,inverse(X_20))),
inference(subst,[],[distributivity2:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(inverse(X_20)))]]) ).
cnf(refute_0_35,plain,
add(X_20,inverse(X_20)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_36,plain,
( add(X_20,multiply(X_21,inverse(X_20))) != multiply(add(X_20,X_21),add(X_20,inverse(X_20)))
| add(X_20,inverse(X_20)) != multiplicative_identity
| add(X_20,multiply(X_21,inverse(X_20))) = multiply(add(X_20,X_21),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,inverse(X_20))),multiply(add(X_20,X_21),add(X_20,inverse(X_20)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_37,plain,
( add(X_20,multiply(X_21,inverse(X_20))) != multiply(add(X_20,X_21),add(X_20,inverse(X_20)))
| add(X_20,multiply(X_21,inverse(X_20))) = multiply(add(X_20,X_21),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_20,inverse(X_20)),multiplicative_identity) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
add(X_20,multiply(X_21,inverse(X_20))) = multiply(add(X_20,X_21),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,inverse(X_20))),multiply(add(X_20,X_21),add(X_20,inverse(X_20)))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(add(X_20,X_21),multiplicative_identity) = add(X_20,X_21),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_20,X_21)))]]) ).
cnf(refute_0_40,plain,
( multiply(add(X_20,X_21),multiplicative_identity) != add(X_20,X_21)
| add(X_20,multiply(X_21,inverse(X_20))) != multiply(add(X_20,X_21),multiplicative_identity)
| add(X_20,multiply(X_21,inverse(X_20))) = add(X_20,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,inverse(X_20))),multiply(add(X_20,X_21),multiplicative_identity)) ),[1],$fot(add(X_20,X_21))]]) ).
cnf(refute_0_41,plain,
( add(X_20,multiply(X_21,inverse(X_20))) != multiply(add(X_20,X_21),multiplicative_identity)
| add(X_20,multiply(X_21,inverse(X_20))) = add(X_20,X_21) ),
inference(resolve,[$cnf( $equal(multiply(add(X_20,X_21),multiplicative_identity),add(X_20,X_21)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
add(X_20,multiply(X_21,inverse(X_20))) = add(X_20,X_21),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,inverse(X_20))),multiply(add(X_20,X_21),multiplicative_identity)) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
add(X_25,multiply(multiplicative_identity,inverse(X_25))) = add(X_25,multiplicative_identity),
inference(subst,[],[refute_0_42:[bind(X_20,$fot(X_25)),bind(X_21,$fot(multiplicative_identity))]]) ).
cnf(refute_0_44,plain,
multiply(multiplicative_identity,inverse(X_25)) = inverse(X_25),
inference(subst,[],[multiplicative_id2:[bind(X,$fot(inverse(X_25)))]]) ).
cnf(refute_0_45,plain,
( multiply(multiplicative_identity,inverse(X_25)) != inverse(X_25)
| add(X_25,multiply(multiplicative_identity,inverse(X_25))) != add(X_25,multiplicative_identity)
| add(X_25,inverse(X_25)) = add(X_25,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_25,multiply(multiplicative_identity,inverse(X_25))),add(X_25,multiplicative_identity)) ),[0,1],$fot(inverse(X_25))]]) ).
cnf(refute_0_46,plain,
( add(X_25,multiply(multiplicative_identity,inverse(X_25))) != add(X_25,multiplicative_identity)
| add(X_25,inverse(X_25)) = add(X_25,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(X_25)),inverse(X_25)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
add(X_25,inverse(X_25)) = add(X_25,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_25,multiply(multiplicative_identity,inverse(X_25))),add(X_25,multiplicative_identity)) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
add(X_25,inverse(X_25)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_49,plain,
( add(X_25,inverse(X_25)) != add(X_25,multiplicative_identity)
| add(X_25,inverse(X_25)) != multiplicative_identity
| multiplicative_identity = add(X_25,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_25,inverse(X_25)),add(X_25,multiplicative_identity)) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_50,plain,
( add(X_25,inverse(X_25)) != add(X_25,multiplicative_identity)
| multiplicative_identity = add(X_25,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_25,inverse(X_25)),multiplicative_identity) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiplicative_identity = add(X_25,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_25,inverse(X_25)),add(X_25,multiplicative_identity)) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiplicative_identity != add(X_25,multiplicative_identity)
| add(X_25,multiplicative_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_25,multiplicative_identity)))]]) ).
cnf(refute_0_53,plain,
add(X_25,multiplicative_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_25,multiplicative_identity)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
add(X_58,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[refute_0_53:[bind(X_25,$fot(X_58))]]) ).
cnf(refute_0_55,plain,
multiply(add(X_58,multiplicative_identity),X_60) = multiply(add(X_58,multiplicative_identity),X_60),
introduced(tautology,[refl,[$fot(multiply(add(X_58,multiplicative_identity),X_60))]]) ).
cnf(refute_0_56,plain,
( multiply(add(X_58,multiplicative_identity),X_60) != multiply(add(X_58,multiplicative_identity),X_60)
| add(X_58,multiplicative_identity) != multiplicative_identity
| multiply(add(X_58,multiplicative_identity),X_60) = multiply(multiplicative_identity,X_60) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_58,multiplicative_identity),X_60),multiply(add(X_58,multiplicative_identity),X_60)) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_57,plain,
( add(X_58,multiplicative_identity) != multiplicative_identity
| multiply(add(X_58,multiplicative_identity),X_60) = multiply(multiplicative_identity,X_60) ),
inference(resolve,[$cnf( $equal(multiply(add(X_58,multiplicative_identity),X_60),multiply(add(X_58,multiplicative_identity),X_60)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(add(X_58,multiplicative_identity),X_60) = multiply(multiplicative_identity,X_60),
inference(resolve,[$cnf( $equal(add(X_58,multiplicative_identity),multiplicative_identity) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_60,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_6,refute_0_59]) ).
cnf(refute_0_61,plain,
( multiply(add(X_58,multiplicative_identity),X_60) != multiply(multiplicative_identity,X_60)
| multiply(multiplicative_identity,X_60) != X_60
| multiply(add(X_58,multiplicative_identity),X_60) = X_60 ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(add(X_58,multiplicative_identity),X_60))),bind(Y0,$fot(multiply(multiplicative_identity,X_60))),bind(Z0,$fot(X_60))]]) ).
cnf(refute_0_62,plain,
( multiply(multiplicative_identity,X_60) != X_60
| multiply(add(X_58,multiplicative_identity),X_60) = X_60 ),
inference(resolve,[$cnf( $equal(multiply(add(X_58,multiplicative_identity),X_60),multiply(multiplicative_identity,X_60)) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(add(X_58,multiplicative_identity),X_60) = X_60,
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,X_60),X_60) )],[refute_0_30,refute_0_62]) ).
cnf(refute_0_64,plain,
( multiply(add(X_58,multiplicative_identity),X_60) != X_60
| multiply(add(X_58,multiplicative_identity),X_60) != add(multiply(X_58,X_60),X_60)
| X_60 = add(multiply(X_58,X_60),X_60) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_58,multiplicative_identity),X_60),add(multiply(X_58,X_60),X_60)) ),[0],$fot(X_60)]]) ).
cnf(refute_0_65,plain,
( multiply(add(X_58,multiplicative_identity),X_60) != add(multiply(X_58,X_60),X_60)
| X_60 = add(multiply(X_58,X_60),X_60) ),
inference(resolve,[$cnf( $equal(multiply(add(X_58,multiplicative_identity),X_60),X_60) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
add(Z,multiply(Y,Z)) = multiply(add(Z,Y),add(Z,Z)),
inference(subst,[],[distributivity2:[bind(X,$fot(Z))]]) ).
cnf(refute_0_67,plain,
add(X_25,multiply(X_25,inverse(X_25))) = add(X_25,X_25),
inference(subst,[],[refute_0_42:[bind(X_20,$fot(X_25)),bind(X_21,$fot(X_25))]]) ).
cnf(refute_0_68,plain,
multiply(X_25,inverse(X_25)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_69,plain,
( multiply(X_25,inverse(X_25)) != additive_identity
| add(X_25,multiply(X_25,inverse(X_25))) != add(X_25,X_25)
| add(X_25,additive_identity) = add(X_25,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_25,multiply(X_25,inverse(X_25))),add(X_25,X_25)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_70,plain,
( add(X_25,multiply(X_25,inverse(X_25))) != add(X_25,X_25)
| add(X_25,additive_identity) = add(X_25,X_25) ),
inference(resolve,[$cnf( $equal(multiply(X_25,inverse(X_25)),additive_identity) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
add(X_25,additive_identity) = add(X_25,X_25),
inference(resolve,[$cnf( $equal(add(X_25,multiply(X_25,inverse(X_25))),add(X_25,X_25)) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
add(X_25,additive_identity) = X_25,
inference(subst,[],[additive_id1:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_73,plain,
( add(X_25,additive_identity) != X_25
| add(X_25,additive_identity) != add(X_25,X_25)
| X_25 = add(X_25,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_25,additive_identity),add(X_25,X_25)) ),[0],$fot(X_25)]]) ).
cnf(refute_0_74,plain,
( add(X_25,additive_identity) != add(X_25,X_25)
| X_25 = add(X_25,X_25) ),
inference(resolve,[$cnf( $equal(add(X_25,additive_identity),X_25) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
X_25 = add(X_25,X_25),
inference(resolve,[$cnf( $equal(add(X_25,additive_identity),add(X_25,X_25)) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
Z = add(Z,Z),
inference(subst,[],[refute_0_75:[bind(X_25,$fot(Z))]]) ).
cnf(refute_0_77,plain,
( Z != add(Z,Z)
| add(Z,Z) = Z ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(Z)),bind(Y0,$fot(add(Z,Z)))]]) ).
cnf(refute_0_78,plain,
add(Z,Z) = Z,
inference(resolve,[$cnf( $equal(Z,add(Z,Z)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( add(Z,Z) != Z
| add(Z,multiply(Y,Z)) != multiply(add(Z,Y),add(Z,Z))
| add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),add(Z,Z))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_80,plain,
( add(Z,multiply(Y,Z)) != multiply(add(Z,Y),add(Z,Z))
| add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z) ),
inference(resolve,[$cnf( $equal(add(Z,Z),Z) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z),
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),add(Z,Z))) )],[refute_0_66,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(add(Z,Y),Z) = multiply(Z,add(Z,Y)),
inference(subst,[],[refute_0_8:[bind(X,$fot(Z)),bind(Y,$fot(add(Z,Y)))]]) ).
cnf(refute_0_83,plain,
( multiply(add(Z,Y),Z) != multiply(Z,add(Z,Y))
| add(Z,multiply(Y,Z)) != multiply(add(Z,Y),Z)
| add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),Z)) ),[1],$fot(multiply(Z,add(Z,Y)))]]) ).
cnf(refute_0_84,plain,
( add(Z,multiply(Y,Z)) != multiply(add(Z,Y),Z)
| add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(add(Z,Y),Z),multiply(Z,add(Z,Y))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)),
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),Z)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
add(X_60,multiply(X_58,X_60)) = multiply(X_60,add(X_60,X_58)),
inference(subst,[],[refute_0_85:[bind(Y,$fot(X_58)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_87,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_88,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_87]) ).
cnf(refute_0_89,plain,
add(multiply(X_58,X_60),X_60) = add(X_60,multiply(X_58,X_60)),
inference(subst,[],[refute_0_88:[bind(X,$fot(X_60)),bind(Y,$fot(multiply(X_58,X_60)))]]) ).
cnf(refute_0_90,plain,
( add(X_60,multiply(X_58,X_60)) != multiply(X_60,add(X_60,X_58))
| add(multiply(X_58,X_60),X_60) != add(X_60,multiply(X_58,X_60))
| add(multiply(X_58,X_60),X_60) = multiply(X_60,add(X_60,X_58)) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(multiply(X_58,X_60),X_60))),bind(Y0,$fot(add(X_60,multiply(X_58,X_60)))),bind(Z0,$fot(multiply(X_60,add(X_60,X_58))))]]) ).
cnf(refute_0_91,plain,
( add(X_60,multiply(X_58,X_60)) != multiply(X_60,add(X_60,X_58))
| add(multiply(X_58,X_60),X_60) = multiply(X_60,add(X_60,X_58)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_58,X_60),X_60),add(X_60,multiply(X_58,X_60))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
add(multiply(X_58,X_60),X_60) = multiply(X_60,add(X_60,X_58)),
inference(resolve,[$cnf( $equal(add(X_60,multiply(X_58,X_60)),multiply(X_60,add(X_60,X_58))) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
( X_60 != add(multiply(X_58,X_60),X_60)
| add(multiply(X_58,X_60),X_60) != multiply(X_60,add(X_60,X_58))
| X_60 = multiply(X_60,add(X_60,X_58)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_60,multiply(X_60,add(X_60,X_58))) ),[0],$fot(add(multiply(X_58,X_60),X_60))]]) ).
cnf(refute_0_94,plain,
( X_60 != add(multiply(X_58,X_60),X_60)
| X_60 = multiply(X_60,add(X_60,X_58)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_58,X_60),X_60),multiply(X_60,add(X_60,X_58))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( multiply(add(X_58,multiplicative_identity),X_60) != add(multiply(X_58,X_60),X_60)
| X_60 = multiply(X_60,add(X_60,X_58)) ),
inference(resolve,[$cnf( $equal(X_60,add(multiply(X_58,X_60),X_60)) )],[refute_0_65,refute_0_94]) ).
cnf(refute_0_96,plain,
X_60 = multiply(X_60,add(X_60,X_58)),
inference(resolve,[$cnf( $equal(multiply(add(X_58,multiplicative_identity),X_60),add(multiply(X_58,X_60),X_60)) )],[refute_0_33,refute_0_95]) ).
cnf(refute_0_97,plain,
( X_60 != multiply(X_60,add(X_60,X_58))
| multiply(X_60,add(X_60,X_58)) = X_60 ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(X_60)),bind(Y0,$fot(multiply(X_60,add(X_60,X_58))))]]) ).
cnf(refute_0_98,plain,
multiply(X_60,add(X_60,X_58)) = X_60,
inference(resolve,[$cnf( $equal(X_60,multiply(X_60,add(X_60,X_58))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
multiply(additive_identity,add(additive_identity,X_59)) = additive_identity,
inference(subst,[],[refute_0_98:[bind(X_58,$fot(X_59)),bind(X_60,$fot(additive_identity))]]) ).
cnf(refute_0_100,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),add(additive_identity,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_101,plain,
( add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),add(additive_identity,X_12))
| add(additive_identity,X_12) != X_12
| add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),add(additive_identity,X_12))) ),[1,1],$fot(X_12)]]) ).
cnf(refute_0_102,plain,
( add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),add(additive_identity,X_12))
| add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),X_12) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_12),X_12) )],[refute_0_16,refute_0_101]) ).
cnf(refute_0_103,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),X_12),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),add(additive_identity,X_12))) )],[refute_0_100,refute_0_102]) ).
cnf(refute_0_104,plain,
multiply(add(X_10,X_12),X_12) = multiply(X_12,add(X_10,X_12)),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_12)),bind(Y,$fot(add(X_10,X_12)))]]) ).
cnf(refute_0_105,plain,
( multiply(add(X_10,X_12),X_12) != multiply(X_12,add(X_10,X_12))
| add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),X_12)
| add(multiply(X_10,additive_identity),X_12) = multiply(X_12,add(X_10,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),X_12)) ),[1],$fot(multiply(X_12,add(X_10,X_12)))]]) ).
cnf(refute_0_106,plain,
( add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),X_12)
| add(multiply(X_10,additive_identity),X_12) = multiply(X_12,add(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_12),X_12),multiply(X_12,add(X_10,X_12))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(X_12,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),X_12)) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity)))) = multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))),
inference(subst,[],[refute_0_107:[bind(X_12,$fot(inverse(inverse(multiply(X_10,additive_identity)))))]]) ).
cnf(refute_0_109,plain,
add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11))),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(inverse(X_11)))]]) ).
cnf(refute_0_110,plain,
add(X_11,inverse(X_11)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_111,plain,
( add(X_11,inverse(X_11)) != multiplicative_identity
| add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))
| add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_112,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))
| add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_11,inverse(X_11)),multiplicative_identity) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
add(multiply(X_10,X_11),inverse(X_11)) = add(inverse(X_11),multiply(X_10,X_11)),
inference(subst,[],[refute_0_88:[bind(X,$fot(inverse(X_11))),bind(Y,$fot(multiply(X_10,X_11)))]]) ).
cnf(refute_0_115,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(multiply(X_10,X_11),inverse(X_11)) != add(inverse(X_11),multiply(X_10,X_11))
| add(inverse(X_11),multiply(X_10,X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) ),[0],$fot(add(inverse(X_11),multiply(X_10,X_11)))]]) ).
cnf(refute_0_116,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),add(inverse(X_11),multiply(X_10,X_11))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(add(X_10,inverse(X_11)),multiplicative_identity) = add(X_10,inverse(X_11)),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,inverse(X_11))))]]) ).
cnf(refute_0_118,plain,
( multiply(add(X_10,inverse(X_11)),multiplicative_identity) != add(X_10,inverse(X_11))
| add(inverse(X_11),multiply(X_10,X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_11),multiply(X_10,X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) ),[1],$fot(add(X_10,inverse(X_11)))]]) ).
cnf(refute_0_119,plain,
( add(inverse(X_11),multiply(X_10,X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,inverse(X_11)),multiplicative_identity),add(X_10,inverse(X_11))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_11),multiply(X_10,X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) )],[refute_0_113,refute_0_120]) ).
cnf(refute_0_122,plain,
add(inverse(inverse(X_38)),multiply(X_38,inverse(X_38))) = add(X_38,inverse(inverse(X_38))),
inference(subst,[],[refute_0_121:[bind(X_10,$fot(X_38)),bind(X_11,$fot(inverse(X_38)))]]) ).
cnf(refute_0_123,plain,
multiply(X_38,inverse(X_38)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_38))]]) ).
cnf(refute_0_124,plain,
( multiply(X_38,inverse(X_38)) != additive_identity
| add(inverse(inverse(X_38)),multiply(X_38,inverse(X_38))) != add(X_38,inverse(inverse(X_38)))
| add(inverse(inverse(X_38)),additive_identity) = add(X_38,inverse(inverse(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_38)),multiply(X_38,inverse(X_38))),add(X_38,inverse(inverse(X_38)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_125,plain,
( add(inverse(inverse(X_38)),multiply(X_38,inverse(X_38))) != add(X_38,inverse(inverse(X_38)))
| add(inverse(inverse(X_38)),additive_identity) = add(X_38,inverse(inverse(X_38))) ),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(X_38)),additive_identity) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
add(inverse(inverse(X_38)),additive_identity) = add(X_38,inverse(inverse(X_38))),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_38)),multiply(X_38,inverse(X_38))),add(X_38,inverse(inverse(X_38)))) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
add(inverse(inverse(X_38)),additive_identity) = inverse(inverse(X_38)),
inference(subst,[],[additive_id1:[bind(X,$fot(inverse(inverse(X_38))))]]) ).
cnf(refute_0_128,plain,
( add(inverse(inverse(X_38)),additive_identity) != add(X_38,inverse(inverse(X_38)))
| add(inverse(inverse(X_38)),additive_identity) != inverse(inverse(X_38))
| inverse(inverse(X_38)) = add(X_38,inverse(inverse(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_38)),additive_identity),add(X_38,inverse(inverse(X_38)))) ),[0],$fot(inverse(inverse(X_38)))]]) ).
cnf(refute_0_129,plain,
( add(inverse(inverse(X_38)),additive_identity) != add(X_38,inverse(inverse(X_38)))
| inverse(inverse(X_38)) = add(X_38,inverse(inverse(X_38))) ),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_38)),additive_identity),inverse(inverse(X_38))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
inverse(inverse(X_38)) = add(X_38,inverse(inverse(X_38))),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_38)),additive_identity),add(X_38,inverse(inverse(X_38)))) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
inverse(inverse(multiply(X_10,additive_identity))) = add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity)))),
inference(subst,[],[refute_0_130:[bind(X_38,$fot(multiply(X_10,additive_identity)))]]) ).
cnf(refute_0_132,plain,
( inverse(inverse(multiply(X_10,additive_identity))) != add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity))))
| add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity)))) = inverse(inverse(multiply(X_10,additive_identity))) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(inverse(multiply(X_10,additive_identity))))),bind(Y0,$fot(add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity))))))]]) ).
cnf(refute_0_133,plain,
add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity)))) = inverse(inverse(multiply(X_10,additive_identity))),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_10,additive_identity))),add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity))))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
( add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity)))) != multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity)))))
| add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity)))) != inverse(inverse(multiply(X_10,additive_identity)))
| inverse(inverse(multiply(X_10,additive_identity))) = multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity)))),multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity)))))) ),[0],$fot(inverse(inverse(multiply(X_10,additive_identity))))]]) ).
cnf(refute_0_135,plain,
( add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity)))) != multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity)))))
| inverse(inverse(multiply(X_10,additive_identity))) = multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity)))),inverse(inverse(multiply(X_10,additive_identity)))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
inverse(inverse(multiply(X_10,additive_identity))) = multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),inverse(inverse(multiply(X_10,additive_identity)))),multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity)))))) )],[refute_0_108,refute_0_135]) ).
cnf(refute_0_137,plain,
add(X_20,multiply(X_21,additive_identity)) = multiply(add(X_20,X_21),add(X_20,additive_identity)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_138,plain,
add(X_20,additive_identity) = X_20,
inference(subst,[],[additive_id1:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_139,plain,
( add(X_20,multiply(X_21,additive_identity)) != multiply(add(X_20,X_21),add(X_20,additive_identity))
| add(X_20,additive_identity) != X_20
| add(X_20,multiply(X_21,additive_identity)) = multiply(add(X_20,X_21),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(add(X_20,X_21),add(X_20,additive_identity))) ),[1,1],$fot(X_20)]]) ).
cnf(refute_0_140,plain,
( add(X_20,multiply(X_21,additive_identity)) != multiply(add(X_20,X_21),add(X_20,additive_identity))
| add(X_20,multiply(X_21,additive_identity)) = multiply(add(X_20,X_21),X_20) ),
inference(resolve,[$cnf( $equal(add(X_20,additive_identity),X_20) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
add(X_20,multiply(X_21,additive_identity)) = multiply(add(X_20,X_21),X_20),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(add(X_20,X_21),add(X_20,additive_identity))) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(add(X_20,X_21),X_20) = multiply(X_20,add(X_20,X_21)),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_20)),bind(Y,$fot(add(X_20,X_21)))]]) ).
cnf(refute_0_143,plain,
( multiply(add(X_20,X_21),X_20) != multiply(X_20,add(X_20,X_21))
| add(X_20,multiply(X_21,additive_identity)) != multiply(add(X_20,X_21),X_20)
| add(X_20,multiply(X_21,additive_identity)) = multiply(X_20,add(X_20,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(add(X_20,X_21),X_20)) ),[1],$fot(multiply(X_20,add(X_20,X_21)))]]) ).
cnf(refute_0_144,plain,
( add(X_20,multiply(X_21,additive_identity)) != multiply(add(X_20,X_21),X_20)
| add(X_20,multiply(X_21,additive_identity)) = multiply(X_20,add(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_20,X_21),X_20),multiply(X_20,add(X_20,X_21))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
add(X_20,multiply(X_21,additive_identity)) = multiply(X_20,add(X_20,X_21)),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(add(X_20,X_21),X_20)) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) = multiply(inverse(X_39),add(inverse(X_39),multiply(X_38,X_39))),
inference(subst,[],[refute_0_145:[bind(X_20,$fot(inverse(X_39))),bind(X_21,$fot(multiply(X_38,X_39)))]]) ).
cnf(refute_0_147,plain,
add(inverse(X_39),multiply(X_38,X_39)) = add(X_38,inverse(X_39)),
inference(subst,[],[refute_0_121:[bind(X_10,$fot(X_38)),bind(X_11,$fot(X_39))]]) ).
cnf(refute_0_148,plain,
( add(inverse(X_39),multiply(X_38,X_39)) != add(X_38,inverse(X_39))
| add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) != multiply(inverse(X_39),add(inverse(X_39),multiply(X_38,X_39)))
| add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) = multiply(inverse(X_39),add(X_38,inverse(X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)),multiply(inverse(X_39),add(inverse(X_39),multiply(X_38,X_39)))) ),[1,1],$fot(add(X_38,inverse(X_39)))]]) ).
cnf(refute_0_149,plain,
( add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) != multiply(inverse(X_39),add(inverse(X_39),multiply(X_38,X_39)))
| add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) = multiply(inverse(X_39),add(X_38,inverse(X_39))) ),
inference(resolve,[$cnf( $equal(add(inverse(X_39),multiply(X_38,X_39)),add(X_38,inverse(X_39))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) = multiply(inverse(X_39),add(X_38,inverse(X_39))),
inference(resolve,[$cnf( $equal(add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)),multiply(inverse(X_39),add(inverse(X_39),multiply(X_38,X_39)))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(add(X_20,X_22),add(X_20,X_21)) = multiply(add(X_20,X_21),add(X_20,X_22)),
inference(subst,[],[commutativity_of_multiply:[bind(X,$fot(add(X_20,X_22))),bind(Y,$fot(add(X_20,X_21)))]]) ).
cnf(refute_0_152,plain,
add(X_20,multiply(X_21,X_22)) = multiply(add(X_20,X_21),add(X_20,X_22)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_153,plain,
( add(X_20,multiply(X_21,X_22)) != multiply(add(X_20,X_21),add(X_20,X_22))
| multiply(add(X_20,X_21),add(X_20,X_22)) = add(X_20,multiply(X_21,X_22)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X_20,multiply(X_21,X_22)))),bind(Y0,$fot(multiply(add(X_20,X_21),add(X_20,X_22))))]]) ).
cnf(refute_0_154,plain,
multiply(add(X_20,X_21),add(X_20,X_22)) = add(X_20,multiply(X_21,X_22)),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,X_22)),multiply(add(X_20,X_21),add(X_20,X_22))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
( multiply(add(X_20,X_21),add(X_20,X_22)) != add(X_20,multiply(X_21,X_22))
| multiply(add(X_20,X_22),add(X_20,X_21)) != multiply(add(X_20,X_21),add(X_20,X_22))
| multiply(add(X_20,X_22),add(X_20,X_21)) = add(X_20,multiply(X_21,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_20,X_22),add(X_20,X_21)),multiply(add(X_20,X_21),add(X_20,X_22))) ),[1],$fot(add(X_20,multiply(X_21,X_22)))]]) ).
cnf(refute_0_156,plain,
( multiply(add(X_20,X_22),add(X_20,X_21)) != multiply(add(X_20,X_21),add(X_20,X_22))
| multiply(add(X_20,X_22),add(X_20,X_21)) = add(X_20,multiply(X_21,X_22)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_20,X_21),add(X_20,X_22)),add(X_20,multiply(X_21,X_22))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(add(X_20,X_22),add(X_20,X_21)) = add(X_20,multiply(X_21,X_22)),
inference(resolve,[$cnf( $equal(multiply(add(X_20,X_22),add(X_20,X_21)),multiply(add(X_20,X_21),add(X_20,X_22))) )],[refute_0_151,refute_0_156]) ).
cnf(refute_0_158,plain,
( add(X,multiply(Y,Z)) != multiply(add(X,Y),add(X,Z))
| multiply(add(X,Y),add(X,Z)) = add(X,multiply(Y,Z)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X,multiply(Y,Z)))),bind(Y0,$fot(multiply(add(X,Y),add(X,Z))))]]) ).
cnf(refute_0_159,plain,
multiply(add(X,Y),add(X,Z)) = add(X,multiply(Y,Z)),
inference(resolve,[$cnf( $equal(add(X,multiply(Y,Z)),multiply(add(X,Y),add(X,Z))) )],[distributivity2,refute_0_158]) ).
cnf(refute_0_160,plain,
multiply(add(X_20,X_22),add(X_20,X_21)) = add(X_20,multiply(X_22,X_21)),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_20)),bind(Y,$fot(X_22)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_161,plain,
( multiply(add(X_20,X_22),add(X_20,X_21)) != add(X_20,multiply(X_21,X_22))
| multiply(add(X_20,X_22),add(X_20,X_21)) != add(X_20,multiply(X_22,X_21))
| add(X_20,multiply(X_22,X_21)) = add(X_20,multiply(X_21,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_20,X_22),add(X_20,X_21)),add(X_20,multiply(X_21,X_22))) ),[0],$fot(add(X_20,multiply(X_22,X_21)))]]) ).
cnf(refute_0_162,plain,
( multiply(add(X_20,X_22),add(X_20,X_21)) != add(X_20,multiply(X_21,X_22))
| add(X_20,multiply(X_22,X_21)) = add(X_20,multiply(X_21,X_22)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_20,X_22),add(X_20,X_21)),add(X_20,multiply(X_22,X_21))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
add(X_20,multiply(X_22,X_21)) = add(X_20,multiply(X_21,X_22)),
inference(resolve,[$cnf( $equal(multiply(add(X_20,X_22),add(X_20,X_21)),add(X_20,multiply(X_21,X_22))) )],[refute_0_157,refute_0_162]) ).
cnf(refute_0_164,plain,
( add(X_20,multiply(X_22,X_21)) != add(X_20,multiply(X_21,X_22))
| add(X_20,multiply(X_21,X_22)) = add(X_20,multiply(X_22,X_21)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X_20,multiply(X_22,X_21)))),bind(Y0,$fot(add(X_20,multiply(X_21,X_22))))]]) ).
cnf(refute_0_165,plain,
add(X_20,multiply(X_21,X_22)) = add(X_20,multiply(X_22,X_21)),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_22,X_21)),add(X_20,multiply(X_21,X_22))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) = add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))),
inference(subst,[],[refute_0_165:[bind(X_20,$fot(inverse(X_39))),bind(X_21,$fot(multiply(X_38,X_39))),bind(X_22,$fot(additive_identity))]]) ).
cnf(refute_0_167,plain,
( add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) != multiply(inverse(X_39),add(X_38,inverse(X_39)))
| add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) != add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39)))
| add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) = multiply(inverse(X_39),add(X_38,inverse(X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)),multiply(inverse(X_39),add(X_38,inverse(X_39)))) ),[0],$fot(add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))))]]) ).
cnf(refute_0_168,plain,
( add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) != multiply(inverse(X_39),add(X_38,inverse(X_39)))
| add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) = multiply(inverse(X_39),add(X_38,inverse(X_39))) ),
inference(resolve,[$cnf( $equal(add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)),add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39)))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
add(X,multiply(X_36,additive_identity)) = add(multiply(X_36,additive_identity),X),
inference(subst,[],[commutativity_of_add:[bind(Y,$fot(multiply(X_36,additive_identity)))]]) ).
cnf(refute_0_170,plain,
add(multiply(X_36,additive_identity),X) = multiply(X,add(X_36,X)),
inference(subst,[],[refute_0_107:[bind(X_10,$fot(X_36)),bind(X_12,$fot(X))]]) ).
cnf(refute_0_171,plain,
( add(X,multiply(X_36,additive_identity)) != add(multiply(X_36,additive_identity),X)
| add(multiply(X_36,additive_identity),X) != multiply(X,add(X_36,X))
| add(X,multiply(X_36,additive_identity)) = multiply(X,add(X_36,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,multiply(X_36,additive_identity)),multiply(X,add(X_36,X))) ),[0],$fot(add(multiply(X_36,additive_identity),X))]]) ).
cnf(refute_0_172,plain,
( add(X,multiply(X_36,additive_identity)) != add(multiply(X_36,additive_identity),X)
| add(X,multiply(X_36,additive_identity)) = multiply(X,add(X_36,X)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_36,additive_identity),X),multiply(X,add(X_36,X))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
add(X,multiply(X_36,additive_identity)) = multiply(X,add(X_36,X)),
inference(resolve,[$cnf( $equal(add(X,multiply(X_36,additive_identity)),add(multiply(X_36,additive_identity),X)) )],[refute_0_169,refute_0_172]) ).
cnf(refute_0_174,plain,
( add(X,multiply(X_36,additive_identity)) != multiply(X,add(X_36,X))
| multiply(X,add(X_36,X)) = add(X,multiply(X_36,additive_identity)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X,multiply(X_36,additive_identity)))),bind(Y0,$fot(multiply(X,add(X_36,X))))]]) ).
cnf(refute_0_175,plain,
multiply(X,add(X_36,X)) = add(X,multiply(X_36,additive_identity)),
inference(resolve,[$cnf( $equal(add(X,multiply(X_36,additive_identity)),multiply(X,add(X_36,X))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(inverse(X_39),add(X_38,inverse(X_39))) = add(inverse(X_39),multiply(X_38,additive_identity)),
inference(subst,[],[refute_0_175:[bind(X,$fot(inverse(X_39))),bind(X_36,$fot(X_38))]]) ).
cnf(refute_0_177,plain,
( multiply(inverse(X_39),add(X_38,inverse(X_39))) != add(inverse(X_39),multiply(X_38,additive_identity))
| add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) != multiply(inverse(X_39),add(X_38,inverse(X_39)))
| add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) = add(inverse(X_39),multiply(X_38,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))),multiply(inverse(X_39),add(X_38,inverse(X_39)))) ),[1],$fot(add(inverse(X_39),multiply(X_38,additive_identity)))]]) ).
cnf(refute_0_178,plain,
( add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) != multiply(inverse(X_39),add(X_38,inverse(X_39)))
| add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) = add(inverse(X_39),multiply(X_38,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_39),add(X_38,inverse(X_39))),add(inverse(X_39),multiply(X_38,additive_identity))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)) != multiply(inverse(X_39),add(X_38,inverse(X_39)))
| add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) = add(inverse(X_39),multiply(X_38,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))),multiply(inverse(X_39),add(X_38,inverse(X_39)))) )],[refute_0_168,refute_0_178]) ).
cnf(refute_0_180,plain,
add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) = add(inverse(X_39),multiply(X_38,additive_identity)),
inference(resolve,[$cnf( $equal(add(inverse(X_39),multiply(multiply(X_38,X_39),additive_identity)),multiply(inverse(X_39),add(X_38,inverse(X_39)))) )],[refute_0_150,refute_0_179]) ).
cnf(refute_0_181,plain,
add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) = multiply(add(inverse(X_39),Y),add(inverse(X_39),multiply(X_38,X_39))),
inference(subst,[],[distributivity2:[bind(X,$fot(inverse(X_39))),bind(Z,$fot(multiply(X_38,X_39)))]]) ).
cnf(refute_0_182,plain,
( add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) != multiply(add(inverse(X_39),Y),add(inverse(X_39),multiply(X_38,X_39)))
| add(inverse(X_39),multiply(X_38,X_39)) != add(X_38,inverse(X_39))
| add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) = multiply(add(inverse(X_39),Y),add(X_38,inverse(X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_39),multiply(Y,multiply(X_38,X_39))),multiply(add(inverse(X_39),Y),add(inverse(X_39),multiply(X_38,X_39)))) ),[1,1],$fot(add(X_38,inverse(X_39)))]]) ).
cnf(refute_0_183,plain,
( add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) != multiply(add(inverse(X_39),Y),add(inverse(X_39),multiply(X_38,X_39)))
| add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) = multiply(add(inverse(X_39),Y),add(X_38,inverse(X_39))) ),
inference(resolve,[$cnf( $equal(add(inverse(X_39),multiply(X_38,X_39)),add(X_38,inverse(X_39))) )],[refute_0_147,refute_0_182]) ).
cnf(refute_0_184,plain,
add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) = multiply(add(inverse(X_39),Y),add(X_38,inverse(X_39))),
inference(resolve,[$cnf( $equal(add(inverse(X_39),multiply(Y,multiply(X_38,X_39))),multiply(add(inverse(X_39),Y),add(inverse(X_39),multiply(X_38,X_39)))) )],[refute_0_181,refute_0_183]) ).
cnf(refute_0_185,plain,
add(multiply(X_10,X_11),X_12) = multiply(add(X_10,X_12),add(X_11,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_186,plain,
add(X_12,X_10) = add(X_10,X_12),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_12)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_187,plain,
( add(X_12,X_10) != add(X_10,X_12)
| add(X_10,X_12) = add(X_12,X_10) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X_12,X_10))),bind(Y0,$fot(add(X_10,X_12)))]]) ).
cnf(refute_0_188,plain,
add(X_10,X_12) = add(X_12,X_10),
inference(resolve,[$cnf( $equal(add(X_12,X_10),add(X_10,X_12)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
( add(X_10,X_12) != add(X_12,X_10)
| add(multiply(X_10,X_11),X_12) != multiply(add(X_10,X_12),add(X_11,X_12))
| add(multiply(X_10,X_11),X_12) = multiply(add(X_12,X_10),add(X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,X_11),X_12),multiply(add(X_10,X_12),add(X_11,X_12))) ),[1,0],$fot(add(X_12,X_10))]]) ).
cnf(refute_0_190,plain,
( add(multiply(X_10,X_11),X_12) != multiply(add(X_10,X_12),add(X_11,X_12))
| add(multiply(X_10,X_11),X_12) = multiply(add(X_12,X_10),add(X_11,X_12)) ),
inference(resolve,[$cnf( $equal(add(X_10,X_12),add(X_12,X_10)) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
add(multiply(X_10,X_11),X_12) = multiply(add(X_12,X_10),add(X_11,X_12)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),X_12),multiply(add(X_10,X_12),add(X_11,X_12))) )],[refute_0_185,refute_0_190]) ).
cnf(refute_0_192,plain,
( add(multiply(X_10,X_11),X_12) != multiply(add(X_12,X_10),add(X_11,X_12))
| multiply(add(X_12,X_10),add(X_11,X_12)) = add(multiply(X_10,X_11),X_12) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(multiply(X_10,X_11),X_12))),bind(Y0,$fot(multiply(add(X_12,X_10),add(X_11,X_12))))]]) ).
cnf(refute_0_193,plain,
multiply(add(X_12,X_10),add(X_11,X_12)) = add(multiply(X_10,X_11),X_12),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),X_12),multiply(add(X_12,X_10),add(X_11,X_12))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
multiply(add(inverse(X_39),Y),add(X_38,inverse(X_39))) = add(multiply(Y,X_38),inverse(X_39)),
inference(subst,[],[refute_0_193:[bind(X_10,$fot(Y)),bind(X_11,$fot(X_38)),bind(X_12,$fot(inverse(X_39)))]]) ).
cnf(refute_0_195,plain,
( multiply(add(inverse(X_39),Y),add(X_38,inverse(X_39))) != add(multiply(Y,X_38),inverse(X_39))
| add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) != multiply(add(inverse(X_39),Y),add(X_38,inverse(X_39)))
| add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) = add(multiply(Y,X_38),inverse(X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_39),multiply(Y,multiply(X_38,X_39))),multiply(add(inverse(X_39),Y),add(X_38,inverse(X_39)))) ),[1],$fot(add(multiply(Y,X_38),inverse(X_39)))]]) ).
cnf(refute_0_196,plain,
( add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) != multiply(add(inverse(X_39),Y),add(X_38,inverse(X_39)))
| add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) = add(multiply(Y,X_38),inverse(X_39)) ),
inference(resolve,[$cnf( $equal(multiply(add(inverse(X_39),Y),add(X_38,inverse(X_39))),add(multiply(Y,X_38),inverse(X_39))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
add(inverse(X_39),multiply(Y,multiply(X_38,X_39))) = add(multiply(Y,X_38),inverse(X_39)),
inference(resolve,[$cnf( $equal(add(inverse(X_39),multiply(Y,multiply(X_38,X_39))),multiply(add(inverse(X_39),Y),add(X_38,inverse(X_39)))) )],[refute_0_184,refute_0_196]) ).
cnf(refute_0_198,plain,
add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) = add(multiply(additive_identity,X_38),inverse(X_39)),
inference(subst,[],[refute_0_197:[bind(Y,$fot(additive_identity))]]) ).
cnf(refute_0_199,plain,
( add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) != add(multiply(additive_identity,X_38),inverse(X_39))
| add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) != add(inverse(X_39),multiply(X_38,additive_identity))
| add(multiply(additive_identity,X_38),inverse(X_39)) = add(inverse(X_39),multiply(X_38,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))),add(inverse(X_39),multiply(X_38,additive_identity))) ),[0],$fot(add(multiply(additive_identity,X_38),inverse(X_39)))]]) ).
cnf(refute_0_200,plain,
( add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))) != add(inverse(X_39),multiply(X_38,additive_identity))
| add(multiply(additive_identity,X_38),inverse(X_39)) = add(inverse(X_39),multiply(X_38,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))),add(multiply(additive_identity,X_38),inverse(X_39))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
add(multiply(additive_identity,X_38),inverse(X_39)) = add(inverse(X_39),multiply(X_38,additive_identity)),
inference(resolve,[$cnf( $equal(add(inverse(X_39),multiply(additive_identity,multiply(X_38,X_39))),add(inverse(X_39),multiply(X_38,additive_identity))) )],[refute_0_180,refute_0_200]) ).
cnf(refute_0_202,plain,
( add(multiply(additive_identity,X_38),inverse(X_39)) != add(inverse(X_39),multiply(X_38,additive_identity))
| add(inverse(X_39),multiply(X_38,additive_identity)) = add(multiply(additive_identity,X_38),inverse(X_39)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(multiply(additive_identity,X_38),inverse(X_39)))),bind(Y0,$fot(add(inverse(X_39),multiply(X_38,additive_identity))))]]) ).
cnf(refute_0_203,plain,
add(inverse(X_39),multiply(X_38,additive_identity)) = add(multiply(additive_identity,X_38),inverse(X_39)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_38),inverse(X_39)),add(inverse(X_39),multiply(X_38,additive_identity))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
add(inverse(inverse(multiply(X_10,additive_identity))),multiply(X_10,additive_identity)) = add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))),
inference(subst,[],[refute_0_203:[bind(X_38,$fot(X_10)),bind(X_39,$fot(inverse(multiply(X_10,additive_identity))))]]) ).
cnf(refute_0_205,plain,
multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))) = add(inverse(inverse(multiply(X_10,additive_identity))),multiply(X_10,additive_identity)),
inference(subst,[],[refute_0_175:[bind(X,$fot(inverse(inverse(multiply(X_10,additive_identity))))),bind(X_36,$fot(X_10))]]) ).
cnf(refute_0_206,plain,
( multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))) != add(inverse(inverse(multiply(X_10,additive_identity))),multiply(X_10,additive_identity))
| add(inverse(inverse(multiply(X_10,additive_identity))),multiply(X_10,additive_identity)) != add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))
| multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))) = add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))))),bind(Y0,$fot(add(inverse(inverse(multiply(X_10,additive_identity))),multiply(X_10,additive_identity)))),bind(Z0,$fot(add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))))]]) ).
cnf(refute_0_207,plain,
( add(inverse(inverse(multiply(X_10,additive_identity))),multiply(X_10,additive_identity)) != add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))
| multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))) = add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))),add(inverse(inverse(multiply(X_10,additive_identity))),multiply(X_10,additive_identity))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))) = add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))),
inference(resolve,[$cnf( $equal(add(inverse(inverse(multiply(X_10,additive_identity))),multiply(X_10,additive_identity)),add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
( multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))) != add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))
| inverse(inverse(multiply(X_10,additive_identity))) != multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity)))))
| inverse(inverse(multiply(X_10,additive_identity))) = add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_10,additive_identity))),multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity)))))) ),[1],$fot(add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))))]]) ).
cnf(refute_0_210,plain,
( inverse(inverse(multiply(X_10,additive_identity))) != multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity)))))
| inverse(inverse(multiply(X_10,additive_identity))) = add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity))))),add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
inverse(inverse(multiply(X_10,additive_identity))) = add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_10,additive_identity))),multiply(inverse(inverse(multiply(X_10,additive_identity))),add(X_10,inverse(inverse(multiply(X_10,additive_identity)))))) )],[refute_0_136,refute_0_210]) ).
cnf(refute_0_212,plain,
add(X_20,multiply(inverse(X_20),X_22)) = multiply(add(X_20,inverse(X_20)),add(X_20,X_22)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_20)),bind(Y,$fot(inverse(X_20))),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_213,plain,
( add(X_20,multiply(inverse(X_20),X_22)) != multiply(add(X_20,inverse(X_20)),add(X_20,X_22))
| add(X_20,inverse(X_20)) != multiplicative_identity
| add(X_20,multiply(inverse(X_20),X_22)) = multiply(multiplicative_identity,add(X_20,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(inverse(X_20),X_22)),multiply(add(X_20,inverse(X_20)),add(X_20,X_22))) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_214,plain,
( add(X_20,multiply(inverse(X_20),X_22)) != multiply(add(X_20,inverse(X_20)),add(X_20,X_22))
| add(X_20,multiply(inverse(X_20),X_22)) = multiply(multiplicative_identity,add(X_20,X_22)) ),
inference(resolve,[$cnf( $equal(add(X_20,inverse(X_20)),multiplicative_identity) )],[refute_0_35,refute_0_213]) ).
cnf(refute_0_215,plain,
add(X_20,multiply(inverse(X_20),X_22)) = multiply(multiplicative_identity,add(X_20,X_22)),
inference(resolve,[$cnf( $equal(add(X_20,multiply(inverse(X_20),X_22)),multiply(add(X_20,inverse(X_20)),add(X_20,X_22))) )],[refute_0_212,refute_0_214]) ).
cnf(refute_0_216,plain,
multiply(multiplicative_identity,add(X_20,X_22)) = add(X_20,X_22),
inference(subst,[],[multiplicative_id2:[bind(X,$fot(add(X_20,X_22)))]]) ).
cnf(refute_0_217,plain,
( multiply(multiplicative_identity,add(X_20,X_22)) != add(X_20,X_22)
| add(X_20,multiply(inverse(X_20),X_22)) != multiply(multiplicative_identity,add(X_20,X_22))
| add(X_20,multiply(inverse(X_20),X_22)) = add(X_20,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(inverse(X_20),X_22)),multiply(multiplicative_identity,add(X_20,X_22))) ),[1],$fot(add(X_20,X_22))]]) ).
cnf(refute_0_218,plain,
( add(X_20,multiply(inverse(X_20),X_22)) != multiply(multiplicative_identity,add(X_20,X_22))
| add(X_20,multiply(inverse(X_20),X_22)) = add(X_20,X_22) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(X_20,X_22)),add(X_20,X_22)) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
add(X_20,multiply(inverse(X_20),X_22)) = add(X_20,X_22),
inference(resolve,[$cnf( $equal(add(X_20,multiply(inverse(X_20),X_22)),multiply(multiplicative_identity,add(X_20,X_22))) )],[refute_0_215,refute_0_218]) ).
cnf(refute_0_220,plain,
add(X_51,multiply(inverse(X_51),inverse(inverse(X_51)))) = add(X_51,inverse(inverse(X_51))),
inference(subst,[],[refute_0_219:[bind(X_20,$fot(X_51)),bind(X_22,$fot(inverse(inverse(X_51))))]]) ).
cnf(refute_0_221,plain,
multiply(inverse(X_51),inverse(inverse(X_51))) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(inverse(X_51)))]]) ).
cnf(refute_0_222,plain,
( multiply(inverse(X_51),inverse(inverse(X_51))) != additive_identity
| add(X_51,multiply(inverse(X_51),inverse(inverse(X_51)))) != add(X_51,inverse(inverse(X_51)))
| add(X_51,additive_identity) = add(X_51,inverse(inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_51,multiply(inverse(X_51),inverse(inverse(X_51)))),add(X_51,inverse(inverse(X_51)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_223,plain,
( add(X_51,multiply(inverse(X_51),inverse(inverse(X_51)))) != add(X_51,inverse(inverse(X_51)))
| add(X_51,additive_identity) = add(X_51,inverse(inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),inverse(inverse(X_51))),additive_identity) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
add(X_51,additive_identity) = add(X_51,inverse(inverse(X_51))),
inference(resolve,[$cnf( $equal(add(X_51,multiply(inverse(X_51),inverse(inverse(X_51)))),add(X_51,inverse(inverse(X_51)))) )],[refute_0_220,refute_0_223]) ).
cnf(refute_0_225,plain,
add(X_51,additive_identity) = X_51,
inference(subst,[],[additive_id1:[bind(X,$fot(X_51))]]) ).
cnf(refute_0_226,plain,
( add(X_51,additive_identity) != X_51
| add(X_51,additive_identity) != add(X_51,inverse(inverse(X_51)))
| X_51 = add(X_51,inverse(inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_51,additive_identity),add(X_51,inverse(inverse(X_51)))) ),[0],$fot(X_51)]]) ).
cnf(refute_0_227,plain,
( add(X_51,additive_identity) != add(X_51,inverse(inverse(X_51)))
| X_51 = add(X_51,inverse(inverse(X_51))) ),
inference(resolve,[$cnf( $equal(add(X_51,additive_identity),X_51) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
( inverse(inverse(X_38)) != add(X_38,inverse(inverse(X_38)))
| add(X_38,inverse(inverse(X_38))) = inverse(inverse(X_38)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(inverse(X_38)))),bind(Y0,$fot(add(X_38,inverse(inverse(X_38)))))]]) ).
cnf(refute_0_229,plain,
add(X_38,inverse(inverse(X_38))) = inverse(inverse(X_38)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_38)),add(X_38,inverse(inverse(X_38)))) )],[refute_0_130,refute_0_228]) ).
cnf(refute_0_230,plain,
add(X_51,inverse(inverse(X_51))) = inverse(inverse(X_51)),
inference(subst,[],[refute_0_229:[bind(X_38,$fot(X_51))]]) ).
cnf(refute_0_231,plain,
( X_51 != add(X_51,inverse(inverse(X_51)))
| add(X_51,inverse(inverse(X_51))) != inverse(inverse(X_51))
| X_51 = inverse(inverse(X_51)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_51,inverse(inverse(X_51))) ),[0],$fot(add(X_51,inverse(inverse(X_51))))]]) ).
cnf(refute_0_232,plain,
( X_51 != add(X_51,inverse(inverse(X_51)))
| X_51 = inverse(inverse(X_51)) ),
inference(resolve,[$cnf( $equal(add(X_51,inverse(inverse(X_51))),inverse(inverse(X_51))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
( add(X_51,additive_identity) != add(X_51,inverse(inverse(X_51)))
| X_51 = inverse(inverse(X_51)) ),
inference(resolve,[$cnf( $equal(X_51,add(X_51,inverse(inverse(X_51)))) )],[refute_0_227,refute_0_232]) ).
cnf(refute_0_234,plain,
X_51 = inverse(inverse(X_51)),
inference(resolve,[$cnf( $equal(add(X_51,additive_identity),add(X_51,inverse(inverse(X_51)))) )],[refute_0_224,refute_0_233]) ).
cnf(refute_0_235,plain,
( X_51 != inverse(inverse(X_51))
| inverse(inverse(X_51)) = X_51 ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(X_51)),bind(Y0,$fot(inverse(inverse(X_51))))]]) ).
cnf(refute_0_236,plain,
inverse(inverse(X_51)) = X_51,
inference(resolve,[$cnf( $equal(X_51,inverse(inverse(X_51))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
inverse(inverse(multiply(X_10,additive_identity))) = multiply(X_10,additive_identity),
inference(subst,[],[refute_0_236:[bind(X_51,$fot(multiply(X_10,additive_identity)))]]) ).
cnf(refute_0_238,plain,
( inverse(inverse(multiply(X_10,additive_identity))) != multiply(X_10,additive_identity)
| inverse(inverse(multiply(X_10,additive_identity))) != add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))
| multiply(X_10,additive_identity) = add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_10,additive_identity))),add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))) ),[0],$fot(multiply(X_10,additive_identity))]]) ).
cnf(refute_0_239,plain,
( inverse(inverse(multiply(X_10,additive_identity))) != add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))
| multiply(X_10,additive_identity) = add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_10,additive_identity))),multiply(X_10,additive_identity)) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
( X_25 != add(X_25,X_25)
| add(X_25,X_25) = X_25 ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(X_25)),bind(Y0,$fot(add(X_25,X_25)))]]) ).
cnf(refute_0_241,plain,
add(X_25,X_25) = X_25,
inference(resolve,[$cnf( $equal(X_25,add(X_25,X_25)) )],[refute_0_75,refute_0_240]) ).
cnf(refute_0_242,plain,
add(X_10,X_10) = X_10,
inference(subst,[],[refute_0_241:[bind(X_25,$fot(X_10))]]) ).
cnf(refute_0_243,plain,
multiply(additive_identity,add(X_10,X_10)) = multiply(additive_identity,add(X_10,X_10)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(X_10,X_10)))]]) ).
cnf(refute_0_244,plain,
( multiply(additive_identity,add(X_10,X_10)) != multiply(additive_identity,add(X_10,X_10))
| add(X_10,X_10) != X_10
| multiply(additive_identity,add(X_10,X_10)) = multiply(additive_identity,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_10,X_10)),multiply(additive_identity,add(X_10,X_10))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_245,plain,
( add(X_10,X_10) != X_10
| multiply(additive_identity,add(X_10,X_10)) = multiply(additive_identity,X_10) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_10,X_10)),multiply(additive_identity,add(X_10,X_10))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
multiply(additive_identity,add(X_10,X_10)) = multiply(additive_identity,X_10),
inference(resolve,[$cnf( $equal(add(X_10,X_10),X_10) )],[refute_0_242,refute_0_245]) ).
cnf(refute_0_247,plain,
add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) = multiply(multiply(X_21,additive_identity),add(X_36,multiply(X_21,additive_identity))),
inference(subst,[],[refute_0_107:[bind(X_10,$fot(X_36)),bind(X_12,$fot(multiply(X_21,additive_identity)))]]) ).
cnf(refute_0_248,plain,
add(X_36,multiply(X_21,additive_identity)) = multiply(X_36,add(X_36,X_21)),
inference(subst,[],[refute_0_145:[bind(X_20,$fot(X_36))]]) ).
cnf(refute_0_249,plain,
( add(X_36,multiply(X_21,additive_identity)) != multiply(X_36,add(X_36,X_21))
| add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) != multiply(multiply(X_21,additive_identity),add(X_36,multiply(X_21,additive_identity)))
| add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) = multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)),multiply(multiply(X_21,additive_identity),add(X_36,multiply(X_21,additive_identity)))) ),[1,1],$fot(multiply(X_36,add(X_36,X_21)))]]) ).
cnf(refute_0_250,plain,
( add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) != multiply(multiply(X_21,additive_identity),add(X_36,multiply(X_21,additive_identity)))
| add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) = multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) ),
inference(resolve,[$cnf( $equal(add(X_36,multiply(X_21,additive_identity)),multiply(X_36,add(X_36,X_21))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) = multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))),
inference(resolve,[$cnf( $equal(add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)),multiply(multiply(X_21,additive_identity),add(X_36,multiply(X_21,additive_identity)))) )],[refute_0_247,refute_0_250]) ).
cnf(refute_0_252,plain,
multiply(add(X_36,X_21),additive_identity) = multiply(additive_identity,add(X_36,X_21)),
inference(subst,[],[refute_0_8:[bind(X,$fot(additive_identity)),bind(Y,$fot(add(X_36,X_21)))]]) ).
cnf(refute_0_253,plain,
( multiply(add(X,Y),Z) != add(multiply(X,Z),multiply(Y,Z))
| add(multiply(X,Z),multiply(Y,Z)) = multiply(add(X,Y),Z) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(add(X,Y),Z))),bind(Y0,$fot(add(multiply(X,Z),multiply(Y,Z))))]]) ).
cnf(refute_0_254,plain,
add(multiply(X,Z),multiply(Y,Z)) = multiply(add(X,Y),Z),
inference(resolve,[$cnf( $equal(multiply(add(X,Y),Z),add(multiply(X,Z),multiply(Y,Z))) )],[distributivity3,refute_0_253]) ).
cnf(refute_0_255,plain,
add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) = multiply(add(X_36,X_21),additive_identity),
inference(subst,[],[refute_0_254:[bind(X,$fot(X_36)),bind(Y,$fot(X_21)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_256,plain,
( multiply(add(X_36,X_21),additive_identity) != multiply(additive_identity,add(X_36,X_21))
| add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) != multiply(add(X_36,X_21),additive_identity)
| add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) = multiply(additive_identity,add(X_36,X_21)) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)))),bind(Y0,$fot(multiply(add(X_36,X_21),additive_identity))),bind(Z0,$fot(multiply(additive_identity,add(X_36,X_21))))]]) ).
cnf(refute_0_257,plain,
( multiply(add(X_36,X_21),additive_identity) != multiply(additive_identity,add(X_36,X_21))
| add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) = multiply(additive_identity,add(X_36,X_21)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)),multiply(add(X_36,X_21),additive_identity)) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) = multiply(additive_identity,add(X_36,X_21)),
inference(resolve,[$cnf( $equal(multiply(add(X_36,X_21),additive_identity),multiply(additive_identity,add(X_36,X_21))) )],[refute_0_252,refute_0_257]) ).
cnf(refute_0_259,plain,
( add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) != multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))
| add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) != multiply(additive_identity,add(X_36,X_21))
| multiply(additive_identity,add(X_36,X_21)) = multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)),multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))) ),[0],$fot(multiply(additive_identity,add(X_36,X_21)))]]) ).
cnf(refute_0_260,plain,
( add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) != multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))
| multiply(additive_identity,add(X_36,X_21)) = multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)),multiply(additive_identity,add(X_36,X_21))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)) = multiply(multiply(X_33,additive_identity),add(X_11,multiply(X_33,additive_identity))),
inference(subst,[],[refute_0_19:[bind(X_12,$fot(multiply(X_33,additive_identity)))]]) ).
cnf(refute_0_262,plain,
add(X_11,multiply(X_33,additive_identity)) = multiply(X_11,add(X_11,X_33)),
inference(subst,[],[refute_0_145:[bind(X_20,$fot(X_11)),bind(X_21,$fot(X_33))]]) ).
cnf(refute_0_263,plain,
( add(X_11,multiply(X_33,additive_identity)) != multiply(X_11,add(X_11,X_33))
| add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)) != multiply(multiply(X_33,additive_identity),add(X_11,multiply(X_33,additive_identity)))
| add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)) = multiply(multiply(X_33,additive_identity),multiply(X_11,add(X_11,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)),multiply(multiply(X_33,additive_identity),add(X_11,multiply(X_33,additive_identity)))) ),[1,1],$fot(multiply(X_11,add(X_11,X_33)))]]) ).
cnf(refute_0_264,plain,
( add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)) != multiply(multiply(X_33,additive_identity),add(X_11,multiply(X_33,additive_identity)))
| add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)) = multiply(multiply(X_33,additive_identity),multiply(X_11,add(X_11,X_33))) ),
inference(resolve,[$cnf( $equal(add(X_11,multiply(X_33,additive_identity)),multiply(X_11,add(X_11,X_33))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)) = multiply(multiply(X_33,additive_identity),multiply(X_11,add(X_11,X_33))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)),multiply(multiply(X_33,additive_identity),add(X_11,multiply(X_33,additive_identity)))) )],[refute_0_261,refute_0_264]) ).
cnf(refute_0_266,plain,
( add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)) != multiply(multiply(X_33,additive_identity),multiply(X_11,add(X_11,X_33)))
| multiply(multiply(X_33,additive_identity),multiply(X_11,add(X_11,X_33))) = add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)))),bind(Y0,$fot(multiply(multiply(X_33,additive_identity),multiply(X_11,add(X_11,X_33)))))]]) ).
cnf(refute_0_267,plain,
multiply(multiply(X_33,additive_identity),multiply(X_11,add(X_11,X_33))) = add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_11),multiply(X_33,additive_identity)),multiply(multiply(X_33,additive_identity),multiply(X_11,add(X_11,X_33)))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) = add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)),
inference(subst,[],[refute_0_267:[bind(X_11,$fot(X_36)),bind(X_33,$fot(X_21))]]) ).
cnf(refute_0_269,plain,
( multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))) != add(multiply(additive_identity,X_36),multiply(X_21,additive_identity))
| multiply(additive_identity,add(X_36,X_21)) != multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))
| multiply(additive_identity,add(X_36,X_21)) = add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_36,X_21)),multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))) ),[1],$fot(add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)))]]) ).
cnf(refute_0_270,plain,
( multiply(additive_identity,add(X_36,X_21)) != multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))
| multiply(additive_identity,add(X_36,X_21)) = add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21))),add(multiply(additive_identity,X_36),multiply(X_21,additive_identity))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
( add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)) != multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))
| multiply(additive_identity,add(X_36,X_21)) = add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_36,X_21)),multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))) )],[refute_0_260,refute_0_270]) ).
cnf(refute_0_272,plain,
multiply(additive_identity,add(X_36,X_21)) = add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(X_36,additive_identity),multiply(X_21,additive_identity)),multiply(multiply(X_21,additive_identity),multiply(X_36,add(X_36,X_21)))) )],[refute_0_251,refute_0_271]) ).
cnf(refute_0_273,plain,
( multiply(additive_identity,add(X_36,X_21)) != add(multiply(additive_identity,X_36),multiply(X_21,additive_identity))
| add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) = multiply(additive_identity,add(X_36,X_21)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(additive_identity,add(X_36,X_21)))),bind(Y0,$fot(add(multiply(additive_identity,X_36),multiply(X_21,additive_identity))))]]) ).
cnf(refute_0_274,plain,
add(multiply(additive_identity,X_36),multiply(X_21,additive_identity)) = multiply(additive_identity,add(X_36,X_21)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_36,X_21)),add(multiply(additive_identity,X_36),multiply(X_21,additive_identity))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)) = multiply(additive_identity,add(X_10,X_10)),
inference(subst,[],[refute_0_274:[bind(X_21,$fot(X_10)),bind(X_36,$fot(X_10))]]) ).
cnf(refute_0_276,plain,
( multiply(additive_identity,add(X_10,X_10)) != multiply(additive_identity,X_10)
| add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)) != multiply(additive_identity,add(X_10,X_10))
| add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)) = multiply(additive_identity,X_10) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)))),bind(Y0,$fot(multiply(additive_identity,add(X_10,X_10)))),bind(Z0,$fot(multiply(additive_identity,X_10)))]]) ).
cnf(refute_0_277,plain,
( multiply(additive_identity,add(X_10,X_10)) != multiply(additive_identity,X_10)
| add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)) = multiply(additive_identity,X_10) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)),multiply(additive_identity,add(X_10,X_10))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)) = multiply(additive_identity,X_10),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_10,X_10)),multiply(additive_identity,X_10)) )],[refute_0_246,refute_0_277]) ).
cnf(refute_0_279,plain,
add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) = add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))),
introduced(tautology,[refl,[$fot(add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))))]]) ).
cnf(refute_0_280,plain,
( add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) != add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))
| inverse(inverse(multiply(X_10,additive_identity))) != multiply(X_10,additive_identity)
| add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) = add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))),add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))) ),[1,1],$fot(multiply(X_10,additive_identity))]]) ).
cnf(refute_0_281,plain,
( inverse(inverse(multiply(X_10,additive_identity))) != multiply(X_10,additive_identity)
| add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) = add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))),add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) = add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_10,additive_identity))),multiply(X_10,additive_identity)) )],[refute_0_237,refute_0_281]) ).
cnf(refute_0_283,plain,
( add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)) != multiply(additive_identity,X_10)
| add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) != add(multiply(additive_identity,X_10),multiply(X_10,additive_identity))
| add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) = multiply(additive_identity,X_10) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))))),bind(Y0,$fot(add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)))),bind(Z0,$fot(multiply(additive_identity,X_10)))]]) ).
cnf(refute_0_284,plain,
( add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)) != multiply(additive_identity,X_10)
| add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) = multiply(additive_identity,X_10) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))),add(multiply(additive_identity,X_10),multiply(X_10,additive_identity))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) = multiply(additive_identity,X_10),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_10),multiply(X_10,additive_identity)),multiply(additive_identity,X_10)) )],[refute_0_278,refute_0_284]) ).
cnf(refute_0_286,plain,
( multiply(X_10,additive_identity) != add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))
| add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))) != multiply(additive_identity,X_10)
| multiply(X_10,additive_identity) = multiply(additive_identity,X_10) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_10,additive_identity),multiply(additive_identity,X_10)) ),[0],$fot(add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))))]]) ).
cnf(refute_0_287,plain,
( multiply(X_10,additive_identity) != add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))
| multiply(X_10,additive_identity) = multiply(additive_identity,X_10) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity)))),multiply(additive_identity,X_10)) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
( inverse(inverse(multiply(X_10,additive_identity))) != add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))
| multiply(X_10,additive_identity) = multiply(additive_identity,X_10) ),
inference(resolve,[$cnf( $equal(multiply(X_10,additive_identity),add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))) )],[refute_0_239,refute_0_287]) ).
cnf(refute_0_289,plain,
multiply(X_10,additive_identity) = multiply(additive_identity,X_10),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_10,additive_identity))),add(multiply(additive_identity,X_10),inverse(inverse(multiply(X_10,additive_identity))))) )],[refute_0_211,refute_0_288]) ).
cnf(refute_0_290,plain,
multiply(add(additive_identity,X_59),additive_identity) = multiply(additive_identity,add(additive_identity,X_59)),
inference(subst,[],[refute_0_289:[bind(X_10,$fot(add(additive_identity,X_59)))]]) ).
cnf(refute_0_291,plain,
( multiply(add(additive_identity,X_59),additive_identity) != multiply(additive_identity,add(additive_identity,X_59))
| multiply(additive_identity,add(additive_identity,X_59)) != additive_identity
| multiply(add(additive_identity,X_59),additive_identity) = additive_identity ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(add(additive_identity,X_59),additive_identity))),bind(Y0,$fot(multiply(additive_identity,add(additive_identity,X_59)))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_292,plain,
( multiply(additive_identity,add(additive_identity,X_59)) != additive_identity
| multiply(add(additive_identity,X_59),additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(add(additive_identity,X_59),additive_identity),multiply(additive_identity,add(additive_identity,X_59))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
multiply(add(additive_identity,X_59),additive_identity) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_59)),additive_identity) )],[refute_0_99,refute_0_292]) ).
cnf(refute_0_294,plain,
( multiply(add(additive_identity,X_59),additive_identity) != multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))
| multiply(add(additive_identity,X_59),additive_identity) != additive_identity
| additive_identity = multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(additive_identity,X_59),additive_identity),multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_295,plain,
( multiply(add(additive_identity,X_59),additive_identity) != multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))
| additive_identity = multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(add(additive_identity,X_59),additive_identity),additive_identity) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
add(multiply(additive_identity,additive_identity),multiply(X_33,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)),
inference(subst,[],[refute_0_145:[bind(X_20,$fot(multiply(additive_identity,additive_identity))),bind(X_21,$fot(X_33))]]) ).
cnf(refute_0_297,plain,
add(multiply(additive_identity,additive_identity),multiply(X_33,additive_identity)) = multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)),
inference(subst,[],[refute_0_24:[bind(X_16,$fot(multiply(X_33,additive_identity)))]]) ).
cnf(refute_0_298,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_33,additive_identity)) != multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity))
| add(multiply(additive_identity,additive_identity),multiply(X_33,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33))
| multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_33,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33))) ),[0],$fot(multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)))]]) ).
cnf(refute_0_299,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_33,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33))
| multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_33,additive_identity)),multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_33,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33))) )],[refute_0_296,refute_0_299]) ).
cnf(refute_0_301,plain,
add(additive_identity,X_33) = X_33,
inference(subst,[],[additive_id2:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_302,plain,
multiply(additive_identity,add(additive_identity,X_33)) = multiply(additive_identity,add(additive_identity,X_33)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(additive_identity,X_33)))]]) ).
cnf(refute_0_303,plain,
( multiply(additive_identity,add(additive_identity,X_33)) != multiply(additive_identity,add(additive_identity,X_33))
| add(additive_identity,X_33) != X_33
| multiply(additive_identity,add(additive_identity,X_33)) = multiply(additive_identity,X_33) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_33)),multiply(additive_identity,add(additive_identity,X_33))) ),[1,1],$fot(X_33)]]) ).
cnf(refute_0_304,plain,
( add(additive_identity,X_33) != X_33
| multiply(additive_identity,add(additive_identity,X_33)) = multiply(additive_identity,X_33) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_33)),multiply(additive_identity,add(additive_identity,X_33))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
multiply(additive_identity,add(additive_identity,X_33)) = multiply(additive_identity,X_33),
inference(resolve,[$cnf( $equal(add(additive_identity,X_33),X_33) )],[refute_0_301,refute_0_304]) ).
cnf(refute_0_306,plain,
( multiply(X,add(Y,Z)) != add(multiply(X,Y),multiply(X,Z))
| add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_307,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[distributivity4,refute_0_306]) ).
cnf(refute_0_308,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_33)) = multiply(additive_identity,add(additive_identity,X_33)),
inference(subst,[],[refute_0_307:[bind(X,$fot(additive_identity)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_309,plain,
add(X_32,multiply(X_33,additive_identity)) = multiply(X_32,add(X_32,X_33)),
inference(subst,[],[refute_0_145:[bind(X_20,$fot(X_32)),bind(X_21,$fot(X_33))]]) ).
cnf(refute_0_310,plain,
multiply(additive_identity,X_33) = multiply(X_33,additive_identity),
inference(subst,[],[commutativity_of_multiply:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_311,plain,
( multiply(additive_identity,X_33) != multiply(X_33,additive_identity)
| multiply(X_33,additive_identity) = multiply(additive_identity,X_33) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(additive_identity,X_33))),bind(Y0,$fot(multiply(X_33,additive_identity)))]]) ).
cnf(refute_0_312,plain,
multiply(X_33,additive_identity) = multiply(additive_identity,X_33),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_33),multiply(X_33,additive_identity)) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
( multiply(X_33,additive_identity) != multiply(additive_identity,X_33)
| add(X_32,multiply(X_33,additive_identity)) != multiply(X_32,add(X_32,X_33))
| add(X_32,multiply(additive_identity,X_33)) = multiply(X_32,add(X_32,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_32,multiply(X_33,additive_identity)),multiply(X_32,add(X_32,X_33))) ),[0,1],$fot(multiply(additive_identity,X_33))]]) ).
cnf(refute_0_314,plain,
( add(X_32,multiply(X_33,additive_identity)) != multiply(X_32,add(X_32,X_33))
| add(X_32,multiply(additive_identity,X_33)) = multiply(X_32,add(X_32,X_33)) ),
inference(resolve,[$cnf( $equal(multiply(X_33,additive_identity),multiply(additive_identity,X_33)) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
add(X_32,multiply(additive_identity,X_33)) = multiply(X_32,add(X_32,X_33)),
inference(resolve,[$cnf( $equal(add(X_32,multiply(X_33,additive_identity)),multiply(X_32,add(X_32,X_33))) )],[refute_0_309,refute_0_314]) ).
cnf(refute_0_316,plain,
( add(X_32,multiply(additive_identity,X_33)) != multiply(X_32,add(X_32,X_33))
| multiply(X_32,add(X_32,X_33)) = add(X_32,multiply(additive_identity,X_33)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X_32,multiply(additive_identity,X_33)))),bind(Y0,$fot(multiply(X_32,add(X_32,X_33))))]]) ).
cnf(refute_0_317,plain,
multiply(X_32,add(X_32,X_33)) = add(X_32,multiply(additive_identity,X_33)),
inference(resolve,[$cnf( $equal(add(X_32,multiply(additive_identity,X_33)),multiply(X_32,add(X_32,X_33))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) = add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_33)),
inference(subst,[],[refute_0_317:[bind(X_32,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_319,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_33))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_33)) != multiply(additive_identity,add(additive_identity,X_33))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) = multiply(additive_identity,add(additive_identity,X_33)) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)))),bind(Y0,$fot(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_33)))),bind(Z0,$fot(multiply(additive_identity,add(additive_identity,X_33))))]]) ).
cnf(refute_0_320,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_33)) != multiply(additive_identity,add(additive_identity,X_33))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) = multiply(additive_identity,add(additive_identity,X_33)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)),add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_33))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) = multiply(additive_identity,add(additive_identity,X_33)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_33)),multiply(additive_identity,add(additive_identity,X_33))) )],[refute_0_308,refute_0_320]) ).
cnf(refute_0_322,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) != multiply(additive_identity,add(additive_identity,X_33))
| multiply(additive_identity,add(additive_identity,X_33)) != multiply(additive_identity,X_33)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) = multiply(additive_identity,X_33) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)))),bind(Y0,$fot(multiply(additive_identity,add(additive_identity,X_33)))),bind(Z0,$fot(multiply(additive_identity,X_33)))]]) ).
cnf(refute_0_323,plain,
( multiply(additive_identity,add(additive_identity,X_33)) != multiply(additive_identity,X_33)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) = multiply(additive_identity,X_33) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)),multiply(additive_identity,add(additive_identity,X_33))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) = multiply(additive_identity,X_33),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_33)),multiply(additive_identity,X_33)) )],[refute_0_305,refute_0_323]) ).
cnf(refute_0_325,plain,
( multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)) != multiply(additive_identity,X_33)
| multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) = multiply(additive_identity,X_33) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)),multiply(additive_identity,X_33)) ),[0],$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)))]]) ).
cnf(refute_0_326,plain,
( multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33))
| multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) = multiply(additive_identity,X_33) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33)),multiply(additive_identity,X_33)) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) = multiply(additive_identity,X_33),
inference(resolve,[$cnf( $equal(multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_33))) )],[refute_0_300,refute_0_326]) ).
cnf(refute_0_328,plain,
multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity)) = multiply(additive_identity,X_59),
inference(subst,[],[refute_0_327:[bind(X_33,$fot(X_59))]]) ).
cnf(refute_0_329,plain,
( multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity)) != multiply(additive_identity,X_59)
| additive_identity != multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))
| additive_identity = multiply(additive_identity,X_59) ),
introduced(tautology,[equality,[$cnf( $equal(additive_identity,multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))) ),[1],$fot(multiply(additive_identity,X_59))]]) ).
cnf(refute_0_330,plain,
( additive_identity != multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))
| additive_identity = multiply(additive_identity,X_59) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity)),multiply(additive_identity,X_59)) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
( multiply(add(additive_identity,X_59),additive_identity) != multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))
| additive_identity = multiply(additive_identity,X_59) ),
inference(resolve,[$cnf( $equal(additive_identity,multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))) )],[refute_0_295,refute_0_330]) ).
cnf(refute_0_332,plain,
additive_identity = multiply(additive_identity,X_59),
inference(resolve,[$cnf( $equal(multiply(add(additive_identity,X_59),additive_identity),multiply(multiply(X_59,additive_identity),multiply(X_59,additive_identity))) )],[refute_0_28,refute_0_331]) ).
cnf(refute_0_333,plain,
additive_identity = multiply(additive_identity,y),
inference(subst,[],[refute_0_332:[bind(X_59,$fot(y))]]) ).
cnf(refute_0_334,plain,
( additive_identity != multiply(additive_identity,y)
| multiply(additive_identity,y) = additive_identity ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(additive_identity,y)))]]) ).
cnf(refute_0_335,plain,
multiply(additive_identity,y) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(additive_identity,y)) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
( multiply(additive_identity,y) != additive_identity
| add(x,multiply(additive_identity,y)) != multiply(z,add(x,additive_identity))
| add(x,additive_identity) = multiply(z,add(x,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(x,multiply(additive_identity,y)),multiply(z,add(x,additive_identity))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_337,plain,
( add(x,multiply(additive_identity,y)) != multiply(z,add(x,additive_identity))
| add(x,additive_identity) = multiply(z,add(x,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,y),additive_identity) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
add(x,additive_identity) = multiply(z,add(x,additive_identity)),
inference(resolve,[$cnf( $equal(add(x,multiply(additive_identity,y)),multiply(z,add(x,additive_identity))) )],[refute_0_13,refute_0_337]) ).
cnf(refute_0_339,plain,
add(additive_identity,x) = x,
inference(subst,[],[additive_id2:[bind(X,$fot(x))]]) ).
cnf(refute_0_340,plain,
add(multiply(X,add(X,Z)),Z) = multiply(add(X,Z),add(add(X,Z),Z)),
inference(subst,[],[distributivity1:[bind(Y,$fot(add(X,Z)))]]) ).
cnf(refute_0_341,plain,
add(multiply(X_36,additive_identity),X_37) = multiply(X_37,add(X_36,X_37)),
inference(subst,[],[refute_0_107:[bind(X_10,$fot(X_36)),bind(X_12,$fot(X_37))]]) ).
cnf(refute_0_342,plain,
add(X_37,X_36) = add(X_36,X_37),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_37)),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_343,plain,
( add(X_37,X_36) != add(X_36,X_37)
| add(X_36,X_37) = add(X_37,X_36) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X_37,X_36))),bind(Y0,$fot(add(X_36,X_37)))]]) ).
cnf(refute_0_344,plain,
add(X_36,X_37) = add(X_37,X_36),
inference(resolve,[$cnf( $equal(add(X_37,X_36),add(X_36,X_37)) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
( add(X_36,X_37) != add(X_37,X_36)
| add(multiply(X_36,additive_identity),X_37) != multiply(X_37,add(X_36,X_37))
| add(multiply(X_36,additive_identity),X_37) = multiply(X_37,add(X_37,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_36,additive_identity),X_37),multiply(X_37,add(X_36,X_37))) ),[1,1],$fot(add(X_37,X_36))]]) ).
cnf(refute_0_346,plain,
( add(multiply(X_36,additive_identity),X_37) != multiply(X_37,add(X_36,X_37))
| add(multiply(X_36,additive_identity),X_37) = multiply(X_37,add(X_37,X_36)) ),
inference(resolve,[$cnf( $equal(add(X_36,X_37),add(X_37,X_36)) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
add(multiply(X_36,additive_identity),X_37) = multiply(X_37,add(X_37,X_36)),
inference(resolve,[$cnf( $equal(add(multiply(X_36,additive_identity),X_37),multiply(X_37,add(X_36,X_37))) )],[refute_0_341,refute_0_346]) ).
cnf(refute_0_348,plain,
add(multiply(Z,additive_identity),add(X,Z)) = multiply(add(X,Z),add(add(X,Z),Z)),
inference(subst,[],[refute_0_347:[bind(X_36,$fot(Z)),bind(X_37,$fot(add(X,Z)))]]) ).
cnf(refute_0_349,plain,
( add(multiply(Z,additive_identity),add(X,Z)) != multiply(add(X,Z),add(add(X,Z),Z))
| multiply(add(X,Z),add(add(X,Z),Z)) = add(multiply(Z,additive_identity),add(X,Z)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(multiply(Z,additive_identity),add(X,Z)))),bind(Y0,$fot(multiply(add(X,Z),add(add(X,Z),Z))))]]) ).
cnf(refute_0_350,plain,
multiply(add(X,Z),add(add(X,Z),Z)) = add(multiply(Z,additive_identity),add(X,Z)),
inference(resolve,[$cnf( $equal(add(multiply(Z,additive_identity),add(X,Z)),multiply(add(X,Z),add(add(X,Z),Z))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
( multiply(add(X,Z),add(add(X,Z),Z)) != add(multiply(Z,additive_identity),add(X,Z))
| add(multiply(X,add(X,Z)),Z) != multiply(add(X,Z),add(add(X,Z),Z))
| add(multiply(X,add(X,Z)),Z) = add(multiply(Z,additive_identity),add(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,add(X,Z)),Z),multiply(add(X,Z),add(add(X,Z),Z))) ),[1],$fot(add(multiply(Z,additive_identity),add(X,Z)))]]) ).
cnf(refute_0_352,plain,
( add(multiply(X,add(X,Z)),Z) != multiply(add(X,Z),add(add(X,Z),Z))
| add(multiply(X,add(X,Z)),Z) = add(multiply(Z,additive_identity),add(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(add(X,Z),add(add(X,Z),Z)),add(multiply(Z,additive_identity),add(X,Z))) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
add(multiply(X,add(X,Z)),Z) = add(multiply(Z,additive_identity),add(X,Z)),
inference(resolve,[$cnf( $equal(add(multiply(X,add(X,Z)),Z),multiply(add(X,Z),add(add(X,Z),Z))) )],[refute_0_340,refute_0_352]) ).
cnf(refute_0_354,plain,
add(multiply(X,add(X,Z)),Z) = add(Z,multiply(X,add(X,Z))),
inference(subst,[],[refute_0_88:[bind(X,$fot(Z)),bind(Y,$fot(multiply(X,add(X,Z))))]]) ).
cnf(refute_0_355,plain,
( add(multiply(X,add(X,Z)),Z) != add(Z,multiply(X,add(X,Z)))
| add(multiply(X,add(X,Z)),Z) != add(multiply(Z,additive_identity),add(X,Z))
| add(Z,multiply(X,add(X,Z))) = add(multiply(Z,additive_identity),add(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,add(X,Z)),Z),add(multiply(Z,additive_identity),add(X,Z))) ),[0],$fot(add(Z,multiply(X,add(X,Z))))]]) ).
cnf(refute_0_356,plain,
( add(multiply(X,add(X,Z)),Z) != add(multiply(Z,additive_identity),add(X,Z))
| add(Z,multiply(X,add(X,Z))) = add(multiply(Z,additive_identity),add(X,Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X,add(X,Z)),Z),add(Z,multiply(X,add(X,Z)))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
add(Z,multiply(X,add(X,Z))) = add(multiply(Z,additive_identity),add(X,Z)),
inference(resolve,[$cnf( $equal(add(multiply(X,add(X,Z)),Z),add(multiply(Z,additive_identity),add(X,Z))) )],[refute_0_353,refute_0_356]) ).
cnf(refute_0_358,plain,
multiply(X,add(X,Z)) = X,
inference(subst,[],[refute_0_98:[bind(X_58,$fot(Z)),bind(X_60,$fot(X))]]) ).
cnf(refute_0_359,plain,
add(Z,multiply(X,add(X,Z))) = add(Z,multiply(X,add(X,Z))),
introduced(tautology,[refl,[$fot(add(Z,multiply(X,add(X,Z))))]]) ).
cnf(refute_0_360,plain,
( multiply(X,add(X,Z)) != X
| add(Z,multiply(X,add(X,Z))) != add(Z,multiply(X,add(X,Z)))
| add(Z,multiply(X,add(X,Z))) = add(Z,X) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(X,add(X,Z))),add(Z,multiply(X,add(X,Z)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_361,plain,
( multiply(X,add(X,Z)) != X
| add(Z,multiply(X,add(X,Z))) = add(Z,X) ),
inference(resolve,[$cnf( $equal(add(Z,multiply(X,add(X,Z))),add(Z,multiply(X,add(X,Z)))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
add(Z,multiply(X,add(X,Z))) = add(Z,X),
inference(resolve,[$cnf( $equal(multiply(X,add(X,Z)),X) )],[refute_0_358,refute_0_361]) ).
cnf(refute_0_363,plain,
( add(Z,multiply(X,add(X,Z))) != add(Z,X)
| add(Z,multiply(X,add(X,Z))) != add(multiply(Z,additive_identity),add(X,Z))
| add(Z,X) = add(multiply(Z,additive_identity),add(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(X,add(X,Z))),add(multiply(Z,additive_identity),add(X,Z))) ),[0],$fot(add(Z,X))]]) ).
cnf(refute_0_364,plain,
( add(Z,multiply(X,add(X,Z))) != add(multiply(Z,additive_identity),add(X,Z))
| add(Z,X) = add(multiply(Z,additive_identity),add(X,Z)) ),
inference(resolve,[$cnf( $equal(add(Z,multiply(X,add(X,Z))),add(Z,X)) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
add(additive_identity,add(X,Z)) = add(X,Z),
inference(subst,[],[additive_id2:[bind(X,$fot(add(X,Z)))]]) ).
cnf(refute_0_366,plain,
add(multiply(Y,Y),Z) = multiply(add(Y,Z),add(Y,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_367,plain,
add(Y,multiply(Z,Z)) = multiply(add(Y,Z),add(Y,Z)),
inference(subst,[],[distributivity2:[bind(X,$fot(Y)),bind(Y,$fot(Z))]]) ).
cnf(refute_0_368,plain,
( add(Y,multiply(Z,Z)) != multiply(add(Y,Z),add(Y,Z))
| multiply(add(Y,Z),add(Y,Z)) = add(Y,multiply(Z,Z)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(Y,multiply(Z,Z)))),bind(Y0,$fot(multiply(add(Y,Z),add(Y,Z))))]]) ).
cnf(refute_0_369,plain,
multiply(add(Y,Z),add(Y,Z)) = add(Y,multiply(Z,Z)),
inference(resolve,[$cnf( $equal(add(Y,multiply(Z,Z)),multiply(add(Y,Z),add(Y,Z))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
( multiply(add(Y,Z),add(Y,Z)) != add(Y,multiply(Z,Z))
| add(multiply(Y,Y),Z) != multiply(add(Y,Z),add(Y,Z))
| add(multiply(Y,Y),Z) = add(Y,multiply(Z,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Y),Z),multiply(add(Y,Z),add(Y,Z))) ),[1],$fot(add(Y,multiply(Z,Z)))]]) ).
cnf(refute_0_371,plain,
( add(multiply(Y,Y),Z) != multiply(add(Y,Z),add(Y,Z))
| add(multiply(Y,Y),Z) = add(Y,multiply(Z,Z)) ),
inference(resolve,[$cnf( $equal(multiply(add(Y,Z),add(Y,Z)),add(Y,multiply(Z,Z))) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
add(multiply(Y,Y),Z) = add(Y,multiply(Z,Z)),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),Z),multiply(add(Y,Z),add(Y,Z))) )],[refute_0_366,refute_0_371]) ).
cnf(refute_0_373,plain,
add(multiply(Y,Y),multiply(additive_identity,additive_identity)) = add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))),
inference(subst,[],[refute_0_372:[bind(Z,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_374,plain,
add(multiply(Y,Y),additive_identity) = add(Y,multiply(additive_identity,additive_identity)),
inference(subst,[],[refute_0_372:[bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_375,plain,
add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,add(Y,additive_identity)),
inference(subst,[],[refute_0_145:[bind(X_20,$fot(Y)),bind(X_21,$fot(additive_identity))]]) ).
cnf(refute_0_376,plain,
( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(multiply(Y,Y),additive_identity) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(Y,Y),additive_identity) = multiply(Y,add(Y,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Y),additive_identity),add(Y,multiply(additive_identity,additive_identity))) ),[1],$fot(multiply(Y,add(Y,additive_identity)))]]) ).
cnf(refute_0_377,plain,
( add(multiply(Y,Y),additive_identity) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(Y,Y),additive_identity) = multiply(Y,add(Y,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,add(Y,additive_identity))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
add(multiply(Y,Y),additive_identity) = multiply(Y,add(Y,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),additive_identity),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_374,refute_0_377]) ).
cnf(refute_0_379,plain,
( add(multiply(Y,Y),additive_identity) != multiply(Y,add(Y,additive_identity))
| add(multiply(Y,Y),additive_identity) != add(Y,multiply(additive_identity,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,add(Y,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Y),additive_identity),multiply(Y,add(Y,additive_identity))) ),[0],$fot(add(Y,multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_380,plain,
( add(multiply(Y,Y),additive_identity) != multiply(Y,add(Y,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,add(Y,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),additive_identity),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_374,refute_0_379]) ).
cnf(refute_0_381,plain,
add(Y,additive_identity) = Y,
inference(subst,[],[additive_id1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_382,plain,
multiply(Y,add(Y,additive_identity)) = multiply(Y,add(Y,additive_identity)),
introduced(tautology,[refl,[$fot(multiply(Y,add(Y,additive_identity)))]]) ).
cnf(refute_0_383,plain,
( multiply(Y,add(Y,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(Y,additive_identity) != Y
| multiply(Y,add(Y,additive_identity)) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(Y,add(Y,additive_identity)),multiply(Y,add(Y,additive_identity))) ),[1,1],$fot(Y)]]) ).
cnf(refute_0_384,plain,
( add(Y,additive_identity) != Y
| multiply(Y,add(Y,additive_identity)) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,additive_identity)),multiply(Y,add(Y,additive_identity))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
multiply(Y,add(Y,additive_identity)) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(Y,additive_identity),Y) )],[refute_0_381,refute_0_384]) ).
cnf(refute_0_386,plain,
( multiply(Y,add(Y,additive_identity)) != multiply(Y,Y)
| add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,add(Y,additive_identity))) ),[1],$fot(multiply(Y,Y))]]) ).
cnf(refute_0_387,plain,
( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,additive_identity)),multiply(Y,Y)) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
( add(multiply(Y,Y),additive_identity) != multiply(Y,add(Y,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,add(Y,additive_identity))) )],[refute_0_380,refute_0_387]) ).
cnf(refute_0_389,plain,
add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),additive_identity),multiply(Y,add(Y,additive_identity))) )],[refute_0_378,refute_0_388]) ).
cnf(refute_0_390,plain,
add(multiply(Y,Y),multiply(additive_identity,additive_identity)) = multiply(multiply(Y,Y),multiply(Y,Y)),
inference(subst,[],[refute_0_389:[bind(Y,$fot(multiply(Y,Y)))]]) ).
cnf(refute_0_391,plain,
( add(multiply(Y,Y),multiply(additive_identity,additive_identity)) != multiply(multiply(Y,Y),multiply(Y,Y))
| add(multiply(Y,Y),multiply(additive_identity,additive_identity)) != add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)))
| multiply(multiply(Y,Y),multiply(Y,Y)) = add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Y),multiply(additive_identity,additive_identity)),add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)))) ),[0],$fot(multiply(multiply(Y,Y),multiply(Y,Y)))]]) ).
cnf(refute_0_392,plain,
( add(multiply(Y,Y),multiply(additive_identity,additive_identity)) != add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)))
| multiply(multiply(Y,Y),multiply(Y,Y)) = add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),multiply(additive_identity,additive_identity)),multiply(multiply(Y,Y),multiply(Y,Y))) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
multiply(multiply(Y,Y),multiply(Y,Y)) = add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),multiply(additive_identity,additive_identity)),add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)))) )],[refute_0_373,refute_0_392]) ).
cnf(refute_0_394,plain,
add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))),
inference(subst,[],[refute_0_19:[bind(X_12,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_395,plain,
add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)) = multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)),
inference(subst,[],[refute_0_389:[bind(Y,$fot(multiply(additive_identity,X_11)))]]) ).
cnf(refute_0_396,plain,
( add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)) != multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11))
| add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity)))
| multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)) = multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity)))) ),[0],$fot(multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)))]]) ).
cnf(refute_0_397,plain,
( add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity)))
| multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)) = multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)),multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)) = multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity)))) )],[refute_0_394,refute_0_397]) ).
cnf(refute_0_399,plain,
add(additive_identity,X_11) = X_11,
inference(subst,[],[additive_id2:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_400,plain,
multiply(additive_identity,add(additive_identity,X_11)) = multiply(additive_identity,add(additive_identity,X_11)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(additive_identity,X_11)))]]) ).
cnf(refute_0_401,plain,
( multiply(additive_identity,add(additive_identity,X_11)) != multiply(additive_identity,add(additive_identity,X_11))
| add(additive_identity,X_11) != X_11
| multiply(additive_identity,add(additive_identity,X_11)) = multiply(additive_identity,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_11)),multiply(additive_identity,add(additive_identity,X_11))) ),[1,1],$fot(X_11)]]) ).
cnf(refute_0_402,plain,
( add(additive_identity,X_11) != X_11
| multiply(additive_identity,add(additive_identity,X_11)) = multiply(additive_identity,X_11) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_11)),multiply(additive_identity,add(additive_identity,X_11))) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
multiply(additive_identity,add(additive_identity,X_11)) = multiply(additive_identity,X_11),
inference(resolve,[$cnf( $equal(add(additive_identity,X_11),X_11) )],[refute_0_399,refute_0_402]) ).
cnf(refute_0_404,plain,
multiply(add(additive_identity,X_11),additive_identity) = multiply(additive_identity,add(additive_identity,X_11)),
inference(subst,[],[refute_0_8:[bind(X,$fot(additive_identity)),bind(Y,$fot(add(additive_identity,X_11)))]]) ).
cnf(refute_0_405,plain,
add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) = multiply(add(additive_identity,X_11),additive_identity),
inference(subst,[],[refute_0_254:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_11)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_406,plain,
( multiply(add(additive_identity,X_11),additive_identity) != multiply(additive_identity,add(additive_identity,X_11))
| add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) != multiply(add(additive_identity,X_11),additive_identity)
| add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) = multiply(additive_identity,add(additive_identity,X_11)) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)))),bind(Y0,$fot(multiply(add(additive_identity,X_11),additive_identity))),bind(Z0,$fot(multiply(additive_identity,add(additive_identity,X_11))))]]) ).
cnf(refute_0_407,plain,
( multiply(add(additive_identity,X_11),additive_identity) != multiply(additive_identity,add(additive_identity,X_11))
| add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) = multiply(additive_identity,add(additive_identity,X_11)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)),multiply(add(additive_identity,X_11),additive_identity)) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) = multiply(additive_identity,add(additive_identity,X_11)),
inference(resolve,[$cnf( $equal(multiply(add(additive_identity,X_11),additive_identity),multiply(additive_identity,add(additive_identity,X_11))) )],[refute_0_404,refute_0_407]) ).
cnf(refute_0_409,plain,
add(X_33,X_32) = add(X_32,X_33),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_33)),bind(Y,$fot(X_32))]]) ).
cnf(refute_0_410,plain,
( add(X_33,X_32) != add(X_32,X_33)
| add(X_32,X_33) = add(X_33,X_32) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X_33,X_32))),bind(Y0,$fot(add(X_32,X_33)))]]) ).
cnf(refute_0_411,plain,
add(X_32,X_33) = add(X_33,X_32),
inference(resolve,[$cnf( $equal(add(X_33,X_32),add(X_32,X_33)) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
( add(X_32,X_33) != add(X_33,X_32)
| add(X_32,multiply(X_33,additive_identity)) != multiply(X_32,add(X_32,X_33))
| add(X_32,multiply(X_33,additive_identity)) = multiply(X_32,add(X_33,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_32,multiply(X_33,additive_identity)),multiply(X_32,add(X_32,X_33))) ),[1,1],$fot(add(X_33,X_32))]]) ).
cnf(refute_0_413,plain,
( add(X_32,multiply(X_33,additive_identity)) != multiply(X_32,add(X_32,X_33))
| add(X_32,multiply(X_33,additive_identity)) = multiply(X_32,add(X_33,X_32)) ),
inference(resolve,[$cnf( $equal(add(X_32,X_33),add(X_33,X_32)) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
add(X_32,multiply(X_33,additive_identity)) = multiply(X_32,add(X_33,X_32)),
inference(resolve,[$cnf( $equal(add(X_32,multiply(X_33,additive_identity)),multiply(X_32,add(X_32,X_33))) )],[refute_0_309,refute_0_413]) ).
cnf(refute_0_415,plain,
( add(X_32,multiply(X_33,additive_identity)) != multiply(X_32,add(X_33,X_32))
| multiply(X_32,add(X_33,X_32)) = add(X_32,multiply(X_33,additive_identity)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X_32,multiply(X_33,additive_identity)))),bind(Y0,$fot(multiply(X_32,add(X_33,X_32))))]]) ).
cnf(refute_0_416,plain,
multiply(X_32,add(X_33,X_32)) = add(X_32,multiply(X_33,additive_identity)),
inference(resolve,[$cnf( $equal(add(X_32,multiply(X_33,additive_identity)),multiply(X_32,add(X_33,X_32))) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) = add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)),
inference(subst,[],[refute_0_416:[bind(X_32,$fot(multiply(additive_identity,additive_identity))),bind(X_33,$fot(X_11))]]) ).
cnf(refute_0_418,plain,
( multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) != add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity))
| add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) != multiply(additive_identity,add(additive_identity,X_11))
| multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) = multiply(additive_identity,add(additive_identity,X_11)) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))))),bind(Y0,$fot(add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)))),bind(Z0,$fot(multiply(additive_identity,add(additive_identity,X_11))))]]) ).
cnf(refute_0_419,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) != multiply(additive_identity,add(additive_identity,X_11))
| multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) = multiply(additive_identity,add(additive_identity,X_11)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))),add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity))) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) = multiply(additive_identity,add(additive_identity,X_11)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)),multiply(additive_identity,add(additive_identity,X_11))) )],[refute_0_408,refute_0_419]) ).
cnf(refute_0_421,plain,
( multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) != multiply(additive_identity,add(additive_identity,X_11))
| multiply(additive_identity,add(additive_identity,X_11)) != multiply(additive_identity,X_11)
| multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) = multiply(additive_identity,X_11) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))))),bind(Y0,$fot(multiply(additive_identity,add(additive_identity,X_11)))),bind(Z0,$fot(multiply(additive_identity,X_11)))]]) ).
cnf(refute_0_422,plain,
( multiply(additive_identity,add(additive_identity,X_11)) != multiply(additive_identity,X_11)
| multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) = multiply(additive_identity,X_11) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))),multiply(additive_identity,add(additive_identity,X_11))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) = multiply(additive_identity,X_11),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_11)),multiply(additive_identity,X_11)) )],[refute_0_403,refute_0_422]) ).
cnf(refute_0_424,plain,
( multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)) != multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity)))
| multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))) != multiply(additive_identity,X_11)
| multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)) = multiply(additive_identity,X_11) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)),multiply(additive_identity,X_11)) ),[0],$fot(multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))))]]) ).
cnf(refute_0_425,plain,
( multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)) != multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity)))
| multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)) = multiply(additive_identity,X_11) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity))),multiply(additive_identity,X_11)) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)) = multiply(additive_identity,X_11),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_11),multiply(additive_identity,X_11)),multiply(multiply(additive_identity,additive_identity),add(X_11,multiply(additive_identity,additive_identity)))) )],[refute_0_398,refute_0_425]) ).
cnf(refute_0_427,plain,
multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)) = multiply(additive_identity,additive_identity),
inference(subst,[],[refute_0_426:[bind(X_11,$fot(additive_identity))]]) ).
cnf(refute_0_428,plain,
add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))) = add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))),
introduced(tautology,[refl,[$fot(add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))))]]) ).
cnf(refute_0_429,plain,
( multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)) != multiply(additive_identity,additive_identity)
| add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))) != add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)))
| add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))) = add(Y,multiply(additive_identity,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))),add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)))) ),[1,1],$fot(multiply(additive_identity,additive_identity))]]) ).
cnf(refute_0_430,plain,
( multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)) != multiply(additive_identity,additive_identity)
| add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))) = add(Y,multiply(additive_identity,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))),add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))) = add(Y,multiply(additive_identity,additive_identity)),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)),multiply(additive_identity,additive_identity)) )],[refute_0_427,refute_0_430]) ).
cnf(refute_0_432,plain,
( multiply(multiply(Y,Y),multiply(Y,Y)) != add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)))
| add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))) != add(Y,multiply(additive_identity,additive_identity))
| multiply(multiply(Y,Y),multiply(Y,Y)) = add(Y,multiply(additive_identity,additive_identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(Y,Y),multiply(Y,Y)),add(Y,multiply(additive_identity,additive_identity))) ),[0],$fot(add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))))]]) ).
cnf(refute_0_433,plain,
( multiply(multiply(Y,Y),multiply(Y,Y)) != add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)))
| multiply(multiply(Y,Y),multiply(Y,Y)) = add(Y,multiply(additive_identity,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
multiply(multiply(Y,Y),multiply(Y,Y)) = add(Y,multiply(additive_identity,additive_identity)),
inference(resolve,[$cnf( $equal(multiply(multiply(Y,Y),multiply(Y,Y)),add(Y,multiply(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)))) )],[refute_0_393,refute_0_433]) ).
cnf(refute_0_435,plain,
add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) = multiply(add(multiply(additive_identity,additive_identity),X_21),add(multiply(additive_identity,additive_identity),X_22)),
inference(subst,[],[distributivity2:[bind(X,$fot(multiply(additive_identity,additive_identity))),bind(Y,$fot(X_21)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_436,plain,
add(multiply(additive_identity,additive_identity),X_22) = multiply(X_22,X_22),
inference(subst,[],[refute_0_24:[bind(X_16,$fot(X_22))]]) ).
cnf(refute_0_437,plain,
( add(multiply(additive_identity,additive_identity),X_22) != multiply(X_22,X_22)
| add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(add(multiply(additive_identity,additive_identity),X_21),add(multiply(additive_identity,additive_identity),X_22))
| add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) = multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)),multiply(add(multiply(additive_identity,additive_identity),X_21),add(multiply(additive_identity,additive_identity),X_22))) ),[1,1],$fot(multiply(X_22,X_22))]]) ).
cnf(refute_0_438,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(add(multiply(additive_identity,additive_identity),X_21),add(multiply(additive_identity,additive_identity),X_22))
| add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) = multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_22),multiply(X_22,X_22)) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) = multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)),multiply(add(multiply(additive_identity,additive_identity),X_21),add(multiply(additive_identity,additive_identity),X_22))) )],[refute_0_435,refute_0_438]) ).
cnf(refute_0_440,plain,
add(multiply(X,multiply(additive_identity,X_15)),Z) = multiply(add(X,Z),add(multiply(additive_identity,X_15),Z)),
inference(subst,[],[distributivity1:[bind(Y,$fot(multiply(additive_identity,X_15)))]]) ).
cnf(refute_0_441,plain,
add(multiply(additive_identity,X_15),Z) = multiply(Z,add(X_15,Z)),
inference(subst,[],[refute_0_19:[bind(X_11,$fot(X_15)),bind(X_12,$fot(Z))]]) ).
cnf(refute_0_442,plain,
( add(multiply(X,multiply(additive_identity,X_15)),Z) != multiply(add(X,Z),add(multiply(additive_identity,X_15),Z))
| add(multiply(additive_identity,X_15),Z) != multiply(Z,add(X_15,Z))
| add(multiply(X,multiply(additive_identity,X_15)),Z) = multiply(add(X,Z),multiply(Z,add(X_15,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,multiply(additive_identity,X_15)),Z),multiply(add(X,Z),add(multiply(additive_identity,X_15),Z))) ),[1,1],$fot(multiply(Z,add(X_15,Z)))]]) ).
cnf(refute_0_443,plain,
( add(multiply(X,multiply(additive_identity,X_15)),Z) != multiply(add(X,Z),add(multiply(additive_identity,X_15),Z))
| add(multiply(X,multiply(additive_identity,X_15)),Z) = multiply(add(X,Z),multiply(Z,add(X_15,Z))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_15),Z),multiply(Z,add(X_15,Z))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
add(multiply(X,multiply(additive_identity,X_15)),Z) = multiply(add(X,Z),multiply(Z,add(X_15,Z))),
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(additive_identity,X_15)),Z),multiply(add(X,Z),add(multiply(additive_identity,X_15),Z))) )],[refute_0_440,refute_0_443]) ).
cnf(refute_0_445,plain,
( additive_identity != multiply(additive_identity,X_59)
| multiply(additive_identity,X_59) = additive_identity ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(additive_identity,X_59)))]]) ).
cnf(refute_0_446,plain,
multiply(additive_identity,X_59) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(additive_identity,X_59)) )],[refute_0_332,refute_0_445]) ).
cnf(refute_0_447,plain,
multiply(additive_identity,X_15) = additive_identity,
inference(subst,[],[refute_0_446:[bind(X_59,$fot(X_15))]]) ).
cnf(refute_0_448,plain,
multiply(X,multiply(additive_identity,X_15)) = multiply(X,multiply(additive_identity,X_15)),
introduced(tautology,[refl,[$fot(multiply(X,multiply(additive_identity,X_15)))]]) ).
cnf(refute_0_449,plain,
( multiply(X,multiply(additive_identity,X_15)) != multiply(X,multiply(additive_identity,X_15))
| multiply(additive_identity,X_15) != additive_identity
| multiply(X,multiply(additive_identity,X_15)) = multiply(X,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiply(additive_identity,X_15)),multiply(X,multiply(additive_identity,X_15))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_450,plain,
( multiply(additive_identity,X_15) != additive_identity
| multiply(X,multiply(additive_identity,X_15)) = multiply(X,additive_identity) ),
inference(resolve,[$cnf( $equal(multiply(X,multiply(additive_identity,X_15)),multiply(X,multiply(additive_identity,X_15))) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
multiply(X,multiply(additive_identity,X_15)) = multiply(X,additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_15),additive_identity) )],[refute_0_447,refute_0_450]) ).
cnf(refute_0_452,plain,
add(multiply(X,multiply(additive_identity,X_15)),Z) = add(multiply(X,multiply(additive_identity,X_15)),Z),
introduced(tautology,[refl,[$fot(add(multiply(X,multiply(additive_identity,X_15)),Z))]]) ).
cnf(refute_0_453,plain,
( multiply(X,multiply(additive_identity,X_15)) != multiply(X,additive_identity)
| add(multiply(X,multiply(additive_identity,X_15)),Z) != add(multiply(X,multiply(additive_identity,X_15)),Z)
| add(multiply(X,multiply(additive_identity,X_15)),Z) = add(multiply(X,additive_identity),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,multiply(additive_identity,X_15)),Z),add(multiply(X,multiply(additive_identity,X_15)),Z)) ),[1,0],$fot(multiply(X,additive_identity))]]) ).
cnf(refute_0_454,plain,
( multiply(X,multiply(additive_identity,X_15)) != multiply(X,additive_identity)
| add(multiply(X,multiply(additive_identity,X_15)),Z) = add(multiply(X,additive_identity),Z) ),
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(additive_identity,X_15)),Z),add(multiply(X,multiply(additive_identity,X_15)),Z)) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
add(multiply(X,multiply(additive_identity,X_15)),Z) = add(multiply(X,additive_identity),Z),
inference(resolve,[$cnf( $equal(multiply(X,multiply(additive_identity,X_15)),multiply(X,additive_identity)) )],[refute_0_451,refute_0_454]) ).
cnf(refute_0_456,plain,
( add(multiply(X,multiply(additive_identity,X_15)),Z) != multiply(add(X,Z),multiply(Z,add(X_15,Z)))
| add(multiply(X,multiply(additive_identity,X_15)),Z) != add(multiply(X,additive_identity),Z)
| add(multiply(X,additive_identity),Z) = multiply(add(X,Z),multiply(Z,add(X_15,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,multiply(additive_identity,X_15)),Z),multiply(add(X,Z),multiply(Z,add(X_15,Z)))) ),[0],$fot(add(multiply(X,additive_identity),Z))]]) ).
cnf(refute_0_457,plain,
( add(multiply(X,multiply(additive_identity,X_15)),Z) != multiply(add(X,Z),multiply(Z,add(X_15,Z)))
| add(multiply(X,additive_identity),Z) = multiply(add(X,Z),multiply(Z,add(X_15,Z))) ),
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(additive_identity,X_15)),Z),add(multiply(X,additive_identity),Z)) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) = add(multiply(X_58,Z),multiply(Z,Z)),
inference(subst,[],[refute_0_372:[bind(Y,$fot(multiply(X_58,Z)))]]) ).
cnf(refute_0_459,plain,
multiply(add(X_58,Z),Z) = add(multiply(X_58,Z),multiply(Z,Z)),
inference(subst,[],[distributivity3:[bind(X,$fot(X_58)),bind(Y,$fot(Z))]]) ).
cnf(refute_0_460,plain,
( multiply(add(X_58,Z),Z) != add(multiply(X_58,Z),multiply(Z,Z))
| add(multiply(X_58,Z),multiply(Z,Z)) = multiply(add(X_58,Z),Z) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(add(X_58,Z),Z))),bind(Y0,$fot(add(multiply(X_58,Z),multiply(Z,Z))))]]) ).
cnf(refute_0_461,plain,
add(multiply(X_58,Z),multiply(Z,Z)) = multiply(add(X_58,Z),Z),
inference(resolve,[$cnf( $equal(multiply(add(X_58,Z),Z),add(multiply(X_58,Z),multiply(Z,Z))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
( add(multiply(X_58,Z),multiply(Z,Z)) != multiply(add(X_58,Z),Z)
| add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) != add(multiply(X_58,Z),multiply(Z,Z))
| add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) = multiply(add(X_58,Z),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z),add(multiply(X_58,Z),multiply(Z,Z))) ),[1],$fot(multiply(add(X_58,Z),Z))]]) ).
cnf(refute_0_463,plain,
( add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) != add(multiply(X_58,Z),multiply(Z,Z))
| add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) = multiply(add(X_58,Z),Z) ),
inference(resolve,[$cnf( $equal(add(multiply(X_58,Z),multiply(Z,Z)),multiply(add(X_58,Z),Z)) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) = multiply(add(X_58,Z),Z),
inference(resolve,[$cnf( $equal(add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z),add(multiply(X_58,Z),multiply(Z,Z))) )],[refute_0_458,refute_0_463]) ).
cnf(refute_0_465,plain,
add(Z,multiply(additive_identity,additive_identity)) = multiply(Z,Z),
inference(subst,[],[refute_0_389:[bind(Y,$fot(Z))]]) ).
cnf(refute_0_466,plain,
( add(Z,multiply(additive_identity,additive_identity)) != multiply(Z,Z)
| multiply(Z,Z) = add(Z,multiply(additive_identity,additive_identity)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(Z,multiply(additive_identity,additive_identity)))),bind(Y0,$fot(multiply(Z,Z)))]]) ).
cnf(refute_0_467,plain,
multiply(Z,Z) = add(Z,multiply(additive_identity,additive_identity)),
inference(resolve,[$cnf( $equal(add(Z,multiply(additive_identity,additive_identity)),multiply(Z,Z)) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
( multiply(Z,Z) != add(Z,multiply(additive_identity,additive_identity))
| add(multiply(Y,Y),Z) != add(Y,multiply(Z,Z))
| add(multiply(Y,Y),Z) = add(Y,add(Z,multiply(additive_identity,additive_identity))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Y),Z),add(Y,multiply(Z,Z))) ),[1,1],$fot(add(Z,multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_469,plain,
( add(multiply(Y,Y),Z) != add(Y,multiply(Z,Z))
| add(multiply(Y,Y),Z) = add(Y,add(Z,multiply(additive_identity,additive_identity))) ),
inference(resolve,[$cnf( $equal(multiply(Z,Z),add(Z,multiply(additive_identity,additive_identity))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
add(multiply(Y,Y),Z) = add(Y,add(Z,multiply(additive_identity,additive_identity))),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),Z),add(Y,multiply(Z,Z))) )],[refute_0_372,refute_0_469]) ).
cnf(refute_0_471,plain,
add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) = add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))),
inference(subst,[],[refute_0_470:[bind(Y,$fot(multiply(X_58,Z)))]]) ).
cnf(refute_0_472,plain,
( add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) != multiply(add(X_58,Z),Z)
| add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) != add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity)))
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = multiply(add(X_58,Z),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z),multiply(add(X_58,Z),Z)) ),[0],$fot(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))))]]) ).
cnf(refute_0_473,plain,
( add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) != multiply(add(X_58,Z),Z)
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = multiply(add(X_58,Z),Z) ),
inference(resolve,[$cnf( $equal(add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z),add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity)))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
multiply(add(X_58,Z),Z) = multiply(Z,add(X_58,Z)),
inference(subst,[],[refute_0_8:[bind(X,$fot(Z)),bind(Y,$fot(add(X_58,Z)))]]) ).
cnf(refute_0_475,plain,
( multiply(add(X_58,Z),Z) != multiply(Z,add(X_58,Z))
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) != multiply(add(X_58,Z),Z)
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = multiply(Z,add(X_58,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))),multiply(add(X_58,Z),Z)) ),[1],$fot(multiply(Z,add(X_58,Z)))]]) ).
cnf(refute_0_476,plain,
( add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) != multiply(add(X_58,Z),Z)
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = multiply(Z,add(X_58,Z)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_58,Z),Z),multiply(Z,add(X_58,Z))) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
( add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z) != multiply(add(X_58,Z),Z)
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = multiply(Z,add(X_58,Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))),multiply(add(X_58,Z),Z)) )],[refute_0_473,refute_0_476]) ).
cnf(refute_0_478,plain,
add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = multiply(Z,add(X_58,Z)),
inference(resolve,[$cnf( $equal(add(multiply(multiply(X_58,Z),multiply(X_58,Z)),Z),multiply(add(X_58,Z),Z)) )],[refute_0_464,refute_0_477]) ).
cnf(refute_0_479,plain,
multiply(Z,add(Z,X_58)) = Z,
inference(subst,[],[refute_0_98:[bind(X_60,$fot(Z))]]) ).
cnf(refute_0_480,plain,
add(Z,multiply(X_58,Z)) = multiply(Z,add(Z,X_58)),
inference(subst,[],[refute_0_85:[bind(Y,$fot(X_58))]]) ).
cnf(refute_0_481,plain,
( multiply(Z,add(Z,X_58)) != Z
| add(Z,multiply(X_58,Z)) != multiply(Z,add(Z,X_58))
| add(Z,multiply(X_58,Z)) = Z ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(Z,multiply(X_58,Z)))),bind(Y0,$fot(multiply(Z,add(Z,X_58)))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_482,plain,
( multiply(Z,add(Z,X_58)) != Z
| add(Z,multiply(X_58,Z)) = Z ),
inference(resolve,[$cnf( $equal(add(Z,multiply(X_58,Z)),multiply(Z,add(Z,X_58))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
add(Z,multiply(X_58,Z)) = Z,
inference(resolve,[$cnf( $equal(multiply(Z,add(Z,X_58)),Z) )],[refute_0_479,refute_0_482]) ).
cnf(refute_0_484,plain,
add(multiply(X_58,Z),Z) = add(Z,multiply(X_58,Z)),
inference(subst,[],[refute_0_88:[bind(X,$fot(Z)),bind(Y,$fot(multiply(X_58,Z)))]]) ).
cnf(refute_0_485,plain,
( add(Z,multiply(X_58,Z)) != Z
| add(multiply(X_58,Z),Z) != add(Z,multiply(X_58,Z))
| add(multiply(X_58,Z),Z) = Z ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(multiply(X_58,Z),Z))),bind(Y0,$fot(add(Z,multiply(X_58,Z)))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_486,plain,
( add(Z,multiply(X_58,Z)) != Z
| add(multiply(X_58,Z),Z) = Z ),
inference(resolve,[$cnf( $equal(add(multiply(X_58,Z),Z),add(Z,multiply(X_58,Z))) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
add(multiply(X_58,Z),Z) = Z,
inference(resolve,[$cnf( $equal(add(Z,multiply(X_58,Z)),Z) )],[refute_0_483,refute_0_486]) ).
cnf(refute_0_488,plain,
add(Z,additive_identity) = Z,
inference(subst,[],[additive_id1:[bind(X,$fot(Z))]]) ).
cnf(refute_0_489,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(subst,[],[refute_0_446:[bind(X_59,$fot(additive_identity))]]) ).
cnf(refute_0_490,plain,
add(Z,multiply(additive_identity,additive_identity)) = add(Z,multiply(additive_identity,additive_identity)),
introduced(tautology,[refl,[$fot(add(Z,multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_491,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(Z,multiply(additive_identity,additive_identity)) != add(Z,multiply(additive_identity,additive_identity))
| add(Z,multiply(additive_identity,additive_identity)) = add(Z,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(additive_identity,additive_identity)),add(Z,multiply(additive_identity,additive_identity))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_492,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(Z,multiply(additive_identity,additive_identity)) = add(Z,additive_identity) ),
inference(resolve,[$cnf( $equal(add(Z,multiply(additive_identity,additive_identity)),add(Z,multiply(additive_identity,additive_identity))) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
add(Z,multiply(additive_identity,additive_identity)) = add(Z,additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),additive_identity) )],[refute_0_489,refute_0_492]) ).
cnf(refute_0_494,plain,
( add(Z,multiply(additive_identity,additive_identity)) != add(Z,additive_identity)
| add(Z,additive_identity) != Z
| add(Z,multiply(additive_identity,additive_identity)) = Z ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(Z,multiply(additive_identity,additive_identity)))),bind(Y0,$fot(add(Z,additive_identity))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_495,plain,
( add(Z,additive_identity) != Z
| add(Z,multiply(additive_identity,additive_identity)) = Z ),
inference(resolve,[$cnf( $equal(add(Z,multiply(additive_identity,additive_identity)),add(Z,additive_identity)) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
add(Z,multiply(additive_identity,additive_identity)) = Z,
inference(resolve,[$cnf( $equal(add(Z,additive_identity),Z) )],[refute_0_488,refute_0_495]) ).
cnf(refute_0_497,plain,
add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))),
introduced(tautology,[refl,[$fot(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))))]]) ).
cnf(refute_0_498,plain,
( add(Z,multiply(additive_identity,additive_identity)) != Z
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) != add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity)))
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = add(multiply(X_58,Z),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))),add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity)))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_499,plain,
( add(Z,multiply(additive_identity,additive_identity)) != Z
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = add(multiply(X_58,Z),Z) ),
inference(resolve,[$cnf( $equal(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))),add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity)))) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = add(multiply(X_58,Z),Z),
inference(resolve,[$cnf( $equal(add(Z,multiply(additive_identity,additive_identity)),Z) )],[refute_0_496,refute_0_499]) ).
cnf(refute_0_501,plain,
( add(multiply(X_58,Z),Z) != Z
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) != add(multiply(X_58,Z),Z)
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = Z ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))))),bind(Y0,$fot(add(multiply(X_58,Z),Z))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_502,plain,
( add(multiply(X_58,Z),Z) != Z
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = Z ),
inference(resolve,[$cnf( $equal(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))),add(multiply(X_58,Z),Z)) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) = Z,
inference(resolve,[$cnf( $equal(add(multiply(X_58,Z),Z),Z) )],[refute_0_487,refute_0_502]) ).
cnf(refute_0_504,plain,
( add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) != Z
| add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) != multiply(Z,add(X_58,Z))
| Z = multiply(Z,add(X_58,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))),multiply(Z,add(X_58,Z))) ),[0],$fot(Z)]]) ).
cnf(refute_0_505,plain,
( add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))) != multiply(Z,add(X_58,Z))
| Z = multiply(Z,add(X_58,Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))),Z) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
Z = multiply(Z,add(X_58,Z)),
inference(resolve,[$cnf( $equal(add(multiply(X_58,Z),add(Z,multiply(additive_identity,additive_identity))),multiply(Z,add(X_58,Z))) )],[refute_0_478,refute_0_505]) ).
cnf(refute_0_507,plain,
( Z != multiply(Z,add(X_58,Z))
| multiply(Z,add(X_58,Z)) = Z ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(Z)),bind(Y0,$fot(multiply(Z,add(X_58,Z))))]]) ).
cnf(refute_0_508,plain,
multiply(Z,add(X_58,Z)) = Z,
inference(resolve,[$cnf( $equal(Z,multiply(Z,add(X_58,Z))) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
multiply(Z,add(X,Z)) = Z,
inference(subst,[],[refute_0_508:[bind(X_58,$fot(X))]]) ).
cnf(refute_0_510,plain,
multiply(add(X,Z),Z) = multiply(Z,add(X,Z)),
inference(subst,[],[refute_0_8:[bind(X,$fot(Z)),bind(Y,$fot(add(X,Z)))]]) ).
cnf(refute_0_511,plain,
( multiply(Z,add(X,Z)) != Z
| multiply(add(X,Z),Z) != multiply(Z,add(X,Z))
| multiply(add(X,Z),Z) = Z ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(add(X,Z),Z))),bind(Y0,$fot(multiply(Z,add(X,Z)))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_512,plain,
( multiply(Z,add(X,Z)) != Z
| multiply(add(X,Z),Z) = Z ),
inference(resolve,[$cnf( $equal(multiply(add(X,Z),Z),multiply(Z,add(X,Z))) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
multiply(add(X,Z),Z) = Z,
inference(resolve,[$cnf( $equal(multiply(Z,add(X,Z)),Z) )],[refute_0_509,refute_0_512]) ).
cnf(refute_0_514,plain,
multiply(Z,add(X_15,Z)) = Z,
inference(subst,[],[refute_0_508:[bind(X_58,$fot(X_15))]]) ).
cnf(refute_0_515,plain,
multiply(add(X,Z),multiply(Z,add(X_15,Z))) = multiply(add(X,Z),multiply(Z,add(X_15,Z))),
introduced(tautology,[refl,[$fot(multiply(add(X,Z),multiply(Z,add(X_15,Z))))]]) ).
cnf(refute_0_516,plain,
( multiply(Z,add(X_15,Z)) != Z
| multiply(add(X,Z),multiply(Z,add(X_15,Z))) != multiply(add(X,Z),multiply(Z,add(X_15,Z)))
| multiply(add(X,Z),multiply(Z,add(X_15,Z))) = multiply(add(X,Z),Z) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X,Z),multiply(Z,add(X_15,Z))),multiply(add(X,Z),multiply(Z,add(X_15,Z)))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_517,plain,
( multiply(Z,add(X_15,Z)) != Z
| multiply(add(X,Z),multiply(Z,add(X_15,Z))) = multiply(add(X,Z),Z) ),
inference(resolve,[$cnf( $equal(multiply(add(X,Z),multiply(Z,add(X_15,Z))),multiply(add(X,Z),multiply(Z,add(X_15,Z)))) )],[refute_0_515,refute_0_516]) ).
cnf(refute_0_518,plain,
multiply(add(X,Z),multiply(Z,add(X_15,Z))) = multiply(add(X,Z),Z),
inference(resolve,[$cnf( $equal(multiply(Z,add(X_15,Z)),Z) )],[refute_0_514,refute_0_517]) ).
cnf(refute_0_519,plain,
( multiply(add(X,Z),Z) != Z
| multiply(add(X,Z),multiply(Z,add(X_15,Z))) != multiply(add(X,Z),Z)
| multiply(add(X,Z),multiply(Z,add(X_15,Z))) = Z ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(add(X,Z),multiply(Z,add(X_15,Z))))),bind(Y0,$fot(multiply(add(X,Z),Z))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_520,plain,
( multiply(add(X,Z),Z) != Z
| multiply(add(X,Z),multiply(Z,add(X_15,Z))) = Z ),
inference(resolve,[$cnf( $equal(multiply(add(X,Z),multiply(Z,add(X_15,Z))),multiply(add(X,Z),Z)) )],[refute_0_518,refute_0_519]) ).
cnf(refute_0_521,plain,
multiply(add(X,Z),multiply(Z,add(X_15,Z))) = Z,
inference(resolve,[$cnf( $equal(multiply(add(X,Z),Z),Z) )],[refute_0_513,refute_0_520]) ).
cnf(refute_0_522,plain,
( multiply(add(X,Z),multiply(Z,add(X_15,Z))) != Z
| add(multiply(X,additive_identity),Z) != multiply(add(X,Z),multiply(Z,add(X_15,Z)))
| add(multiply(X,additive_identity),Z) = Z ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,additive_identity),Z),multiply(add(X,Z),multiply(Z,add(X_15,Z)))) ),[1],$fot(Z)]]) ).
cnf(refute_0_523,plain,
( add(multiply(X,additive_identity),Z) != multiply(add(X,Z),multiply(Z,add(X_15,Z)))
| add(multiply(X,additive_identity),Z) = Z ),
inference(resolve,[$cnf( $equal(multiply(add(X,Z),multiply(Z,add(X_15,Z))),Z) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
( add(multiply(X,multiply(additive_identity,X_15)),Z) != multiply(add(X,Z),multiply(Z,add(X_15,Z)))
| add(multiply(X,additive_identity),Z) = Z ),
inference(resolve,[$cnf( $equal(add(multiply(X,additive_identity),Z),multiply(add(X,Z),multiply(Z,add(X_15,Z)))) )],[refute_0_457,refute_0_523]) ).
cnf(refute_0_525,plain,
add(multiply(X,additive_identity),Z) = Z,
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(additive_identity,X_15)),Z),multiply(add(X,Z),multiply(Z,add(X_15,Z)))) )],[refute_0_444,refute_0_524]) ).
cnf(refute_0_526,plain,
add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) = multiply(X_21,X_22),
inference(subst,[],[refute_0_525:[bind(X,$fot(additive_identity)),bind(Z,$fot(multiply(X_21,X_22)))]]) ).
cnf(refute_0_527,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(X_21,X_22)
| add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))
| multiply(X_21,X_22) = multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)),multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))) ),[0],$fot(multiply(X_21,X_22))]]) ).
cnf(refute_0_528,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))
| multiply(X_21,X_22) = multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)),multiply(X_21,X_22)) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
add(multiply(additive_identity,additive_identity),X_21) = X_21,
inference(subst,[],[refute_0_525:[bind(X,$fot(additive_identity)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_530,plain,
multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)) = multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)),
introduced(tautology,[refl,[$fot(multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)))]]) ).
cnf(refute_0_531,plain,
( multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)) != multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))
| add(multiply(additive_identity,additive_identity),X_21) != X_21
| multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)) = multiply(X_21,multiply(X_22,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)),multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))) ),[1,0],$fot(X_21)]]) ).
cnf(refute_0_532,plain,
( add(multiply(additive_identity,additive_identity),X_21) != X_21
| multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)) = multiply(X_21,multiply(X_22,X_22)) ),
inference(resolve,[$cnf( $equal(multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)),multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)) = multiply(X_21,multiply(X_22,X_22)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_21),X_21) )],[refute_0_529,refute_0_532]) ).
cnf(refute_0_534,plain,
( multiply(X_21,X_22) != multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))
| multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)) != multiply(X_21,multiply(X_22,X_22))
| multiply(X_21,X_22) = multiply(X_21,multiply(X_22,X_22)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_21,X_22),multiply(X_21,multiply(X_22,X_22))) ),[0],$fot(multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)))]]) ).
cnf(refute_0_535,plain,
( multiply(X_21,X_22) != multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))
| multiply(X_21,X_22) = multiply(X_21,multiply(X_22,X_22)) ),
inference(resolve,[$cnf( $equal(multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22)),multiply(X_21,multiply(X_22,X_22))) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))
| multiply(X_21,X_22) = multiply(X_21,multiply(X_22,X_22)) ),
inference(resolve,[$cnf( $equal(multiply(X_21,X_22),multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))) )],[refute_0_528,refute_0_535]) ).
cnf(refute_0_537,plain,
multiply(X_21,X_22) = multiply(X_21,multiply(X_22,X_22)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)),multiply(add(multiply(additive_identity,additive_identity),X_21),multiply(X_22,X_22))) )],[refute_0_439,refute_0_536]) ).
cnf(refute_0_538,plain,
( multiply(X_21,X_22) != multiply(X_21,multiply(X_22,X_22))
| multiply(X_21,multiply(X_22,X_22)) = multiply(X_21,X_22) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X_21,X_22))),bind(Y0,$fot(multiply(X_21,multiply(X_22,X_22))))]]) ).
cnf(refute_0_539,plain,
multiply(X_21,multiply(X_22,X_22)) = multiply(X_21,X_22),
inference(resolve,[$cnf( $equal(multiply(X_21,X_22),multiply(X_21,multiply(X_22,X_22))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
multiply(Y,multiply(Y,Y)) = multiply(Y,Y),
inference(subst,[],[refute_0_539:[bind(X_21,$fot(Y)),bind(X_22,$fot(Y))]]) ).
cnf(refute_0_541,plain,
add(multiply(additive_identity,additive_identity),X_21) = multiply(X_21,X_21),
inference(subst,[],[refute_0_24:[bind(X_16,$fot(X_21))]]) ).
cnf(refute_0_542,plain,
( add(multiply(additive_identity,additive_identity),X_21) != multiply(X_21,X_21)
| add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(add(multiply(additive_identity,additive_identity),X_21),add(multiply(additive_identity,additive_identity),X_22))
| add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) = multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)),multiply(add(multiply(additive_identity,additive_identity),X_21),add(multiply(additive_identity,additive_identity),X_22))) ),[1,0],$fot(multiply(X_21,X_21))]]) ).
cnf(refute_0_543,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(add(multiply(additive_identity,additive_identity),X_21),add(multiply(additive_identity,additive_identity),X_22))
| add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) = multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_21),multiply(X_21,X_21)) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) = multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)),multiply(add(multiply(additive_identity,additive_identity),X_21),add(multiply(additive_identity,additive_identity),X_22))) )],[refute_0_435,refute_0_543]) ).
cnf(refute_0_545,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(X_21,X_22)
| add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))
| multiply(X_21,X_22) = multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)),multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))) ),[0],$fot(multiply(X_21,X_22))]]) ).
cnf(refute_0_546,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))
| multiply(X_21,X_22) = multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)),multiply(X_21,X_22)) )],[refute_0_526,refute_0_545]) ).
cnf(refute_0_547,plain,
add(multiply(additive_identity,additive_identity),X_22) = X_22,
inference(subst,[],[refute_0_525:[bind(X,$fot(additive_identity)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_548,plain,
multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)) = multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)),
introduced(tautology,[refl,[$fot(multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)))]]) ).
cnf(refute_0_549,plain,
( multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)) != multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))
| add(multiply(additive_identity,additive_identity),X_22) != X_22
| multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)) = multiply(multiply(X_21,X_21),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)),multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))) ),[1,1],$fot(X_22)]]) ).
cnf(refute_0_550,plain,
( add(multiply(additive_identity,additive_identity),X_22) != X_22
| multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)) = multiply(multiply(X_21,X_21),X_22) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)),multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)) = multiply(multiply(X_21,X_21),X_22),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_22),X_22) )],[refute_0_547,refute_0_550]) ).
cnf(refute_0_552,plain,
( multiply(X_21,X_22) != multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))
| multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)) != multiply(multiply(X_21,X_21),X_22)
| multiply(X_21,X_22) = multiply(multiply(X_21,X_21),X_22) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_21,X_22),multiply(multiply(X_21,X_21),X_22)) ),[0],$fot(multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)))]]) ).
cnf(refute_0_553,plain,
( multiply(X_21,X_22) != multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))
| multiply(X_21,X_22) = multiply(multiply(X_21,X_21),X_22) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22)),multiply(multiply(X_21,X_21),X_22)) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)) != multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))
| multiply(X_21,X_22) = multiply(multiply(X_21,X_21),X_22) ),
inference(resolve,[$cnf( $equal(multiply(X_21,X_22),multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))) )],[refute_0_546,refute_0_553]) ).
cnf(refute_0_555,plain,
multiply(X_21,X_22) = multiply(multiply(X_21,X_21),X_22),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_21,X_22)),multiply(multiply(X_21,X_21),add(multiply(additive_identity,additive_identity),X_22))) )],[refute_0_544,refute_0_554]) ).
cnf(refute_0_556,plain,
( multiply(X_21,X_22) != multiply(multiply(X_21,X_21),X_22)
| multiply(multiply(X_21,X_21),X_22) = multiply(X_21,X_22) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X_21,X_22))),bind(Y0,$fot(multiply(multiply(X_21,X_21),X_22)))]]) ).
cnf(refute_0_557,plain,
multiply(multiply(X_21,X_21),X_22) = multiply(X_21,X_22),
inference(resolve,[$cnf( $equal(multiply(X_21,X_22),multiply(multiply(X_21,X_21),X_22)) )],[refute_0_555,refute_0_556]) ).
cnf(refute_0_558,plain,
multiply(multiply(Y,Y),multiply(Y,Y)) = multiply(Y,multiply(Y,Y)),
inference(subst,[],[refute_0_557:[bind(X_21,$fot(Y)),bind(X_22,$fot(multiply(Y,Y)))]]) ).
cnf(refute_0_559,plain,
( multiply(Y,multiply(Y,Y)) != multiply(Y,Y)
| multiply(multiply(Y,Y),multiply(Y,Y)) != multiply(Y,multiply(Y,Y))
| multiply(multiply(Y,Y),multiply(Y,Y)) = multiply(Y,Y) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(multiply(Y,Y),multiply(Y,Y)))),bind(Y0,$fot(multiply(Y,multiply(Y,Y)))),bind(Z0,$fot(multiply(Y,Y)))]]) ).
cnf(refute_0_560,plain,
( multiply(Y,multiply(Y,Y)) != multiply(Y,Y)
| multiply(multiply(Y,Y),multiply(Y,Y)) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(multiply(multiply(Y,Y),multiply(Y,Y)),multiply(Y,multiply(Y,Y))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
multiply(multiply(Y,Y),multiply(Y,Y)) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(multiply(Y,multiply(Y,Y)),multiply(Y,Y)) )],[refute_0_540,refute_0_560]) ).
cnf(refute_0_562,plain,
( multiply(multiply(Y,Y),multiply(Y,Y)) != multiply(Y,Y)
| multiply(multiply(Y,Y),multiply(Y,Y)) != add(Y,multiply(additive_identity,additive_identity))
| multiply(Y,Y) = add(Y,multiply(additive_identity,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(Y,Y),multiply(Y,Y)),add(Y,multiply(additive_identity,additive_identity))) ),[0],$fot(multiply(Y,Y))]]) ).
cnf(refute_0_563,plain,
( multiply(multiply(Y,Y),multiply(Y,Y)) != add(Y,multiply(additive_identity,additive_identity))
| multiply(Y,Y) = add(Y,multiply(additive_identity,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(Y,Y),multiply(Y,Y)),multiply(Y,Y)) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
add(Y,multiply(additive_identity,additive_identity)) = add(Y,multiply(additive_identity,additive_identity)),
introduced(tautology,[refl,[$fot(add(Y,multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_565,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(Y,multiply(additive_identity,additive_identity)) != add(Y,multiply(additive_identity,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = add(Y,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),add(Y,multiply(additive_identity,additive_identity))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_566,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(Y,multiply(additive_identity,additive_identity)) = add(Y,additive_identity) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
add(Y,multiply(additive_identity,additive_identity)) = add(Y,additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),additive_identity) )],[refute_0_489,refute_0_566]) ).
cnf(refute_0_568,plain,
( add(Y,multiply(additive_identity,additive_identity)) != add(Y,additive_identity)
| add(Y,additive_identity) != Y
| add(Y,multiply(additive_identity,additive_identity)) = Y ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(Y,multiply(additive_identity,additive_identity)))),bind(Y0,$fot(add(Y,additive_identity))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_569,plain,
( add(Y,additive_identity) != Y
| add(Y,multiply(additive_identity,additive_identity)) = Y ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),add(Y,additive_identity)) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
add(Y,multiply(additive_identity,additive_identity)) = Y,
inference(resolve,[$cnf( $equal(add(Y,additive_identity),Y) )],[refute_0_381,refute_0_569]) ).
cnf(refute_0_571,plain,
( multiply(Y,Y) != add(Y,multiply(additive_identity,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) != Y
| multiply(Y,Y) = Y ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(Y,Y),Y) ),[0],$fot(add(Y,multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_572,plain,
( multiply(Y,Y) != add(Y,multiply(additive_identity,additive_identity))
| multiply(Y,Y) = Y ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),Y) )],[refute_0_570,refute_0_571]) ).
cnf(refute_0_573,plain,
( multiply(multiply(Y,Y),multiply(Y,Y)) != add(Y,multiply(additive_identity,additive_identity))
| multiply(Y,Y) = Y ),
inference(resolve,[$cnf( $equal(multiply(Y,Y),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_563,refute_0_572]) ).
cnf(refute_0_574,plain,
multiply(Y,Y) = Y,
inference(resolve,[$cnf( $equal(multiply(multiply(Y,Y),multiply(Y,Y)),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_434,refute_0_573]) ).
cnf(refute_0_575,plain,
multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) = multiply(X_33,additive_identity),
inference(subst,[],[refute_0_574:[bind(Y,$fot(multiply(X_33,additive_identity)))]]) ).
cnf(refute_0_576,plain,
( multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) != multiply(X_33,additive_identity)
| multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) != multiply(additive_identity,X_33)
| multiply(X_33,additive_identity) = multiply(additive_identity,X_33) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)),multiply(additive_identity,X_33)) ),[0],$fot(multiply(X_33,additive_identity))]]) ).
cnf(refute_0_577,plain,
( multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) != multiply(additive_identity,X_33)
| multiply(X_33,additive_identity) = multiply(additive_identity,X_33) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)),multiply(X_33,additive_identity)) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
multiply(additive_identity,X_33) = additive_identity,
inference(subst,[],[refute_0_446:[bind(X_59,$fot(X_33))]]) ).
cnf(refute_0_579,plain,
( multiply(X_33,additive_identity) != multiply(additive_identity,X_33)
| multiply(additive_identity,X_33) != additive_identity
| multiply(X_33,additive_identity) = additive_identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_33,additive_identity),additive_identity) ),[0],$fot(multiply(additive_identity,X_33))]]) ).
cnf(refute_0_580,plain,
( multiply(X_33,additive_identity) != multiply(additive_identity,X_33)
| multiply(X_33,additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_33),additive_identity) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
( multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)) != multiply(additive_identity,X_33)
| multiply(X_33,additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(X_33,additive_identity),multiply(additive_identity,X_33)) )],[refute_0_577,refute_0_580]) ).
cnf(refute_0_582,plain,
multiply(X_33,additive_identity) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(multiply(X_33,additive_identity),multiply(X_33,additive_identity)),multiply(additive_identity,X_33)) )],[refute_0_327,refute_0_581]) ).
cnf(refute_0_583,plain,
multiply(Z,additive_identity) = additive_identity,
inference(subst,[],[refute_0_582:[bind(X_33,$fot(Z))]]) ).
cnf(refute_0_584,plain,
add(multiply(Z,additive_identity),add(X,Z)) = add(multiply(Z,additive_identity),add(X,Z)),
introduced(tautology,[refl,[$fot(add(multiply(Z,additive_identity),add(X,Z)))]]) ).
cnf(refute_0_585,plain,
( multiply(Z,additive_identity) != additive_identity
| add(multiply(Z,additive_identity),add(X,Z)) != add(multiply(Z,additive_identity),add(X,Z))
| add(multiply(Z,additive_identity),add(X,Z)) = add(additive_identity,add(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Z,additive_identity),add(X,Z)),add(multiply(Z,additive_identity),add(X,Z))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_586,plain,
( multiply(Z,additive_identity) != additive_identity
| add(multiply(Z,additive_identity),add(X,Z)) = add(additive_identity,add(X,Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(Z,additive_identity),add(X,Z)),add(multiply(Z,additive_identity),add(X,Z))) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
add(multiply(Z,additive_identity),add(X,Z)) = add(additive_identity,add(X,Z)),
inference(resolve,[$cnf( $equal(multiply(Z,additive_identity),additive_identity) )],[refute_0_583,refute_0_586]) ).
cnf(refute_0_588,plain,
( add(multiply(Z,additive_identity),add(X,Z)) != add(additive_identity,add(X,Z))
| add(additive_identity,add(X,Z)) != add(X,Z)
| add(multiply(Z,additive_identity),add(X,Z)) = add(X,Z) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(multiply(Z,additive_identity),add(X,Z)))),bind(Y0,$fot(add(additive_identity,add(X,Z)))),bind(Z0,$fot(add(X,Z)))]]) ).
cnf(refute_0_589,plain,
( add(additive_identity,add(X,Z)) != add(X,Z)
| add(multiply(Z,additive_identity),add(X,Z)) = add(X,Z) ),
inference(resolve,[$cnf( $equal(add(multiply(Z,additive_identity),add(X,Z)),add(additive_identity,add(X,Z))) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
add(multiply(Z,additive_identity),add(X,Z)) = add(X,Z),
inference(resolve,[$cnf( $equal(add(additive_identity,add(X,Z)),add(X,Z)) )],[refute_0_365,refute_0_589]) ).
cnf(refute_0_591,plain,
( add(Z,X) != add(multiply(Z,additive_identity),add(X,Z))
| add(multiply(Z,additive_identity),add(X,Z)) != add(X,Z)
| add(Z,X) = add(X,Z) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(Z,X),add(X,Z)) ),[0],$fot(add(multiply(Z,additive_identity),add(X,Z)))]]) ).
cnf(refute_0_592,plain,
( add(Z,X) != add(multiply(Z,additive_identity),add(X,Z))
| add(Z,X) = add(X,Z) ),
inference(resolve,[$cnf( $equal(add(multiply(Z,additive_identity),add(X,Z)),add(X,Z)) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
( add(Z,multiply(X,add(X,Z))) != add(multiply(Z,additive_identity),add(X,Z))
| add(Z,X) = add(X,Z) ),
inference(resolve,[$cnf( $equal(add(Z,X),add(multiply(Z,additive_identity),add(X,Z))) )],[refute_0_364,refute_0_592]) ).
cnf(refute_0_594,plain,
add(Z,X) = add(X,Z),
inference(resolve,[$cnf( $equal(add(Z,multiply(X,add(X,Z))),add(multiply(Z,additive_identity),add(X,Z))) )],[refute_0_357,refute_0_593]) ).
cnf(refute_0_595,plain,
( add(Z,X) != add(X,Z)
| add(X,Z) = add(Z,X) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(Z,X))),bind(Y0,$fot(add(X,Z)))]]) ).
cnf(refute_0_596,plain,
add(X,Z) = add(Z,X),
inference(resolve,[$cnf( $equal(add(Z,X),add(X,Z)) )],[refute_0_594,refute_0_595]) ).
cnf(refute_0_597,plain,
add(x,additive_identity) = add(additive_identity,x),
inference(subst,[],[refute_0_596:[bind(X,$fot(x)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_598,plain,
( add(additive_identity,x) != x
| add(x,additive_identity) != add(additive_identity,x)
| add(x,additive_identity) = x ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(add(x,additive_identity))),bind(Y0,$fot(add(additive_identity,x))),bind(Z0,$fot(x))]]) ).
cnf(refute_0_599,plain,
( add(additive_identity,x) != x
| add(x,additive_identity) = x ),
inference(resolve,[$cnf( $equal(add(x,additive_identity),add(additive_identity,x)) )],[refute_0_597,refute_0_598]) ).
cnf(refute_0_600,plain,
add(x,additive_identity) = x,
inference(resolve,[$cnf( $equal(add(additive_identity,x),x) )],[refute_0_339,refute_0_599]) ).
cnf(refute_0_601,plain,
( add(x,additive_identity) != multiply(z,add(x,additive_identity))
| add(x,additive_identity) != x
| x = multiply(z,add(x,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(x,additive_identity),multiply(z,add(x,additive_identity))) ),[0],$fot(x)]]) ).
cnf(refute_0_602,plain,
( add(x,additive_identity) != multiply(z,add(x,additive_identity))
| x = multiply(z,add(x,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(x,additive_identity),x) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
multiply(z,x) = multiply(x,z),
inference(subst,[],[refute_0_8:[bind(X,$fot(x)),bind(Y,$fot(z))]]) ).
cnf(refute_0_604,plain,
multiply(z,add(additive_identity,x)) = multiply(z,add(additive_identity,x)),
introduced(tautology,[refl,[$fot(multiply(z,add(additive_identity,x)))]]) ).
cnf(refute_0_605,plain,
( multiply(z,add(additive_identity,x)) != multiply(z,add(additive_identity,x))
| add(additive_identity,x) != x
| multiply(z,add(additive_identity,x)) = multiply(z,x) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(z,add(additive_identity,x)),multiply(z,add(additive_identity,x))) ),[1,1],$fot(x)]]) ).
cnf(refute_0_606,plain,
( add(additive_identity,x) != x
| multiply(z,add(additive_identity,x)) = multiply(z,x) ),
inference(resolve,[$cnf( $equal(multiply(z,add(additive_identity,x)),multiply(z,add(additive_identity,x))) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
multiply(z,add(additive_identity,x)) = multiply(z,x),
inference(resolve,[$cnf( $equal(add(additive_identity,x),x) )],[refute_0_339,refute_0_606]) ).
cnf(refute_0_608,plain,
( multiply(z,add(additive_identity,x)) != multiply(z,x)
| multiply(z,x) != multiply(x,z)
| multiply(z,add(additive_identity,x)) = multiply(x,z) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(z,add(additive_identity,x)))),bind(Y0,$fot(multiply(z,x))),bind(Z0,$fot(multiply(x,z)))]]) ).
cnf(refute_0_609,plain,
( multiply(z,x) != multiply(x,z)
| multiply(z,add(additive_identity,x)) = multiply(x,z) ),
inference(resolve,[$cnf( $equal(multiply(z,add(additive_identity,x)),multiply(z,x)) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
multiply(z,add(additive_identity,x)) = multiply(x,z),
inference(resolve,[$cnf( $equal(multiply(z,x),multiply(x,z)) )],[refute_0_603,refute_0_609]) ).
cnf(refute_0_611,plain,
add(x,multiply(y,X_22)) = multiply(add(x,y),add(x,X_22)),
inference(subst,[],[distributivity2:[bind(X,$fot(x)),bind(Y,$fot(y)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_612,plain,
( add(x,multiply(y,X_22)) != multiply(add(x,y),add(x,X_22))
| add(x,y) != z
| add(x,multiply(y,X_22)) = multiply(z,add(x,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(add(x,multiply(y,X_22)),multiply(add(x,y),add(x,X_22))) ),[1,0],$fot(z)]]) ).
cnf(refute_0_613,plain,
( add(x,multiply(y,X_22)) != multiply(add(x,y),add(x,X_22))
| add(x,multiply(y,X_22)) = multiply(z,add(x,X_22)) ),
inference(resolve,[$cnf( $equal(add(x,y),z) )],[x_times_y,refute_0_612]) ).
cnf(refute_0_614,plain,
add(x,multiply(y,X_22)) = multiply(z,add(x,X_22)),
inference(resolve,[$cnf( $equal(add(x,multiply(y,X_22)),multiply(add(x,y),add(x,X_22))) )],[refute_0_611,refute_0_613]) ).
cnf(refute_0_615,plain,
add(x,multiply(y,X_24)) = multiply(z,add(x,X_24)),
inference(subst,[],[refute_0_614:[bind(X_22,$fot(X_24))]]) ).
cnf(refute_0_616,plain,
add(X_24,x) = add(x,X_24),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_24)),bind(Y,$fot(x))]]) ).
cnf(refute_0_617,plain,
( add(X_24,x) != add(x,X_24)
| add(x,X_24) = add(X_24,x) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X_24,x))),bind(Y0,$fot(add(x,X_24)))]]) ).
cnf(refute_0_618,plain,
add(x,X_24) = add(X_24,x),
inference(resolve,[$cnf( $equal(add(X_24,x),add(x,X_24)) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
( add(x,X_24) != add(X_24,x)
| add(x,multiply(y,X_24)) != multiply(z,add(x,X_24))
| add(x,multiply(y,X_24)) = multiply(z,add(X_24,x)) ),
introduced(tautology,[equality,[$cnf( $equal(add(x,multiply(y,X_24)),multiply(z,add(x,X_24))) ),[1,1],$fot(add(X_24,x))]]) ).
cnf(refute_0_620,plain,
( add(x,multiply(y,X_24)) != multiply(z,add(x,X_24))
| add(x,multiply(y,X_24)) = multiply(z,add(X_24,x)) ),
inference(resolve,[$cnf( $equal(add(x,X_24),add(X_24,x)) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
add(x,multiply(y,X_24)) = multiply(z,add(X_24,x)),
inference(resolve,[$cnf( $equal(add(x,multiply(y,X_24)),multiply(z,add(x,X_24))) )],[refute_0_615,refute_0_620]) ).
cnf(refute_0_622,plain,
( add(x,multiply(y,X_24)) != multiply(z,add(X_24,x))
| add(x,multiply(y,X_24)) != multiply(z,add(x,X_24))
| multiply(z,add(x,X_24)) = multiply(z,add(X_24,x)) ),
introduced(tautology,[equality,[$cnf( $equal(add(x,multiply(y,X_24)),multiply(z,add(X_24,x))) ),[0],$fot(multiply(z,add(x,X_24)))]]) ).
cnf(refute_0_623,plain,
( add(x,multiply(y,X_24)) != multiply(z,add(X_24,x))
| multiply(z,add(x,X_24)) = multiply(z,add(X_24,x)) ),
inference(resolve,[$cnf( $equal(add(x,multiply(y,X_24)),multiply(z,add(x,X_24))) )],[refute_0_615,refute_0_622]) ).
cnf(refute_0_624,plain,
multiply(z,add(x,X_24)) = multiply(z,add(X_24,x)),
inference(resolve,[$cnf( $equal(add(x,multiply(y,X_24)),multiply(z,add(X_24,x))) )],[refute_0_621,refute_0_623]) ).
cnf(refute_0_625,plain,
multiply(z,add(x,additive_identity)) = multiply(z,add(additive_identity,x)),
inference(subst,[],[refute_0_624:[bind(X_24,$fot(additive_identity))]]) ).
cnf(refute_0_626,plain,
( multiply(z,add(additive_identity,x)) != multiply(x,z)
| multiply(z,add(x,additive_identity)) != multiply(z,add(additive_identity,x))
| multiply(z,add(x,additive_identity)) = multiply(x,z) ),
inference(subst,[],[refute_0_60:[bind(X0,$fot(multiply(z,add(x,additive_identity)))),bind(Y0,$fot(multiply(z,add(additive_identity,x)))),bind(Z0,$fot(multiply(x,z)))]]) ).
cnf(refute_0_627,plain,
( multiply(z,add(additive_identity,x)) != multiply(x,z)
| multiply(z,add(x,additive_identity)) = multiply(x,z) ),
inference(resolve,[$cnf( $equal(multiply(z,add(x,additive_identity)),multiply(z,add(additive_identity,x))) )],[refute_0_625,refute_0_626]) ).
cnf(refute_0_628,plain,
multiply(z,add(x,additive_identity)) = multiply(x,z),
inference(resolve,[$cnf( $equal(multiply(z,add(additive_identity,x)),multiply(x,z)) )],[refute_0_610,refute_0_627]) ).
cnf(refute_0_629,plain,
( multiply(z,add(x,additive_identity)) != multiply(x,z)
| x != multiply(z,add(x,additive_identity))
| x = multiply(x,z) ),
introduced(tautology,[equality,[$cnf( $equal(x,multiply(z,add(x,additive_identity))) ),[1],$fot(multiply(x,z))]]) ).
cnf(refute_0_630,plain,
( x != multiply(z,add(x,additive_identity))
| x = multiply(x,z) ),
inference(resolve,[$cnf( $equal(multiply(z,add(x,additive_identity)),multiply(x,z)) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
( add(x,additive_identity) != multiply(z,add(x,additive_identity))
| x = multiply(x,z) ),
inference(resolve,[$cnf( $equal(x,multiply(z,add(x,additive_identity))) )],[refute_0_602,refute_0_630]) ).
cnf(refute_0_632,plain,
x = multiply(x,z),
inference(resolve,[$cnf( $equal(add(x,additive_identity),multiply(z,add(x,additive_identity))) )],[refute_0_338,refute_0_631]) ).
cnf(refute_0_633,plain,
( x != multiply(x,z)
| multiply(x,z) = x ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(x)),bind(Y0,$fot(multiply(x,z)))]]) ).
cnf(refute_0_634,plain,
x != multiply(x,z),
inference(resolve,[$cnf( $equal(multiply(x,z),x) )],[refute_0_633,prove_sum]) ).
cnf(refute_0_635,plain,
$false,
inference(resolve,[$cnf( $equal(x,multiply(x,z)) )],[refute_0_632,refute_0_634]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO017-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 1 20:41:19 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.00/1.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.00/1.16
% 1.00/1.16 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.00/1.21
%------------------------------------------------------------------------------