%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO016-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 23:44:40 EDT 2022
% Result : Unsatisfiable 0.56s 0.76s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 129
% Number of leaves : 168
% Syntax : Number of clauses : 730 ( 365 unt; 0 nHn; 394 RR)
% Number of literals : 1254 (1253 equ; 526 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 1096 ( 94 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,
multiply(x,y) = z ).
cnf(prove_sum,negated_conjecture,
add(x,z) != x ).
cnf(refute_0_0,plain,
multiply(add(y,X_62),add(x,z)) = add(multiply(y,add(x,z)),multiply(X_62,add(x,z))),
inference(subst,[],[distributivity3:[bind(X,$fot(y)),bind(Y,$fot(X_62)),bind(Z,$fot(add(x,z)))]]) ).
cnf(refute_0_1,plain,
add(multiply(X,y),z) = multiply(add(X,z),add(y,z)),
inference(subst,[],[distributivity1:[bind(Y,$fot(y)),bind(Z,$fot(z))]]) ).
cnf(refute_0_2,plain,
add(Z,multiply(Y,Z)) = multiply(add(Z,Y),add(Z,Z)),
inference(subst,[],[distributivity2:[bind(X,$fot(Z))]]) ).
cnf(refute_0_3,plain,
add(X_18,multiply(X_19,inverse(X_18))) = multiply(add(X_18,X_19),add(X_18,inverse(X_18))),
inference(subst,[],[distributivity2:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(inverse(X_18)))]]) ).
cnf(refute_0_4,plain,
add(X_18,inverse(X_18)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_5,plain,
( add(X_18,multiply(X_19,inverse(X_18))) != multiply(add(X_18,X_19),add(X_18,inverse(X_18)))
| add(X_18,inverse(X_18)) != multiplicative_identity
| add(X_18,multiply(X_19,inverse(X_18))) = multiply(add(X_18,X_19),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_18,multiply(X_19,inverse(X_18))),multiply(add(X_18,X_19),add(X_18,inverse(X_18)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_6,plain,
( add(X_18,multiply(X_19,inverse(X_18))) != multiply(add(X_18,X_19),add(X_18,inverse(X_18)))
| add(X_18,multiply(X_19,inverse(X_18))) = multiply(add(X_18,X_19),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_18,inverse(X_18)),multiplicative_identity) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
add(X_18,multiply(X_19,inverse(X_18))) = multiply(add(X_18,X_19),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_18,multiply(X_19,inverse(X_18))),multiply(add(X_18,X_19),add(X_18,inverse(X_18)))) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(add(X_18,X_19),multiplicative_identity) = add(X_18,X_19),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_18,X_19)))]]) ).
cnf(refute_0_9,plain,
( multiply(add(X_18,X_19),multiplicative_identity) != add(X_18,X_19)
| add(X_18,multiply(X_19,inverse(X_18))) != multiply(add(X_18,X_19),multiplicative_identity)
| add(X_18,multiply(X_19,inverse(X_18))) = add(X_18,X_19) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_18,multiply(X_19,inverse(X_18))),multiply(add(X_18,X_19),multiplicative_identity)) ),[1],$fot(add(X_18,X_19))]]) ).
cnf(refute_0_10,plain,
( add(X_18,multiply(X_19,inverse(X_18))) != multiply(add(X_18,X_19),multiplicative_identity)
| add(X_18,multiply(X_19,inverse(X_18))) = add(X_18,X_19) ),
inference(resolve,[$cnf( $equal(multiply(add(X_18,X_19),multiplicative_identity),add(X_18,X_19)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
add(X_18,multiply(X_19,inverse(X_18))) = add(X_18,X_19),
inference(resolve,[$cnf( $equal(add(X_18,multiply(X_19,inverse(X_18))),multiply(add(X_18,X_19),multiplicative_identity)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
add(X_49,multiply(X_49,inverse(X_49))) = add(X_49,X_49),
inference(subst,[],[refute_0_11:[bind(X_18,$fot(X_49)),bind(X_19,$fot(X_49))]]) ).
cnf(refute_0_13,plain,
multiply(X_49,inverse(X_49)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_14,plain,
( multiply(X_49,inverse(X_49)) != additive_identity
| add(X_49,multiply(X_49,inverse(X_49))) != add(X_49,X_49)
| add(X_49,additive_identity) = add(X_49,X_49) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_49,multiply(X_49,inverse(X_49))),add(X_49,X_49)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_15,plain,
( add(X_49,multiply(X_49,inverse(X_49))) != add(X_49,X_49)
| add(X_49,additive_identity) = add(X_49,X_49) ),
inference(resolve,[$cnf( $equal(multiply(X_49,inverse(X_49)),additive_identity) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
add(X_49,additive_identity) = add(X_49,X_49),
inference(resolve,[$cnf( $equal(add(X_49,multiply(X_49,inverse(X_49))),add(X_49,X_49)) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
add(X_49,additive_identity) = X_49,
inference(subst,[],[additive_id1:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_18,plain,
( add(X_49,additive_identity) != X_49
| add(X_49,additive_identity) != add(X_49,X_49)
| X_49 = add(X_49,X_49) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_49,additive_identity),add(X_49,X_49)) ),[0],$fot(X_49)]]) ).
cnf(refute_0_19,plain,
( add(X_49,additive_identity) != add(X_49,X_49)
| X_49 = add(X_49,X_49) ),
inference(resolve,[$cnf( $equal(add(X_49,additive_identity),X_49) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
X_49 = add(X_49,X_49),
inference(resolve,[$cnf( $equal(add(X_49,additive_identity),add(X_49,X_49)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
Z = add(Z,Z),
inference(subst,[],[refute_0_20:[bind(X_49,$fot(Z))]]) ).
cnf(refute_0_22,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_24,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( Z != add(Z,Z)
| add(Z,Z) = Z ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(Z)),bind(Y0,$fot(add(Z,Z)))]]) ).
cnf(refute_0_26,plain,
add(Z,Z) = Z,
inference(resolve,[$cnf( $equal(Z,add(Z,Z)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( add(Z,Z) != Z
| add(Z,multiply(Y,Z)) != multiply(add(Z,Y),add(Z,Z))
| add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),add(Z,Z))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_28,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( $equal(add(Z,Z),Z) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z),
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),add(Z,Z))) )],[refute_0_2,refute_0_28]) ).
cnf(refute_0_30,plain,
add(X,multiply(multiply(additive_identity,X_24),Z)) = multiply(add(X,multiply(additive_identity,X_24)),add(X,Z)),
inference(subst,[],[distributivity2:[bind(Y,$fot(multiply(additive_identity,X_24)))]]) ).
cnf(refute_0_31,plain,
add(X_18,multiply(additive_identity,X_20)) = multiply(add(X_18,additive_identity),add(X_18,X_20)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_18)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_32,plain,
add(X_18,additive_identity) = X_18,
inference(subst,[],[additive_id1:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_33,plain,
( add(X_18,multiply(additive_identity,X_20)) != multiply(add(X_18,additive_identity),add(X_18,X_20))
| add(X_18,additive_identity) != X_18
| add(X_18,multiply(additive_identity,X_20)) = multiply(X_18,add(X_18,X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_18,multiply(additive_identity,X_20)),multiply(add(X_18,additive_identity),add(X_18,X_20))) ),[1,0],$fot(X_18)]]) ).
cnf(refute_0_34,plain,
( add(X_18,multiply(additive_identity,X_20)) != multiply(add(X_18,additive_identity),add(X_18,X_20))
| add(X_18,multiply(additive_identity,X_20)) = multiply(X_18,add(X_18,X_20)) ),
inference(resolve,[$cnf( $equal(add(X_18,additive_identity),X_18) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
add(X_18,multiply(additive_identity,X_20)) = multiply(X_18,add(X_18,X_20)),
inference(resolve,[$cnf( $equal(add(X_18,multiply(additive_identity,X_20)),multiply(add(X_18,additive_identity),add(X_18,X_20))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
add(X,multiply(additive_identity,X_24)) = multiply(X,add(X,X_24)),
inference(subst,[],[refute_0_35:[bind(X_18,$fot(X)),bind(X_20,$fot(X_24))]]) ).
cnf(refute_0_37,plain,
( add(X,multiply(multiply(additive_identity,X_24),Z)) != multiply(add(X,multiply(additive_identity,X_24)),add(X,Z))
| add(X,multiply(additive_identity,X_24)) != multiply(X,add(X,X_24))
| add(X,multiply(multiply(additive_identity,X_24),Z)) = multiply(multiply(X,add(X,X_24)),add(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,multiply(multiply(additive_identity,X_24),Z)),multiply(add(X,multiply(additive_identity,X_24)),add(X,Z))) ),[1,0],$fot(multiply(X,add(X,X_24)))]]) ).
cnf(refute_0_38,plain,
( add(X,multiply(multiply(additive_identity,X_24),Z)) != multiply(add(X,multiply(additive_identity,X_24)),add(X,Z))
| add(X,multiply(multiply(additive_identity,X_24),Z)) = multiply(multiply(X,add(X,X_24)),add(X,Z)) ),
inference(resolve,[$cnf( $equal(add(X,multiply(additive_identity,X_24)),multiply(X,add(X,X_24))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
add(X,multiply(multiply(additive_identity,X_24),Z)) = multiply(multiply(X,add(X,X_24)),add(X,Z)),
inference(resolve,[$cnf( $equal(add(X,multiply(multiply(additive_identity,X_24),Z)),multiply(add(X,multiply(additive_identity,X_24)),add(X,Z))) )],[refute_0_30,refute_0_38]) ).
cnf(refute_0_40,plain,
add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) = multiply(multiply(additive_identity,X_31),add(multiply(additive_identity,X_31),X_20)),
inference(subst,[],[refute_0_35:[bind(X_18,$fot(multiply(additive_identity,X_31)))]]) ).
cnf(refute_0_41,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,$fot(X_12))]]) ).
cnf(refute_0_42,plain,
add(additive_identity,X_12) = X_12,
inference(subst,[],[additive_id2:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_43,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_44,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( $equal(add(additive_identity,X_12),X_12) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
add(multiply(additive_identity,X_11),X_12) = multiply(X_12,add(X_11,X_12)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_11),X_12),multiply(add(additive_identity,X_12),add(X_11,X_12))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
add(multiply(additive_identity,X_31),X_20) = multiply(X_20,add(X_31,X_20)),
inference(subst,[],[refute_0_45:[bind(X_11,$fot(X_31)),bind(X_12,$fot(X_20))]]) ).
cnf(refute_0_47,plain,
( add(multiply(additive_identity,X_31),X_20) != multiply(X_20,add(X_31,X_20))
| add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(multiply(additive_identity,X_31),add(multiply(additive_identity,X_31),X_20))
| add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) = multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)),multiply(multiply(additive_identity,X_31),add(multiply(additive_identity,X_31),X_20))) ),[1,1],$fot(multiply(X_20,add(X_31,X_20)))]]) ).
cnf(refute_0_48,plain,
( add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(multiply(additive_identity,X_31),add(multiply(additive_identity,X_31),X_20))
| add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) = multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),X_20),multiply(X_20,add(X_31,X_20))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) = multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)),multiply(multiply(additive_identity,X_31),add(multiply(additive_identity,X_31),X_20))) )],[refute_0_40,refute_0_48]) ).
cnf(refute_0_50,plain,
( multiply(X,add(Y,Z)) != add(multiply(X,Y),multiply(X,Z))
| add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_51,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[distributivity4,refute_0_50]) ).
cnf(refute_0_52,plain,
add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) = multiply(additive_identity,add(X_31,X_20)),
inference(subst,[],[refute_0_51:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_31)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_53,plain,
( add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))
| add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(additive_identity,add(X_31,X_20))
| multiply(additive_identity,add(X_31,X_20)) = multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)),multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))) ),[0],$fot(multiply(additive_identity,add(X_31,X_20)))]]) ).
cnf(refute_0_54,plain,
( add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))
| multiply(additive_identity,add(X_31,X_20)) = multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)),multiply(additive_identity,add(X_31,X_20))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(additive_identity,add(X_31,X_20)) = multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)),multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))) )],[refute_0_49,refute_0_54]) ).
cnf(refute_0_56,plain,
add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(X_10,additive_identity),add(multiply(X_10,additive_identity),X_24)),
inference(subst,[],[refute_0_35:[bind(X_18,$fot(multiply(X_10,additive_identity))),bind(X_20,$fot(X_24))]]) ).
cnf(refute_0_57,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),add(additive_identity,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_58,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_59,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( $equal(add(additive_identity,X_12),X_12) )],[refute_0_42,refute_0_58]) ).
cnf(refute_0_60,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),X_12),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),add(additive_identity,X_12))) )],[refute_0_57,refute_0_59]) ).
cnf(refute_0_61,plain,
( multiply(X,Y) != multiply(Y,X)
| multiply(Y,X) = multiply(X,Y) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_62,plain,
multiply(Y,X) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(Y,X)) )],[commutativity_of_multiply,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(add(X_10,X_12),X_12) = multiply(X_12,add(X_10,X_12)),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_12)),bind(Y,$fot(add(X_10,X_12)))]]) ).
cnf(refute_0_64,plain,
( multiply(add(X_10,X_12),X_12) != multiply(X_12,add(X_10,X_12))
| add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),X_12)
| add(multiply(X_10,additive_identity),X_12) = multiply(X_12,add(X_10,X_12)) ),
introduced(tautology,[equality,[$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_65,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( $equal(multiply(add(X_10,X_12),X_12),multiply(X_12,add(X_10,X_12))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(X_12,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),X_12)) )],[refute_0_60,refute_0_65]) ).
cnf(refute_0_67,plain,
add(multiply(X_10,additive_identity),X_24) = multiply(X_24,add(X_10,X_24)),
inference(subst,[],[refute_0_66:[bind(X_12,$fot(X_24))]]) ).
cnf(refute_0_68,plain,
( add(multiply(X_10,additive_identity),X_24) != multiply(X_24,add(X_10,X_24))
| add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(X_10,additive_identity),add(multiply(X_10,additive_identity),X_24))
| add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(X_10,additive_identity),add(multiply(X_10,additive_identity),X_24))) ),[1,1],$fot(multiply(X_24,add(X_10,X_24)))]]) ).
cnf(refute_0_69,plain,
( add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(X_10,additive_identity),add(multiply(X_10,additive_identity),X_24))
| add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_24),multiply(X_24,add(X_10,X_24))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(X_10,additive_identity),add(multiply(X_10,additive_identity),X_24))) )],[refute_0_56,refute_0_69]) ).
cnf(refute_0_71,plain,
add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) = multiply(multiply(additive_identity,X_20),add(X_31,multiply(additive_identity,X_20))),
inference(subst,[],[refute_0_45:[bind(X_11,$fot(X_31)),bind(X_12,$fot(multiply(additive_identity,X_20)))]]) ).
cnf(refute_0_72,plain,
add(X_31,multiply(additive_identity,X_20)) = multiply(X_31,add(X_31,X_20)),
inference(subst,[],[refute_0_35:[bind(X_18,$fot(X_31))]]) ).
cnf(refute_0_73,plain,
( add(X_31,multiply(additive_identity,X_20)) != multiply(X_31,add(X_31,X_20))
| add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(multiply(additive_identity,X_20),add(X_31,multiply(additive_identity,X_20)))
| add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) = multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)),multiply(multiply(additive_identity,X_20),add(X_31,multiply(additive_identity,X_20)))) ),[1,1],$fot(multiply(X_31,add(X_31,X_20)))]]) ).
cnf(refute_0_74,plain,
( add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(multiply(additive_identity,X_20),add(X_31,multiply(additive_identity,X_20)))
| add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) = multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20))) ),
inference(resolve,[$cnf( $equal(add(X_31,multiply(additive_identity,X_20)),multiply(X_31,add(X_31,X_20))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) = multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)),multiply(multiply(additive_identity,X_20),add(X_31,multiply(additive_identity,X_20)))) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
( add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20)))
| add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(additive_identity,add(X_31,X_20))
| multiply(additive_identity,add(X_31,X_20)) = multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)),multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20)))) ),[0],$fot(multiply(additive_identity,add(X_31,X_20)))]]) ).
cnf(refute_0_77,plain,
( add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20)))
| multiply(additive_identity,add(X_31,X_20)) = multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)),multiply(additive_identity,add(X_31,X_20))) )],[refute_0_52,refute_0_76]) ).
cnf(refute_0_78,plain,
add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(additive_identity,X_24),add(X_10,multiply(additive_identity,X_24))),
inference(subst,[],[refute_0_66:[bind(X_12,$fot(multiply(additive_identity,X_24)))]]) ).
cnf(refute_0_79,plain,
add(X_10,multiply(additive_identity,X_24)) = multiply(X_10,add(X_10,X_24)),
inference(subst,[],[refute_0_35:[bind(X_18,$fot(X_10)),bind(X_20,$fot(X_24))]]) ).
cnf(refute_0_80,plain,
( add(X_10,multiply(additive_identity,X_24)) != multiply(X_10,add(X_10,X_24))
| add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(additive_identity,X_24),add(X_10,multiply(additive_identity,X_24)))
| add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(additive_identity,X_24),multiply(X_10,add(X_10,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(additive_identity,X_24),add(X_10,multiply(additive_identity,X_24)))) ),[1,1],$fot(multiply(X_10,add(X_10,X_24)))]]) ).
cnf(refute_0_81,plain,
( add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(additive_identity,X_24),add(X_10,multiply(additive_identity,X_24)))
| add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(additive_identity,X_24),multiply(X_10,add(X_10,X_24))) ),
inference(resolve,[$cnf( $equal(add(X_10,multiply(additive_identity,X_24)),multiply(X_10,add(X_10,X_24))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(additive_identity,X_24),multiply(X_10,add(X_10,X_24))),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(additive_identity,X_24),add(X_10,multiply(additive_identity,X_24)))) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(additive_identity,X_24),multiply(X_10,add(X_10,X_24)))
| multiply(multiply(additive_identity,X_24),multiply(X_10,add(X_10,X_24))) = add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)))),bind(Y0,$fot(multiply(multiply(additive_identity,X_24),multiply(X_10,add(X_10,X_24)))))]]) ).
cnf(refute_0_84,plain,
multiply(multiply(additive_identity,X_24),multiply(X_10,add(X_10,X_24))) = add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(additive_identity,X_24),multiply(X_10,add(X_10,X_24)))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20))) = add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)),
inference(subst,[],[refute_0_84:[bind(X_10,$fot(X_31)),bind(X_24,$fot(X_20))]]) ).
cnf(refute_0_86,plain,
( multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20))) != add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))
| multiply(additive_identity,add(X_31,X_20)) != multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20)))
| multiply(additive_identity,add(X_31,X_20)) = add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_31,X_20)),multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20)))) ),[1],$fot(add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)))]]) ).
cnf(refute_0_87,plain,
( multiply(additive_identity,add(X_31,X_20)) != multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20)))
| multiply(additive_identity,add(X_31,X_20)) = add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20))),add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)) != multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20)))
| multiply(additive_identity,add(X_31,X_20)) = add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_31,X_20)),multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20)))) )],[refute_0_77,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(additive_identity,add(X_31,X_20)) = add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),multiply(additive_identity,X_20)),multiply(multiply(additive_identity,X_20),multiply(X_31,add(X_31,X_20)))) )],[refute_0_75,refute_0_88]) ).
cnf(refute_0_90,plain,
( multiply(additive_identity,add(X_31,X_20)) != add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))
| add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) = multiply(additive_identity,add(X_31,X_20)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(additive_identity,add(X_31,X_20)))),bind(Y0,$fot(add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))))]]) ).
cnf(refute_0_91,plain,
add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) = multiply(additive_identity,add(X_31,X_20)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_31,X_20)),add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) = multiply(additive_identity,add(X_10,X_24)),
inference(subst,[],[refute_0_91:[bind(X_20,$fot(X_24)),bind(X_31,$fot(X_10))]]) ).
cnf(refute_0_93,plain,
( add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))
| add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) != multiply(additive_identity,add(X_10,X_24))
| multiply(additive_identity,add(X_10,X_24)) = multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))) ),[0],$fot(multiply(additive_identity,add(X_10,X_24)))]]) ).
cnf(refute_0_94,plain,
( add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))
| multiply(additive_identity,add(X_10,X_24)) = multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)),multiply(additive_identity,add(X_10,X_24))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
multiply(additive_identity,add(X_10,X_24)) = multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))) )],[refute_0_70,refute_0_94]) ).
cnf(refute_0_96,plain,
add(multiply(X,multiply(X_13,additive_identity)),Z) = multiply(add(X,Z),add(multiply(X_13,additive_identity),Z)),
inference(subst,[],[distributivity1:[bind(Y,$fot(multiply(X_13,additive_identity)))]]) ).
cnf(refute_0_97,plain,
add(multiply(X_13,additive_identity),Z) = multiply(Z,add(X_13,Z)),
inference(subst,[],[refute_0_66:[bind(X_10,$fot(X_13)),bind(X_12,$fot(Z))]]) ).
cnf(refute_0_98,plain,
( add(multiply(X,multiply(X_13,additive_identity)),Z) != multiply(add(X,Z),add(multiply(X_13,additive_identity),Z))
| add(multiply(X_13,additive_identity),Z) != multiply(Z,add(X_13,Z))
| add(multiply(X,multiply(X_13,additive_identity)),Z) = multiply(add(X,Z),multiply(Z,add(X_13,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,multiply(X_13,additive_identity)),Z),multiply(add(X,Z),add(multiply(X_13,additive_identity),Z))) ),[1,1],$fot(multiply(Z,add(X_13,Z)))]]) ).
cnf(refute_0_99,plain,
( add(multiply(X,multiply(X_13,additive_identity)),Z) != multiply(add(X,Z),add(multiply(X_13,additive_identity),Z))
| add(multiply(X,multiply(X_13,additive_identity)),Z) = multiply(add(X,Z),multiply(Z,add(X_13,Z))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_13,additive_identity),Z),multiply(Z,add(X_13,Z))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
add(multiply(X,multiply(X_13,additive_identity)),Z) = multiply(add(X,Z),multiply(Z,add(X_13,Z))),
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(X_13,additive_identity)),Z),multiply(add(X,Z),add(multiply(X_13,additive_identity),Z))) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
add(additive_identity,Z) = Z,
inference(subst,[],[additive_id2:[bind(X,$fot(Z))]]) ).
cnf(refute_0_102,plain,
add(multiply(multiplicative_identity,additive_identity),X_14) = multiply(X_14,add(multiplicative_identity,X_14)),
inference(subst,[],[refute_0_66:[bind(X_10,$fot(multiplicative_identity)),bind(X_12,$fot(X_14))]]) ).
cnf(refute_0_103,plain,
multiply(multiplicative_identity,additive_identity) = additive_identity,
inference(subst,[],[multiplicative_id2:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_104,plain,
( multiply(multiplicative_identity,additive_identity) != additive_identity
| add(multiply(multiplicative_identity,additive_identity),X_14) != multiply(X_14,add(multiplicative_identity,X_14))
| add(additive_identity,X_14) = multiply(X_14,add(multiplicative_identity,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(multiplicative_identity,additive_identity),X_14),multiply(X_14,add(multiplicative_identity,X_14))) ),[0,0],$fot(additive_identity)]]) ).
cnf(refute_0_105,plain,
( add(multiply(multiplicative_identity,additive_identity),X_14) != multiply(X_14,add(multiplicative_identity,X_14))
| add(additive_identity,X_14) = multiply(X_14,add(multiplicative_identity,X_14)) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,additive_identity),additive_identity) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
add(additive_identity,X_14) = multiply(X_14,add(multiplicative_identity,X_14)),
inference(resolve,[$cnf( $equal(add(multiply(multiplicative_identity,additive_identity),X_14),multiply(X_14,add(multiplicative_identity,X_14))) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
add(additive_identity,X_14) = X_14,
inference(subst,[],[additive_id2:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_108,plain,
( add(additive_identity,X_14) != X_14
| add(additive_identity,X_14) != multiply(X_14,add(multiplicative_identity,X_14))
| X_14 = multiply(X_14,add(multiplicative_identity,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_identity,X_14),multiply(X_14,add(multiplicative_identity,X_14))) ),[0],$fot(X_14)]]) ).
cnf(refute_0_109,plain,
( add(additive_identity,X_14) != multiply(X_14,add(multiplicative_identity,X_14))
| X_14 = multiply(X_14,add(multiplicative_identity,X_14)) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_14),X_14) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
X_14 = multiply(X_14,add(multiplicative_identity,X_14)),
inference(resolve,[$cnf( $equal(add(additive_identity,X_14),multiply(X_14,add(multiplicative_identity,X_14))) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(X_42,additive_identity) = multiply(multiply(X_42,additive_identity),add(multiplicative_identity,multiply(X_42,additive_identity))),
inference(subst,[],[refute_0_110:[bind(X_14,$fot(multiply(X_42,additive_identity)))]]) ).
cnf(refute_0_112,plain,
add(X,multiply(X_13,additive_identity)) = add(multiply(X_13,additive_identity),X),
inference(subst,[],[commutativity_of_add:[bind(Y,$fot(multiply(X_13,additive_identity)))]]) ).
cnf(refute_0_113,plain,
add(multiply(X_13,additive_identity),X) = multiply(X,add(X_13,X)),
inference(subst,[],[refute_0_66:[bind(X_10,$fot(X_13)),bind(X_12,$fot(X))]]) ).
cnf(refute_0_114,plain,
( add(X,multiply(X_13,additive_identity)) != add(multiply(X_13,additive_identity),X)
| add(multiply(X_13,additive_identity),X) != multiply(X,add(X_13,X))
| add(X,multiply(X_13,additive_identity)) = multiply(X,add(X_13,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,multiply(X_13,additive_identity)),multiply(X,add(X_13,X))) ),[0],$fot(add(multiply(X_13,additive_identity),X))]]) ).
cnf(refute_0_115,plain,
( add(X,multiply(X_13,additive_identity)) != add(multiply(X_13,additive_identity),X)
| add(X,multiply(X_13,additive_identity)) = multiply(X,add(X_13,X)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_13,additive_identity),X),multiply(X,add(X_13,X))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
add(X,multiply(X_13,additive_identity)) = multiply(X,add(X_13,X)),
inference(resolve,[$cnf( $equal(add(X,multiply(X_13,additive_identity)),add(multiply(X_13,additive_identity),X)) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
add(multiplicative_identity,multiply(X_42,additive_identity)) = multiply(multiplicative_identity,add(X_42,multiplicative_identity)),
inference(subst,[],[refute_0_116:[bind(X,$fot(multiplicative_identity)),bind(X_13,$fot(X_42))]]) ).
cnf(refute_0_118,plain,
( multiply(X_42,additive_identity) != multiply(multiply(X_42,additive_identity),add(multiplicative_identity,multiply(X_42,additive_identity)))
| add(multiplicative_identity,multiply(X_42,additive_identity)) != multiply(multiplicative_identity,add(X_42,multiplicative_identity))
| multiply(X_42,additive_identity) = multiply(multiply(X_42,additive_identity),multiply(multiplicative_identity,add(X_42,multiplicative_identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_42,additive_identity),multiply(multiply(X_42,additive_identity),add(multiplicative_identity,multiply(X_42,additive_identity)))) ),[1,1],$fot(multiply(multiplicative_identity,add(X_42,multiplicative_identity)))]]) ).
cnf(refute_0_119,plain,
( multiply(X_42,additive_identity) != multiply(multiply(X_42,additive_identity),add(multiplicative_identity,multiply(X_42,additive_identity)))
| multiply(X_42,additive_identity) = multiply(multiply(X_42,additive_identity),multiply(multiplicative_identity,add(X_42,multiplicative_identity))) ),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,multiply(X_42,additive_identity)),multiply(multiplicative_identity,add(X_42,multiplicative_identity))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(X_42,additive_identity) = multiply(multiply(X_42,additive_identity),multiply(multiplicative_identity,add(X_42,multiplicative_identity))),
inference(resolve,[$cnf( $equal(multiply(X_42,additive_identity),multiply(multiply(X_42,additive_identity),add(multiplicative_identity,multiply(X_42,additive_identity)))) )],[refute_0_111,refute_0_119]) ).
cnf(refute_0_121,plain,
( multiply(additive_identity,add(X_10,X_24)) != multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))
| multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,add(X_10,X_24)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(additive_identity,add(X_10,X_24)))),bind(Y0,$fot(multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))))]]) ).
cnf(refute_0_122,plain,
multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,add(X_10,X_24)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_10,X_24)),multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))) )],[refute_0_95,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(multiply(X_42,additive_identity),multiply(multiplicative_identity,add(X_42,multiplicative_identity))) = multiply(additive_identity,add(X_42,multiplicative_identity)),
inference(subst,[],[refute_0_122:[bind(X_10,$fot(X_42)),bind(X_24,$fot(multiplicative_identity))]]) ).
cnf(refute_0_124,plain,
( multiply(X_42,additive_identity) != multiply(multiply(X_42,additive_identity),multiply(multiplicative_identity,add(X_42,multiplicative_identity)))
| multiply(multiply(X_42,additive_identity),multiply(multiplicative_identity,add(X_42,multiplicative_identity))) != multiply(additive_identity,add(X_42,multiplicative_identity))
| multiply(X_42,additive_identity) = multiply(additive_identity,add(X_42,multiplicative_identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_42,additive_identity),multiply(additive_identity,add(X_42,multiplicative_identity))) ),[0],$fot(multiply(multiply(X_42,additive_identity),multiply(multiplicative_identity,add(X_42,multiplicative_identity))))]]) ).
cnf(refute_0_125,plain,
( multiply(X_42,additive_identity) != multiply(multiply(X_42,additive_identity),multiply(multiplicative_identity,add(X_42,multiplicative_identity)))
| multiply(X_42,additive_identity) = multiply(additive_identity,add(X_42,multiplicative_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_42,additive_identity),multiply(multiplicative_identity,add(X_42,multiplicative_identity))),multiply(additive_identity,add(X_42,multiplicative_identity))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(X_42,additive_identity) = multiply(additive_identity,add(X_42,multiplicative_identity)),
inference(resolve,[$cnf( $equal(multiply(X_42,additive_identity),multiply(multiply(X_42,additive_identity),multiply(multiplicative_identity,add(X_42,multiplicative_identity)))) )],[refute_0_120,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(additive_identity,multiplicative_identity) = additive_identity,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_128,plain,
add(multiplicative_identity,multiply(Y,inverse(X_29))) = multiply(add(multiplicative_identity,Y),add(multiplicative_identity,inverse(X_29))),
inference(subst,[],[distributivity2:[bind(X,$fot(multiplicative_identity)),bind(Z,$fot(inverse(X_29)))]]) ).
cnf(refute_0_129,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,$fot(inverse(X_11)))]]) ).
cnf(refute_0_130,plain,
add(X_11,inverse(X_11)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_131,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_132,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( $equal(add(X_11,inverse(X_11)),multiplicative_identity) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_135,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_134]) ).
cnf(refute_0_136,plain,
add(multiply(X_10,X_11),inverse(X_11)) = add(inverse(X_11),multiply(X_10,X_11)),
inference(subst,[],[refute_0_135:[bind(X,$fot(inverse(X_11))),bind(Y,$fot(multiply(X_10,X_11)))]]) ).
cnf(refute_0_137,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(multiply(X_10,X_11),inverse(X_11)) != add(inverse(X_11),multiply(X_10,X_11))
| add(inverse(X_11),multiply(X_10,X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
introduced(tautology,[equality,[$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_138,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( $equal(add(multiply(X_10,X_11),inverse(X_11)),add(inverse(X_11),multiply(X_10,X_11))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(add(X_10,inverse(X_11)),multiplicative_identity) = add(X_10,inverse(X_11)),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,inverse(X_11))))]]) ).
cnf(refute_0_140,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_141,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( $equal(multiply(add(X_10,inverse(X_11)),multiplicative_identity),add(X_10,inverse(X_11))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_11),multiply(X_10,X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) )],[refute_0_133,refute_0_142]) ).
cnf(refute_0_144,plain,
add(inverse(X_28),multiply(multiplicative_identity,X_28)) = add(multiplicative_identity,inverse(X_28)),
inference(subst,[],[refute_0_143:[bind(X_10,$fot(multiplicative_identity)),bind(X_11,$fot(X_28))]]) ).
cnf(refute_0_145,plain,
multiply(multiplicative_identity,X_28) = X_28,
inference(subst,[],[multiplicative_id2:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_146,plain,
( multiply(multiplicative_identity,X_28) != X_28
| add(inverse(X_28),multiply(multiplicative_identity,X_28)) != add(multiplicative_identity,inverse(X_28))
| add(inverse(X_28),X_28) = add(multiplicative_identity,inverse(X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_28),multiply(multiplicative_identity,X_28)),add(multiplicative_identity,inverse(X_28))) ),[0,1],$fot(X_28)]]) ).
cnf(refute_0_147,plain,
( add(inverse(X_28),multiply(multiplicative_identity,X_28)) != add(multiplicative_identity,inverse(X_28))
| add(inverse(X_28),X_28) = add(multiplicative_identity,inverse(X_28)) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,X_28),X_28) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
add(inverse(X_28),X_28) = add(multiplicative_identity,inverse(X_28)),
inference(resolve,[$cnf( $equal(add(inverse(X_28),multiply(multiplicative_identity,X_28)),add(multiplicative_identity,inverse(X_28))) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
add(X_28,inverse(X_28)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_150,plain,
add(multiply(X_22,X_22),Y) = add(Y,multiply(X_22,X_22)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(X_22,X_22)))]]) ).
cnf(refute_0_151,plain,
add(multiply(Y,Y),Z) = multiply(add(Y,Z),add(Y,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_152,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_153,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_24:[bind(X0,$fot(add(Y,multiply(Z,Z)))),bind(Y0,$fot(multiply(add(Y,Z),add(Y,Z))))]]) ).
cnf(refute_0_154,plain,
multiply(add(Y,Z),add(Y,Z)) = add(Y,multiply(Z,Z)),
inference(resolve,[$cnf( $equal(add(Y,multiply(Z,Z)),multiply(add(Y,Z),add(Y,Z))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
( multiply(add(Y,Z),add(Y,Z)) != add(Y,multiply(Z,Z))
| add(multiply(Y,Y),Z) != multiply(add(Y,Z),add(Y,Z))
| add(multiply(Y,Y),Z) = add(Y,multiply(Z,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Y),Z),multiply(add(Y,Z),add(Y,Z))) ),[1],$fot(add(Y,multiply(Z,Z)))]]) ).
cnf(refute_0_156,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( $equal(multiply(add(Y,Z),add(Y,Z)),add(Y,multiply(Z,Z))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
add(multiply(Y,Y),Z) = add(Y,multiply(Z,Z)),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),Z),multiply(add(Y,Z),add(Y,Z))) )],[refute_0_151,refute_0_156]) ).
cnf(refute_0_158,plain,
add(multiply(Y,Y),X_22) = add(Y,multiply(X_22,X_22)),
inference(subst,[],[refute_0_157:[bind(Z,$fot(X_22))]]) ).
cnf(refute_0_159,plain,
( add(multiply(Y,Y),X_22) != add(Y,multiply(X_22,X_22))
| add(Y,multiply(X_22,X_22)) = add(multiply(Y,Y),X_22) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(multiply(Y,Y),X_22))),bind(Y0,$fot(add(Y,multiply(X_22,X_22))))]]) ).
cnf(refute_0_160,plain,
add(Y,multiply(X_22,X_22)) = add(multiply(Y,Y),X_22),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),X_22),add(Y,multiply(X_22,X_22))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
( add(Y,multiply(X_22,X_22)) != add(multiply(Y,Y),X_22)
| add(multiply(X_22,X_22),Y) != add(Y,multiply(X_22,X_22))
| add(multiply(X_22,X_22),Y) = add(multiply(Y,Y),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_22,X_22),Y),add(Y,multiply(X_22,X_22))) ),[1],$fot(add(multiply(Y,Y),X_22))]]) ).
cnf(refute_0_162,plain,
( add(multiply(X_22,X_22),Y) != add(Y,multiply(X_22,X_22))
| add(multiply(X_22,X_22),Y) = add(multiply(Y,Y),X_22) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(X_22,X_22)),add(multiply(Y,Y),X_22)) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
add(multiply(X_22,X_22),Y) = add(multiply(Y,Y),X_22),
inference(resolve,[$cnf( $equal(add(multiply(X_22,X_22),Y),add(Y,multiply(X_22,X_22))) )],[refute_0_150,refute_0_162]) ).
cnf(refute_0_164,plain,
add(multiply(additive_identity,additive_identity),Y) = add(Y,multiply(additive_identity,additive_identity)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_165,plain,
add(multiply(Y,Y),additive_identity) = add(Y,multiply(additive_identity,additive_identity)),
inference(subst,[],[refute_0_157:[bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_166,plain,
add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,add(Y,additive_identity)),
inference(subst,[],[refute_0_35:[bind(X_18,$fot(Y)),bind(X_20,$fot(additive_identity))]]) ).
cnf(refute_0_167,plain,
( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(multiply(Y,Y),additive_identity) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(Y,Y),additive_identity) = multiply(Y,add(Y,additive_identity)) ),
introduced(tautology,[equality,[$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_168,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( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,add(Y,additive_identity))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
add(multiply(Y,Y),additive_identity) = multiply(Y,add(Y,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),additive_identity),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
( add(multiply(Y,Y),additive_identity) != multiply(Y,add(Y,additive_identity))
| add(multiply(Y,Y),additive_identity) != add(Y,multiply(additive_identity,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,add(Y,additive_identity)) ),
introduced(tautology,[equality,[$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_171,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( $equal(add(multiply(Y,Y),additive_identity),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_165,refute_0_170]) ).
cnf(refute_0_172,plain,
add(Y,additive_identity) = Y,
inference(subst,[],[additive_id1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_173,plain,
multiply(Y,add(Y,additive_identity)) = multiply(Y,add(Y,additive_identity)),
introduced(tautology,[refl,[$fot(multiply(Y,add(Y,additive_identity)))]]) ).
cnf(refute_0_174,plain,
( multiply(Y,add(Y,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(Y,additive_identity) != Y
| multiply(Y,add(Y,additive_identity)) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(Y,add(Y,additive_identity)),multiply(Y,add(Y,additive_identity))) ),[1,1],$fot(Y)]]) ).
cnf(refute_0_175,plain,
( add(Y,additive_identity) != Y
| multiply(Y,add(Y,additive_identity)) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,additive_identity)),multiply(Y,add(Y,additive_identity))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(Y,add(Y,additive_identity)) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(Y,additive_identity),Y) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
( multiply(Y,add(Y,additive_identity)) != multiply(Y,Y)
| add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,add(Y,additive_identity))) ),[1],$fot(multiply(Y,Y))]]) ).
cnf(refute_0_178,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( $equal(multiply(Y,add(Y,additive_identity)),multiply(Y,Y)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( add(multiply(Y,Y),additive_identity) != multiply(Y,add(Y,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,add(Y,additive_identity))) )],[refute_0_171,refute_0_178]) ).
cnf(refute_0_180,plain,
add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),additive_identity),multiply(Y,add(Y,additive_identity))) )],[refute_0_169,refute_0_179]) ).
cnf(refute_0_181,plain,
( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,Y)
| add(multiply(additive_identity,additive_identity),Y) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) ),[1],$fot(multiply(Y,Y))]]) ).
cnf(refute_0_182,plain,
( add(multiply(additive_identity,additive_identity),Y) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,Y)) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_164,refute_0_182]) ).
cnf(refute_0_184,plain,
add(additive_identity,Y) = Y,
inference(subst,[],[additive_id2:[bind(X,$fot(Y))]]) ).
cnf(refute_0_185,plain,
multiply(additive_identity,additive_identity) = multiply(multiply(additive_identity,additive_identity),add(multiplicative_identity,multiply(additive_identity,additive_identity))),
inference(subst,[],[refute_0_110:[bind(X_14,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_186,plain,
add(multiplicative_identity,multiply(additive_identity,additive_identity)) = multiply(multiplicative_identity,multiplicative_identity),
inference(subst,[],[refute_0_180:[bind(Y,$fot(multiplicative_identity))]]) ).
cnf(refute_0_187,plain,
( multiply(additive_identity,additive_identity) != multiply(multiply(additive_identity,additive_identity),add(multiplicative_identity,multiply(additive_identity,additive_identity)))
| add(multiplicative_identity,multiply(additive_identity,additive_identity)) != multiply(multiplicative_identity,multiplicative_identity)
| multiply(additive_identity,additive_identity) = multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,additive_identity),multiply(multiply(additive_identity,additive_identity),add(multiplicative_identity,multiply(additive_identity,additive_identity)))) ),[1,1],$fot(multiply(multiplicative_identity,multiplicative_identity))]]) ).
cnf(refute_0_188,plain,
( multiply(additive_identity,additive_identity) != multiply(multiply(additive_identity,additive_identity),add(multiplicative_identity,multiply(additive_identity,additive_identity)))
| multiply(additive_identity,additive_identity) = multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) ),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,multiply(additive_identity,additive_identity)),multiply(multiplicative_identity,multiplicative_identity)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
multiply(additive_identity,additive_identity) = multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),multiply(multiply(additive_identity,additive_identity),add(multiplicative_identity,multiply(additive_identity,additive_identity)))) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_24)),
inference(subst,[],[refute_0_35:[bind(X_18,$fot(multiply(additive_identity,additive_identity))),bind(X_20,$fot(X_24))]]) ).
cnf(refute_0_191,plain,
add(multiply(additive_identity,additive_identity),X_14) = multiply(X_14,add(additive_identity,X_14)),
inference(subst,[],[refute_0_66:[bind(X_10,$fot(additive_identity)),bind(X_12,$fot(X_14))]]) ).
cnf(refute_0_192,plain,
( add(multiply(additive_identity,additive_identity),X_14) != multiply(X_14,add(additive_identity,X_14))
| add(additive_identity,X_14) != X_14
| add(multiply(additive_identity,additive_identity),X_14) = multiply(X_14,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_14),multiply(X_14,add(additive_identity,X_14))) ),[1,1],$fot(X_14)]]) ).
cnf(refute_0_193,plain,
( add(multiply(additive_identity,additive_identity),X_14) != multiply(X_14,add(additive_identity,X_14))
| add(multiply(additive_identity,additive_identity),X_14) = multiply(X_14,X_14) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_14),X_14) )],[refute_0_107,refute_0_192]) ).
cnf(refute_0_194,plain,
add(multiply(additive_identity,additive_identity),X_14) = multiply(X_14,X_14),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_14),multiply(X_14,add(additive_identity,X_14))) )],[refute_0_191,refute_0_193]) ).
cnf(refute_0_195,plain,
add(multiply(additive_identity,additive_identity),X_24) = multiply(X_24,X_24),
inference(subst,[],[refute_0_194:[bind(X_14,$fot(X_24))]]) ).
cnf(refute_0_196,plain,
( add(multiply(additive_identity,additive_identity),X_24) != multiply(X_24,X_24)
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_24))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_24))) ),[1,1],$fot(multiply(X_24,X_24))]]) ).
cnf(refute_0_197,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_24))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_24),multiply(X_24,X_24)) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) = multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_24))) )],[refute_0_190,refute_0_197]) ).
cnf(refute_0_199,plain,
add(additive_identity,X_24) = X_24,
inference(subst,[],[additive_id2:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_200,plain,
multiply(additive_identity,add(additive_identity,X_24)) = multiply(additive_identity,add(additive_identity,X_24)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(additive_identity,X_24)))]]) ).
cnf(refute_0_201,plain,
( multiply(additive_identity,add(additive_identity,X_24)) != multiply(additive_identity,add(additive_identity,X_24))
| add(additive_identity,X_24) != X_24
| multiply(additive_identity,add(additive_identity,X_24)) = multiply(additive_identity,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_24)),multiply(additive_identity,add(additive_identity,X_24))) ),[1,1],$fot(X_24)]]) ).
cnf(refute_0_202,plain,
( add(additive_identity,X_24) != X_24
| multiply(additive_identity,add(additive_identity,X_24)) = multiply(additive_identity,X_24) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_24)),multiply(additive_identity,add(additive_identity,X_24))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
multiply(additive_identity,add(additive_identity,X_24)) = multiply(additive_identity,X_24),
inference(resolve,[$cnf( $equal(add(additive_identity,X_24),X_24) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) = multiply(additive_identity,add(additive_identity,X_24)),
inference(subst,[],[refute_0_51:[bind(X,$fot(additive_identity)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_205,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_206,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_24,refute_0_205]) ).
cnf(refute_0_207,plain,
( multiply(additive_identity,add(additive_identity,X_24)) != multiply(additive_identity,X_24)
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) != multiply(additive_identity,add(additive_identity,X_24))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) = multiply(additive_identity,X_24) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)))),bind(Y0,$fot(multiply(additive_identity,add(additive_identity,X_24)))),bind(Z0,$fot(multiply(additive_identity,X_24)))]]) ).
cnf(refute_0_208,plain,
( multiply(additive_identity,add(additive_identity,X_24)) != multiply(additive_identity,X_24)
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) = multiply(additive_identity,X_24) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)),multiply(additive_identity,add(additive_identity,X_24))) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) = multiply(additive_identity,X_24),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_24)),multiply(additive_identity,X_24)) )],[refute_0_203,refute_0_208]) ).
cnf(refute_0_210,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) != multiply(additive_identity,X_24)
| multiply(additive_identity,X_24) = multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24))) ),[0],$fot(multiply(additive_identity,X_24))]]) ).
cnf(refute_0_211,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)) != multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24))
| multiply(additive_identity,X_24) = multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)),multiply(additive_identity,X_24)) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
multiply(additive_identity,X_24) = multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_24)),multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24))) )],[refute_0_198,refute_0_211]) ).
cnf(refute_0_213,plain,
( multiply(additive_identity,X_24) != multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24))
| multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24)) = multiply(additive_identity,X_24) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(additive_identity,X_24))),bind(Y0,$fot(multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24))))]]) ).
cnf(refute_0_214,plain,
multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24)) = multiply(additive_identity,X_24),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_24),multiply(multiply(additive_identity,additive_identity),multiply(X_24,X_24))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) = multiply(additive_identity,multiplicative_identity),
inference(subst,[],[refute_0_214:[bind(X_24,$fot(multiplicative_identity))]]) ).
cnf(refute_0_216,plain,
( multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) != multiply(additive_identity,multiplicative_identity)
| multiply(additive_identity,multiplicative_identity) != additive_identity
| multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) = additive_identity ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)))),bind(Y0,$fot(multiply(additive_identity,multiplicative_identity))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_217,plain,
( multiply(additive_identity,multiplicative_identity) != additive_identity
| multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)),multiply(additive_identity,multiplicative_identity)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,multiplicative_identity),additive_identity) )],[refute_0_127,refute_0_217]) ).
cnf(refute_0_219,plain,
( multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) != additive_identity
| multiply(additive_identity,additive_identity) != multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity))
| multiply(additive_identity,additive_identity) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,additive_identity),multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity))) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_220,plain,
( multiply(additive_identity,additive_identity) != multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity))
| multiply(additive_identity,additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)),additive_identity) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity))) )],[refute_0_189,refute_0_220]) ).
cnf(refute_0_222,plain,
add(multiply(additive_identity,additive_identity),Y) = add(multiply(additive_identity,additive_identity),Y),
introduced(tautology,[refl,[$fot(add(multiply(additive_identity,additive_identity),Y))]]) ).
cnf(refute_0_223,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(multiply(additive_identity,additive_identity),Y) != add(multiply(additive_identity,additive_identity),Y)
| add(multiply(additive_identity,additive_identity),Y) = add(additive_identity,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(multiply(additive_identity,additive_identity),Y)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_224,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(multiply(additive_identity,additive_identity),Y) = add(additive_identity,Y) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(multiply(additive_identity,additive_identity),Y)) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
add(multiply(additive_identity,additive_identity),Y) = add(additive_identity,Y),
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),additive_identity) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
( add(multiply(additive_identity,additive_identity),Y) != add(additive_identity,Y)
| add(additive_identity,Y) != Y
| add(multiply(additive_identity,additive_identity),Y) = Y ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),Y))),bind(Y0,$fot(add(additive_identity,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_227,plain,
( add(additive_identity,Y) != Y
| add(multiply(additive_identity,additive_identity),Y) = Y ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(additive_identity,Y)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
add(multiply(additive_identity,additive_identity),Y) = Y,
inference(resolve,[$cnf( $equal(add(additive_identity,Y),Y) )],[refute_0_184,refute_0_227]) ).
cnf(refute_0_229,plain,
( add(multiply(additive_identity,additive_identity),Y) != Y
| add(multiply(additive_identity,additive_identity),Y) != multiply(Y,Y)
| Y = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),multiply(Y,Y)) ),[0],$fot(Y)]]) ).
cnf(refute_0_230,plain,
( add(multiply(additive_identity,additive_identity),Y) != multiply(Y,Y)
| Y = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),Y) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
Y = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),multiply(Y,Y)) )],[refute_0_183,refute_0_230]) ).
cnf(refute_0_232,plain,
( Y != multiply(Y,Y)
| multiply(Y,Y) = Y ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(Y)),bind(Y0,$fot(multiply(Y,Y)))]]) ).
cnf(refute_0_233,plain,
multiply(Y,Y) = Y,
inference(resolve,[$cnf( $equal(Y,multiply(Y,Y)) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
multiply(X_22,X_22) = X_22,
inference(subst,[],[refute_0_233:[bind(Y,$fot(X_22))]]) ).
cnf(refute_0_235,plain,
add(multiply(X_22,X_22),Y) = add(multiply(X_22,X_22),Y),
introduced(tautology,[refl,[$fot(add(multiply(X_22,X_22),Y))]]) ).
cnf(refute_0_236,plain,
( multiply(X_22,X_22) != X_22
| add(multiply(X_22,X_22),Y) != add(multiply(X_22,X_22),Y)
| add(multiply(X_22,X_22),Y) = add(X_22,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_22,X_22),Y),add(multiply(X_22,X_22),Y)) ),[1,0],$fot(X_22)]]) ).
cnf(refute_0_237,plain,
( multiply(X_22,X_22) != X_22
| add(multiply(X_22,X_22),Y) = add(X_22,Y) ),
inference(resolve,[$cnf( $equal(add(multiply(X_22,X_22),Y),add(multiply(X_22,X_22),Y)) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
add(multiply(X_22,X_22),Y) = add(X_22,Y),
inference(resolve,[$cnf( $equal(multiply(X_22,X_22),X_22) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
( add(multiply(X_22,X_22),Y) != add(X_22,Y)
| add(multiply(X_22,X_22),Y) != add(multiply(Y,Y),X_22)
| add(X_22,Y) = add(multiply(Y,Y),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_22,X_22),Y),add(multiply(Y,Y),X_22)) ),[0],$fot(add(X_22,Y))]]) ).
cnf(refute_0_240,plain,
( add(multiply(X_22,X_22),Y) != add(multiply(Y,Y),X_22)
| add(X_22,Y) = add(multiply(Y,Y),X_22) ),
inference(resolve,[$cnf( $equal(add(multiply(X_22,X_22),Y),add(X_22,Y)) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
add(multiply(Y,Y),X_22) = add(multiply(Y,Y),X_22),
introduced(tautology,[refl,[$fot(add(multiply(Y,Y),X_22))]]) ).
cnf(refute_0_242,plain,
( multiply(Y,Y) != Y
| add(multiply(Y,Y),X_22) != add(multiply(Y,Y),X_22)
| add(multiply(Y,Y),X_22) = add(Y,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Y),X_22),add(multiply(Y,Y),X_22)) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_243,plain,
( multiply(Y,Y) != Y
| add(multiply(Y,Y),X_22) = add(Y,X_22) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),X_22),add(multiply(Y,Y),X_22)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
add(multiply(Y,Y),X_22) = add(Y,X_22),
inference(resolve,[$cnf( $equal(multiply(Y,Y),Y) )],[refute_0_233,refute_0_243]) ).
cnf(refute_0_245,plain,
( add(X_22,Y) != add(multiply(Y,Y),X_22)
| add(multiply(Y,Y),X_22) != add(Y,X_22)
| add(X_22,Y) = add(Y,X_22) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_22,Y),add(Y,X_22)) ),[0],$fot(add(multiply(Y,Y),X_22))]]) ).
cnf(refute_0_246,plain,
( add(X_22,Y) != add(multiply(Y,Y),X_22)
| add(X_22,Y) = add(Y,X_22) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),X_22),add(Y,X_22)) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
( add(multiply(X_22,X_22),Y) != add(multiply(Y,Y),X_22)
| add(X_22,Y) = add(Y,X_22) ),
inference(resolve,[$cnf( $equal(add(X_22,Y),add(multiply(Y,Y),X_22)) )],[refute_0_240,refute_0_246]) ).
cnf(refute_0_248,plain,
add(X_22,Y) = add(Y,X_22),
inference(resolve,[$cnf( $equal(add(multiply(X_22,X_22),Y),add(multiply(Y,Y),X_22)) )],[refute_0_163,refute_0_247]) ).
cnf(refute_0_249,plain,
( add(X_22,Y) != add(Y,X_22)
| add(Y,X_22) = add(X_22,Y) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(X_22,Y))),bind(Y0,$fot(add(Y,X_22)))]]) ).
cnf(refute_0_250,plain,
add(Y,X_22) = add(X_22,Y),
inference(resolve,[$cnf( $equal(add(X_22,Y),add(Y,X_22)) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
add(inverse(X_28),X_28) = add(X_28,inverse(X_28)),
inference(subst,[],[refute_0_250:[bind(Y,$fot(inverse(X_28))),bind(X_22,$fot(X_28))]]) ).
cnf(refute_0_252,plain,
( add(X_28,inverse(X_28)) != multiplicative_identity
| add(inverse(X_28),X_28) != add(X_28,inverse(X_28))
| add(inverse(X_28),X_28) = multiplicative_identity ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(inverse(X_28),X_28))),bind(Y0,$fot(add(X_28,inverse(X_28)))),bind(Z0,$fot(multiplicative_identity))]]) ).
cnf(refute_0_253,plain,
( add(X_28,inverse(X_28)) != multiplicative_identity
| add(inverse(X_28),X_28) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(inverse(X_28),X_28),add(X_28,inverse(X_28))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
add(inverse(X_28),X_28) = multiplicative_identity,
inference(resolve,[$cnf( $equal(add(X_28,inverse(X_28)),multiplicative_identity) )],[refute_0_149,refute_0_253]) ).
cnf(refute_0_255,plain,
( add(inverse(X_28),X_28) != add(multiplicative_identity,inverse(X_28))
| add(inverse(X_28),X_28) != multiplicative_identity
| multiplicative_identity = add(multiplicative_identity,inverse(X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_28),X_28),add(multiplicative_identity,inverse(X_28))) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_256,plain,
( add(inverse(X_28),X_28) != add(multiplicative_identity,inverse(X_28))
| multiplicative_identity = add(multiplicative_identity,inverse(X_28)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_28),X_28),multiplicative_identity) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
multiplicative_identity = add(multiplicative_identity,inverse(X_28)),
inference(resolve,[$cnf( $equal(add(inverse(X_28),X_28),add(multiplicative_identity,inverse(X_28))) )],[refute_0_148,refute_0_256]) ).
cnf(refute_0_258,plain,
multiplicative_identity = add(multiplicative_identity,inverse(X_29)),
inference(subst,[],[refute_0_257:[bind(X_28,$fot(X_29))]]) ).
cnf(refute_0_259,plain,
( multiplicative_identity != add(multiplicative_identity,inverse(X_29))
| add(multiplicative_identity,inverse(X_29)) = multiplicative_identity ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(multiplicative_identity,inverse(X_29))))]]) ).
cnf(refute_0_260,plain,
add(multiplicative_identity,inverse(X_29)) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(multiplicative_identity,inverse(X_29))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
( add(multiplicative_identity,multiply(Y,inverse(X_29))) != multiply(add(multiplicative_identity,Y),add(multiplicative_identity,inverse(X_29)))
| add(multiplicative_identity,inverse(X_29)) != multiplicative_identity
| add(multiplicative_identity,multiply(Y,inverse(X_29))) = multiply(add(multiplicative_identity,Y),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiplicative_identity,multiply(Y,inverse(X_29))),multiply(add(multiplicative_identity,Y),add(multiplicative_identity,inverse(X_29)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_262,plain,
( add(multiplicative_identity,multiply(Y,inverse(X_29))) != multiply(add(multiplicative_identity,Y),add(multiplicative_identity,inverse(X_29)))
| add(multiplicative_identity,multiply(Y,inverse(X_29))) = multiply(add(multiplicative_identity,Y),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,inverse(X_29)),multiplicative_identity) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
add(multiplicative_identity,multiply(Y,inverse(X_29))) = multiply(add(multiplicative_identity,Y),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,multiply(Y,inverse(X_29))),multiply(add(multiplicative_identity,Y),add(multiplicative_identity,inverse(X_29)))) )],[refute_0_128,refute_0_262]) ).
cnf(refute_0_264,plain,
multiply(add(multiplicative_identity,Y),multiplicative_identity) = add(multiplicative_identity,Y),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(multiplicative_identity,Y)))]]) ).
cnf(refute_0_265,plain,
( multiply(add(multiplicative_identity,Y),multiplicative_identity) != add(multiplicative_identity,Y)
| add(multiplicative_identity,multiply(Y,inverse(X_29))) != multiply(add(multiplicative_identity,Y),multiplicative_identity)
| add(multiplicative_identity,multiply(Y,inverse(X_29))) = add(multiplicative_identity,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiplicative_identity,multiply(Y,inverse(X_29))),multiply(add(multiplicative_identity,Y),multiplicative_identity)) ),[1],$fot(add(multiplicative_identity,Y))]]) ).
cnf(refute_0_266,plain,
( add(multiplicative_identity,multiply(Y,inverse(X_29))) != multiply(add(multiplicative_identity,Y),multiplicative_identity)
| add(multiplicative_identity,multiply(Y,inverse(X_29))) = add(multiplicative_identity,Y) ),
inference(resolve,[$cnf( $equal(multiply(add(multiplicative_identity,Y),multiplicative_identity),add(multiplicative_identity,Y)) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
add(multiplicative_identity,multiply(Y,inverse(X_29))) = add(multiplicative_identity,Y),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,multiply(Y,inverse(X_29))),multiply(add(multiplicative_identity,Y),multiplicative_identity)) )],[refute_0_263,refute_0_266]) ).
cnf(refute_0_268,plain,
add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) = add(multiplicative_identity,multiply(X_13,additive_identity)),
inference(subst,[],[refute_0_267:[bind(Y,$fot(multiply(X_13,additive_identity))),bind(X_29,$fot(X_46))]]) ).
cnf(refute_0_269,plain,
add(multiplicative_identity,multiply(X_13,additive_identity)) = multiply(multiplicative_identity,add(X_13,multiplicative_identity)),
inference(subst,[],[refute_0_116:[bind(X,$fot(multiplicative_identity))]]) ).
cnf(refute_0_270,plain,
( add(multiplicative_identity,multiply(X_13,additive_identity)) != multiply(multiplicative_identity,add(X_13,multiplicative_identity))
| add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) != add(multiplicative_identity,multiply(X_13,additive_identity))
| add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) = multiply(multiplicative_identity,add(X_13,multiplicative_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))),add(multiplicative_identity,multiply(X_13,additive_identity))) ),[1],$fot(multiply(multiplicative_identity,add(X_13,multiplicative_identity)))]]) ).
cnf(refute_0_271,plain,
( add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) != add(multiplicative_identity,multiply(X_13,additive_identity))
| add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) = multiply(multiplicative_identity,add(X_13,multiplicative_identity)) ),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,multiply(X_13,additive_identity)),multiply(multiplicative_identity,add(X_13,multiplicative_identity))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) = multiply(multiplicative_identity,add(X_13,multiplicative_identity)),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))),add(multiplicative_identity,multiply(X_13,additive_identity))) )],[refute_0_268,refute_0_271]) ).
cnf(refute_0_273,plain,
add(multiplicative_identity,multiply(X_46,inverse(X_46))) = add(multiplicative_identity,X_46),
inference(subst,[],[refute_0_267:[bind(Y,$fot(X_46)),bind(X_29,$fot(X_46))]]) ).
cnf(refute_0_274,plain,
multiply(X_46,inverse(X_46)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_46))]]) ).
cnf(refute_0_275,plain,
( multiply(X_46,inverse(X_46)) != additive_identity
| add(multiplicative_identity,multiply(X_46,inverse(X_46))) != add(multiplicative_identity,X_46)
| add(multiplicative_identity,additive_identity) = add(multiplicative_identity,X_46) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiplicative_identity,multiply(X_46,inverse(X_46))),add(multiplicative_identity,X_46)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_276,plain,
( add(multiplicative_identity,multiply(X_46,inverse(X_46))) != add(multiplicative_identity,X_46)
| add(multiplicative_identity,additive_identity) = add(multiplicative_identity,X_46) ),
inference(resolve,[$cnf( $equal(multiply(X_46,inverse(X_46)),additive_identity) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
add(multiplicative_identity,additive_identity) = add(multiplicative_identity,X_46),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,multiply(X_46,inverse(X_46))),add(multiplicative_identity,X_46)) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
add(additive_identity,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[additive_id2:[bind(X,$fot(multiplicative_identity))]]) ).
cnf(refute_0_279,plain,
add(multiplicative_identity,additive_identity) = add(additive_identity,multiplicative_identity),
inference(subst,[],[refute_0_250:[bind(Y,$fot(multiplicative_identity)),bind(X_22,$fot(additive_identity))]]) ).
cnf(refute_0_280,plain,
( add(additive_identity,multiplicative_identity) != multiplicative_identity
| add(multiplicative_identity,additive_identity) != add(additive_identity,multiplicative_identity)
| add(multiplicative_identity,additive_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(multiplicative_identity,additive_identity))),bind(Y0,$fot(add(additive_identity,multiplicative_identity))),bind(Z0,$fot(multiplicative_identity))]]) ).
cnf(refute_0_281,plain,
( add(additive_identity,multiplicative_identity) != multiplicative_identity
| add(multiplicative_identity,additive_identity) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,additive_identity),add(additive_identity,multiplicative_identity)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
add(multiplicative_identity,additive_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(add(additive_identity,multiplicative_identity),multiplicative_identity) )],[refute_0_278,refute_0_281]) ).
cnf(refute_0_283,plain,
( add(multiplicative_identity,additive_identity) != add(multiplicative_identity,X_46)
| add(multiplicative_identity,additive_identity) != multiplicative_identity
| multiplicative_identity = add(multiplicative_identity,X_46) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiplicative_identity,additive_identity),add(multiplicative_identity,X_46)) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_284,plain,
( add(multiplicative_identity,additive_identity) != add(multiplicative_identity,X_46)
| multiplicative_identity = add(multiplicative_identity,X_46) ),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,additive_identity),multiplicative_identity) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
multiplicative_identity = add(multiplicative_identity,X_46),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,additive_identity),add(multiplicative_identity,X_46)) )],[refute_0_277,refute_0_284]) ).
cnf(refute_0_286,plain,
( multiplicative_identity != add(multiplicative_identity,X_46)
| add(multiplicative_identity,X_46) = multiplicative_identity ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(multiplicative_identity,X_46)))]]) ).
cnf(refute_0_287,plain,
add(multiplicative_identity,X_46) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(multiplicative_identity,X_46)) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) = multiplicative_identity,
inference(subst,[],[refute_0_287:[bind(X_46,$fot(multiply(multiply(X_13,additive_identity),inverse(X_46))))]]) ).
cnf(refute_0_289,plain,
( add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) != multiply(multiplicative_identity,add(X_13,multiplicative_identity))
| add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) != multiplicative_identity
| multiplicative_identity = multiply(multiplicative_identity,add(X_13,multiplicative_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))),multiply(multiplicative_identity,add(X_13,multiplicative_identity))) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_290,plain,
( add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) != multiply(multiplicative_identity,add(X_13,multiplicative_identity))
| multiplicative_identity = multiply(multiplicative_identity,add(X_13,multiplicative_identity)) ),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))),multiplicative_identity) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
multiply(multiplicative_identity,add(X_13,multiplicative_identity)) = add(X_13,multiplicative_identity),
inference(subst,[],[multiplicative_id2:[bind(X,$fot(add(X_13,multiplicative_identity)))]]) ).
cnf(refute_0_292,plain,
( multiply(multiplicative_identity,add(X_13,multiplicative_identity)) != add(X_13,multiplicative_identity)
| multiplicative_identity != multiply(multiplicative_identity,add(X_13,multiplicative_identity))
| multiplicative_identity = add(X_13,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiplicative_identity,multiply(multiplicative_identity,add(X_13,multiplicative_identity))) ),[1],$fot(add(X_13,multiplicative_identity))]]) ).
cnf(refute_0_293,plain,
( multiplicative_identity != multiply(multiplicative_identity,add(X_13,multiplicative_identity))
| multiplicative_identity = add(X_13,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(X_13,multiplicative_identity)),add(X_13,multiplicative_identity)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
( add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))) != multiply(multiplicative_identity,add(X_13,multiplicative_identity))
| multiplicative_identity = add(X_13,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiplicative_identity,multiply(multiplicative_identity,add(X_13,multiplicative_identity))) )],[refute_0_290,refute_0_293]) ).
cnf(refute_0_295,plain,
multiplicative_identity = add(X_13,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,multiply(multiply(X_13,additive_identity),inverse(X_46))),multiply(multiplicative_identity,add(X_13,multiplicative_identity))) )],[refute_0_272,refute_0_294]) ).
cnf(refute_0_296,plain,
( multiplicative_identity != add(X_13,multiplicative_identity)
| add(X_13,multiplicative_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_13,multiplicative_identity)))]]) ).
cnf(refute_0_297,plain,
add(X_13,multiplicative_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_13,multiplicative_identity)) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
add(X_42,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[refute_0_297:[bind(X_13,$fot(X_42))]]) ).
cnf(refute_0_299,plain,
multiply(additive_identity,add(X_42,multiplicative_identity)) = multiply(additive_identity,add(X_42,multiplicative_identity)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(X_42,multiplicative_identity)))]]) ).
cnf(refute_0_300,plain,
( multiply(additive_identity,add(X_42,multiplicative_identity)) != multiply(additive_identity,add(X_42,multiplicative_identity))
| add(X_42,multiplicative_identity) != multiplicative_identity
| multiply(additive_identity,add(X_42,multiplicative_identity)) = multiply(additive_identity,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_42,multiplicative_identity)),multiply(additive_identity,add(X_42,multiplicative_identity))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_301,plain,
( add(X_42,multiplicative_identity) != multiplicative_identity
| multiply(additive_identity,add(X_42,multiplicative_identity)) = multiply(additive_identity,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_42,multiplicative_identity)),multiply(additive_identity,add(X_42,multiplicative_identity))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
multiply(additive_identity,add(X_42,multiplicative_identity)) = multiply(additive_identity,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_42,multiplicative_identity),multiplicative_identity) )],[refute_0_298,refute_0_301]) ).
cnf(refute_0_303,plain,
( multiply(additive_identity,add(X_42,multiplicative_identity)) != multiply(additive_identity,multiplicative_identity)
| multiply(additive_identity,multiplicative_identity) != additive_identity
| multiply(additive_identity,add(X_42,multiplicative_identity)) = additive_identity ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(multiply(additive_identity,add(X_42,multiplicative_identity)))),bind(Y0,$fot(multiply(additive_identity,multiplicative_identity))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_304,plain,
( multiply(additive_identity,multiplicative_identity) != additive_identity
| multiply(additive_identity,add(X_42,multiplicative_identity)) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_42,multiplicative_identity)),multiply(additive_identity,multiplicative_identity)) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
multiply(additive_identity,add(X_42,multiplicative_identity)) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,multiplicative_identity),additive_identity) )],[refute_0_127,refute_0_304]) ).
cnf(refute_0_306,plain,
( multiply(X_42,additive_identity) != multiply(additive_identity,add(X_42,multiplicative_identity))
| multiply(additive_identity,add(X_42,multiplicative_identity)) != additive_identity
| multiply(X_42,additive_identity) = additive_identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_42,additive_identity),additive_identity) ),[0],$fot(multiply(additive_identity,add(X_42,multiplicative_identity)))]]) ).
cnf(refute_0_307,plain,
( multiply(X_42,additive_identity) != multiply(additive_identity,add(X_42,multiplicative_identity))
| multiply(X_42,additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_42,multiplicative_identity)),additive_identity) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
multiply(X_42,additive_identity) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(X_42,additive_identity),multiply(additive_identity,add(X_42,multiplicative_identity))) )],[refute_0_126,refute_0_307]) ).
cnf(refute_0_309,plain,
multiply(X,additive_identity) = additive_identity,
inference(subst,[],[refute_0_308:[bind(X_42,$fot(X))]]) ).
cnf(refute_0_310,plain,
multiply(X_13,additive_identity) = additive_identity,
inference(subst,[],[refute_0_308:[bind(X_42,$fot(X_13))]]) ).
cnf(refute_0_311,plain,
multiply(X,multiply(X_13,additive_identity)) = multiply(X,multiply(X_13,additive_identity)),
introduced(tautology,[refl,[$fot(multiply(X,multiply(X_13,additive_identity)))]]) ).
cnf(refute_0_312,plain,
( multiply(X,multiply(X_13,additive_identity)) != multiply(X,multiply(X_13,additive_identity))
| multiply(X_13,additive_identity) != additive_identity
| multiply(X,multiply(X_13,additive_identity)) = multiply(X,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiply(X_13,additive_identity)),multiply(X,multiply(X_13,additive_identity))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_313,plain,
( multiply(X_13,additive_identity) != additive_identity
| multiply(X,multiply(X_13,additive_identity)) = multiply(X,additive_identity) ),
inference(resolve,[$cnf( $equal(multiply(X,multiply(X_13,additive_identity)),multiply(X,multiply(X_13,additive_identity))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
multiply(X,multiply(X_13,additive_identity)) = multiply(X,additive_identity),
inference(resolve,[$cnf( $equal(multiply(X_13,additive_identity),additive_identity) )],[refute_0_310,refute_0_313]) ).
cnf(refute_0_315,plain,
( multiply(X,multiply(X_13,additive_identity)) != multiply(X,additive_identity)
| multiply(X,additive_identity) != additive_identity
| multiply(X,multiply(X_13,additive_identity)) = additive_identity ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(multiply(X,multiply(X_13,additive_identity)))),bind(Y0,$fot(multiply(X,additive_identity))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_316,plain,
( multiply(X,additive_identity) != additive_identity
| multiply(X,multiply(X_13,additive_identity)) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(X,multiply(X_13,additive_identity)),multiply(X,additive_identity)) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
multiply(X,multiply(X_13,additive_identity)) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(X,additive_identity),additive_identity) )],[refute_0_309,refute_0_316]) ).
cnf(refute_0_318,plain,
add(multiply(X,multiply(X_13,additive_identity)),Z) = add(multiply(X,multiply(X_13,additive_identity)),Z),
introduced(tautology,[refl,[$fot(add(multiply(X,multiply(X_13,additive_identity)),Z))]]) ).
cnf(refute_0_319,plain,
( multiply(X,multiply(X_13,additive_identity)) != additive_identity
| add(multiply(X,multiply(X_13,additive_identity)),Z) != add(multiply(X,multiply(X_13,additive_identity)),Z)
| add(multiply(X,multiply(X_13,additive_identity)),Z) = add(additive_identity,Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,multiply(X_13,additive_identity)),Z),add(multiply(X,multiply(X_13,additive_identity)),Z)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_320,plain,
( multiply(X,multiply(X_13,additive_identity)) != additive_identity
| add(multiply(X,multiply(X_13,additive_identity)),Z) = add(additive_identity,Z) ),
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(X_13,additive_identity)),Z),add(multiply(X,multiply(X_13,additive_identity)),Z)) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
add(multiply(X,multiply(X_13,additive_identity)),Z) = add(additive_identity,Z),
inference(resolve,[$cnf( $equal(multiply(X,multiply(X_13,additive_identity)),additive_identity) )],[refute_0_317,refute_0_320]) ).
cnf(refute_0_322,plain,
( add(multiply(X,multiply(X_13,additive_identity)),Z) != add(additive_identity,Z)
| add(additive_identity,Z) != Z
| add(multiply(X,multiply(X_13,additive_identity)),Z) = Z ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(multiply(X,multiply(X_13,additive_identity)),Z))),bind(Y0,$fot(add(additive_identity,Z))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_323,plain,
( add(additive_identity,Z) != Z
| add(multiply(X,multiply(X_13,additive_identity)),Z) = Z ),
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(X_13,additive_identity)),Z),add(additive_identity,Z)) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
add(multiply(X,multiply(X_13,additive_identity)),Z) = Z,
inference(resolve,[$cnf( $equal(add(additive_identity,Z),Z) )],[refute_0_101,refute_0_323]) ).
cnf(refute_0_325,plain,
( add(multiply(X,multiply(X_13,additive_identity)),Z) != Z
| add(multiply(X,multiply(X_13,additive_identity)),Z) != multiply(add(X,Z),multiply(Z,add(X_13,Z)))
| Z = multiply(add(X,Z),multiply(Z,add(X_13,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,multiply(X_13,additive_identity)),Z),multiply(add(X,Z),multiply(Z,add(X_13,Z)))) ),[0],$fot(Z)]]) ).
cnf(refute_0_326,plain,
( add(multiply(X,multiply(X_13,additive_identity)),Z) != multiply(add(X,Z),multiply(Z,add(X_13,Z)))
| Z = multiply(add(X,Z),multiply(Z,add(X_13,Z))) ),
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(X_13,additive_identity)),Z),Z) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
Z = multiply(add(X,Z),multiply(Z,add(X_13,Z))),
inference(resolve,[$cnf( $equal(add(multiply(X,multiply(X_13,additive_identity)),Z),multiply(add(X,Z),multiply(Z,add(X_13,Z)))) )],[refute_0_100,refute_0_326]) ).
cnf(refute_0_328,plain,
multiply(add(X,Z),Z) = multiply(Z,add(X,Z)),
inference(subst,[],[refute_0_62:[bind(X,$fot(Z)),bind(Y,$fot(add(X,Z)))]]) ).
cnf(refute_0_329,plain,
add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = multiply(add(multiply(X_10,additive_identity),X_19),add(multiply(X_10,additive_identity),X_20)),
inference(subst,[],[distributivity2:[bind(X,$fot(multiply(X_10,additive_identity))),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_330,plain,
add(multiply(X_10,additive_identity),X_20) = multiply(X_20,add(X_10,X_20)),
inference(subst,[],[refute_0_66:[bind(X_12,$fot(X_20))]]) ).
cnf(refute_0_331,plain,
( add(multiply(X_10,additive_identity),X_20) != multiply(X_20,add(X_10,X_20))
| add(multiply(X_10,additive_identity),multiply(X_19,X_20)) != multiply(add(multiply(X_10,additive_identity),X_19),add(multiply(X_10,additive_identity),X_20))
| add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_19,X_20)),multiply(add(multiply(X_10,additive_identity),X_19),add(multiply(X_10,additive_identity),X_20))) ),[1,1],$fot(multiply(X_20,add(X_10,X_20)))]]) ).
cnf(refute_0_332,plain,
( add(multiply(X_10,additive_identity),multiply(X_19,X_20)) != multiply(add(multiply(X_10,additive_identity),X_19),add(multiply(X_10,additive_identity),X_20))
| add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_20),multiply(X_20,add(X_10,X_20))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_19,X_20)),multiply(add(multiply(X_10,additive_identity),X_19),add(multiply(X_10,additive_identity),X_20))) )],[refute_0_329,refute_0_332]) ).
cnf(refute_0_334,plain,
add(additive_identity,multiply(X_19,X_20)) = multiply(X_19,X_20),
inference(subst,[],[additive_id2:[bind(X,$fot(multiply(X_19,X_20)))]]) ).
cnf(refute_0_335,plain,
multiply(X_10,additive_identity) = additive_identity,
inference(subst,[],[refute_0_308:[bind(X_42,$fot(X_10))]]) ).
cnf(refute_0_336,plain,
add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = add(multiply(X_10,additive_identity),multiply(X_19,X_20)),
introduced(tautology,[refl,[$fot(add(multiply(X_10,additive_identity),multiply(X_19,X_20)))]]) ).
cnf(refute_0_337,plain,
( multiply(X_10,additive_identity) != additive_identity
| add(multiply(X_10,additive_identity),multiply(X_19,X_20)) != add(multiply(X_10,additive_identity),multiply(X_19,X_20))
| add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = add(additive_identity,multiply(X_19,X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_19,X_20)),add(multiply(X_10,additive_identity),multiply(X_19,X_20))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_338,plain,
( multiply(X_10,additive_identity) != additive_identity
| add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = add(additive_identity,multiply(X_19,X_20)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_19,X_20)),add(multiply(X_10,additive_identity),multiply(X_19,X_20))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = add(additive_identity,multiply(X_19,X_20)),
inference(resolve,[$cnf( $equal(multiply(X_10,additive_identity),additive_identity) )],[refute_0_335,refute_0_338]) ).
cnf(refute_0_340,plain,
( add(multiply(X_10,additive_identity),multiply(X_19,X_20)) != add(additive_identity,multiply(X_19,X_20))
| add(additive_identity,multiply(X_19,X_20)) != multiply(X_19,X_20)
| add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = multiply(X_19,X_20) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(multiply(X_10,additive_identity),multiply(X_19,X_20)))),bind(Y0,$fot(add(additive_identity,multiply(X_19,X_20)))),bind(Z0,$fot(multiply(X_19,X_20)))]]) ).
cnf(refute_0_341,plain,
( add(additive_identity,multiply(X_19,X_20)) != multiply(X_19,X_20)
| add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = multiply(X_19,X_20) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_19,X_20)),add(additive_identity,multiply(X_19,X_20))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
add(multiply(X_10,additive_identity),multiply(X_19,X_20)) = multiply(X_19,X_20),
inference(resolve,[$cnf( $equal(add(additive_identity,multiply(X_19,X_20)),multiply(X_19,X_20)) )],[refute_0_334,refute_0_341]) ).
cnf(refute_0_343,plain,
( add(multiply(X_10,additive_identity),multiply(X_19,X_20)) != multiply(X_19,X_20)
| add(multiply(X_10,additive_identity),multiply(X_19,X_20)) != multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))
| multiply(X_19,X_20) = multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_19,X_20)),multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))) ),[0],$fot(multiply(X_19,X_20))]]) ).
cnf(refute_0_344,plain,
( add(multiply(X_10,additive_identity),multiply(X_19,X_20)) != multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))
| multiply(X_19,X_20) = multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_19,X_20)),multiply(X_19,X_20)) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
add(additive_identity,X_19) = X_19,
inference(subst,[],[additive_id2:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_346,plain,
add(multiply(X_10,additive_identity),X_19) = add(multiply(X_10,additive_identity),X_19),
introduced(tautology,[refl,[$fot(add(multiply(X_10,additive_identity),X_19))]]) ).
cnf(refute_0_347,plain,
( multiply(X_10,additive_identity) != additive_identity
| add(multiply(X_10,additive_identity),X_19) != add(multiply(X_10,additive_identity),X_19)
| add(multiply(X_10,additive_identity),X_19) = add(additive_identity,X_19) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),X_19),add(multiply(X_10,additive_identity),X_19)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_348,plain,
( multiply(X_10,additive_identity) != additive_identity
| add(multiply(X_10,additive_identity),X_19) = add(additive_identity,X_19) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_19),add(multiply(X_10,additive_identity),X_19)) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
add(multiply(X_10,additive_identity),X_19) = add(additive_identity,X_19),
inference(resolve,[$cnf( $equal(multiply(X_10,additive_identity),additive_identity) )],[refute_0_335,refute_0_348]) ).
cnf(refute_0_350,plain,
( add(multiply(X_10,additive_identity),X_19) != add(additive_identity,X_19)
| add(additive_identity,X_19) != X_19
| add(multiply(X_10,additive_identity),X_19) = X_19 ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(multiply(X_10,additive_identity),X_19))),bind(Y0,$fot(add(additive_identity,X_19))),bind(Z0,$fot(X_19))]]) ).
cnf(refute_0_351,plain,
( add(additive_identity,X_19) != X_19
| add(multiply(X_10,additive_identity),X_19) = X_19 ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_19),add(additive_identity,X_19)) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
add(multiply(X_10,additive_identity),X_19) = X_19,
inference(resolve,[$cnf( $equal(add(additive_identity,X_19),X_19) )],[refute_0_345,refute_0_351]) ).
cnf(refute_0_353,plain,
multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))) = multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))),
introduced(tautology,[refl,[$fot(multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))))]]) ).
cnf(refute_0_354,plain,
( multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))) != multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))
| add(multiply(X_10,additive_identity),X_19) != X_19
| multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))) = multiply(X_19,multiply(X_20,add(X_10,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))),multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))) ),[1,0],$fot(X_19)]]) ).
cnf(refute_0_355,plain,
( add(multiply(X_10,additive_identity),X_19) != X_19
| multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))) = multiply(X_19,multiply(X_20,add(X_10,X_20))) ),
inference(resolve,[$cnf( $equal(multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))),multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))) = multiply(X_19,multiply(X_20,add(X_10,X_20))),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_19),X_19) )],[refute_0_352,refute_0_355]) ).
cnf(refute_0_357,plain,
( multiply(X_19,X_20) != multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))
| multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))) != multiply(X_19,multiply(X_20,add(X_10,X_20)))
| multiply(X_19,X_20) = multiply(X_19,multiply(X_20,add(X_10,X_20))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_19,X_20),multiply(X_19,multiply(X_20,add(X_10,X_20)))) ),[0],$fot(multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))))]]) ).
cnf(refute_0_358,plain,
( multiply(X_19,X_20) != multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))
| multiply(X_19,X_20) = multiply(X_19,multiply(X_20,add(X_10,X_20))) ),
inference(resolve,[$cnf( $equal(multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20))),multiply(X_19,multiply(X_20,add(X_10,X_20)))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
( add(multiply(X_10,additive_identity),multiply(X_19,X_20)) != multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))
| multiply(X_19,X_20) = multiply(X_19,multiply(X_20,add(X_10,X_20))) ),
inference(resolve,[$cnf( $equal(multiply(X_19,X_20),multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))) )],[refute_0_344,refute_0_358]) ).
cnf(refute_0_360,plain,
multiply(X_19,X_20) = multiply(X_19,multiply(X_20,add(X_10,X_20))),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_19,X_20)),multiply(add(multiply(X_10,additive_identity),X_19),multiply(X_20,add(X_10,X_20)))) )],[refute_0_333,refute_0_359]) ).
cnf(refute_0_361,plain,
( multiply(X_19,X_20) != multiply(X_19,multiply(X_20,add(X_10,X_20)))
| multiply(X_19,multiply(X_20,add(X_10,X_20))) = multiply(X_19,X_20) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(X_19,X_20))),bind(Y0,$fot(multiply(X_19,multiply(X_20,add(X_10,X_20)))))]]) ).
cnf(refute_0_362,plain,
multiply(X_19,multiply(X_20,add(X_10,X_20))) = multiply(X_19,X_20),
inference(resolve,[$cnf( $equal(multiply(X_19,X_20),multiply(X_19,multiply(X_20,add(X_10,X_20)))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
multiply(add(X,Z),multiply(Z,add(X_13,Z))) = multiply(add(X,Z),Z),
inference(subst,[],[refute_0_362:[bind(X_10,$fot(X_13)),bind(X_19,$fot(add(X,Z))),bind(X_20,$fot(Z))]]) ).
cnf(refute_0_364,plain,
( multiply(add(X,Z),Z) != multiply(Z,add(X,Z))
| multiply(add(X,Z),multiply(Z,add(X_13,Z))) != multiply(add(X,Z),Z)
| multiply(add(X,Z),multiply(Z,add(X_13,Z))) = multiply(Z,add(X,Z)) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(multiply(add(X,Z),multiply(Z,add(X_13,Z))))),bind(Y0,$fot(multiply(add(X,Z),Z))),bind(Z0,$fot(multiply(Z,add(X,Z))))]]) ).
cnf(refute_0_365,plain,
( multiply(add(X,Z),Z) != multiply(Z,add(X,Z))
| multiply(add(X,Z),multiply(Z,add(X_13,Z))) = multiply(Z,add(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(add(X,Z),multiply(Z,add(X_13,Z))),multiply(add(X,Z),Z)) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
multiply(add(X,Z),multiply(Z,add(X_13,Z))) = multiply(Z,add(X,Z)),
inference(resolve,[$cnf( $equal(multiply(add(X,Z),Z),multiply(Z,add(X,Z))) )],[refute_0_328,refute_0_365]) ).
cnf(refute_0_367,plain,
( Z != multiply(add(X,Z),multiply(Z,add(X_13,Z)))
| multiply(add(X,Z),multiply(Z,add(X_13,Z))) != multiply(Z,add(X,Z))
| Z = multiply(Z,add(X,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(Z,multiply(Z,add(X,Z))) ),[0],$fot(multiply(add(X,Z),multiply(Z,add(X_13,Z))))]]) ).
cnf(refute_0_368,plain,
( Z != multiply(add(X,Z),multiply(Z,add(X_13,Z)))
| Z = multiply(Z,add(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(add(X,Z),multiply(Z,add(X_13,Z))),multiply(Z,add(X,Z))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
Z = multiply(Z,add(X,Z)),
inference(resolve,[$cnf( $equal(Z,multiply(add(X,Z),multiply(Z,add(X_13,Z)))) )],[refute_0_327,refute_0_368]) ).
cnf(refute_0_370,plain,
( Z != multiply(Z,add(X,Z))
| multiply(Z,add(X,Z)) = Z ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(Z)),bind(Y0,$fot(multiply(Z,add(X,Z))))]]) ).
cnf(refute_0_371,plain,
multiply(Z,add(X,Z)) = Z,
inference(resolve,[$cnf( $equal(Z,multiply(Z,add(X,Z))) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
multiply(X_24,add(X_10,X_24)) = X_24,
inference(subst,[],[refute_0_371:[bind(X,$fot(X_10)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_373,plain,
multiply(additive_identity,multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,multiply(X_24,add(X_10,X_24))),
introduced(tautology,[refl,[$fot(multiply(additive_identity,multiply(X_24,add(X_10,X_24))))]]) ).
cnf(refute_0_374,plain,
( multiply(X_24,add(X_10,X_24)) != X_24
| multiply(additive_identity,multiply(X_24,add(X_10,X_24))) != multiply(additive_identity,multiply(X_24,add(X_10,X_24)))
| multiply(additive_identity,multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,multiply(X_24,add(X_10,X_24))),multiply(additive_identity,multiply(X_24,add(X_10,X_24)))) ),[1,1],$fot(X_24)]]) ).
cnf(refute_0_375,plain,
( multiply(X_24,add(X_10,X_24)) != X_24
| multiply(additive_identity,multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,X_24) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,multiply(X_24,add(X_10,X_24))),multiply(additive_identity,multiply(X_24,add(X_10,X_24)))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
multiply(additive_identity,multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,X_24),
inference(resolve,[$cnf( $equal(multiply(X_24,add(X_10,X_24)),X_24) )],[refute_0_372,refute_0_375]) ).
cnf(refute_0_377,plain,
multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) = multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))),
introduced(tautology,[refl,[$fot(multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))))]]) ).
cnf(refute_0_378,plain,
( multiply(X_10,additive_identity) != additive_identity
| multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) != multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))
| multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,multiply(X_24,add(X_10,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))),multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_379,plain,
( multiply(X_10,additive_identity) != additive_identity
| multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,multiply(X_24,add(X_10,X_24))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))),multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,multiply(X_24,add(X_10,X_24))),
inference(resolve,[$cnf( $equal(multiply(X_10,additive_identity),additive_identity) )],[refute_0_335,refute_0_379]) ).
cnf(refute_0_381,plain,
( multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) != multiply(additive_identity,multiply(X_24,add(X_10,X_24)))
| multiply(additive_identity,multiply(X_24,add(X_10,X_24))) != multiply(additive_identity,X_24)
| multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,X_24) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))))),bind(Y0,$fot(multiply(additive_identity,multiply(X_24,add(X_10,X_24))))),bind(Z0,$fot(multiply(additive_identity,X_24)))]]) ).
cnf(refute_0_382,plain,
( multiply(additive_identity,multiply(X_24,add(X_10,X_24))) != multiply(additive_identity,X_24)
| multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,X_24) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))),multiply(additive_identity,multiply(X_24,add(X_10,X_24)))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) = multiply(additive_identity,X_24),
inference(resolve,[$cnf( $equal(multiply(additive_identity,multiply(X_24,add(X_10,X_24))),multiply(additive_identity,X_24)) )],[refute_0_376,refute_0_382]) ).
cnf(refute_0_384,plain,
( multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))) != multiply(additive_identity,X_24)
| multiply(additive_identity,add(X_10,X_24)) != multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))
| multiply(additive_identity,add(X_10,X_24)) = multiply(additive_identity,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_10,X_24)),multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))) ),[1],$fot(multiply(additive_identity,X_24))]]) ).
cnf(refute_0_385,plain,
( multiply(additive_identity,add(X_10,X_24)) != multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))
| multiply(additive_identity,add(X_10,X_24)) = multiply(additive_identity,X_24) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24))),multiply(additive_identity,X_24)) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
multiply(additive_identity,add(X_10,X_24)) = multiply(additive_identity,X_24),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_10,X_24)),multiply(multiply(X_10,additive_identity),multiply(X_24,add(X_10,X_24)))) )],[refute_0_95,refute_0_385]) ).
cnf(refute_0_387,plain,
multiply(additive_identity,add(X_31,X_20)) = multiply(additive_identity,X_20),
inference(subst,[],[refute_0_386:[bind(X_10,$fot(X_31)),bind(X_24,$fot(X_20))]]) ).
cnf(refute_0_388,plain,
( multiply(additive_identity,add(X_31,X_20)) != multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))
| multiply(additive_identity,add(X_31,X_20)) != multiply(additive_identity,X_20)
| multiply(additive_identity,X_20) = multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_31,X_20)),multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))) ),[0],$fot(multiply(additive_identity,X_20))]]) ).
cnf(refute_0_389,plain,
( multiply(additive_identity,add(X_31,X_20)) != multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))
| multiply(additive_identity,X_20) = multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_31,X_20)),multiply(additive_identity,X_20)) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
multiply(X_20,add(X_31,X_20)) = X_20,
inference(subst,[],[refute_0_371:[bind(X,$fot(X_31)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_391,plain,
multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) = multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))),
introduced(tautology,[refl,[$fot(multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))))]]) ).
cnf(refute_0_392,plain,
( multiply(X_20,add(X_31,X_20)) != X_20
| multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) != multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))
| multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) = multiply(multiply(additive_identity,X_31),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))),multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))) ),[1,1],$fot(X_20)]]) ).
cnf(refute_0_393,plain,
( multiply(X_20,add(X_31,X_20)) != X_20
| multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) = multiply(multiply(additive_identity,X_31),X_20) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))),multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) = multiply(multiply(additive_identity,X_31),X_20),
inference(resolve,[$cnf( $equal(multiply(X_20,add(X_31,X_20)),X_20) )],[refute_0_390,refute_0_393]) ).
cnf(refute_0_395,plain,
( multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))) != multiply(multiply(additive_identity,X_31),X_20)
| multiply(additive_identity,X_20) != multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))
| multiply(additive_identity,X_20) = multiply(multiply(additive_identity,X_31),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,X_20),multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))) ),[1],$fot(multiply(multiply(additive_identity,X_31),X_20))]]) ).
cnf(refute_0_396,plain,
( multiply(additive_identity,X_20) != multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))
| multiply(additive_identity,X_20) = multiply(multiply(additive_identity,X_31),X_20) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20))),multiply(multiply(additive_identity,X_31),X_20)) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
( multiply(additive_identity,add(X_31,X_20)) != multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))
| multiply(additive_identity,X_20) = multiply(multiply(additive_identity,X_31),X_20) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_20),multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))) )],[refute_0_389,refute_0_396]) ).
cnf(refute_0_398,plain,
multiply(additive_identity,X_20) = multiply(multiply(additive_identity,X_31),X_20),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_31,X_20)),multiply(multiply(additive_identity,X_31),multiply(X_20,add(X_31,X_20)))) )],[refute_0_55,refute_0_397]) ).
cnf(refute_0_399,plain,
( multiply(additive_identity,X_20) != multiply(multiply(additive_identity,X_31),X_20)
| multiply(multiply(additive_identity,X_31),X_20) = multiply(additive_identity,X_20) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(additive_identity,X_20))),bind(Y0,$fot(multiply(multiply(additive_identity,X_31),X_20)))]]) ).
cnf(refute_0_400,plain,
multiply(multiply(additive_identity,X_31),X_20) = multiply(additive_identity,X_20),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_20),multiply(multiply(additive_identity,X_31),X_20)) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
multiply(multiply(additive_identity,X_24),Z) = multiply(additive_identity,Z),
inference(subst,[],[refute_0_400:[bind(X_20,$fot(Z)),bind(X_31,$fot(X_24))]]) ).
cnf(refute_0_402,plain,
add(X,multiply(multiply(additive_identity,X_24),Z)) = add(X,multiply(multiply(additive_identity,X_24),Z)),
introduced(tautology,[refl,[$fot(add(X,multiply(multiply(additive_identity,X_24),Z)))]]) ).
cnf(refute_0_403,plain,
( multiply(multiply(additive_identity,X_24),Z) != multiply(additive_identity,Z)
| add(X,multiply(multiply(additive_identity,X_24),Z)) != add(X,multiply(multiply(additive_identity,X_24),Z))
| add(X,multiply(multiply(additive_identity,X_24),Z)) = add(X,multiply(additive_identity,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,multiply(multiply(additive_identity,X_24),Z)),add(X,multiply(multiply(additive_identity,X_24),Z))) ),[1,1],$fot(multiply(additive_identity,Z))]]) ).
cnf(refute_0_404,plain,
( multiply(multiply(additive_identity,X_24),Z) != multiply(additive_identity,Z)
| add(X,multiply(multiply(additive_identity,X_24),Z)) = add(X,multiply(additive_identity,Z)) ),
inference(resolve,[$cnf( $equal(add(X,multiply(multiply(additive_identity,X_24),Z)),add(X,multiply(multiply(additive_identity,X_24),Z))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
add(X,multiply(multiply(additive_identity,X_24),Z)) = add(X,multiply(additive_identity,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_24),Z),multiply(additive_identity,Z)) )],[refute_0_401,refute_0_404]) ).
cnf(refute_0_406,plain,
( add(X,multiply(multiply(additive_identity,X_24),Z)) != multiply(multiply(X,add(X,X_24)),add(X,Z))
| add(X,multiply(multiply(additive_identity,X_24),Z)) != add(X,multiply(additive_identity,Z))
| add(X,multiply(additive_identity,Z)) = multiply(multiply(X,add(X,X_24)),add(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,multiply(multiply(additive_identity,X_24),Z)),multiply(multiply(X,add(X,X_24)),add(X,Z))) ),[0],$fot(add(X,multiply(additive_identity,Z)))]]) ).
cnf(refute_0_407,plain,
( add(X,multiply(multiply(additive_identity,X_24),Z)) != multiply(multiply(X,add(X,X_24)),add(X,Z))
| add(X,multiply(additive_identity,Z)) = multiply(multiply(X,add(X,X_24)),add(X,Z)) ),
inference(resolve,[$cnf( $equal(add(X,multiply(multiply(additive_identity,X_24),Z)),add(X,multiply(additive_identity,Z))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
add(X,multiply(additive_identity,Z)) = multiply(multiply(X,add(X,X_24)),add(X,Z)),
inference(resolve,[$cnf( $equal(add(X,multiply(multiply(additive_identity,X_24),Z)),multiply(multiply(X,add(X,X_24)),add(X,Z))) )],[refute_0_39,refute_0_407]) ).
cnf(refute_0_409,plain,
( multiply(additive_identity,add(X_31,X_20)) != multiply(additive_identity,X_20)
| multiply(additive_identity,add(X_31,X_20)) != add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))
| multiply(additive_identity,X_20) = add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_31,X_20)),add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))) ),[0],$fot(multiply(additive_identity,X_20))]]) ).
cnf(refute_0_410,plain,
( multiply(additive_identity,add(X_31,X_20)) != add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))
| multiply(additive_identity,X_20) = add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_31,X_20)),multiply(additive_identity,X_20)) )],[refute_0_387,refute_0_409]) ).
cnf(refute_0_411,plain,
multiply(additive_identity,add(X_20,additive_identity)) = multiply(additive_identity,additive_identity),
inference(subst,[],[refute_0_386:[bind(X_10,$fot(X_20)),bind(X_24,$fot(additive_identity))]]) ).
cnf(refute_0_412,plain,
( multiply(additive_identity,add(X_20,additive_identity)) != multiply(additive_identity,additive_identity)
| multiply(additive_identity,additive_identity) != additive_identity
| multiply(additive_identity,add(X_20,additive_identity)) = additive_identity ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(multiply(additive_identity,add(X_20,additive_identity)))),bind(Y0,$fot(multiply(additive_identity,additive_identity))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_413,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| multiply(additive_identity,add(X_20,additive_identity)) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_20,additive_identity)),multiply(additive_identity,additive_identity)) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
multiply(additive_identity,add(X_20,additive_identity)) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),additive_identity) )],[refute_0_221,refute_0_413]) ).
cnf(refute_0_415,plain,
add(X_41,multiply(X_42,additive_identity)) = multiply(X_41,add(X_42,X_41)),
inference(subst,[],[refute_0_116:[bind(X,$fot(X_41)),bind(X_13,$fot(X_42))]]) ).
cnf(refute_0_416,plain,
multiply(additive_identity,X_42) = multiply(X_42,additive_identity),
inference(subst,[],[commutativity_of_multiply:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_417,plain,
( multiply(additive_identity,X_42) != multiply(X_42,additive_identity)
| multiply(X_42,additive_identity) = multiply(additive_identity,X_42) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(additive_identity,X_42))),bind(Y0,$fot(multiply(X_42,additive_identity)))]]) ).
cnf(refute_0_418,plain,
multiply(X_42,additive_identity) = multiply(additive_identity,X_42),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_42),multiply(X_42,additive_identity)) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
( multiply(X_42,additive_identity) != multiply(additive_identity,X_42)
| add(X_41,multiply(X_42,additive_identity)) != multiply(X_41,add(X_42,X_41))
| add(X_41,multiply(additive_identity,X_42)) = multiply(X_41,add(X_42,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_41,multiply(X_42,additive_identity)),multiply(X_41,add(X_42,X_41))) ),[0,1],$fot(multiply(additive_identity,X_42))]]) ).
cnf(refute_0_420,plain,
( add(X_41,multiply(X_42,additive_identity)) != multiply(X_41,add(X_42,X_41))
| add(X_41,multiply(additive_identity,X_42)) = multiply(X_41,add(X_42,X_41)) ),
inference(resolve,[$cnf( $equal(multiply(X_42,additive_identity),multiply(additive_identity,X_42)) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
add(X_41,multiply(additive_identity,X_42)) = multiply(X_41,add(X_42,X_41)),
inference(resolve,[$cnf( $equal(add(X_41,multiply(X_42,additive_identity)),multiply(X_41,add(X_42,X_41))) )],[refute_0_415,refute_0_420]) ).
cnf(refute_0_422,plain,
add(additive_identity,multiply(additive_identity,X_20)) = multiply(additive_identity,add(X_20,additive_identity)),
inference(subst,[],[refute_0_421:[bind(X_41,$fot(additive_identity)),bind(X_42,$fot(X_20))]]) ).
cnf(refute_0_423,plain,
( multiply(additive_identity,add(X_20,additive_identity)) != additive_identity
| add(additive_identity,multiply(additive_identity,X_20)) != multiply(additive_identity,add(X_20,additive_identity))
| add(additive_identity,multiply(additive_identity,X_20)) = additive_identity ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(additive_identity,multiply(additive_identity,X_20)))),bind(Y0,$fot(multiply(additive_identity,add(X_20,additive_identity)))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_424,plain,
( multiply(additive_identity,add(X_20,additive_identity)) != additive_identity
| add(additive_identity,multiply(additive_identity,X_20)) = additive_identity ),
inference(resolve,[$cnf( $equal(add(additive_identity,multiply(additive_identity,X_20)),multiply(additive_identity,add(X_20,additive_identity))) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
add(additive_identity,multiply(additive_identity,X_20)) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_20,additive_identity)),additive_identity) )],[refute_0_414,refute_0_424]) ).
cnf(refute_0_426,plain,
multiply(X_31,additive_identity) = additive_identity,
inference(subst,[],[refute_0_308:[bind(X_42,$fot(X_31))]]) ).
cnf(refute_0_427,plain,
add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) = add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)),
introduced(tautology,[refl,[$fot(add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)))]]) ).
cnf(refute_0_428,plain,
( multiply(X_31,additive_identity) != additive_identity
| add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) != add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))
| add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) = add(additive_identity,multiply(additive_identity,X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)),add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_429,plain,
( multiply(X_31,additive_identity) != additive_identity
| add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) = add(additive_identity,multiply(additive_identity,X_20)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)),add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) = add(additive_identity,multiply(additive_identity,X_20)),
inference(resolve,[$cnf( $equal(multiply(X_31,additive_identity),additive_identity) )],[refute_0_426,refute_0_429]) ).
cnf(refute_0_431,plain,
( add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) != add(additive_identity,multiply(additive_identity,X_20))
| add(additive_identity,multiply(additive_identity,X_20)) != additive_identity
| add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) = additive_identity ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)))),bind(Y0,$fot(add(additive_identity,multiply(additive_identity,X_20)))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_432,plain,
( add(additive_identity,multiply(additive_identity,X_20)) != additive_identity
| add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) = additive_identity ),
inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)),add(additive_identity,multiply(additive_identity,X_20))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) = additive_identity,
inference(resolve,[$cnf( $equal(add(additive_identity,multiply(additive_identity,X_20)),additive_identity) )],[refute_0_425,refute_0_432]) ).
cnf(refute_0_434,plain,
( multiply(additive_identity,X_20) != add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))
| add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)) != additive_identity
| multiply(additive_identity,X_20) = additive_identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(additive_identity,X_20),additive_identity) ),[0],$fot(add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)))]]) ).
cnf(refute_0_435,plain,
( multiply(additive_identity,X_20) != add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))
| multiply(additive_identity,X_20) = additive_identity ),
inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(additive_identity,X_20)),additive_identity) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
( multiply(additive_identity,add(X_31,X_20)) != add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))
| multiply(additive_identity,X_20) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_20),add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))) )],[refute_0_410,refute_0_435]) ).
cnf(refute_0_437,plain,
multiply(additive_identity,X_20) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_31,X_20)),add(multiply(X_31,additive_identity),multiply(additive_identity,X_20))) )],[refute_0_89,refute_0_436]) ).
cnf(refute_0_438,plain,
multiply(additive_identity,Z) = additive_identity,
inference(subst,[],[refute_0_437:[bind(X_20,$fot(Z))]]) ).
cnf(refute_0_439,plain,
add(X,multiply(additive_identity,Z)) = add(X,multiply(additive_identity,Z)),
introduced(tautology,[refl,[$fot(add(X,multiply(additive_identity,Z)))]]) ).
cnf(refute_0_440,plain,
( multiply(additive_identity,Z) != additive_identity
| add(X,multiply(additive_identity,Z)) != add(X,multiply(additive_identity,Z))
| add(X,multiply(additive_identity,Z)) = add(X,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,multiply(additive_identity,Z)),add(X,multiply(additive_identity,Z))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_441,plain,
( multiply(additive_identity,Z) != additive_identity
| add(X,multiply(additive_identity,Z)) = add(X,additive_identity) ),
inference(resolve,[$cnf( $equal(add(X,multiply(additive_identity,Z)),add(X,multiply(additive_identity,Z))) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
add(X,multiply(additive_identity,Z)) = add(X,additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,Z),additive_identity) )],[refute_0_438,refute_0_441]) ).
cnf(refute_0_443,plain,
( add(X,multiply(additive_identity,Z)) != add(X,additive_identity)
| add(X,additive_identity) != X
| add(X,multiply(additive_identity,Z)) = X ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(X,multiply(additive_identity,Z)))),bind(Y0,$fot(add(X,additive_identity))),bind(Z0,$fot(X))]]) ).
cnf(refute_0_444,plain,
( add(X,additive_identity) != X
| add(X,multiply(additive_identity,Z)) = X ),
inference(resolve,[$cnf( $equal(add(X,multiply(additive_identity,Z)),add(X,additive_identity)) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
add(X,multiply(additive_identity,Z)) = X,
inference(resolve,[$cnf( $equal(add(X,additive_identity),X) )],[additive_id1,refute_0_444]) ).
cnf(refute_0_446,plain,
( add(X,multiply(additive_identity,Z)) != X
| add(X,multiply(additive_identity,Z)) != multiply(multiply(X,add(X,X_24)),add(X,Z))
| X = multiply(multiply(X,add(X,X_24)),add(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,multiply(additive_identity,Z)),multiply(multiply(X,add(X,X_24)),add(X,Z))) ),[0],$fot(X)]]) ).
cnf(refute_0_447,plain,
( add(X,multiply(additive_identity,Z)) != multiply(multiply(X,add(X,X_24)),add(X,Z))
| X = multiply(multiply(X,add(X,X_24)),add(X,Z)) ),
inference(resolve,[$cnf( $equal(add(X,multiply(additive_identity,Z)),X) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
X = multiply(multiply(X,add(X,X_24)),add(X,Z)),
inference(resolve,[$cnf( $equal(add(X,multiply(additive_identity,Z)),multiply(multiply(X,add(X,X_24)),add(X,Z))) )],[refute_0_408,refute_0_447]) ).
cnf(refute_0_449,plain,
add(multiply(X,Y),multiply(additive_identity,X_24)) = multiply(add(X,multiply(additive_identity,X_24)),add(Y,multiply(additive_identity,X_24))),
inference(subst,[],[distributivity1:[bind(Z,$fot(multiply(additive_identity,X_24)))]]) ).
cnf(refute_0_450,plain,
( add(X,multiply(additive_identity,X_24)) != multiply(X,add(X,X_24))
| add(multiply(X,Y),multiply(additive_identity,X_24)) != multiply(add(X,multiply(additive_identity,X_24)),add(Y,multiply(additive_identity,X_24)))
| add(multiply(X,Y),multiply(additive_identity,X_24)) = multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,Y),multiply(additive_identity,X_24)),multiply(add(X,multiply(additive_identity,X_24)),add(Y,multiply(additive_identity,X_24)))) ),[1,0],$fot(multiply(X,add(X,X_24)))]]) ).
cnf(refute_0_451,plain,
( add(multiply(X,Y),multiply(additive_identity,X_24)) != multiply(add(X,multiply(additive_identity,X_24)),add(Y,multiply(additive_identity,X_24)))
| add(multiply(X,Y),multiply(additive_identity,X_24)) = multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))) ),
inference(resolve,[$cnf( $equal(add(X,multiply(additive_identity,X_24)),multiply(X,add(X,X_24))) )],[refute_0_36,refute_0_450]) ).
cnf(refute_0_452,plain,
add(multiply(X,Y),multiply(additive_identity,X_24)) = multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),multiply(additive_identity,X_24)),multiply(add(X,multiply(additive_identity,X_24)),add(Y,multiply(additive_identity,X_24)))) )],[refute_0_449,refute_0_451]) ).
cnf(refute_0_453,plain,
add(additive_identity,multiply(X,Y)) = multiply(X,Y),
inference(subst,[],[additive_id2:[bind(X,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_454,plain,
add(multiply(X,Y),additive_identity) = add(additive_identity,multiply(X,Y)),
inference(subst,[],[refute_0_250:[bind(Y,$fot(multiply(X,Y))),bind(X_22,$fot(additive_identity))]]) ).
cnf(refute_0_455,plain,
( add(multiply(X,Y),additive_identity) != add(additive_identity,multiply(X,Y))
| add(additive_identity,multiply(X,Y)) != multiply(X,Y)
| add(multiply(X,Y),additive_identity) = multiply(X,Y) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(multiply(X,Y),additive_identity))),bind(Y0,$fot(add(additive_identity,multiply(X,Y)))),bind(Z0,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_456,plain,
( add(additive_identity,multiply(X,Y)) != multiply(X,Y)
| add(multiply(X,Y),additive_identity) = multiply(X,Y) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),additive_identity),add(additive_identity,multiply(X,Y))) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
add(multiply(X,Y),additive_identity) = multiply(X,Y),
inference(resolve,[$cnf( $equal(add(additive_identity,multiply(X,Y)),multiply(X,Y)) )],[refute_0_453,refute_0_456]) ).
cnf(refute_0_458,plain,
multiply(additive_identity,X_24) = additive_identity,
inference(subst,[],[refute_0_437:[bind(X_20,$fot(X_24))]]) ).
cnf(refute_0_459,plain,
add(multiply(X,Y),multiply(additive_identity,X_24)) = add(multiply(X,Y),multiply(additive_identity,X_24)),
introduced(tautology,[refl,[$fot(add(multiply(X,Y),multiply(additive_identity,X_24)))]]) ).
cnf(refute_0_460,plain,
( multiply(additive_identity,X_24) != additive_identity
| add(multiply(X,Y),multiply(additive_identity,X_24)) != add(multiply(X,Y),multiply(additive_identity,X_24))
| add(multiply(X,Y),multiply(additive_identity,X_24)) = add(multiply(X,Y),additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,Y),multiply(additive_identity,X_24)),add(multiply(X,Y),multiply(additive_identity,X_24))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_461,plain,
( multiply(additive_identity,X_24) != additive_identity
| add(multiply(X,Y),multiply(additive_identity,X_24)) = add(multiply(X,Y),additive_identity) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),multiply(additive_identity,X_24)),add(multiply(X,Y),multiply(additive_identity,X_24))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
add(multiply(X,Y),multiply(additive_identity,X_24)) = add(multiply(X,Y),additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_24),additive_identity) )],[refute_0_458,refute_0_461]) ).
cnf(refute_0_463,plain,
( add(multiply(X,Y),multiply(additive_identity,X_24)) != add(multiply(X,Y),additive_identity)
| add(multiply(X,Y),additive_identity) != multiply(X,Y)
| add(multiply(X,Y),multiply(additive_identity,X_24)) = multiply(X,Y) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(multiply(X,Y),multiply(additive_identity,X_24)))),bind(Y0,$fot(add(multiply(X,Y),additive_identity))),bind(Z0,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_464,plain,
( add(multiply(X,Y),additive_identity) != multiply(X,Y)
| add(multiply(X,Y),multiply(additive_identity,X_24)) = multiply(X,Y) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),multiply(additive_identity,X_24)),add(multiply(X,Y),additive_identity)) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
add(multiply(X,Y),multiply(additive_identity,X_24)) = multiply(X,Y),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),additive_identity),multiply(X,Y)) )],[refute_0_457,refute_0_464]) ).
cnf(refute_0_466,plain,
( add(multiply(X,Y),multiply(additive_identity,X_24)) != multiply(X,Y)
| add(multiply(X,Y),multiply(additive_identity,X_24)) != multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))
| multiply(X,Y) = multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,Y),multiply(additive_identity,X_24)),multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))) ),[0],$fot(multiply(X,Y))]]) ).
cnf(refute_0_467,plain,
( add(multiply(X,Y),multiply(additive_identity,X_24)) != multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))
| multiply(X,Y) = multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),multiply(additive_identity,X_24)),multiply(X,Y)) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
add(Y,multiply(additive_identity,X_24)) = add(Y,multiply(additive_identity,X_24)),
introduced(tautology,[refl,[$fot(add(Y,multiply(additive_identity,X_24)))]]) ).
cnf(refute_0_469,plain,
( multiply(additive_identity,X_24) != additive_identity
| add(Y,multiply(additive_identity,X_24)) != add(Y,multiply(additive_identity,X_24))
| add(Y,multiply(additive_identity,X_24)) = add(Y,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(additive_identity,X_24)),add(Y,multiply(additive_identity,X_24))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_470,plain,
( multiply(additive_identity,X_24) != additive_identity
| add(Y,multiply(additive_identity,X_24)) = add(Y,additive_identity) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,X_24)),add(Y,multiply(additive_identity,X_24))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
add(Y,multiply(additive_identity,X_24)) = add(Y,additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_24),additive_identity) )],[refute_0_458,refute_0_470]) ).
cnf(refute_0_472,plain,
( add(Y,multiply(additive_identity,X_24)) != add(Y,additive_identity)
| add(Y,additive_identity) != Y
| add(Y,multiply(additive_identity,X_24)) = Y ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(Y,multiply(additive_identity,X_24)))),bind(Y0,$fot(add(Y,additive_identity))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_473,plain,
( add(Y,additive_identity) != Y
| add(Y,multiply(additive_identity,X_24)) = Y ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,X_24)),add(Y,additive_identity)) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
add(Y,multiply(additive_identity,X_24)) = Y,
inference(resolve,[$cnf( $equal(add(Y,additive_identity),Y) )],[refute_0_172,refute_0_473]) ).
cnf(refute_0_475,plain,
multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))) = multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))),
introduced(tautology,[refl,[$fot(multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))))]]) ).
cnf(refute_0_476,plain,
( multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))) != multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))
| add(Y,multiply(additive_identity,X_24)) != Y
| multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))) = multiply(multiply(X,add(X,X_24)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))),multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))) ),[1,1],$fot(Y)]]) ).
cnf(refute_0_477,plain,
( add(Y,multiply(additive_identity,X_24)) != Y
| multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))) = multiply(multiply(X,add(X,X_24)),Y) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))),multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))) = multiply(multiply(X,add(X,X_24)),Y),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,X_24)),Y) )],[refute_0_474,refute_0_477]) ).
cnf(refute_0_479,plain,
( multiply(X,Y) != multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))
| multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))) != multiply(multiply(X,add(X,X_24)),Y)
| multiply(X,Y) = multiply(multiply(X,add(X,X_24)),Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,Y),multiply(multiply(X,add(X,X_24)),Y)) ),[0],$fot(multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))))]]) ).
cnf(refute_0_480,plain,
( multiply(X,Y) != multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))
| multiply(X,Y) = multiply(multiply(X,add(X,X_24)),Y) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24))),multiply(multiply(X,add(X,X_24)),Y)) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
( add(multiply(X,Y),multiply(additive_identity,X_24)) != multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))
| multiply(X,Y) = multiply(multiply(X,add(X,X_24)),Y) ),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))) )],[refute_0_467,refute_0_480]) ).
cnf(refute_0_482,plain,
multiply(X,Y) = multiply(multiply(X,add(X,X_24)),Y),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),multiply(additive_identity,X_24)),multiply(multiply(X,add(X,X_24)),add(Y,multiply(additive_identity,X_24)))) )],[refute_0_452,refute_0_481]) ).
cnf(refute_0_483,plain,
( multiply(X,Y) != multiply(multiply(X,add(X,X_24)),Y)
| multiply(multiply(X,add(X,X_24)),Y) = multiply(X,Y) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(multiply(multiply(X,add(X,X_24)),Y)))]]) ).
cnf(refute_0_484,plain,
multiply(multiply(X,add(X,X_24)),Y) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(multiply(X,add(X,X_24)),Y)) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
multiply(multiply(X,add(X,X_24)),add(X,Z)) = multiply(X,add(X,Z)),
inference(subst,[],[refute_0_484:[bind(Y,$fot(add(X,Z)))]]) ).
cnf(refute_0_486,plain,
( X != multiply(multiply(X,add(X,X_24)),add(X,Z))
| multiply(multiply(X,add(X,X_24)),add(X,Z)) != multiply(X,add(X,Z))
| X = multiply(X,add(X,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,multiply(X,add(X,Z))) ),[0],$fot(multiply(multiply(X,add(X,X_24)),add(X,Z)))]]) ).
cnf(refute_0_487,plain,
( X != multiply(multiply(X,add(X,X_24)),add(X,Z))
| X = multiply(X,add(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,add(X,X_24)),add(X,Z)),multiply(X,add(X,Z))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
X = multiply(X,add(X,Z)),
inference(resolve,[$cnf( $equal(X,multiply(multiply(X,add(X,X_24)),add(X,Z))) )],[refute_0_448,refute_0_487]) ).
cnf(refute_0_489,plain,
( X != multiply(X,add(X,Z))
| multiply(X,add(X,Z)) = X ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,add(X,Z))))]]) ).
cnf(refute_0_490,plain,
multiply(X,add(X,Z)) = X,
inference(resolve,[$cnf( $equal(X,multiply(X,add(X,Z))) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
multiply(Z,add(Z,Y)) = Z,
inference(subst,[],[refute_0_490:[bind(X,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_492,plain,
multiply(add(Z,Y),Z) = multiply(Z,add(Z,Y)),
inference(subst,[],[refute_0_62:[bind(X,$fot(Z)),bind(Y,$fot(add(Z,Y)))]]) ).
cnf(refute_0_493,plain,
( multiply(Z,add(Z,Y)) != Z
| multiply(add(Z,Y),Z) != multiply(Z,add(Z,Y))
| multiply(add(Z,Y),Z) = Z ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(multiply(add(Z,Y),Z))),bind(Y0,$fot(multiply(Z,add(Z,Y)))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_494,plain,
( multiply(Z,add(Z,Y)) != Z
| multiply(add(Z,Y),Z) = Z ),
inference(resolve,[$cnf( $equal(multiply(add(Z,Y),Z),multiply(Z,add(Z,Y))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
multiply(add(Z,Y),Z) = Z,
inference(resolve,[$cnf( $equal(multiply(Z,add(Z,Y)),Z) )],[refute_0_491,refute_0_494]) ).
cnf(refute_0_496,plain,
( multiply(add(Z,Y),Z) != Z
| add(Z,multiply(Y,Z)) != multiply(add(Z,Y),Z)
| add(Z,multiply(Y,Z)) = Z ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),Z)) ),[1],$fot(Z)]]) ).
cnf(refute_0_497,plain,
( add(Z,multiply(Y,Z)) != multiply(add(Z,Y),Z)
| add(Z,multiply(Y,Z)) = Z ),
inference(resolve,[$cnf( $equal(multiply(add(Z,Y),Z),Z) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
add(Z,multiply(Y,Z)) = Z,
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),Z)) )],[refute_0_29,refute_0_497]) ).
cnf(refute_0_499,plain,
add(y,multiply(x,y)) = y,
inference(subst,[],[refute_0_498:[bind(Y,$fot(x)),bind(Z,$fot(y))]]) ).
cnf(refute_0_500,plain,
( multiply(x,y) != z
| add(y,multiply(x,y)) != y
| add(y,z) = y ),
introduced(tautology,[equality,[$cnf( $equal(add(y,multiply(x,y)),y) ),[0,1],$fot(z)]]) ).
cnf(refute_0_501,plain,
( add(y,multiply(x,y)) != y
| add(y,z) = y ),
inference(resolve,[$cnf( $equal(multiply(x,y),z) )],[x_times_y,refute_0_500]) ).
cnf(refute_0_502,plain,
add(y,z) = y,
inference(resolve,[$cnf( $equal(add(y,multiply(x,y)),y) )],[refute_0_499,refute_0_501]) ).
cnf(refute_0_503,plain,
( add(multiply(X,y),z) != multiply(add(X,z),add(y,z))
| add(y,z) != y
| add(multiply(X,y),z) = multiply(add(X,z),y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,y),z),multiply(add(X,z),add(y,z))) ),[1,1],$fot(y)]]) ).
cnf(refute_0_504,plain,
( add(multiply(X,y),z) != multiply(add(X,z),add(y,z))
| add(multiply(X,y),z) = multiply(add(X,z),y) ),
inference(resolve,[$cnf( $equal(add(y,z),y) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
add(multiply(X,y),z) = multiply(add(X,z),y),
inference(resolve,[$cnf( $equal(add(multiply(X,y),z),multiply(add(X,z),add(y,z))) )],[refute_0_1,refute_0_504]) ).
cnf(refute_0_506,plain,
add(multiply(X,add(X,Z)),Z) = multiply(add(X,Z),add(add(X,Z),Z)),
inference(subst,[],[distributivity1:[bind(Y,$fot(add(X,Z)))]]) ).
cnf(refute_0_507,plain,
add(multiply(X_13,additive_identity),X_14) = multiply(X_14,add(X_13,X_14)),
inference(subst,[],[refute_0_66:[bind(X_10,$fot(X_13)),bind(X_12,$fot(X_14))]]) ).
cnf(refute_0_508,plain,
add(X_14,X_13) = add(X_13,X_14),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_14)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_509,plain,
( add(X_14,X_13) != add(X_13,X_14)
| add(X_13,X_14) = add(X_14,X_13) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(X_14,X_13))),bind(Y0,$fot(add(X_13,X_14)))]]) ).
cnf(refute_0_510,plain,
add(X_13,X_14) = add(X_14,X_13),
inference(resolve,[$cnf( $equal(add(X_14,X_13),add(X_13,X_14)) )],[refute_0_508,refute_0_509]) ).
cnf(refute_0_511,plain,
( add(X_13,X_14) != add(X_14,X_13)
| add(multiply(X_13,additive_identity),X_14) != multiply(X_14,add(X_13,X_14))
| add(multiply(X_13,additive_identity),X_14) = multiply(X_14,add(X_14,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_13,additive_identity),X_14),multiply(X_14,add(X_13,X_14))) ),[1,1],$fot(add(X_14,X_13))]]) ).
cnf(refute_0_512,plain,
( add(multiply(X_13,additive_identity),X_14) != multiply(X_14,add(X_13,X_14))
| add(multiply(X_13,additive_identity),X_14) = multiply(X_14,add(X_14,X_13)) ),
inference(resolve,[$cnf( $equal(add(X_13,X_14),add(X_14,X_13)) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
add(multiply(X_13,additive_identity),X_14) = multiply(X_14,add(X_14,X_13)),
inference(resolve,[$cnf( $equal(add(multiply(X_13,additive_identity),X_14),multiply(X_14,add(X_13,X_14))) )],[refute_0_507,refute_0_512]) ).
cnf(refute_0_514,plain,
add(multiply(Z,additive_identity),add(X,Z)) = multiply(add(X,Z),add(add(X,Z),Z)),
inference(subst,[],[refute_0_513:[bind(X_13,$fot(Z)),bind(X_14,$fot(add(X,Z)))]]) ).
cnf(refute_0_515,plain,
( add(multiply(Z,additive_identity),add(X,Z)) != multiply(add(X,Z),add(add(X,Z),Z))
| multiply(add(X,Z),add(add(X,Z),Z)) = add(multiply(Z,additive_identity),add(X,Z)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(multiply(Z,additive_identity),add(X,Z)))),bind(Y0,$fot(multiply(add(X,Z),add(add(X,Z),Z))))]]) ).
cnf(refute_0_516,plain,
multiply(add(X,Z),add(add(X,Z),Z)) = add(multiply(Z,additive_identity),add(X,Z)),
inference(resolve,[$cnf( $equal(add(multiply(Z,additive_identity),add(X,Z)),multiply(add(X,Z),add(add(X,Z),Z))) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
( multiply(add(X,Z),add(add(X,Z),Z)) != add(multiply(Z,additive_identity),add(X,Z))
| add(multiply(X,add(X,Z)),Z) != multiply(add(X,Z),add(add(X,Z),Z))
| add(multiply(X,add(X,Z)),Z) = add(multiply(Z,additive_identity),add(X,Z)) ),
introduced(tautology,[equality,[$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_518,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( $equal(multiply(add(X,Z),add(add(X,Z),Z)),add(multiply(Z,additive_identity),add(X,Z))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
add(multiply(X,add(X,Z)),Z) = add(multiply(Z,additive_identity),add(X,Z)),
inference(resolve,[$cnf( $equal(add(multiply(X,add(X,Z)),Z),multiply(add(X,Z),add(add(X,Z),Z))) )],[refute_0_506,refute_0_518]) ).
cnf(refute_0_520,plain,
add(multiply(X,add(X,Z)),Z) = add(Z,multiply(X,add(X,Z))),
inference(subst,[],[refute_0_250:[bind(Y,$fot(multiply(X,add(X,Z)))),bind(X_22,$fot(Z))]]) ).
cnf(refute_0_521,plain,
( add(multiply(X,add(X,Z)),Z) != add(Z,multiply(X,add(X,Z)))
| add(multiply(X,add(X,Z)),Z) != add(multiply(Z,additive_identity),add(X,Z))
| add(Z,multiply(X,add(X,Z))) = add(multiply(Z,additive_identity),add(X,Z)) ),
introduced(tautology,[equality,[$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_522,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( $equal(add(multiply(X,add(X,Z)),Z),add(Z,multiply(X,add(X,Z)))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
add(Z,multiply(X,add(X,Z))) = add(multiply(Z,additive_identity),add(X,Z)),
inference(resolve,[$cnf( $equal(add(multiply(X,add(X,Z)),Z),add(multiply(Z,additive_identity),add(X,Z))) )],[refute_0_519,refute_0_522]) ).
cnf(refute_0_524,plain,
add(Z,multiply(X,add(X,Z))) = add(Z,multiply(X,add(X,Z))),
introduced(tautology,[refl,[$fot(add(Z,multiply(X,add(X,Z))))]]) ).
cnf(refute_0_525,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_526,plain,
( multiply(X,add(X,Z)) != X
| add(Z,multiply(X,add(X,Z))) = add(Z,X) ),
inference(resolve,[$cnf( $equal(add(Z,multiply(X,add(X,Z))),add(Z,multiply(X,add(X,Z)))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
add(Z,multiply(X,add(X,Z))) = add(Z,X),
inference(resolve,[$cnf( $equal(multiply(X,add(X,Z)),X) )],[refute_0_490,refute_0_526]) ).
cnf(refute_0_528,plain,
( add(Z,multiply(X,add(X,Z))) != add(Z,X)
| add(Z,multiply(X,add(X,Z))) != add(multiply(Z,additive_identity),add(X,Z))
| add(Z,X) = add(multiply(Z,additive_identity),add(X,Z)) ),
introduced(tautology,[equality,[$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_529,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( $equal(add(Z,multiply(X,add(X,Z))),add(Z,X)) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
add(additive_identity,add(X,Z)) = add(X,Z),
inference(subst,[],[additive_id2:[bind(X,$fot(add(X,Z)))]]) ).
cnf(refute_0_531,plain,
multiply(Z,additive_identity) = additive_identity,
inference(subst,[],[refute_0_308:[bind(X_42,$fot(Z))]]) ).
cnf(refute_0_532,plain,
add(multiply(Z,additive_identity),add(X,Z)) = add(multiply(Z,additive_identity),add(X,Z)),
introduced(tautology,[refl,[$fot(add(multiply(Z,additive_identity),add(X,Z)))]]) ).
cnf(refute_0_533,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_534,plain,
( multiply(Z,additive_identity) != additive_identity
| add(multiply(Z,additive_identity),add(X,Z)) = add(additive_identity,add(X,Z)) ),
inference(resolve,[$cnf( $equal(add(multiply(Z,additive_identity),add(X,Z)),add(multiply(Z,additive_identity),add(X,Z))) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
add(multiply(Z,additive_identity),add(X,Z)) = add(additive_identity,add(X,Z)),
inference(resolve,[$cnf( $equal(multiply(Z,additive_identity),additive_identity) )],[refute_0_531,refute_0_534]) ).
cnf(refute_0_536,plain,
( add(multiply(Z,additive_identity),add(X,Z)) != add(additive_identity,add(X,Z))
| add(additive_identity,add(X,Z)) != add(X,Z)
| add(multiply(Z,additive_identity),add(X,Z)) = add(X,Z) ),
inference(subst,[],[refute_0_206:[bind(X0,$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_537,plain,
( add(additive_identity,add(X,Z)) != add(X,Z)
| add(multiply(Z,additive_identity),add(X,Z)) = add(X,Z) ),
inference(resolve,[$cnf( $equal(add(multiply(Z,additive_identity),add(X,Z)),add(additive_identity,add(X,Z))) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
add(multiply(Z,additive_identity),add(X,Z)) = add(X,Z),
inference(resolve,[$cnf( $equal(add(additive_identity,add(X,Z)),add(X,Z)) )],[refute_0_530,refute_0_537]) ).
cnf(refute_0_539,plain,
( add(Z,X) != add(multiply(Z,additive_identity),add(X,Z))
| add(multiply(Z,additive_identity),add(X,Z)) != add(X,Z)
| add(Z,X) = add(X,Z) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(Z,X),add(X,Z)) ),[0],$fot(add(multiply(Z,additive_identity),add(X,Z)))]]) ).
cnf(refute_0_540,plain,
( add(Z,X) != add(multiply(Z,additive_identity),add(X,Z))
| add(Z,X) = add(X,Z) ),
inference(resolve,[$cnf( $equal(add(multiply(Z,additive_identity),add(X,Z)),add(X,Z)) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
( add(Z,multiply(X,add(X,Z))) != add(multiply(Z,additive_identity),add(X,Z))
| add(Z,X) = add(X,Z) ),
inference(resolve,[$cnf( $equal(add(Z,X),add(multiply(Z,additive_identity),add(X,Z))) )],[refute_0_529,refute_0_540]) ).
cnf(refute_0_542,plain,
add(Z,X) = add(X,Z),
inference(resolve,[$cnf( $equal(add(Z,multiply(X,add(X,Z))),add(multiply(Z,additive_identity),add(X,Z))) )],[refute_0_523,refute_0_541]) ).
cnf(refute_0_543,plain,
( add(Z,X) != add(X,Z)
| add(X,Z) = add(Z,X) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(Z,X))),bind(Y0,$fot(add(X,Z)))]]) ).
cnf(refute_0_544,plain,
add(X,Z) = add(Z,X),
inference(resolve,[$cnf( $equal(add(Z,X),add(X,Z)) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
add(multiply(X,y),z) = add(z,multiply(X,y)),
inference(subst,[],[refute_0_544:[bind(X,$fot(multiply(X,y))),bind(Z,$fot(z))]]) ).
cnf(refute_0_546,plain,
( add(multiply(X,y),z) != multiply(add(X,z),y)
| add(multiply(X,y),z) != add(z,multiply(X,y))
| add(z,multiply(X,y)) = multiply(add(X,z),y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,y),z),multiply(add(X,z),y)) ),[0],$fot(add(z,multiply(X,y)))]]) ).
cnf(refute_0_547,plain,
( add(multiply(X,y),z) != multiply(add(X,z),y)
| add(z,multiply(X,y)) = multiply(add(X,z),y) ),
inference(resolve,[$cnf( $equal(add(multiply(X,y),z),add(z,multiply(X,y))) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
multiply(add(X,z),y) = multiply(y,add(X,z)),
inference(subst,[],[refute_0_62:[bind(X,$fot(y)),bind(Y,$fot(add(X,z)))]]) ).
cnf(refute_0_549,plain,
( multiply(add(X,z),y) != multiply(y,add(X,z))
| add(z,multiply(X,y)) != multiply(add(X,z),y)
| add(z,multiply(X,y)) = multiply(y,add(X,z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(z,multiply(X,y)),multiply(add(X,z),y)) ),[1],$fot(multiply(y,add(X,z)))]]) ).
cnf(refute_0_550,plain,
( add(z,multiply(X,y)) != multiply(add(X,z),y)
| add(z,multiply(X,y)) = multiply(y,add(X,z)) ),
inference(resolve,[$cnf( $equal(multiply(add(X,z),y),multiply(y,add(X,z))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
( add(multiply(X,y),z) != multiply(add(X,z),y)
| add(z,multiply(X,y)) = multiply(y,add(X,z)) ),
inference(resolve,[$cnf( $equal(add(z,multiply(X,y)),multiply(add(X,z),y)) )],[refute_0_547,refute_0_550]) ).
cnf(refute_0_552,plain,
add(z,multiply(X,y)) = multiply(y,add(X,z)),
inference(resolve,[$cnf( $equal(add(multiply(X,y),z),multiply(add(X,z),y)) )],[refute_0_505,refute_0_551]) ).
cnf(refute_0_553,plain,
add(z,multiply(x,y)) = multiply(y,add(x,z)),
inference(subst,[],[refute_0_552:[bind(X,$fot(x))]]) ).
cnf(refute_0_554,plain,
( multiply(x,y) != z
| add(z,multiply(x,y)) != multiply(y,add(x,z))
| add(z,z) = multiply(y,add(x,z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(z,multiply(x,y)),multiply(y,add(x,z))) ),[0,1],$fot(z)]]) ).
cnf(refute_0_555,plain,
( add(z,multiply(x,y)) != multiply(y,add(x,z))
| add(z,z) = multiply(y,add(x,z)) ),
inference(resolve,[$cnf( $equal(multiply(x,y),z) )],[x_times_y,refute_0_554]) ).
cnf(refute_0_556,plain,
add(z,z) = multiply(y,add(x,z)),
inference(resolve,[$cnf( $equal(add(z,multiply(x,y)),multiply(y,add(x,z))) )],[refute_0_553,refute_0_555]) ).
cnf(refute_0_557,plain,
( X_49 != add(X_49,X_49)
| add(X_49,X_49) = X_49 ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(X_49)),bind(Y0,$fot(add(X_49,X_49)))]]) ).
cnf(refute_0_558,plain,
add(X_49,X_49) = X_49,
inference(resolve,[$cnf( $equal(X_49,add(X_49,X_49)) )],[refute_0_20,refute_0_557]) ).
cnf(refute_0_559,plain,
add(z,z) = z,
inference(subst,[],[refute_0_558:[bind(X_49,$fot(z))]]) ).
cnf(refute_0_560,plain,
( add(z,z) != multiply(y,add(x,z))
| add(z,z) != z
| z = multiply(y,add(x,z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(z,z),multiply(y,add(x,z))) ),[0],$fot(z)]]) ).
cnf(refute_0_561,plain,
( add(z,z) != multiply(y,add(x,z))
| z = multiply(y,add(x,z)) ),
inference(resolve,[$cnf( $equal(add(z,z),z) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
z = multiply(y,add(x,z)),
inference(resolve,[$cnf( $equal(add(z,z),multiply(y,add(x,z))) )],[refute_0_556,refute_0_561]) ).
cnf(refute_0_563,plain,
( z != multiply(y,add(x,z))
| multiply(y,add(x,z)) = z ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(z)),bind(Y0,$fot(multiply(y,add(x,z))))]]) ).
cnf(refute_0_564,plain,
multiply(y,add(x,z)) = z,
inference(resolve,[$cnf( $equal(z,multiply(y,add(x,z))) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
( multiply(add(y,X_62),add(x,z)) != add(multiply(y,add(x,z)),multiply(X_62,add(x,z)))
| multiply(y,add(x,z)) != z
| multiply(add(y,X_62),add(x,z)) = add(z,multiply(X_62,add(x,z))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(y,X_62),add(x,z)),add(multiply(y,add(x,z)),multiply(X_62,add(x,z)))) ),[1,0],$fot(z)]]) ).
cnf(refute_0_566,plain,
( multiply(add(y,X_62),add(x,z)) != add(multiply(y,add(x,z)),multiply(X_62,add(x,z)))
| multiply(add(y,X_62),add(x,z)) = add(z,multiply(X_62,add(x,z))) ),
inference(resolve,[$cnf( $equal(multiply(y,add(x,z)),z) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
multiply(add(y,X_62),add(x,z)) = add(z,multiply(X_62,add(x,z))),
inference(resolve,[$cnf( $equal(multiply(add(y,X_62),add(x,z)),add(multiply(y,add(x,z)),multiply(X_62,add(x,z)))) )],[refute_0_0,refute_0_566]) ).
cnf(refute_0_568,plain,
multiply(add(y,X_62),add(x,z)) = multiply(add(x,z),add(y,X_62)),
inference(subst,[],[refute_0_62:[bind(X,$fot(add(x,z))),bind(Y,$fot(add(y,X_62)))]]) ).
cnf(refute_0_569,plain,
( multiply(add(y,X_62),add(x,z)) != multiply(add(x,z),add(y,X_62))
| multiply(add(y,X_62),add(x,z)) != add(z,multiply(X_62,add(x,z)))
| multiply(add(x,z),add(y,X_62)) = add(z,multiply(X_62,add(x,z))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(y,X_62),add(x,z)),add(z,multiply(X_62,add(x,z)))) ),[0],$fot(multiply(add(x,z),add(y,X_62)))]]) ).
cnf(refute_0_570,plain,
( multiply(add(y,X_62),add(x,z)) != add(z,multiply(X_62,add(x,z)))
| multiply(add(x,z),add(y,X_62)) = add(z,multiply(X_62,add(x,z))) ),
inference(resolve,[$cnf( $equal(multiply(add(y,X_62),add(x,z)),multiply(add(x,z),add(y,X_62))) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
add(z,multiply(Y,add(x,z))) = multiply(add(z,Y),add(z,add(x,z))),
inference(subst,[],[distributivity2:[bind(X,$fot(z)),bind(Z,$fot(add(x,z)))]]) ).
cnf(refute_0_572,plain,
add(add(x,z),multiply(y,add(x,z))) = add(x,z),
inference(subst,[],[refute_0_498:[bind(Y,$fot(y)),bind(Z,$fot(add(x,z)))]]) ).
cnf(refute_0_573,plain,
( multiply(y,add(x,z)) != z
| add(add(x,z),multiply(y,add(x,z))) != add(x,z)
| add(add(x,z),z) = add(x,z) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(x,z),multiply(y,add(x,z))),add(x,z)) ),[0,1],$fot(z)]]) ).
cnf(refute_0_574,plain,
( add(add(x,z),multiply(y,add(x,z))) != add(x,z)
| add(add(x,z),z) = add(x,z) ),
inference(resolve,[$cnf( $equal(multiply(y,add(x,z)),z) )],[refute_0_564,refute_0_573]) ).
cnf(refute_0_575,plain,
add(add(x,z),z) = add(x,z),
inference(resolve,[$cnf( $equal(add(add(x,z),multiply(y,add(x,z))),add(x,z)) )],[refute_0_572,refute_0_574]) ).
cnf(refute_0_576,plain,
add(add(x,z),z) = add(z,add(x,z)),
inference(subst,[],[refute_0_544:[bind(X,$fot(add(x,z))),bind(Z,$fot(z))]]) ).
cnf(refute_0_577,plain,
( add(add(x,z),z) != add(x,z)
| add(add(x,z),z) != add(z,add(x,z))
| add(z,add(x,z)) = add(x,z) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(x,z),z),add(x,z)) ),[0],$fot(add(z,add(x,z)))]]) ).
cnf(refute_0_578,plain,
( add(add(x,z),z) != add(x,z)
| add(z,add(x,z)) = add(x,z) ),
inference(resolve,[$cnf( $equal(add(add(x,z),z),add(z,add(x,z))) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
add(z,add(x,z)) = add(x,z),
inference(resolve,[$cnf( $equal(add(add(x,z),z),add(x,z)) )],[refute_0_575,refute_0_578]) ).
cnf(refute_0_580,plain,
( add(z,multiply(Y,add(x,z))) != multiply(add(z,Y),add(z,add(x,z)))
| add(z,add(x,z)) != add(x,z)
| add(z,multiply(Y,add(x,z))) = multiply(add(z,Y),add(x,z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(z,multiply(Y,add(x,z))),multiply(add(z,Y),add(z,add(x,z)))) ),[1,1],$fot(add(x,z))]]) ).
cnf(refute_0_581,plain,
( add(z,multiply(Y,add(x,z))) != multiply(add(z,Y),add(z,add(x,z)))
| add(z,multiply(Y,add(x,z))) = multiply(add(z,Y),add(x,z)) ),
inference(resolve,[$cnf( $equal(add(z,add(x,z)),add(x,z)) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
add(z,multiply(Y,add(x,z))) = multiply(add(z,Y),add(x,z)),
inference(resolve,[$cnf( $equal(add(z,multiply(Y,add(x,z))),multiply(add(z,Y),add(z,add(x,z)))) )],[refute_0_571,refute_0_581]) ).
cnf(refute_0_583,plain,
add(multiply(Y,x),z) = add(z,multiply(Y,x)),
inference(subst,[],[refute_0_544:[bind(X,$fot(multiply(Y,x))),bind(Z,$fot(z))]]) ).
cnf(refute_0_584,plain,
add(multiply(X_10,X_11),X_12) = multiply(add(X_10,X_12),add(X_11,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_585,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_586,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_24:[bind(X0,$fot(add(X_12,X_10))),bind(Y0,$fot(add(X_10,X_12)))]]) ).
cnf(refute_0_587,plain,
add(X_10,X_12) = add(X_12,X_10),
inference(resolve,[$cnf( $equal(add(X_12,X_10),add(X_10,X_12)) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
( add(X_10,X_12) != add(X_12,X_10)
| add(multiply(X_10,X_11),X_12) != multiply(add(X_10,X_12),add(X_11,X_12))
| add(multiply(X_10,X_11),X_12) = multiply(add(X_12,X_10),add(X_11,X_12)) ),
introduced(tautology,[equality,[$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_589,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( $equal(add(X_10,X_12),add(X_12,X_10)) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
add(multiply(X_10,X_11),X_12) = multiply(add(X_12,X_10),add(X_11,X_12)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),X_12),multiply(add(X_10,X_12),add(X_11,X_12))) )],[refute_0_584,refute_0_589]) ).
cnf(refute_0_591,plain,
( add(multiply(X_10,X_11),X_12) != multiply(add(X_12,X_10),add(X_11,X_12))
| multiply(add(X_12,X_10),add(X_11,X_12)) = add(multiply(X_10,X_11),X_12) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(multiply(X_10,X_11),X_12))),bind(Y0,$fot(multiply(add(X_12,X_10),add(X_11,X_12))))]]) ).
cnf(refute_0_592,plain,
multiply(add(X_12,X_10),add(X_11,X_12)) = add(multiply(X_10,X_11),X_12),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),X_12),multiply(add(X_12,X_10),add(X_11,X_12))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
multiply(add(z,Y),add(x,z)) = add(multiply(Y,x),z),
inference(subst,[],[refute_0_592:[bind(X_10,$fot(Y)),bind(X_11,$fot(x)),bind(X_12,$fot(z))]]) ).
cnf(refute_0_594,plain,
( multiply(add(z,Y),add(x,z)) != add(multiply(Y,x),z)
| add(multiply(Y,x),z) != add(z,multiply(Y,x))
| multiply(add(z,Y),add(x,z)) = add(z,multiply(Y,x)) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(multiply(add(z,Y),add(x,z)))),bind(Y0,$fot(add(multiply(Y,x),z))),bind(Z0,$fot(add(z,multiply(Y,x))))]]) ).
cnf(refute_0_595,plain,
( add(multiply(Y,x),z) != add(z,multiply(Y,x))
| multiply(add(z,Y),add(x,z)) = add(z,multiply(Y,x)) ),
inference(resolve,[$cnf( $equal(multiply(add(z,Y),add(x,z)),add(multiply(Y,x),z)) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
multiply(add(z,Y),add(x,z)) = add(z,multiply(Y,x)),
inference(resolve,[$cnf( $equal(add(multiply(Y,x),z),add(z,multiply(Y,x))) )],[refute_0_583,refute_0_595]) ).
cnf(refute_0_597,plain,
( multiply(add(z,Y),add(x,z)) != add(z,multiply(Y,x))
| add(z,multiply(Y,add(x,z))) != multiply(add(z,Y),add(x,z))
| add(z,multiply(Y,add(x,z))) = add(z,multiply(Y,x)) ),
introduced(tautology,[equality,[$cnf( $equal(add(z,multiply(Y,add(x,z))),multiply(add(z,Y),add(x,z))) ),[1],$fot(add(z,multiply(Y,x)))]]) ).
cnf(refute_0_598,plain,
( add(z,multiply(Y,add(x,z))) != multiply(add(z,Y),add(x,z))
| add(z,multiply(Y,add(x,z))) = add(z,multiply(Y,x)) ),
inference(resolve,[$cnf( $equal(multiply(add(z,Y),add(x,z)),add(z,multiply(Y,x))) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
add(z,multiply(Y,add(x,z))) = add(z,multiply(Y,x)),
inference(resolve,[$cnf( $equal(add(z,multiply(Y,add(x,z))),multiply(add(z,Y),add(x,z))) )],[refute_0_582,refute_0_598]) ).
cnf(refute_0_600,plain,
add(z,multiply(X_62,add(x,z))) = add(z,multiply(X_62,x)),
inference(subst,[],[refute_0_599:[bind(Y,$fot(X_62))]]) ).
cnf(refute_0_601,plain,
( multiply(add(x,z),add(y,X_62)) != add(z,multiply(X_62,add(x,z)))
| add(z,multiply(X_62,add(x,z))) != add(z,multiply(X_62,x))
| multiply(add(x,z),add(y,X_62)) = add(z,multiply(X_62,x)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(x,z),add(y,X_62)),add(z,multiply(X_62,x))) ),[0],$fot(add(z,multiply(X_62,add(x,z))))]]) ).
cnf(refute_0_602,plain,
( multiply(add(x,z),add(y,X_62)) != add(z,multiply(X_62,add(x,z)))
| multiply(add(x,z),add(y,X_62)) = add(z,multiply(X_62,x)) ),
inference(resolve,[$cnf( $equal(add(z,multiply(X_62,add(x,z))),add(z,multiply(X_62,x))) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
( multiply(add(y,X_62),add(x,z)) != add(z,multiply(X_62,add(x,z)))
| multiply(add(x,z),add(y,X_62)) = add(z,multiply(X_62,x)) ),
inference(resolve,[$cnf( $equal(multiply(add(x,z),add(y,X_62)),add(z,multiply(X_62,add(x,z)))) )],[refute_0_570,refute_0_602]) ).
cnf(refute_0_604,plain,
multiply(add(x,z),add(y,X_62)) = add(z,multiply(X_62,x)),
inference(resolve,[$cnf( $equal(multiply(add(y,X_62),add(x,z)),add(z,multiply(X_62,add(x,z)))) )],[refute_0_567,refute_0_603]) ).
cnf(refute_0_605,plain,
multiply(add(x,z),add(y,add(x,inverse(z)))) = add(z,multiply(add(x,inverse(z)),x)),
inference(subst,[],[refute_0_604:[bind(X_62,$fot(add(x,inverse(z))))]]) ).
cnf(refute_0_606,plain,
add(add(x,inverse(z)),multiply(y,add(x,inverse(z)))) = add(x,inverse(z)),
inference(subst,[],[refute_0_498:[bind(Y,$fot(y)),bind(Z,$fot(add(x,inverse(z))))]]) ).
cnf(refute_0_607,plain,
multiply(add(X_61,x),y) = add(multiply(X_61,y),multiply(x,y)),
inference(subst,[],[distributivity3:[bind(X,$fot(X_61)),bind(Y,$fot(x)),bind(Z,$fot(y))]]) ).
cnf(refute_0_608,plain,
( multiply(add(X_61,x),y) != add(multiply(X_61,y),multiply(x,y))
| multiply(x,y) != z
| multiply(add(X_61,x),y) = add(multiply(X_61,y),z) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_61,x),y),add(multiply(X_61,y),multiply(x,y))) ),[1,1],$fot(z)]]) ).
cnf(refute_0_609,plain,
( multiply(add(X_61,x),y) != add(multiply(X_61,y),multiply(x,y))
| multiply(add(X_61,x),y) = add(multiply(X_61,y),z) ),
inference(resolve,[$cnf( $equal(multiply(x,y),z) )],[x_times_y,refute_0_608]) ).
cnf(refute_0_610,plain,
multiply(add(X_61,x),y) = add(multiply(X_61,y),z),
inference(resolve,[$cnf( $equal(multiply(add(X_61,x),y),add(multiply(X_61,y),multiply(x,y))) )],[refute_0_607,refute_0_609]) ).
cnf(refute_0_611,plain,
multiply(add(X_61,x),y) = multiply(y,add(X_61,x)),
inference(subst,[],[refute_0_62:[bind(X,$fot(y)),bind(Y,$fot(add(X_61,x)))]]) ).
cnf(refute_0_612,plain,
( multiply(add(X_61,x),y) != multiply(y,add(X_61,x))
| multiply(add(X_61,x),y) != add(multiply(X_61,y),z)
| multiply(y,add(X_61,x)) = add(multiply(X_61,y),z) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_61,x),y),add(multiply(X_61,y),z)) ),[0],$fot(multiply(y,add(X_61,x)))]]) ).
cnf(refute_0_613,plain,
( multiply(add(X_61,x),y) != add(multiply(X_61,y),z)
| multiply(y,add(X_61,x)) = add(multiply(X_61,y),z) ),
inference(resolve,[$cnf( $equal(multiply(add(X_61,x),y),multiply(y,add(X_61,x))) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
add(z,multiply(X_61,y)) = multiply(y,add(X_61,z)),
inference(subst,[],[refute_0_552:[bind(X,$fot(X_61))]]) ).
cnf(refute_0_615,plain,
add(multiply(X_61,y),z) = add(z,multiply(X_61,y)),
inference(subst,[],[refute_0_544:[bind(X,$fot(multiply(X_61,y))),bind(Z,$fot(z))]]) ).
cnf(refute_0_616,plain,
( add(multiply(X_61,y),z) != add(z,multiply(X_61,y))
| add(z,multiply(X_61,y)) != multiply(y,add(X_61,z))
| add(multiply(X_61,y),z) = multiply(y,add(X_61,z)) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(multiply(X_61,y),z))),bind(Y0,$fot(add(z,multiply(X_61,y)))),bind(Z0,$fot(multiply(y,add(X_61,z))))]]) ).
cnf(refute_0_617,plain,
( add(z,multiply(X_61,y)) != multiply(y,add(X_61,z))
| add(multiply(X_61,y),z) = multiply(y,add(X_61,z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_61,y),z),add(z,multiply(X_61,y))) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
add(multiply(X_61,y),z) = multiply(y,add(X_61,z)),
inference(resolve,[$cnf( $equal(add(z,multiply(X_61,y)),multiply(y,add(X_61,z))) )],[refute_0_614,refute_0_617]) ).
cnf(refute_0_619,plain,
( multiply(y,add(X_61,x)) != add(multiply(X_61,y),z)
| add(multiply(X_61,y),z) != multiply(y,add(X_61,z))
| multiply(y,add(X_61,x)) = multiply(y,add(X_61,z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(y,add(X_61,x)),multiply(y,add(X_61,z))) ),[0],$fot(add(multiply(X_61,y),z))]]) ).
cnf(refute_0_620,plain,
( multiply(y,add(X_61,x)) != add(multiply(X_61,y),z)
| multiply(y,add(X_61,x)) = multiply(y,add(X_61,z)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_61,y),z),multiply(y,add(X_61,z))) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
( multiply(add(X_61,x),y) != add(multiply(X_61,y),z)
| multiply(y,add(X_61,x)) = multiply(y,add(X_61,z)) ),
inference(resolve,[$cnf( $equal(multiply(y,add(X_61,x)),add(multiply(X_61,y),z)) )],[refute_0_613,refute_0_620]) ).
cnf(refute_0_622,plain,
multiply(y,add(X_61,x)) = multiply(y,add(X_61,z)),
inference(resolve,[$cnf( $equal(multiply(add(X_61,x),y),add(multiply(X_61,y),z)) )],[refute_0_610,refute_0_621]) ).
cnf(refute_0_623,plain,
multiply(y,add(X_66,x)) = multiply(y,add(X_66,z)),
inference(subst,[],[refute_0_622:[bind(X_61,$fot(X_66))]]) ).
cnf(refute_0_624,plain,
add(z,X_66) = add(X_66,z),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(z)),bind(Y,$fot(X_66))]]) ).
cnf(refute_0_625,plain,
( add(z,X_66) != add(X_66,z)
| add(X_66,z) = add(z,X_66) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(z,X_66))),bind(Y0,$fot(add(X_66,z)))]]) ).
cnf(refute_0_626,plain,
add(X_66,z) = add(z,X_66),
inference(resolve,[$cnf( $equal(add(z,X_66),add(X_66,z)) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
( multiply(y,add(X_66,x)) != multiply(y,add(X_66,z))
| add(X_66,z) != add(z,X_66)
| multiply(y,add(X_66,x)) = multiply(y,add(z,X_66)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(y,add(X_66,x)),multiply(y,add(X_66,z))) ),[1,1],$fot(add(z,X_66))]]) ).
cnf(refute_0_628,plain,
( multiply(y,add(X_66,x)) != multiply(y,add(X_66,z))
| multiply(y,add(X_66,x)) = multiply(y,add(z,X_66)) ),
inference(resolve,[$cnf( $equal(add(X_66,z),add(z,X_66)) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
multiply(y,add(X_66,x)) = multiply(y,add(z,X_66)),
inference(resolve,[$cnf( $equal(multiply(y,add(X_66,x)),multiply(y,add(X_66,z))) )],[refute_0_623,refute_0_628]) ).
cnf(refute_0_630,plain,
multiply(y,add(inverse(z),x)) = multiply(y,add(z,inverse(z))),
inference(subst,[],[refute_0_629:[bind(X_66,$fot(inverse(z)))]]) ).
cnf(refute_0_631,plain,
add(z,inverse(z)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(z))]]) ).
cnf(refute_0_632,plain,
( multiply(y,add(inverse(z),x)) != multiply(y,add(z,inverse(z)))
| add(z,inverse(z)) != multiplicative_identity
| multiply(y,add(inverse(z),x)) = multiply(y,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(y,add(inverse(z),x)),multiply(y,add(z,inverse(z)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_633,plain,
( multiply(y,add(inverse(z),x)) != multiply(y,add(z,inverse(z)))
| multiply(y,add(inverse(z),x)) = multiply(y,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(z,inverse(z)),multiplicative_identity) )],[refute_0_631,refute_0_632]) ).
cnf(refute_0_634,plain,
multiply(y,add(inverse(z),x)) = multiply(y,multiplicative_identity),
inference(resolve,[$cnf( $equal(multiply(y,add(inverse(z),x)),multiply(y,add(z,inverse(z)))) )],[refute_0_630,refute_0_633]) ).
cnf(refute_0_635,plain,
multiply(y,add(X_75,x)) = multiply(y,add(z,X_75)),
inference(subst,[],[refute_0_629:[bind(X_66,$fot(X_75))]]) ).
cnf(refute_0_636,plain,
add(x,X_75) = add(X_75,x),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(x)),bind(Y,$fot(X_75))]]) ).
cnf(refute_0_637,plain,
( add(x,X_75) != add(X_75,x)
| add(X_75,x) = add(x,X_75) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(x,X_75))),bind(Y0,$fot(add(X_75,x)))]]) ).
cnf(refute_0_638,plain,
add(X_75,x) = add(x,X_75),
inference(resolve,[$cnf( $equal(add(x,X_75),add(X_75,x)) )],[refute_0_636,refute_0_637]) ).
cnf(refute_0_639,plain,
( multiply(y,add(X_75,x)) != multiply(y,add(z,X_75))
| add(X_75,x) != add(x,X_75)
| multiply(y,add(x,X_75)) = multiply(y,add(z,X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(y,add(X_75,x)),multiply(y,add(z,X_75))) ),[0,1],$fot(add(x,X_75))]]) ).
cnf(refute_0_640,plain,
( multiply(y,add(X_75,x)) != multiply(y,add(z,X_75))
| multiply(y,add(x,X_75)) = multiply(y,add(z,X_75)) ),
inference(resolve,[$cnf( $equal(add(X_75,x),add(x,X_75)) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
multiply(y,add(x,X_75)) = multiply(y,add(z,X_75)),
inference(resolve,[$cnf( $equal(multiply(y,add(X_75,x)),multiply(y,add(z,X_75))) )],[refute_0_635,refute_0_640]) ).
cnf(refute_0_642,plain,
( multiply(y,add(x,X_75)) != multiply(y,add(z,X_75))
| multiply(y,add(z,X_75)) = multiply(y,add(x,X_75)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(y,add(x,X_75)))),bind(Y0,$fot(multiply(y,add(z,X_75))))]]) ).
cnf(refute_0_643,plain,
multiply(y,add(z,X_75)) = multiply(y,add(x,X_75)),
inference(resolve,[$cnf( $equal(multiply(y,add(x,X_75)),multiply(y,add(z,X_75))) )],[refute_0_641,refute_0_642]) ).
cnf(refute_0_644,plain,
multiply(y,add(z,inverse(z))) = multiply(y,add(x,inverse(z))),
inference(subst,[],[refute_0_643:[bind(X_75,$fot(inverse(z)))]]) ).
cnf(refute_0_645,plain,
( multiply(y,add(inverse(z),x)) != multiply(y,add(z,inverse(z)))
| multiply(y,add(z,inverse(z))) != multiply(y,add(x,inverse(z)))
| multiply(y,add(inverse(z),x)) = multiply(y,add(x,inverse(z))) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(multiply(y,add(inverse(z),x)))),bind(Y0,$fot(multiply(y,add(z,inverse(z))))),bind(Z0,$fot(multiply(y,add(x,inverse(z)))))]]) ).
cnf(refute_0_646,plain,
( multiply(y,add(z,inverse(z))) != multiply(y,add(x,inverse(z)))
| multiply(y,add(inverse(z),x)) = multiply(y,add(x,inverse(z))) ),
inference(resolve,[$cnf( $equal(multiply(y,add(inverse(z),x)),multiply(y,add(z,inverse(z)))) )],[refute_0_630,refute_0_645]) ).
cnf(refute_0_647,plain,
multiply(y,add(inverse(z),x)) = multiply(y,add(x,inverse(z))),
inference(resolve,[$cnf( $equal(multiply(y,add(z,inverse(z))),multiply(y,add(x,inverse(z)))) )],[refute_0_644,refute_0_646]) ).
cnf(refute_0_648,plain,
( multiply(y,add(inverse(z),x)) != multiply(y,add(x,inverse(z)))
| multiply(y,add(inverse(z),x)) != multiply(y,multiplicative_identity)
| multiply(y,add(x,inverse(z))) = multiply(y,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(y,add(inverse(z),x)),multiply(y,multiplicative_identity)) ),[0],$fot(multiply(y,add(x,inverse(z))))]]) ).
cnf(refute_0_649,plain,
( multiply(y,add(inverse(z),x)) != multiply(y,multiplicative_identity)
| multiply(y,add(x,inverse(z))) = multiply(y,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(y,add(inverse(z),x)),multiply(y,add(x,inverse(z)))) )],[refute_0_647,refute_0_648]) ).
cnf(refute_0_650,plain,
multiply(y,multiplicative_identity) = y,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(y))]]) ).
cnf(refute_0_651,plain,
( multiply(y,add(x,inverse(z))) != multiply(y,multiplicative_identity)
| multiply(y,multiplicative_identity) != y
| multiply(y,add(x,inverse(z))) = y ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(y,add(x,inverse(z))),y) ),[0],$fot(multiply(y,multiplicative_identity))]]) ).
cnf(refute_0_652,plain,
( multiply(y,add(x,inverse(z))) != multiply(y,multiplicative_identity)
| multiply(y,add(x,inverse(z))) = y ),
inference(resolve,[$cnf( $equal(multiply(y,multiplicative_identity),y) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
( multiply(y,add(inverse(z),x)) != multiply(y,multiplicative_identity)
| multiply(y,add(x,inverse(z))) = y ),
inference(resolve,[$cnf( $equal(multiply(y,add(x,inverse(z))),multiply(y,multiplicative_identity)) )],[refute_0_649,refute_0_652]) ).
cnf(refute_0_654,plain,
multiply(y,add(x,inverse(z))) = y,
inference(resolve,[$cnf( $equal(multiply(y,add(inverse(z),x)),multiply(y,multiplicative_identity)) )],[refute_0_634,refute_0_653]) ).
cnf(refute_0_655,plain,
( multiply(y,add(x,inverse(z))) != y
| add(add(x,inverse(z)),multiply(y,add(x,inverse(z)))) != add(x,inverse(z))
| add(add(x,inverse(z)),y) = add(x,inverse(z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(x,inverse(z)),multiply(y,add(x,inverse(z)))),add(x,inverse(z))) ),[0,1],$fot(y)]]) ).
cnf(refute_0_656,plain,
( add(add(x,inverse(z)),multiply(y,add(x,inverse(z)))) != add(x,inverse(z))
| add(add(x,inverse(z)),y) = add(x,inverse(z)) ),
inference(resolve,[$cnf( $equal(multiply(y,add(x,inverse(z))),y) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
add(add(x,inverse(z)),y) = add(x,inverse(z)),
inference(resolve,[$cnf( $equal(add(add(x,inverse(z)),multiply(y,add(x,inverse(z)))),add(x,inverse(z))) )],[refute_0_606,refute_0_656]) ).
cnf(refute_0_658,plain,
add(add(x,inverse(z)),y) = add(y,add(x,inverse(z))),
inference(subst,[],[refute_0_544:[bind(X,$fot(add(x,inverse(z)))),bind(Z,$fot(y))]]) ).
cnf(refute_0_659,plain,
( add(add(x,inverse(z)),y) != add(x,inverse(z))
| add(add(x,inverse(z)),y) != add(y,add(x,inverse(z)))
| add(y,add(x,inverse(z))) = add(x,inverse(z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(x,inverse(z)),y),add(x,inverse(z))) ),[0],$fot(add(y,add(x,inverse(z))))]]) ).
cnf(refute_0_660,plain,
( add(add(x,inverse(z)),y) != add(x,inverse(z))
| add(y,add(x,inverse(z))) = add(x,inverse(z)) ),
inference(resolve,[$cnf( $equal(add(add(x,inverse(z)),y),add(y,add(x,inverse(z)))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
add(y,add(x,inverse(z))) = add(x,inverse(z)),
inference(resolve,[$cnf( $equal(add(add(x,inverse(z)),y),add(x,inverse(z))) )],[refute_0_657,refute_0_660]) ).
cnf(refute_0_662,plain,
( multiply(add(x,z),add(y,add(x,inverse(z)))) != add(z,multiply(add(x,inverse(z)),x))
| add(y,add(x,inverse(z))) != add(x,inverse(z))
| multiply(add(x,z),add(x,inverse(z))) = add(z,multiply(add(x,inverse(z)),x)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(x,z),add(y,add(x,inverse(z)))),add(z,multiply(add(x,inverse(z)),x))) ),[0,1],$fot(add(x,inverse(z)))]]) ).
cnf(refute_0_663,plain,
( multiply(add(x,z),add(y,add(x,inverse(z)))) != add(z,multiply(add(x,inverse(z)),x))
| multiply(add(x,z),add(x,inverse(z))) = add(z,multiply(add(x,inverse(z)),x)) ),
inference(resolve,[$cnf( $equal(add(y,add(x,inverse(z))),add(x,inverse(z))) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
multiply(add(x,z),add(x,inverse(z))) = add(z,multiply(add(x,inverse(z)),x)),
inference(resolve,[$cnf( $equal(multiply(add(x,z),add(y,add(x,inverse(z)))),add(z,multiply(add(x,inverse(z)),x))) )],[refute_0_605,refute_0_663]) ).
cnf(refute_0_665,plain,
add(additive_identity,x) = x,
inference(subst,[],[additive_id2:[bind(X,$fot(x))]]) ).
cnf(refute_0_666,plain,
add(x,additive_identity) = add(additive_identity,x),
inference(subst,[],[refute_0_544:[bind(X,$fot(x)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_667,plain,
( add(additive_identity,x) != x
| add(x,additive_identity) != add(additive_identity,x)
| add(x,additive_identity) = x ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(x,additive_identity))),bind(Y0,$fot(add(additive_identity,x))),bind(Z0,$fot(x))]]) ).
cnf(refute_0_668,plain,
( add(additive_identity,x) != x
| add(x,additive_identity) = x ),
inference(resolve,[$cnf( $equal(add(x,additive_identity),add(additive_identity,x)) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
add(x,additive_identity) = x,
inference(resolve,[$cnf( $equal(add(additive_identity,x),x) )],[refute_0_665,refute_0_668]) ).
cnf(refute_0_670,plain,
multiply(z,inverse(z)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(z))]]) ).
cnf(refute_0_671,plain,
add(x,multiply(z,inverse(z))) = add(x,multiply(z,inverse(z))),
introduced(tautology,[refl,[$fot(add(x,multiply(z,inverse(z))))]]) ).
cnf(refute_0_672,plain,
( multiply(z,inverse(z)) != additive_identity
| add(x,multiply(z,inverse(z))) != add(x,multiply(z,inverse(z)))
| add(x,multiply(z,inverse(z))) = add(x,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(x,multiply(z,inverse(z))),add(x,multiply(z,inverse(z)))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_673,plain,
( multiply(z,inverse(z)) != additive_identity
| add(x,multiply(z,inverse(z))) = add(x,additive_identity) ),
inference(resolve,[$cnf( $equal(add(x,multiply(z,inverse(z))),add(x,multiply(z,inverse(z)))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
add(x,multiply(z,inverse(z))) = add(x,additive_identity),
inference(resolve,[$cnf( $equal(multiply(z,inverse(z)),additive_identity) )],[refute_0_670,refute_0_673]) ).
cnf(refute_0_675,plain,
( add(x,multiply(z,inverse(z))) != add(x,additive_identity)
| add(x,additive_identity) != x
| add(x,multiply(z,inverse(z))) = x ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(x,multiply(z,inverse(z))))),bind(Y0,$fot(add(x,additive_identity))),bind(Z0,$fot(x))]]) ).
cnf(refute_0_676,plain,
( add(x,additive_identity) != x
| add(x,multiply(z,inverse(z))) = x ),
inference(resolve,[$cnf( $equal(add(x,multiply(z,inverse(z))),add(x,additive_identity)) )],[refute_0_674,refute_0_675]) ).
cnf(refute_0_677,plain,
add(x,multiply(z,inverse(z))) = x,
inference(resolve,[$cnf( $equal(add(x,additive_identity),x) )],[refute_0_669,refute_0_676]) ).
cnf(refute_0_678,plain,
( add(X,multiply(Y,Z)) != multiply(add(X,Y),add(X,Z))
| multiply(add(X,Y),add(X,Z)) = add(X,multiply(Y,Z)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(add(X,multiply(Y,Z)))),bind(Y0,$fot(multiply(add(X,Y),add(X,Z))))]]) ).
cnf(refute_0_679,plain,
multiply(add(X,Y),add(X,Z)) = add(X,multiply(Y,Z)),
inference(resolve,[$cnf( $equal(add(X,multiply(Y,Z)),multiply(add(X,Y),add(X,Z))) )],[distributivity2,refute_0_678]) ).
cnf(refute_0_680,plain,
multiply(add(x,z),add(x,inverse(z))) = add(x,multiply(z,inverse(z))),
inference(subst,[],[refute_0_679:[bind(X,$fot(x)),bind(Y,$fot(z)),bind(Z,$fot(inverse(z)))]]) ).
cnf(refute_0_681,plain,
( multiply(add(x,z),add(x,inverse(z))) != add(x,multiply(z,inverse(z)))
| add(x,multiply(z,inverse(z))) != x
| multiply(add(x,z),add(x,inverse(z))) = x ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(multiply(add(x,z),add(x,inverse(z))))),bind(Y0,$fot(add(x,multiply(z,inverse(z))))),bind(Z0,$fot(x))]]) ).
cnf(refute_0_682,plain,
( add(x,multiply(z,inverse(z))) != x
| multiply(add(x,z),add(x,inverse(z))) = x ),
inference(resolve,[$cnf( $equal(multiply(add(x,z),add(x,inverse(z))),add(x,multiply(z,inverse(z)))) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
multiply(add(x,z),add(x,inverse(z))) = x,
inference(resolve,[$cnf( $equal(add(x,multiply(z,inverse(z))),x) )],[refute_0_677,refute_0_682]) ).
cnf(refute_0_684,plain,
( multiply(add(x,z),add(x,inverse(z))) != add(z,multiply(add(x,inverse(z)),x))
| multiply(add(x,z),add(x,inverse(z))) != x
| x = add(z,multiply(add(x,inverse(z)),x)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(x,z),add(x,inverse(z))),add(z,multiply(add(x,inverse(z)),x))) ),[0],$fot(x)]]) ).
cnf(refute_0_685,plain,
( multiply(add(x,z),add(x,inverse(z))) != add(z,multiply(add(x,inverse(z)),x))
| x = add(z,multiply(add(x,inverse(z)),x)) ),
inference(resolve,[$cnf( $equal(multiply(add(x,z),add(x,inverse(z))),x) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
add(z,x) = add(x,z),
inference(subst,[],[refute_0_544:[bind(X,$fot(z)),bind(Z,$fot(x))]]) ).
cnf(refute_0_687,plain,
multiply(x,add(x,inverse(z))) = x,
inference(subst,[],[refute_0_490:[bind(X,$fot(x)),bind(Z,$fot(inverse(z)))]]) ).
cnf(refute_0_688,plain,
add(z,multiply(x,add(x,inverse(z)))) = add(z,multiply(x,add(x,inverse(z)))),
introduced(tautology,[refl,[$fot(add(z,multiply(x,add(x,inverse(z)))))]]) ).
cnf(refute_0_689,plain,
( multiply(x,add(x,inverse(z))) != x
| add(z,multiply(x,add(x,inverse(z)))) != add(z,multiply(x,add(x,inverse(z))))
| add(z,multiply(x,add(x,inverse(z)))) = add(z,x) ),
introduced(tautology,[equality,[$cnf( $equal(add(z,multiply(x,add(x,inverse(z)))),add(z,multiply(x,add(x,inverse(z))))) ),[1,1],$fot(x)]]) ).
cnf(refute_0_690,plain,
( multiply(x,add(x,inverse(z))) != x
| add(z,multiply(x,add(x,inverse(z)))) = add(z,x) ),
inference(resolve,[$cnf( $equal(add(z,multiply(x,add(x,inverse(z)))),add(z,multiply(x,add(x,inverse(z))))) )],[refute_0_688,refute_0_689]) ).
cnf(refute_0_691,plain,
add(z,multiply(x,add(x,inverse(z)))) = add(z,x),
inference(resolve,[$cnf( $equal(multiply(x,add(x,inverse(z))),x) )],[refute_0_687,refute_0_690]) ).
cnf(refute_0_692,plain,
( add(z,multiply(x,add(x,inverse(z)))) != add(z,x)
| add(z,x) != add(x,z)
| add(z,multiply(x,add(x,inverse(z)))) = add(x,z) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(z,multiply(x,add(x,inverse(z)))))),bind(Y0,$fot(add(z,x))),bind(Z0,$fot(add(x,z)))]]) ).
cnf(refute_0_693,plain,
( add(z,x) != add(x,z)
| add(z,multiply(x,add(x,inverse(z)))) = add(x,z) ),
inference(resolve,[$cnf( $equal(add(z,multiply(x,add(x,inverse(z)))),add(z,x)) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
add(z,multiply(x,add(x,inverse(z)))) = add(x,z),
inference(resolve,[$cnf( $equal(add(z,x),add(x,z)) )],[refute_0_686,refute_0_693]) ).
cnf(refute_0_695,plain,
multiply(add(x,z),add(y,X_72)) = add(z,multiply(X_72,x)),
inference(subst,[],[refute_0_604:[bind(X_62,$fot(X_72))]]) ).
cnf(refute_0_696,plain,
multiply(x,X_72) = multiply(X_72,x),
inference(subst,[],[commutativity_of_multiply:[bind(X,$fot(x)),bind(Y,$fot(X_72))]]) ).
cnf(refute_0_697,plain,
( multiply(x,X_72) != multiply(X_72,x)
| multiply(X_72,x) = multiply(x,X_72) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(x,X_72))),bind(Y0,$fot(multiply(X_72,x)))]]) ).
cnf(refute_0_698,plain,
multiply(X_72,x) = multiply(x,X_72),
inference(resolve,[$cnf( $equal(multiply(x,X_72),multiply(X_72,x)) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
( multiply(X_72,x) != multiply(x,X_72)
| multiply(add(x,z),add(y,X_72)) != add(z,multiply(X_72,x))
| multiply(add(x,z),add(y,X_72)) = add(z,multiply(x,X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(x,z),add(y,X_72)),add(z,multiply(X_72,x))) ),[1,1],$fot(multiply(x,X_72))]]) ).
cnf(refute_0_700,plain,
( multiply(add(x,z),add(y,X_72)) != add(z,multiply(X_72,x))
| multiply(add(x,z),add(y,X_72)) = add(z,multiply(x,X_72)) ),
inference(resolve,[$cnf( $equal(multiply(X_72,x),multiply(x,X_72)) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
multiply(add(x,z),add(y,X_72)) = add(z,multiply(x,X_72)),
inference(resolve,[$cnf( $equal(multiply(add(x,z),add(y,X_72)),add(z,multiply(X_72,x))) )],[refute_0_695,refute_0_700]) ).
cnf(refute_0_702,plain,
( multiply(add(x,z),add(y,X_72)) != add(z,multiply(X_72,x))
| multiply(add(x,z),add(y,X_72)) != add(z,multiply(x,X_72))
| add(z,multiply(X_72,x)) = add(z,multiply(x,X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(x,z),add(y,X_72)),add(z,multiply(x,X_72))) ),[0],$fot(add(z,multiply(X_72,x)))]]) ).
cnf(refute_0_703,plain,
( multiply(add(x,z),add(y,X_72)) != add(z,multiply(x,X_72))
| add(z,multiply(X_72,x)) = add(z,multiply(x,X_72)) ),
inference(resolve,[$cnf( $equal(multiply(add(x,z),add(y,X_72)),add(z,multiply(X_72,x))) )],[refute_0_695,refute_0_702]) ).
cnf(refute_0_704,plain,
add(z,multiply(X_72,x)) = add(z,multiply(x,X_72)),
inference(resolve,[$cnf( $equal(multiply(add(x,z),add(y,X_72)),add(z,multiply(x,X_72))) )],[refute_0_701,refute_0_703]) ).
cnf(refute_0_705,plain,
add(z,multiply(add(x,inverse(z)),x)) = add(z,multiply(x,add(x,inverse(z)))),
inference(subst,[],[refute_0_704:[bind(X_72,$fot(add(x,inverse(z))))]]) ).
cnf(refute_0_706,plain,
( add(z,multiply(add(x,inverse(z)),x)) != add(z,multiply(x,add(x,inverse(z))))
| add(z,multiply(x,add(x,inverse(z)))) != add(x,z)
| add(z,multiply(add(x,inverse(z)),x)) = add(x,z) ),
inference(subst,[],[refute_0_206:[bind(X0,$fot(add(z,multiply(add(x,inverse(z)),x)))),bind(Y0,$fot(add(z,multiply(x,add(x,inverse(z)))))),bind(Z0,$fot(add(x,z)))]]) ).
cnf(refute_0_707,plain,
( add(z,multiply(x,add(x,inverse(z)))) != add(x,z)
| add(z,multiply(add(x,inverse(z)),x)) = add(x,z) ),
inference(resolve,[$cnf( $equal(add(z,multiply(add(x,inverse(z)),x)),add(z,multiply(x,add(x,inverse(z))))) )],[refute_0_705,refute_0_706]) ).
cnf(refute_0_708,plain,
add(z,multiply(add(x,inverse(z)),x)) = add(x,z),
inference(resolve,[$cnf( $equal(add(z,multiply(x,add(x,inverse(z)))),add(x,z)) )],[refute_0_694,refute_0_707]) ).
cnf(refute_0_709,plain,
( add(z,multiply(add(x,inverse(z)),x)) != add(x,z)
| x != add(z,multiply(add(x,inverse(z)),x))
| x = add(x,z) ),
introduced(tautology,[equality,[$cnf( $equal(x,add(z,multiply(add(x,inverse(z)),x))) ),[1],$fot(add(x,z))]]) ).
cnf(refute_0_710,plain,
( x != add(z,multiply(add(x,inverse(z)),x))
| x = add(x,z) ),
inference(resolve,[$cnf( $equal(add(z,multiply(add(x,inverse(z)),x)),add(x,z)) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
( multiply(add(x,z),add(x,inverse(z))) != add(z,multiply(add(x,inverse(z)),x))
| x = add(x,z) ),
inference(resolve,[$cnf( $equal(x,add(z,multiply(add(x,inverse(z)),x))) )],[refute_0_685,refute_0_710]) ).
cnf(refute_0_712,plain,
x = add(x,z),
inference(resolve,[$cnf( $equal(multiply(add(x,z),add(x,inverse(z))),add(z,multiply(add(x,inverse(z)),x))) )],[refute_0_664,refute_0_711]) ).
cnf(refute_0_713,plain,
( x != add(x,z)
| add(x,z) = x ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(x)),bind(Y0,$fot(add(x,z)))]]) ).
cnf(refute_0_714,plain,
x != add(x,z),
inference(resolve,[$cnf( $equal(add(x,z),x) )],[refute_0_713,prove_sum]) ).
cnf(refute_0_715,plain,
$false,
inference(resolve,[$cnf( $equal(x,add(x,z)) )],[refute_0_712,refute_0_714]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : BOO016-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Wed Jun 1 15:35:29 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.11/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.56/0.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.76
% 0.56/0.76 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.61/0.84
%------------------------------------------------------------------------------