TSTP Solution File: BOO003-4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO003-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 23:44:23 EDT 2022
% Result : Unsatisfiable 0.42s 0.59s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 78
% Syntax : Number of clauses : 356 ( 187 unt; 0 nHn; 169 RR)
% Number of literals : 596 ( 595 equ; 242 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 589 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X) ).
cnf(commutativity_of_multiply,axiom,
multiply(X,Y) = multiply(Y,X) ).
cnf(distributivity1,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ).
cnf(distributivity2,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity ).
cnf(prove_a_times_a_is_a,negated_conjecture,
multiply(a,a) != a ).
cnf(refute_0_0,plain,
add(Z,multiply(Y,Z)) = multiply(add(Z,Y),add(Z,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Z))]]) ).
cnf(refute_0_1,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),add(X_10,inverse(X_10))),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(inverse(X_10)))]]) ).
cnf(refute_0_2,plain,
add(X_10,inverse(X_10)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_3,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),add(X_10,inverse(X_10)))
| add(X_10,inverse(X_10)) != multiplicative_identity
| add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_4,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),add(X_10,inverse(X_10)))
| add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(add(X_10,X_11),multiplicative_identity) = add(X_10,X_11),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_7,plain,
( multiply(add(X_10,X_11),multiplicative_identity) != add(X_10,X_11)
| add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),multiplicative_identity)
| add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) ),[1],$fot(add(X_10,X_11))]]) ).
cnf(refute_0_8,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),multiplicative_identity)
| add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),multiplicative_identity),add(X_10,X_11)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
add(X_13,multiply(X_13,inverse(X_13))) = add(X_13,X_13),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(X_13)),bind(X_11,$fot(X_13))]]) ).
cnf(refute_0_11,plain,
multiply(X_13,inverse(X_13)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_12,plain,
( multiply(X_13,inverse(X_13)) != additive_identity
| add(X_13,multiply(X_13,inverse(X_13))) != add(X_13,X_13)
| add(X_13,additive_identity) = add(X_13,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,multiply(X_13,inverse(X_13))),add(X_13,X_13)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_13,plain,
( add(X_13,multiply(X_13,inverse(X_13))) != add(X_13,X_13)
| add(X_13,additive_identity) = add(X_13,X_13) ),
inference(resolve,[$cnf( $equal(multiply(X_13,inverse(X_13)),additive_identity) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
add(X_13,additive_identity) = add(X_13,X_13),
inference(resolve,[$cnf( $equal(add(X_13,multiply(X_13,inverse(X_13))),add(X_13,X_13)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
add(X_13,additive_identity) = X_13,
inference(subst,[],[additive_id1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_16,plain,
( add(X_13,additive_identity) != X_13
| add(X_13,additive_identity) != add(X_13,X_13)
| X_13 = add(X_13,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,additive_identity),add(X_13,X_13)) ),[0],$fot(X_13)]]) ).
cnf(refute_0_17,plain,
( add(X_13,additive_identity) != add(X_13,X_13)
| X_13 = add(X_13,X_13) ),
inference(resolve,[$cnf( $equal(add(X_13,additive_identity),X_13) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
X_13 = add(X_13,X_13),
inference(resolve,[$cnf( $equal(add(X_13,additive_identity),add(X_13,X_13)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
Z = add(Z,Z),
inference(subst,[],[refute_0_18:[bind(X_13,$fot(Z))]]) ).
cnf(refute_0_20,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_21,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( Z != add(Z,Z)
| add(Z,Z) = Z ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(Z)),bind(Y0,$fot(add(Z,Z)))]]) ).
cnf(refute_0_24,plain,
add(Z,Z) = Z,
inference(resolve,[$cnf( $equal(Z,add(Z,Z)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
( add(Z,Z) != Z
| add(Z,multiply(Y,Z)) != multiply(add(Z,Y),add(Z,Z))
| add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),add(Z,Z))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_26,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( $equal(add(Z,Z),Z) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
add(Z,multiply(Y,Z)) = multiply(add(Z,Y),Z),
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),add(Z,Z))) )],[refute_0_0,refute_0_26]) ).
cnf(refute_0_28,plain,
( multiply(X,Y) != multiply(Y,X)
| multiply(Y,X) = multiply(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_29,plain,
multiply(Y,X) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(Y,X)) )],[commutativity_of_multiply,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(add(Z,Y),Z) = multiply(Z,add(Z,Y)),
inference(subst,[],[refute_0_29:[bind(X,$fot(Z)),bind(Y,$fot(add(Z,Y)))]]) ).
cnf(refute_0_31,plain,
( multiply(add(Z,Y),Z) != multiply(Z,add(Z,Y))
| add(Z,multiply(Y,Z)) != multiply(add(Z,Y),Z)
| add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),Z)) ),[1],$fot(multiply(Z,add(Z,Y)))]]) ).
cnf(refute_0_32,plain,
( add(Z,multiply(Y,Z)) != multiply(add(Z,Y),Z)
| add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(add(Z,Y),Z),multiply(Z,add(Z,Y))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
add(Z,multiply(Y,Z)) = multiply(Z,add(Z,Y)),
inference(resolve,[$cnf( $equal(add(Z,multiply(Y,Z)),multiply(add(Z,Y),Z)) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
add(X_28,multiply(X_28,X_28)) = multiply(X_28,add(X_28,X_28)),
inference(subst,[],[refute_0_33:[bind(Y,$fot(X_28)),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_35,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),add(X_10,additive_identity)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_36,plain,
add(X_10,additive_identity) = X_10,
inference(subst,[],[additive_id1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_37,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),add(X_10,additive_identity))
| add(X_10,additive_identity) != X_10
| add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),add(X_10,additive_identity))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_38,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),add(X_10,additive_identity))
| add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10) ),
inference(resolve,[$cnf( $equal(add(X_10,additive_identity),X_10) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),add(X_10,additive_identity))) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(add(X_10,X_11),X_10) = multiply(X_10,add(X_10,X_11)),
inference(subst,[],[refute_0_29:[bind(X,$fot(X_10)),bind(Y,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_41,plain,
( multiply(add(X_10,X_11),X_10) != multiply(X_10,add(X_10,X_11))
| add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),X_10)
| add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),X_10)) ),[1],$fot(multiply(X_10,add(X_10,X_11)))]]) ).
cnf(refute_0_42,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),X_10)
| add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),X_10),multiply(X_10,add(X_10,X_11))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),X_10)) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
add(X_21,multiply(additive_identity,additive_identity)) = multiply(X_21,add(X_21,additive_identity)),
inference(subst,[],[refute_0_43:[bind(X_10,$fot(X_21)),bind(X_11,$fot(additive_identity))]]) ).
cnf(refute_0_45,plain,
add(X_21,additive_identity) = X_21,
inference(subst,[],[additive_id1:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_46,plain,
( add(X_21,multiply(additive_identity,additive_identity)) != multiply(X_21,add(X_21,additive_identity))
| add(X_21,additive_identity) != X_21
| add(X_21,multiply(additive_identity,additive_identity)) = multiply(X_21,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_21,multiply(additive_identity,additive_identity)),multiply(X_21,add(X_21,additive_identity))) ),[1,1],$fot(X_21)]]) ).
cnf(refute_0_47,plain,
( add(X_21,multiply(additive_identity,additive_identity)) != multiply(X_21,add(X_21,additive_identity))
| add(X_21,multiply(additive_identity,additive_identity)) = multiply(X_21,X_21) ),
inference(resolve,[$cnf( $equal(add(X_21,additive_identity),X_21) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
add(X_21,multiply(additive_identity,additive_identity)) = multiply(X_21,X_21),
inference(resolve,[$cnf( $equal(add(X_21,multiply(additive_identity,additive_identity)),multiply(X_21,add(X_21,additive_identity))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
add(X_28,multiply(additive_identity,additive_identity)) = multiply(X_28,X_28),
inference(subst,[],[refute_0_48:[bind(X_21,$fot(X_28))]]) ).
cnf(refute_0_50,plain,
( add(X_28,multiply(additive_identity,additive_identity)) != multiply(X_28,X_28)
| multiply(X_28,X_28) = add(X_28,multiply(additive_identity,additive_identity)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X_28,multiply(additive_identity,additive_identity)))),bind(Y0,$fot(multiply(X_28,X_28)))]]) ).
cnf(refute_0_51,plain,
multiply(X_28,X_28) = add(X_28,multiply(additive_identity,additive_identity)),
inference(resolve,[$cnf( $equal(add(X_28,multiply(additive_identity,additive_identity)),multiply(X_28,X_28)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiply(X_28,X_28) != add(X_28,multiply(additive_identity,additive_identity))
| add(X_28,multiply(X_28,X_28)) != multiply(X_28,add(X_28,X_28))
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,add(X_28,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_28,multiply(X_28,X_28)),multiply(X_28,add(X_28,X_28))) ),[0,1],$fot(add(X_28,multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_53,plain,
( add(X_28,multiply(X_28,X_28)) != multiply(X_28,add(X_28,X_28))
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,add(X_28,X_28)) ),
inference(resolve,[$cnf( $equal(multiply(X_28,X_28),add(X_28,multiply(additive_identity,additive_identity))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,add(X_28,X_28)),
inference(resolve,[$cnf( $equal(add(X_28,multiply(X_28,X_28)),multiply(X_28,add(X_28,X_28))) )],[refute_0_34,refute_0_53]) ).
cnf(refute_0_55,plain,
( X_13 != add(X_13,X_13)
| add(X_13,X_13) = X_13 ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(X_13)),bind(Y0,$fot(add(X_13,X_13)))]]) ).
cnf(refute_0_56,plain,
add(X_13,X_13) = X_13,
inference(resolve,[$cnf( $equal(X_13,add(X_13,X_13)) )],[refute_0_18,refute_0_55]) ).
cnf(refute_0_57,plain,
add(X_28,X_28) = X_28,
inference(subst,[],[refute_0_56:[bind(X_13,$fot(X_28))]]) ).
cnf(refute_0_58,plain,
multiply(X_28,add(X_28,X_28)) = multiply(X_28,add(X_28,X_28)),
introduced(tautology,[refl,[$fot(multiply(X_28,add(X_28,X_28)))]]) ).
cnf(refute_0_59,plain,
( multiply(X_28,add(X_28,X_28)) != multiply(X_28,add(X_28,X_28))
| add(X_28,X_28) != X_28
| multiply(X_28,add(X_28,X_28)) = multiply(X_28,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_28,add(X_28,X_28)),multiply(X_28,add(X_28,X_28))) ),[1,1],$fot(X_28)]]) ).
cnf(refute_0_60,plain,
( add(X_28,X_28) != X_28
| multiply(X_28,add(X_28,X_28)) = multiply(X_28,X_28) ),
inference(resolve,[$cnf( $equal(multiply(X_28,add(X_28,X_28)),multiply(X_28,add(X_28,X_28))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(X_28,add(X_28,X_28)) = multiply(X_28,X_28),
inference(resolve,[$cnf( $equal(add(X_28,X_28),X_28) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
( multiply(X_28,add(X_28,X_28)) != multiply(X_28,X_28)
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != multiply(X_28,add(X_28,X_28))
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),multiply(X_28,add(X_28,X_28))) ),[1],$fot(multiply(X_28,X_28))]]) ).
cnf(refute_0_63,plain,
( add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != multiply(X_28,add(X_28,X_28))
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,X_28) ),
inference(resolve,[$cnf( $equal(multiply(X_28,add(X_28,X_28)),multiply(X_28,X_28)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,X_28),
inference(resolve,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),multiply(X_28,add(X_28,X_28))) )],[refute_0_54,refute_0_63]) ).
cnf(refute_0_65,plain,
add(X_28,additive_identity) = X_28,
inference(subst,[],[additive_id1:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_66,plain,
multiply(additive_identity,add(additive_identity,X_41)) = add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_41)),
inference(subst,[],[distributivity2:[bind(X,$fot(additive_identity)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_67,plain,
add(multiply(additive_identity,additive_identity),Y) = add(Y,multiply(additive_identity,additive_identity)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_68,plain,
add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y),
inference(subst,[],[refute_0_48:[bind(X_21,$fot(Y))]]) ).
cnf(refute_0_69,plain,
( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,Y)
| add(multiply(additive_identity,additive_identity),Y) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) ),[1],$fot(multiply(Y,Y))]]) ).
cnf(refute_0_70,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( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,Y)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_41)) = multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41)),
inference(subst,[],[refute_0_71:[bind(Y,$fot(multiply(additive_identity,X_41)))]]) ).
cnf(refute_0_73,plain,
( multiply(additive_identity,add(additive_identity,X_41)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_41))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_41)) != multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))
| multiply(additive_identity,add(additive_identity,X_41)) = multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(additive_identity,add(additive_identity,X_41)),multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))) ),[0],$fot(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_41)))]]) ).
cnf(refute_0_74,plain,
( multiply(additive_identity,add(additive_identity,X_41)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_41))
| multiply(additive_identity,add(additive_identity,X_41)) = multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_41)),multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(additive_identity,add(additive_identity,X_41)) = multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_41)),add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_41))) )],[refute_0_66,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(X_39,add(X_40,multiplicative_identity)) = add(multiply(X_39,X_40),multiply(X_39,multiplicative_identity)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(multiplicative_identity))]]) ).
cnf(refute_0_77,plain,
multiply(X_39,multiplicative_identity) = X_39,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_78,plain,
( multiply(X_39,add(X_40,multiplicative_identity)) != add(multiply(X_39,X_40),multiply(X_39,multiplicative_identity))
| multiply(X_39,multiplicative_identity) != X_39
| multiply(X_39,add(X_40,multiplicative_identity)) = add(multiply(X_39,X_40),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_39,add(X_40,multiplicative_identity)),add(multiply(X_39,X_40),multiply(X_39,multiplicative_identity))) ),[1,1],$fot(X_39)]]) ).
cnf(refute_0_79,plain,
( multiply(X_39,add(X_40,multiplicative_identity)) != add(multiply(X_39,X_40),multiply(X_39,multiplicative_identity))
| multiply(X_39,add(X_40,multiplicative_identity)) = add(multiply(X_39,X_40),X_39) ),
inference(resolve,[$cnf( $equal(multiply(X_39,multiplicative_identity),X_39) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(X_39,add(X_40,multiplicative_identity)) = add(multiply(X_39,X_40),X_39),
inference(resolve,[$cnf( $equal(multiply(X_39,add(X_40,multiplicative_identity)),add(multiply(X_39,X_40),multiply(X_39,multiplicative_identity))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
add(X_13,multiply(multiplicative_identity,inverse(X_13))) = add(X_13,multiplicative_identity),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(X_13)),bind(X_11,$fot(multiplicative_identity))]]) ).
cnf(refute_0_82,plain,
multiply(X,multiplicative_identity) = multiply(multiplicative_identity,X),
inference(subst,[],[commutativity_of_multiply:[bind(Y,$fot(multiplicative_identity))]]) ).
cnf(refute_0_83,plain,
( multiply(X,multiplicative_identity) != X
| multiply(X,multiplicative_identity) != multiply(multiplicative_identity,X)
| multiply(multiplicative_identity,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiplicative_identity),X) ),[0],$fot(multiply(multiplicative_identity,X))]]) ).
cnf(refute_0_84,plain,
( multiply(X,multiplicative_identity) != X
| multiply(multiplicative_identity,X) = X ),
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),multiply(multiplicative_identity,X)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(multiplicative_identity,X) = X,
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),X) )],[multiplicative_id1,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(multiplicative_identity,inverse(X_13)) = inverse(X_13),
inference(subst,[],[refute_0_85:[bind(X,$fot(inverse(X_13)))]]) ).
cnf(refute_0_87,plain,
( multiply(multiplicative_identity,inverse(X_13)) != inverse(X_13)
| add(X_13,multiply(multiplicative_identity,inverse(X_13))) != add(X_13,multiplicative_identity)
| add(X_13,inverse(X_13)) = add(X_13,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,multiply(multiplicative_identity,inverse(X_13))),add(X_13,multiplicative_identity)) ),[0,1],$fot(inverse(X_13))]]) ).
cnf(refute_0_88,plain,
( add(X_13,multiply(multiplicative_identity,inverse(X_13))) != add(X_13,multiplicative_identity)
| add(X_13,inverse(X_13)) = add(X_13,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(X_13)),inverse(X_13)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
add(X_13,inverse(X_13)) = add(X_13,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_13,multiply(multiplicative_identity,inverse(X_13))),add(X_13,multiplicative_identity)) )],[refute_0_81,refute_0_88]) ).
cnf(refute_0_90,plain,
add(X_13,inverse(X_13)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_91,plain,
( add(X_13,inverse(X_13)) != add(X_13,multiplicative_identity)
| add(X_13,inverse(X_13)) != multiplicative_identity
| multiplicative_identity = add(X_13,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,inverse(X_13)),add(X_13,multiplicative_identity)) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_92,plain,
( add(X_13,inverse(X_13)) != add(X_13,multiplicative_identity)
| multiplicative_identity = add(X_13,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_13,inverse(X_13)),multiplicative_identity) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
multiplicative_identity = add(X_13,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_13,inverse(X_13)),add(X_13,multiplicative_identity)) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
( multiplicative_identity != add(X_13,multiplicative_identity)
| add(X_13,multiplicative_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_13,multiplicative_identity)))]]) ).
cnf(refute_0_95,plain,
add(X_13,multiplicative_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_13,multiplicative_identity)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
add(X_40,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[refute_0_95:[bind(X_13,$fot(X_40))]]) ).
cnf(refute_0_97,plain,
multiply(X_39,add(X_40,multiplicative_identity)) = multiply(X_39,add(X_40,multiplicative_identity)),
introduced(tautology,[refl,[$fot(multiply(X_39,add(X_40,multiplicative_identity)))]]) ).
cnf(refute_0_98,plain,
( multiply(X_39,add(X_40,multiplicative_identity)) != multiply(X_39,add(X_40,multiplicative_identity))
| add(X_40,multiplicative_identity) != multiplicative_identity
| multiply(X_39,add(X_40,multiplicative_identity)) = multiply(X_39,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_39,add(X_40,multiplicative_identity)),multiply(X_39,add(X_40,multiplicative_identity))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_99,plain,
( add(X_40,multiplicative_identity) != multiplicative_identity
| multiply(X_39,add(X_40,multiplicative_identity)) = multiply(X_39,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(X_39,add(X_40,multiplicative_identity)),multiply(X_39,add(X_40,multiplicative_identity))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
multiply(X_39,add(X_40,multiplicative_identity)) = multiply(X_39,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_40,multiplicative_identity),multiplicative_identity) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_102,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_22,refute_0_101]) ).
cnf(refute_0_103,plain,
( multiply(X_39,add(X_40,multiplicative_identity)) != multiply(X_39,multiplicative_identity)
| multiply(X_39,multiplicative_identity) != X_39
| multiply(X_39,add(X_40,multiplicative_identity)) = X_39 ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(multiply(X_39,add(X_40,multiplicative_identity)))),bind(Y0,$fot(multiply(X_39,multiplicative_identity))),bind(Z0,$fot(X_39))]]) ).
cnf(refute_0_104,plain,
( multiply(X_39,multiplicative_identity) != X_39
| multiply(X_39,add(X_40,multiplicative_identity)) = X_39 ),
inference(resolve,[$cnf( $equal(multiply(X_39,add(X_40,multiplicative_identity)),multiply(X_39,multiplicative_identity)) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(X_39,add(X_40,multiplicative_identity)) = X_39,
inference(resolve,[$cnf( $equal(multiply(X_39,multiplicative_identity),X_39) )],[refute_0_77,refute_0_104]) ).
cnf(refute_0_106,plain,
( multiply(X_39,add(X_40,multiplicative_identity)) != X_39
| multiply(X_39,add(X_40,multiplicative_identity)) != add(multiply(X_39,X_40),X_39)
| X_39 = add(multiply(X_39,X_40),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_39,add(X_40,multiplicative_identity)),add(multiply(X_39,X_40),X_39)) ),[0],$fot(X_39)]]) ).
cnf(refute_0_107,plain,
( multiply(X_39,add(X_40,multiplicative_identity)) != add(multiply(X_39,X_40),X_39)
| X_39 = add(multiply(X_39,X_40),X_39) ),
inference(resolve,[$cnf( $equal(multiply(X_39,add(X_40,multiplicative_identity)),X_39) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
add(Y,multiply(Y,Z)) = multiply(add(Y,Y),add(Y,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_109,plain,
Y = add(Y,Y),
inference(subst,[],[refute_0_18:[bind(X_13,$fot(Y))]]) ).
cnf(refute_0_110,plain,
( Y != add(Y,Y)
| add(Y,Y) = Y ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(Y)),bind(Y0,$fot(add(Y,Y)))]]) ).
cnf(refute_0_111,plain,
add(Y,Y) = Y,
inference(resolve,[$cnf( $equal(Y,add(Y,Y)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( add(Y,Y) != Y
| add(Y,multiply(Y,Z)) != multiply(add(Y,Y),add(Y,Z))
| add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_113,plain,
( add(Y,multiply(Y,Z)) != multiply(add(Y,Y),add(Y,Z))
| add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)) ),
inference(resolve,[$cnf( $equal(add(Y,Y),Y) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) )],[refute_0_108,refute_0_113]) ).
cnf(refute_0_115,plain,
add(X_39,multiply(X_39,X_40)) = multiply(X_39,add(X_39,X_40)),
inference(subst,[],[refute_0_114:[bind(Y,$fot(X_39)),bind(Z,$fot(X_40))]]) ).
cnf(refute_0_116,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_117,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_116]) ).
cnf(refute_0_118,plain,
add(multiply(X_39,X_40),X_39) = add(X_39,multiply(X_39,X_40)),
inference(subst,[],[refute_0_117:[bind(X,$fot(X_39)),bind(Y,$fot(multiply(X_39,X_40)))]]) ).
cnf(refute_0_119,plain,
( add(X_39,multiply(X_39,X_40)) != multiply(X_39,add(X_39,X_40))
| add(multiply(X_39,X_40),X_39) != add(X_39,multiply(X_39,X_40))
| add(multiply(X_39,X_40),X_39) = multiply(X_39,add(X_39,X_40)) ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(add(multiply(X_39,X_40),X_39))),bind(Y0,$fot(add(X_39,multiply(X_39,X_40)))),bind(Z0,$fot(multiply(X_39,add(X_39,X_40))))]]) ).
cnf(refute_0_120,plain,
( add(X_39,multiply(X_39,X_40)) != multiply(X_39,add(X_39,X_40))
| add(multiply(X_39,X_40),X_39) = multiply(X_39,add(X_39,X_40)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_39,X_40),X_39),add(X_39,multiply(X_39,X_40))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
add(multiply(X_39,X_40),X_39) = multiply(X_39,add(X_39,X_40)),
inference(resolve,[$cnf( $equal(add(X_39,multiply(X_39,X_40)),multiply(X_39,add(X_39,X_40))) )],[refute_0_115,refute_0_120]) ).
cnf(refute_0_122,plain,
( X_39 != add(multiply(X_39,X_40),X_39)
| add(multiply(X_39,X_40),X_39) != multiply(X_39,add(X_39,X_40))
| X_39 = multiply(X_39,add(X_39,X_40)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_39,multiply(X_39,add(X_39,X_40))) ),[0],$fot(add(multiply(X_39,X_40),X_39))]]) ).
cnf(refute_0_123,plain,
( X_39 != add(multiply(X_39,X_40),X_39)
| X_39 = multiply(X_39,add(X_39,X_40)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_39,X_40),X_39),multiply(X_39,add(X_39,X_40))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
( multiply(X_39,add(X_40,multiplicative_identity)) != add(multiply(X_39,X_40),X_39)
| X_39 = multiply(X_39,add(X_39,X_40)) ),
inference(resolve,[$cnf( $equal(X_39,add(multiply(X_39,X_40),X_39)) )],[refute_0_107,refute_0_123]) ).
cnf(refute_0_125,plain,
X_39 = multiply(X_39,add(X_39,X_40)),
inference(resolve,[$cnf( $equal(multiply(X_39,add(X_40,multiplicative_identity)),add(multiply(X_39,X_40),X_39)) )],[refute_0_80,refute_0_124]) ).
cnf(refute_0_126,plain,
( X_39 != multiply(X_39,add(X_39,X_40))
| multiply(X_39,add(X_39,X_40)) = X_39 ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(X_39)),bind(Y0,$fot(multiply(X_39,add(X_39,X_40))))]]) ).
cnf(refute_0_127,plain,
multiply(X_39,add(X_39,X_40)) = X_39,
inference(resolve,[$cnf( $equal(X_39,multiply(X_39,add(X_39,X_40))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
multiply(additive_identity,add(additive_identity,X_41)) = additive_identity,
inference(subst,[],[refute_0_127:[bind(X_39,$fot(additive_identity)),bind(X_40,$fot(X_41))]]) ).
cnf(refute_0_129,plain,
( multiply(additive_identity,add(additive_identity,X_41)) != multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))
| multiply(additive_identity,add(additive_identity,X_41)) != additive_identity
| additive_identity = multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_41)),multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_130,plain,
( multiply(additive_identity,add(additive_identity,X_41)) != multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))
| additive_identity = multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_41)),additive_identity) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
add(X_10,multiply(additive_identity,X_12)) = multiply(add(X_10,additive_identity),add(X_10,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_132,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
| add(X_10,additive_identity) != X_10
| add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_133,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
| add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(add(X_10,additive_identity),X_10) )],[refute_0_36,refute_0_132]) ).
cnf(refute_0_134,plain,
add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) )],[refute_0_131,refute_0_133]) ).
cnf(refute_0_135,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),
inference(subst,[],[refute_0_134:[bind(X_10,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_136,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),
inference(subst,[],[refute_0_71:[bind(Y,$fot(multiply(additive_identity,X_12)))]]) ).
cnf(refute_0_137,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) ),[0],$fot(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)))]]) ).
cnf(refute_0_138,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
add(X_12,additive_identity) = X_12,
inference(subst,[],[additive_id1:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_141,plain,
multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,add(X_12,additive_identity)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(X_12,additive_identity)))]]) ).
cnf(refute_0_142,plain,
( multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| add(X_12,additive_identity) != X_12
| multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) ),[1,1],$fot(X_12)]]) ).
cnf(refute_0_143,plain,
( add(X_12,additive_identity) != X_12
| multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(add(X_12,additive_identity),X_12) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
( multiply(X,add(Y,Z)) != add(multiply(X,Y),multiply(X,Z))
| add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_146,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[distributivity2,refute_0_145]) ).
cnf(refute_0_147,plain,
add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) = multiply(additive_identity,add(X_12,additive_identity)),
inference(subst,[],[refute_0_146:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_12)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_148,plain,
add(multiply(additive_identity,X_24),Y) = add(Y,multiply(additive_identity,X_24)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,X_24)))]]) ).
cnf(refute_0_149,plain,
add(Y,multiply(additive_identity,X_24)) = multiply(Y,add(Y,X_24)),
inference(subst,[],[refute_0_134:[bind(X_10,$fot(Y)),bind(X_12,$fot(X_24))]]) ).
cnf(refute_0_150,plain,
( add(Y,multiply(additive_identity,X_24)) != multiply(Y,add(Y,X_24))
| add(multiply(additive_identity,X_24),Y) != add(Y,multiply(additive_identity,X_24))
| add(multiply(additive_identity,X_24),Y) = multiply(Y,add(Y,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_24),Y),add(Y,multiply(additive_identity,X_24))) ),[1],$fot(multiply(Y,add(Y,X_24)))]]) ).
cnf(refute_0_151,plain,
( add(multiply(additive_identity,X_24),Y) != add(Y,multiply(additive_identity,X_24))
| add(multiply(additive_identity,X_24),Y) = multiply(Y,add(Y,X_24)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,X_24)),multiply(Y,add(Y,X_24))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
add(multiply(additive_identity,X_24),Y) = multiply(Y,add(Y,X_24)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_24),Y),add(Y,multiply(additive_identity,X_24))) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
( add(multiply(additive_identity,X_24),Y) != multiply(Y,add(Y,X_24))
| multiply(Y,add(Y,X_24)) = add(multiply(additive_identity,X_24),Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(multiply(additive_identity,X_24),Y))),bind(Y0,$fot(multiply(Y,add(Y,X_24))))]]) ).
cnf(refute_0_154,plain,
multiply(Y,add(Y,X_24)) = add(multiply(additive_identity,X_24),Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_24),Y),multiply(Y,add(Y,X_24))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)),
inference(subst,[],[refute_0_154:[bind(Y,$fot(multiply(additive_identity,additive_identity))),bind(X_24,$fot(X_12))]]) ).
cnf(refute_0_156,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)) ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)))),bind(Y0,$fot(add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)))),bind(Z0,$fot(multiply(additive_identity,add(X_12,additive_identity))))]]) ).
cnf(refute_0_157,plain,
( add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_147,refute_0_157]) ).
cnf(refute_0_159,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12) ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)))),bind(Y0,$fot(multiply(additive_identity,add(X_12,additive_identity)))),bind(Z0,$fot(multiply(additive_identity,X_12)))]]) ).
cnf(refute_0_160,plain,
( multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,X_12)) )],[refute_0_144,refute_0_160]) ).
cnf(refute_0_162,plain,
( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),multiply(additive_identity,X_12)) ),[0],$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)))]]) ).
cnf(refute_0_163,plain,
( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),multiply(additive_identity,X_12)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_139,refute_0_163]) ).
cnf(refute_0_165,plain,
multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41)) = multiply(additive_identity,X_41),
inference(subst,[],[refute_0_164:[bind(X_12,$fot(X_41))]]) ).
cnf(refute_0_166,plain,
( multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41)) != multiply(additive_identity,X_41)
| additive_identity != multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))
| additive_identity = multiply(additive_identity,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(additive_identity,multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))) ),[1],$fot(multiply(additive_identity,X_41))]]) ).
cnf(refute_0_167,plain,
( additive_identity != multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))
| additive_identity = multiply(additive_identity,X_41) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41)),multiply(additive_identity,X_41)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
( multiply(additive_identity,add(additive_identity,X_41)) != multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))
| additive_identity = multiply(additive_identity,X_41) ),
inference(resolve,[$cnf( $equal(additive_identity,multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))) )],[refute_0_130,refute_0_167]) ).
cnf(refute_0_169,plain,
additive_identity = multiply(additive_identity,X_41),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_41)),multiply(multiply(additive_identity,X_41),multiply(additive_identity,X_41))) )],[refute_0_75,refute_0_168]) ).
cnf(refute_0_170,plain,
( additive_identity != multiply(additive_identity,X_41)
| multiply(additive_identity,X_41) = additive_identity ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(additive_identity,X_41)))]]) ).
cnf(refute_0_171,plain,
multiply(additive_identity,X_41) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(additive_identity,X_41)) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(subst,[],[refute_0_171:[bind(X_41,$fot(additive_identity))]]) ).
cnf(refute_0_173,plain,
add(X_28,multiply(additive_identity,additive_identity)) = add(X_28,multiply(additive_identity,additive_identity)),
introduced(tautology,[refl,[$fot(add(X_28,multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_174,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(X_28,multiply(additive_identity,additive_identity)) != add(X_28,multiply(additive_identity,additive_identity))
| add(X_28,multiply(additive_identity,additive_identity)) = add(X_28,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_28,multiply(additive_identity,additive_identity)),add(X_28,multiply(additive_identity,additive_identity))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_175,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(X_28,multiply(additive_identity,additive_identity)) = add(X_28,additive_identity) ),
inference(resolve,[$cnf( $equal(add(X_28,multiply(additive_identity,additive_identity)),add(X_28,multiply(additive_identity,additive_identity))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
add(X_28,multiply(additive_identity,additive_identity)) = add(X_28,additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),additive_identity) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
( add(X_28,multiply(additive_identity,additive_identity)) != add(X_28,additive_identity)
| add(X_28,additive_identity) != X_28
| add(X_28,multiply(additive_identity,additive_identity)) = X_28 ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(add(X_28,multiply(additive_identity,additive_identity)))),bind(Y0,$fot(add(X_28,additive_identity))),bind(Z0,$fot(X_28))]]) ).
cnf(refute_0_178,plain,
( add(X_28,additive_identity) != X_28
| add(X_28,multiply(additive_identity,additive_identity)) = X_28 ),
inference(resolve,[$cnf( $equal(add(X_28,multiply(additive_identity,additive_identity)),add(X_28,additive_identity)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
add(X_28,multiply(additive_identity,additive_identity)) = X_28,
inference(resolve,[$cnf( $equal(add(X_28,additive_identity),X_28) )],[refute_0_65,refute_0_178]) ).
cnf(refute_0_180,plain,
add(add(Y,X_36),multiply(Y,add(Y,X_36))) = multiply(add(Y,X_36),add(add(Y,X_36),Y)),
inference(subst,[],[refute_0_33:[bind(Z,$fot(add(Y,X_36)))]]) ).
cnf(refute_0_181,plain,
add(multiply(additive_identity,X_36),Y) = multiply(Y,add(Y,X_36)),
inference(subst,[],[refute_0_152:[bind(X_24,$fot(X_36))]]) ).
cnf(refute_0_182,plain,
( add(multiply(additive_identity,X_36),Y) != multiply(Y,add(Y,X_36))
| multiply(Y,add(Y,X_36)) = add(multiply(additive_identity,X_36),Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(multiply(additive_identity,X_36),Y))),bind(Y0,$fot(multiply(Y,add(Y,X_36))))]]) ).
cnf(refute_0_183,plain,
multiply(Y,add(Y,X_36)) = add(multiply(additive_identity,X_36),Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_36),Y),multiply(Y,add(Y,X_36))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
( multiply(Y,add(Y,X_36)) != add(multiply(additive_identity,X_36),Y)
| add(add(Y,X_36),multiply(Y,add(Y,X_36))) != multiply(add(Y,X_36),add(add(Y,X_36),Y))
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = multiply(add(Y,X_36),add(add(Y,X_36),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(Y,X_36),multiply(Y,add(Y,X_36))),multiply(add(Y,X_36),add(add(Y,X_36),Y))) ),[0,1],$fot(add(multiply(additive_identity,X_36),Y))]]) ).
cnf(refute_0_185,plain,
( add(add(Y,X_36),multiply(Y,add(Y,X_36))) != multiply(add(Y,X_36),add(add(Y,X_36),Y))
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = multiply(add(Y,X_36),add(add(Y,X_36),Y)) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,X_36)),add(multiply(additive_identity,X_36),Y)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = multiply(add(Y,X_36),add(add(Y,X_36),Y)),
inference(resolve,[$cnf( $equal(add(add(Y,X_36),multiply(Y,add(Y,X_36))),multiply(add(Y,X_36),add(add(Y,X_36),Y))) )],[refute_0_180,refute_0_185]) ).
cnf(refute_0_187,plain,
add(multiply(X_22,additive_identity),Y) = add(Y,multiply(X_22,additive_identity)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(X_22,additive_identity)))]]) ).
cnf(refute_0_188,plain,
add(Y,multiply(X_22,additive_identity)) = multiply(Y,add(Y,X_22)),
inference(subst,[],[refute_0_43:[bind(X_10,$fot(Y)),bind(X_11,$fot(X_22))]]) ).
cnf(refute_0_189,plain,
( add(Y,multiply(X_22,additive_identity)) != multiply(Y,add(Y,X_22))
| add(multiply(X_22,additive_identity),Y) != add(Y,multiply(X_22,additive_identity))
| add(multiply(X_22,additive_identity),Y) = multiply(Y,add(Y,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_22,additive_identity),Y),add(Y,multiply(X_22,additive_identity))) ),[1],$fot(multiply(Y,add(Y,X_22)))]]) ).
cnf(refute_0_190,plain,
( add(multiply(X_22,additive_identity),Y) != add(Y,multiply(X_22,additive_identity))
| add(multiply(X_22,additive_identity),Y) = multiply(Y,add(Y,X_22)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(X_22,additive_identity)),multiply(Y,add(Y,X_22))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
add(multiply(X_22,additive_identity),Y) = multiply(Y,add(Y,X_22)),
inference(resolve,[$cnf( $equal(add(multiply(X_22,additive_identity),Y),add(Y,multiply(X_22,additive_identity))) )],[refute_0_187,refute_0_190]) ).
cnf(refute_0_192,plain,
add(multiply(X_12,additive_identity),X_10) = multiply(X_10,add(X_10,X_12)),
inference(subst,[],[refute_0_191:[bind(Y,$fot(X_10)),bind(X_22,$fot(X_12))]]) ).
cnf(refute_0_193,plain,
( add(multiply(X_12,additive_identity),X_10) != multiply(X_10,add(X_10,X_12))
| multiply(X_10,add(X_10,X_12)) = add(multiply(X_12,additive_identity),X_10) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(multiply(X_12,additive_identity),X_10))),bind(Y0,$fot(multiply(X_10,add(X_10,X_12))))]]) ).
cnf(refute_0_194,plain,
multiply(X_10,add(X_10,X_12)) = add(multiply(X_12,additive_identity),X_10),
inference(resolve,[$cnf( $equal(add(multiply(X_12,additive_identity),X_10),multiply(X_10,add(X_10,X_12))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
( multiply(X_10,add(X_10,X_12)) != add(multiply(X_12,additive_identity),X_10)
| add(X_10,multiply(additive_identity,X_12)) != multiply(X_10,add(X_10,X_12))
| add(X_10,multiply(additive_identity,X_12)) = add(multiply(X_12,additive_identity),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(X_10,add(X_10,X_12))) ),[1],$fot(add(multiply(X_12,additive_identity),X_10))]]) ).
cnf(refute_0_196,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(X_10,add(X_10,X_12))
| add(X_10,multiply(additive_identity,X_12)) = add(multiply(X_12,additive_identity),X_10) ),
inference(resolve,[$cnf( $equal(multiply(X_10,add(X_10,X_12)),add(multiply(X_12,additive_identity),X_10)) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
add(X_10,multiply(additive_identity,X_12)) = add(multiply(X_12,additive_identity),X_10),
inference(resolve,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(X_10,add(X_10,X_12))) )],[refute_0_134,refute_0_196]) ).
cnf(refute_0_198,plain,
add(add(Y,X_36),multiply(additive_identity,Y)) = add(multiply(Y,additive_identity),add(Y,X_36)),
inference(subst,[],[refute_0_197:[bind(X_10,$fot(add(Y,X_36))),bind(X_12,$fot(Y))]]) ).
cnf(refute_0_199,plain,
add(X_21,multiply(X_22,additive_identity)) = multiply(X_21,add(X_21,X_22)),
inference(subst,[],[refute_0_43:[bind(X_10,$fot(X_21)),bind(X_11,$fot(X_22))]]) ).
cnf(refute_0_200,plain,
add(X_22,X_21) = add(X_21,X_22),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_22)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_201,plain,
( add(X_22,X_21) != add(X_21,X_22)
| add(X_21,X_22) = add(X_22,X_21) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X_22,X_21))),bind(Y0,$fot(add(X_21,X_22)))]]) ).
cnf(refute_0_202,plain,
add(X_21,X_22) = add(X_22,X_21),
inference(resolve,[$cnf( $equal(add(X_22,X_21),add(X_21,X_22)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
( add(X_21,X_22) != add(X_22,X_21)
| add(X_21,multiply(X_22,additive_identity)) != multiply(X_21,add(X_21,X_22))
| add(X_21,multiply(X_22,additive_identity)) = multiply(X_21,add(X_22,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_21,multiply(X_22,additive_identity)),multiply(X_21,add(X_21,X_22))) ),[1,1],$fot(add(X_22,X_21))]]) ).
cnf(refute_0_204,plain,
( add(X_21,multiply(X_22,additive_identity)) != multiply(X_21,add(X_21,X_22))
| add(X_21,multiply(X_22,additive_identity)) = multiply(X_21,add(X_22,X_21)) ),
inference(resolve,[$cnf( $equal(add(X_21,X_22),add(X_22,X_21)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
add(X_21,multiply(X_22,additive_identity)) = multiply(X_21,add(X_22,X_21)),
inference(resolve,[$cnf( $equal(add(X_21,multiply(X_22,additive_identity)),multiply(X_21,add(X_21,X_22))) )],[refute_0_199,refute_0_204]) ).
cnf(refute_0_206,plain,
add(X_33,multiply(X_34,additive_identity)) = multiply(X_33,add(X_34,X_33)),
inference(subst,[],[refute_0_205:[bind(X_21,$fot(X_33)),bind(X_22,$fot(X_34))]]) ).
cnf(refute_0_207,plain,
multiply(additive_identity,X_34) = multiply(X_34,additive_identity),
inference(subst,[],[commutativity_of_multiply:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_34))]]) ).
cnf(refute_0_208,plain,
( multiply(additive_identity,X_34) != multiply(X_34,additive_identity)
| multiply(X_34,additive_identity) = multiply(additive_identity,X_34) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiply(additive_identity,X_34))),bind(Y0,$fot(multiply(X_34,additive_identity)))]]) ).
cnf(refute_0_209,plain,
multiply(X_34,additive_identity) = multiply(additive_identity,X_34),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_34),multiply(X_34,additive_identity)) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
( multiply(X_34,additive_identity) != multiply(additive_identity,X_34)
| add(X_33,multiply(X_34,additive_identity)) != multiply(X_33,add(X_34,X_33))
| add(X_33,multiply(additive_identity,X_34)) = multiply(X_33,add(X_34,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_33,multiply(X_34,additive_identity)),multiply(X_33,add(X_34,X_33))) ),[0,1],$fot(multiply(additive_identity,X_34))]]) ).
cnf(refute_0_211,plain,
( add(X_33,multiply(X_34,additive_identity)) != multiply(X_33,add(X_34,X_33))
| add(X_33,multiply(additive_identity,X_34)) = multiply(X_33,add(X_34,X_33)) ),
inference(resolve,[$cnf( $equal(multiply(X_34,additive_identity),multiply(additive_identity,X_34)) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
add(X_33,multiply(additive_identity,X_34)) = multiply(X_33,add(X_34,X_33)),
inference(resolve,[$cnf( $equal(add(X_33,multiply(X_34,additive_identity)),multiply(X_33,add(X_34,X_33))) )],[refute_0_206,refute_0_211]) ).
cnf(refute_0_213,plain,
( add(X_33,multiply(additive_identity,X_34)) != multiply(X_33,add(X_34,X_33))
| multiply(X_33,add(X_34,X_33)) = add(X_33,multiply(additive_identity,X_34)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X_33,multiply(additive_identity,X_34)))),bind(Y0,$fot(multiply(X_33,add(X_34,X_33))))]]) ).
cnf(refute_0_214,plain,
multiply(X_33,add(X_34,X_33)) = add(X_33,multiply(additive_identity,X_34)),
inference(resolve,[$cnf( $equal(add(X_33,multiply(additive_identity,X_34)),multiply(X_33,add(X_34,X_33))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
multiply(add(Y,X_36),add(Y,add(Y,X_36))) = add(add(Y,X_36),multiply(additive_identity,Y)),
inference(subst,[],[refute_0_214:[bind(X_33,$fot(add(Y,X_36))),bind(X_34,$fot(Y))]]) ).
cnf(refute_0_216,plain,
( multiply(add(Y,X_36),add(Y,add(Y,X_36))) != add(add(Y,X_36),multiply(additive_identity,Y))
| add(add(Y,X_36),multiply(additive_identity,Y)) != add(multiply(Y,additive_identity),add(Y,X_36))
| multiply(add(Y,X_36),add(Y,add(Y,X_36))) = add(multiply(Y,additive_identity),add(Y,X_36)) ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(multiply(add(Y,X_36),add(Y,add(Y,X_36))))),bind(Y0,$fot(add(add(Y,X_36),multiply(additive_identity,Y)))),bind(Z0,$fot(add(multiply(Y,additive_identity),add(Y,X_36))))]]) ).
cnf(refute_0_217,plain,
( add(add(Y,X_36),multiply(additive_identity,Y)) != add(multiply(Y,additive_identity),add(Y,X_36))
| multiply(add(Y,X_36),add(Y,add(Y,X_36))) = add(multiply(Y,additive_identity),add(Y,X_36)) ),
inference(resolve,[$cnf( $equal(multiply(add(Y,X_36),add(Y,add(Y,X_36))),add(add(Y,X_36),multiply(additive_identity,Y))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
multiply(add(Y,X_36),add(Y,add(Y,X_36))) = add(multiply(Y,additive_identity),add(Y,X_36)),
inference(resolve,[$cnf( $equal(add(add(Y,X_36),multiply(additive_identity,Y)),add(multiply(Y,additive_identity),add(Y,X_36))) )],[refute_0_198,refute_0_217]) ).
cnf(refute_0_219,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_11,X_10)),
inference(subst,[],[refute_0_205:[bind(X_21,$fot(X_10)),bind(X_22,$fot(X_11))]]) ).
cnf(refute_0_220,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(X_10,add(X_10,X_11))
| add(X_10,multiply(X_11,additive_identity)) != multiply(X_10,add(X_11,X_10))
| multiply(X_10,add(X_11,X_10)) = multiply(X_10,add(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(X_10,add(X_10,X_11))) ),[0],$fot(multiply(X_10,add(X_11,X_10)))]]) ).
cnf(refute_0_221,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(X_10,add(X_10,X_11))
| multiply(X_10,add(X_11,X_10)) = multiply(X_10,add(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(X_10,add(X_11,X_10))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
multiply(X_10,add(X_11,X_10)) = multiply(X_10,add(X_10,X_11)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(X_10,add(X_10,X_11))) )],[refute_0_43,refute_0_221]) ).
cnf(refute_0_223,plain,
( multiply(X_10,add(X_11,X_10)) != multiply(X_10,add(X_10,X_11))
| multiply(X_10,add(X_10,X_11)) = multiply(X_10,add(X_11,X_10)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiply(X_10,add(X_11,X_10)))),bind(Y0,$fot(multiply(X_10,add(X_10,X_11))))]]) ).
cnf(refute_0_224,plain,
multiply(X_10,add(X_10,X_11)) = multiply(X_10,add(X_11,X_10)),
inference(resolve,[$cnf( $equal(multiply(X_10,add(X_11,X_10)),multiply(X_10,add(X_10,X_11))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
multiply(add(Y,X_36),add(add(Y,X_36),Y)) = multiply(add(Y,X_36),add(Y,add(Y,X_36))),
inference(subst,[],[refute_0_224:[bind(X_10,$fot(add(Y,X_36))),bind(X_11,$fot(Y))]]) ).
cnf(refute_0_226,plain,
( multiply(add(Y,X_36),add(Y,add(Y,X_36))) != add(multiply(Y,additive_identity),add(Y,X_36))
| multiply(add(Y,X_36),add(add(Y,X_36),Y)) != multiply(add(Y,X_36),add(Y,add(Y,X_36)))
| multiply(add(Y,X_36),add(add(Y,X_36),Y)) = add(multiply(Y,additive_identity),add(Y,X_36)) ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(multiply(add(Y,X_36),add(add(Y,X_36),Y)))),bind(Y0,$fot(multiply(add(Y,X_36),add(Y,add(Y,X_36))))),bind(Z0,$fot(add(multiply(Y,additive_identity),add(Y,X_36))))]]) ).
cnf(refute_0_227,plain,
( multiply(add(Y,X_36),add(Y,add(Y,X_36))) != add(multiply(Y,additive_identity),add(Y,X_36))
| multiply(add(Y,X_36),add(add(Y,X_36),Y)) = add(multiply(Y,additive_identity),add(Y,X_36)) ),
inference(resolve,[$cnf( $equal(multiply(add(Y,X_36),add(add(Y,X_36),Y)),multiply(add(Y,X_36),add(Y,add(Y,X_36)))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
multiply(add(Y,X_36),add(add(Y,X_36),Y)) = add(multiply(Y,additive_identity),add(Y,X_36)),
inference(resolve,[$cnf( $equal(multiply(add(Y,X_36),add(Y,add(Y,X_36))),add(multiply(Y,additive_identity),add(Y,X_36))) )],[refute_0_218,refute_0_227]) ).
cnf(refute_0_229,plain,
( multiply(add(Y,X_36),add(add(Y,X_36),Y)) != add(multiply(Y,additive_identity),add(Y,X_36))
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) != multiply(add(Y,X_36),add(add(Y,X_36),Y))
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = add(multiply(Y,additive_identity),add(Y,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)),multiply(add(Y,X_36),add(add(Y,X_36),Y))) ),[1],$fot(add(multiply(Y,additive_identity),add(Y,X_36)))]]) ).
cnf(refute_0_230,plain,
( add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) != multiply(add(Y,X_36),add(add(Y,X_36),Y))
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = add(multiply(Y,additive_identity),add(Y,X_36)) ),
inference(resolve,[$cnf( $equal(multiply(add(Y,X_36),add(add(Y,X_36),Y)),add(multiply(Y,additive_identity),add(Y,X_36))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = add(multiply(Y,additive_identity),add(Y,X_36)),
inference(resolve,[$cnf( $equal(add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)),multiply(add(Y,X_36),add(add(Y,X_36),Y))) )],[refute_0_186,refute_0_230]) ).
cnf(refute_0_232,plain,
add(add(Y,X_36),Y) = add(Y,add(Y,X_36)),
inference(subst,[],[refute_0_117:[bind(X,$fot(Y)),bind(Y,$fot(add(Y,X_36)))]]) ).
cnf(refute_0_233,plain,
add(X,additive_identity) = add(additive_identity,X),
inference(subst,[],[commutativity_of_add:[bind(Y,$fot(additive_identity))]]) ).
cnf(refute_0_234,plain,
( add(X,additive_identity) != X
| add(X,additive_identity) != add(additive_identity,X)
| add(additive_identity,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(add(X,additive_identity),X) ),[0],$fot(add(additive_identity,X))]]) ).
cnf(refute_0_235,plain,
( add(X,additive_identity) != X
| add(additive_identity,X) = X ),
inference(resolve,[$cnf( $equal(add(X,additive_identity),add(additive_identity,X)) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
add(additive_identity,X) = X,
inference(resolve,[$cnf( $equal(add(X,additive_identity),X) )],[additive_id1,refute_0_235]) ).
cnf(refute_0_237,plain,
add(additive_identity,Y) = Y,
inference(subst,[],[refute_0_236:[bind(X,$fot(Y))]]) ).
cnf(refute_0_238,plain,
multiply(additive_identity,X_36) = additive_identity,
inference(subst,[],[refute_0_171:[bind(X_41,$fot(X_36))]]) ).
cnf(refute_0_239,plain,
add(multiply(additive_identity,X_36),Y) = add(multiply(additive_identity,X_36),Y),
introduced(tautology,[refl,[$fot(add(multiply(additive_identity,X_36),Y))]]) ).
cnf(refute_0_240,plain,
( multiply(additive_identity,X_36) != additive_identity
| add(multiply(additive_identity,X_36),Y) != add(multiply(additive_identity,X_36),Y)
| add(multiply(additive_identity,X_36),Y) = add(additive_identity,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_36),Y),add(multiply(additive_identity,X_36),Y)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_241,plain,
( multiply(additive_identity,X_36) != additive_identity
| add(multiply(additive_identity,X_36),Y) = add(additive_identity,Y) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_36),Y),add(multiply(additive_identity,X_36),Y)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
add(multiply(additive_identity,X_36),Y) = add(additive_identity,Y),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_36),additive_identity) )],[refute_0_238,refute_0_241]) ).
cnf(refute_0_243,plain,
( add(multiply(additive_identity,X_36),Y) != add(additive_identity,Y)
| add(additive_identity,Y) != Y
| add(multiply(additive_identity,X_36),Y) = Y ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(add(multiply(additive_identity,X_36),Y))),bind(Y0,$fot(add(additive_identity,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_244,plain,
( add(additive_identity,Y) != Y
| add(multiply(additive_identity,X_36),Y) = Y ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_36),Y),add(additive_identity,Y)) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
add(multiply(additive_identity,X_36),Y) = Y,
inference(resolve,[$cnf( $equal(add(additive_identity,Y),Y) )],[refute_0_237,refute_0_244]) ).
cnf(refute_0_246,plain,
add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)),
introduced(tautology,[refl,[$fot(add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)))]]) ).
cnf(refute_0_247,plain,
( add(multiply(additive_identity,X_36),Y) != Y
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) != add(add(Y,X_36),add(multiply(additive_identity,X_36),Y))
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = add(add(Y,X_36),Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)),add(add(Y,X_36),add(multiply(additive_identity,X_36),Y))) ),[1,1],$fot(Y)]]) ).
cnf(refute_0_248,plain,
( add(multiply(additive_identity,X_36),Y) != Y
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = add(add(Y,X_36),Y) ),
inference(resolve,[$cnf( $equal(add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)),add(add(Y,X_36),add(multiply(additive_identity,X_36),Y))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = add(add(Y,X_36),Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_36),Y),Y) )],[refute_0_245,refute_0_248]) ).
cnf(refute_0_250,plain,
( add(add(Y,X_36),Y) != add(Y,add(Y,X_36))
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) != add(add(Y,X_36),Y)
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = add(Y,add(Y,X_36)) ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)))),bind(Y0,$fot(add(add(Y,X_36),Y))),bind(Z0,$fot(add(Y,add(Y,X_36))))]]) ).
cnf(refute_0_251,plain,
( add(add(Y,X_36),Y) != add(Y,add(Y,X_36))
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = add(Y,add(Y,X_36)) ),
inference(resolve,[$cnf( $equal(add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)),add(add(Y,X_36),Y)) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) = add(Y,add(Y,X_36)),
inference(resolve,[$cnf( $equal(add(add(Y,X_36),Y),add(Y,add(Y,X_36))) )],[refute_0_232,refute_0_251]) ).
cnf(refute_0_253,plain,
( add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) != add(Y,add(Y,X_36))
| add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) != add(multiply(Y,additive_identity),add(Y,X_36))
| add(Y,add(Y,X_36)) = add(multiply(Y,additive_identity),add(Y,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)),add(multiply(Y,additive_identity),add(Y,X_36))) ),[0],$fot(add(Y,add(Y,X_36)))]]) ).
cnf(refute_0_254,plain,
( add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) != add(multiply(Y,additive_identity),add(Y,X_36))
| add(Y,add(Y,X_36)) = add(multiply(Y,additive_identity),add(Y,X_36)) ),
inference(resolve,[$cnf( $equal(add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)),add(Y,add(Y,X_36))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
add(X,multiply(Y,add(X,Y))) = multiply(add(X,Y),add(X,add(X,Y))),
inference(subst,[],[distributivity1:[bind(Z,$fot(add(X,Y)))]]) ).
cnf(refute_0_256,plain,
add(add(X,Y),multiply(X,additive_identity)) = multiply(add(X,Y),add(X,add(X,Y))),
inference(subst,[],[refute_0_205:[bind(X_21,$fot(add(X,Y))),bind(X_22,$fot(X))]]) ).
cnf(refute_0_257,plain,
( add(add(X,Y),multiply(X,additive_identity)) != multiply(add(X,Y),add(X,add(X,Y)))
| multiply(add(X,Y),add(X,add(X,Y))) = add(add(X,Y),multiply(X,additive_identity)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(add(X,Y),multiply(X,additive_identity)))),bind(Y0,$fot(multiply(add(X,Y),add(X,add(X,Y)))))]]) ).
cnf(refute_0_258,plain,
multiply(add(X,Y),add(X,add(X,Y))) = add(add(X,Y),multiply(X,additive_identity)),
inference(resolve,[$cnf( $equal(add(add(X,Y),multiply(X,additive_identity)),multiply(add(X,Y),add(X,add(X,Y)))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
( multiply(add(X,Y),add(X,add(X,Y))) != add(add(X,Y),multiply(X,additive_identity))
| add(X,multiply(Y,add(X,Y))) != multiply(add(X,Y),add(X,add(X,Y)))
| add(X,multiply(Y,add(X,Y))) = add(add(X,Y),multiply(X,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,multiply(Y,add(X,Y))),multiply(add(X,Y),add(X,add(X,Y)))) ),[1],$fot(add(add(X,Y),multiply(X,additive_identity)))]]) ).
cnf(refute_0_260,plain,
( add(X,multiply(Y,add(X,Y))) != multiply(add(X,Y),add(X,add(X,Y)))
| add(X,multiply(Y,add(X,Y))) = add(add(X,Y),multiply(X,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(add(X,Y),add(X,add(X,Y))),add(add(X,Y),multiply(X,additive_identity))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
add(X,multiply(Y,add(X,Y))) = add(add(X,Y),multiply(X,additive_identity)),
inference(resolve,[$cnf( $equal(add(X,multiply(Y,add(X,Y))),multiply(add(X,Y),add(X,add(X,Y)))) )],[refute_0_255,refute_0_260]) ).
cnf(refute_0_262,plain,
add(add(X,Y),multiply(X,additive_identity)) = add(multiply(X,additive_identity),add(X,Y)),
inference(subst,[],[refute_0_117:[bind(X,$fot(multiply(X,additive_identity))),bind(Y,$fot(add(X,Y)))]]) ).
cnf(refute_0_263,plain,
( add(X,multiply(Y,add(X,Y))) != add(add(X,Y),multiply(X,additive_identity))
| add(add(X,Y),multiply(X,additive_identity)) != add(multiply(X,additive_identity),add(X,Y))
| add(X,multiply(Y,add(X,Y))) = add(multiply(X,additive_identity),add(X,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,multiply(Y,add(X,Y))),add(multiply(X,additive_identity),add(X,Y))) ),[0],$fot(add(add(X,Y),multiply(X,additive_identity)))]]) ).
cnf(refute_0_264,plain,
( add(X,multiply(Y,add(X,Y))) != add(add(X,Y),multiply(X,additive_identity))
| add(X,multiply(Y,add(X,Y))) = add(multiply(X,additive_identity),add(X,Y)) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),multiply(X,additive_identity)),add(multiply(X,additive_identity),add(X,Y))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
add(X,multiply(Y,add(X,Y))) = add(multiply(X,additive_identity),add(X,Y)),
inference(resolve,[$cnf( $equal(add(X,multiply(Y,add(X,Y))),add(add(X,Y),multiply(X,additive_identity))) )],[refute_0_261,refute_0_264]) ).
cnf(refute_0_266,plain,
multiply(add(X_40,X_41),add(X_40,X_41)) = add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)),
inference(subst,[],[distributivity2:[bind(X,$fot(add(X_40,X_41))),bind(Y,$fot(X_40)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_267,plain,
add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = multiply(add(X_40,X_41),add(X_40,X_41)),
inference(subst,[],[refute_0_71:[bind(Y,$fot(add(X_40,X_41)))]]) ).
cnf(refute_0_268,plain,
( add(multiply(additive_identity,additive_identity),add(X_40,X_41)) != multiply(add(X_40,X_41),add(X_40,X_41))
| multiply(add(X_40,X_41),add(X_40,X_41)) = add(multiply(additive_identity,additive_identity),add(X_40,X_41)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),add(X_40,X_41)))),bind(Y0,$fot(multiply(add(X_40,X_41),add(X_40,X_41))))]]) ).
cnf(refute_0_269,plain,
multiply(add(X_40,X_41),add(X_40,X_41)) = add(multiply(additive_identity,additive_identity),add(X_40,X_41)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),add(X_40,X_41)),multiply(add(X_40,X_41),add(X_40,X_41))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
( multiply(add(X_40,X_41),add(X_40,X_41)) != add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41))
| multiply(add(X_40,X_41),add(X_40,X_41)) != add(multiply(additive_identity,additive_identity),add(X_40,X_41))
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_40,X_41),add(X_40,X_41)),add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41))) ),[0],$fot(add(multiply(additive_identity,additive_identity),add(X_40,X_41)))]]) ).
cnf(refute_0_271,plain,
( multiply(add(X_40,X_41),add(X_40,X_41)) != add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41))
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_40,X_41),add(X_40,X_41)),add(multiply(additive_identity,additive_identity),add(X_40,X_41))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)),
inference(resolve,[$cnf( $equal(multiply(add(X_40,X_41),add(X_40,X_41)),add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41))) )],[refute_0_266,refute_0_271]) ).
cnf(refute_0_273,plain,
multiply(add(X_40,X_41),X_40) = multiply(X_40,add(X_40,X_41)),
inference(subst,[],[refute_0_29:[bind(X,$fot(X_40)),bind(Y,$fot(add(X_40,X_41)))]]) ).
cnf(refute_0_274,plain,
add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))) = add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))),
introduced(tautology,[refl,[$fot(add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))))]]) ).
cnf(refute_0_275,plain,
( multiply(add(X_40,X_41),X_40) != multiply(X_40,add(X_40,X_41))
| add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))) != add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41)))
| add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))),add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41)))) ),[1,0],$fot(multiply(X_40,add(X_40,X_41)))]]) ).
cnf(refute_0_276,plain,
( multiply(add(X_40,X_41),X_40) != multiply(X_40,add(X_40,X_41))
| add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))),add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41)))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))),
inference(resolve,[$cnf( $equal(multiply(add(X_40,X_41),X_40),multiply(X_40,add(X_40,X_41))) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
multiply(add(X_10,X_12),add(X_10,X_11)) = multiply(add(X_10,X_11),add(X_10,X_12)),
inference(subst,[],[commutativity_of_multiply:[bind(X,$fot(add(X_10,X_12))),bind(Y,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_279,plain,
add(X_10,multiply(X_11,X_12)) = multiply(add(X_10,X_11),add(X_10,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_280,plain,
( add(X_10,multiply(X_11,X_12)) != multiply(add(X_10,X_11),add(X_10,X_12))
| multiply(add(X_10,X_11),add(X_10,X_12)) = add(X_10,multiply(X_11,X_12)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X_10,multiply(X_11,X_12)))),bind(Y0,$fot(multiply(add(X_10,X_11),add(X_10,X_12))))]]) ).
cnf(refute_0_281,plain,
multiply(add(X_10,X_11),add(X_10,X_12)) = add(X_10,multiply(X_11,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,X_12)),multiply(add(X_10,X_11),add(X_10,X_12))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
( multiply(add(X_10,X_11),add(X_10,X_12)) != add(X_10,multiply(X_11,X_12))
| multiply(add(X_10,X_12),add(X_10,X_11)) != multiply(add(X_10,X_11),add(X_10,X_12))
| multiply(add(X_10,X_12),add(X_10,X_11)) = add(X_10,multiply(X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_10,X_12),add(X_10,X_11)),multiply(add(X_10,X_11),add(X_10,X_12))) ),[1],$fot(add(X_10,multiply(X_11,X_12)))]]) ).
cnf(refute_0_283,plain,
( multiply(add(X_10,X_12),add(X_10,X_11)) != multiply(add(X_10,X_11),add(X_10,X_12))
| multiply(add(X_10,X_12),add(X_10,X_11)) = add(X_10,multiply(X_11,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),add(X_10,X_12)),add(X_10,multiply(X_11,X_12))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
multiply(add(X_10,X_12),add(X_10,X_11)) = add(X_10,multiply(X_11,X_12)),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_12),add(X_10,X_11)),multiply(add(X_10,X_11),add(X_10,X_12))) )],[refute_0_278,refute_0_283]) ).
cnf(refute_0_285,plain,
( add(X,multiply(Y,Z)) != multiply(add(X,Y),add(X,Z))
| multiply(add(X,Y),add(X,Z)) = add(X,multiply(Y,Z)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X,multiply(Y,Z)))),bind(Y0,$fot(multiply(add(X,Y),add(X,Z))))]]) ).
cnf(refute_0_286,plain,
multiply(add(X,Y),add(X,Z)) = add(X,multiply(Y,Z)),
inference(resolve,[$cnf( $equal(add(X,multiply(Y,Z)),multiply(add(X,Y),add(X,Z))) )],[distributivity1,refute_0_285]) ).
cnf(refute_0_287,plain,
multiply(add(X_10,X_12),add(X_10,X_11)) = add(X_10,multiply(X_12,X_11)),
inference(subst,[],[refute_0_286:[bind(X,$fot(X_10)),bind(Y,$fot(X_12)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_288,plain,
( multiply(add(X_10,X_12),add(X_10,X_11)) != add(X_10,multiply(X_11,X_12))
| multiply(add(X_10,X_12),add(X_10,X_11)) != add(X_10,multiply(X_12,X_11))
| add(X_10,multiply(X_12,X_11)) = add(X_10,multiply(X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_10,X_12),add(X_10,X_11)),add(X_10,multiply(X_11,X_12))) ),[0],$fot(add(X_10,multiply(X_12,X_11)))]]) ).
cnf(refute_0_289,plain,
( multiply(add(X_10,X_12),add(X_10,X_11)) != add(X_10,multiply(X_11,X_12))
| add(X_10,multiply(X_12,X_11)) = add(X_10,multiply(X_11,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_12),add(X_10,X_11)),add(X_10,multiply(X_12,X_11))) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
add(X_10,multiply(X_12,X_11)) = add(X_10,multiply(X_11,X_12)),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_12),add(X_10,X_11)),add(X_10,multiply(X_11,X_12))) )],[refute_0_284,refute_0_289]) ).
cnf(refute_0_291,plain,
( add(X_10,multiply(X_12,X_11)) != add(X_10,multiply(X_11,X_12))
| add(X_10,multiply(X_11,X_12)) = add(X_10,multiply(X_12,X_11)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X_10,multiply(X_12,X_11)))),bind(Y0,$fot(add(X_10,multiply(X_11,X_12))))]]) ).
cnf(refute_0_292,plain,
add(X_10,multiply(X_11,X_12)) = add(X_10,multiply(X_12,X_11)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_12,X_11)),add(X_10,multiply(X_11,X_12))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)) = add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))),
inference(subst,[],[refute_0_292:[bind(X_10,$fot(multiply(add(X_40,X_41),X_40))),bind(X_11,$fot(add(X_40,X_41))),bind(X_12,$fot(X_41))]]) ).
cnf(refute_0_294,plain,
( add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))) != add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))
| add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)) != add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41)))
| add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)))),bind(Y0,$fot(add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))))),bind(Z0,$fot(add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))))]]) ).
cnf(refute_0_295,plain,
( add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))) != add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))
| add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)),add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41)))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))),
inference(resolve,[$cnf( $equal(add(multiply(add(X_40,X_41),X_40),multiply(X_41,add(X_40,X_41))),add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))) )],[refute_0_277,refute_0_295]) ).
cnf(refute_0_297,plain,
( add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)) != add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) != add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41))
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),add(X_40,X_41)),add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41))) ),[1],$fot(add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))))]]) ).
cnf(refute_0_298,plain,
( add(multiply(additive_identity,additive_identity),add(X_40,X_41)) != add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41))
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41)),add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),add(X_40,X_41)),add(multiply(add(X_40,X_41),X_40),multiply(add(X_40,X_41),X_41))) )],[refute_0_272,refute_0_298]) ).
cnf(refute_0_300,plain,
add(additive_identity,add(X_40,X_41)) = add(X_40,X_41),
inference(subst,[],[refute_0_236:[bind(X,$fot(add(X_40,X_41)))]]) ).
cnf(refute_0_301,plain,
add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(multiply(additive_identity,additive_identity),add(X_40,X_41)),
introduced(tautology,[refl,[$fot(add(multiply(additive_identity,additive_identity),add(X_40,X_41)))]]) ).
cnf(refute_0_302,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) != add(multiply(additive_identity,additive_identity),add(X_40,X_41))
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(additive_identity,add(X_40,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),add(X_40,X_41)),add(multiply(additive_identity,additive_identity),add(X_40,X_41))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_303,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(additive_identity,add(X_40,X_41)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),add(X_40,X_41)),add(multiply(additive_identity,additive_identity),add(X_40,X_41))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(additive_identity,add(X_40,X_41)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),additive_identity) )],[refute_0_172,refute_0_303]) ).
cnf(refute_0_305,plain,
( add(multiply(additive_identity,additive_identity),add(X_40,X_41)) != add(additive_identity,add(X_40,X_41))
| add(additive_identity,add(X_40,X_41)) != add(X_40,X_41)
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(X_40,X_41) ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),add(X_40,X_41)))),bind(Y0,$fot(add(additive_identity,add(X_40,X_41)))),bind(Z0,$fot(add(X_40,X_41)))]]) ).
cnf(refute_0_306,plain,
( add(additive_identity,add(X_40,X_41)) != add(X_40,X_41)
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(X_40,X_41) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),add(X_40,X_41)),add(additive_identity,add(X_40,X_41))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
add(multiply(additive_identity,additive_identity),add(X_40,X_41)) = add(X_40,X_41),
inference(resolve,[$cnf( $equal(add(additive_identity,add(X_40,X_41)),add(X_40,X_41)) )],[refute_0_300,refute_0_306]) ).
cnf(refute_0_308,plain,
( add(multiply(additive_identity,additive_identity),add(X_40,X_41)) != add(X_40,X_41)
| add(multiply(additive_identity,additive_identity),add(X_40,X_41)) != add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))
| add(X_40,X_41) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),add(X_40,X_41)),add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))) ),[0],$fot(add(X_40,X_41))]]) ).
cnf(refute_0_309,plain,
( add(multiply(additive_identity,additive_identity),add(X_40,X_41)) != add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))
| add(X_40,X_41) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),add(X_40,X_41)),add(X_40,X_41)) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
multiply(X_40,add(X_40,X_41)) = X_40,
inference(subst,[],[refute_0_127:[bind(X_39,$fot(X_40)),bind(X_40,$fot(X_41))]]) ).
cnf(refute_0_311,plain,
add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) = add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))),
introduced(tautology,[refl,[$fot(add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))))]]) ).
cnf(refute_0_312,plain,
( multiply(X_40,add(X_40,X_41)) != X_40
| add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) != add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))
| add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) = add(X_40,multiply(X_41,add(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))),add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))) ),[1,0],$fot(X_40)]]) ).
cnf(refute_0_313,plain,
( multiply(X_40,add(X_40,X_41)) != X_40
| add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) = add(X_40,multiply(X_41,add(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))),add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) = add(X_40,multiply(X_41,add(X_40,X_41))),
inference(resolve,[$cnf( $equal(multiply(X_40,add(X_40,X_41)),X_40) )],[refute_0_310,refute_0_313]) ).
cnf(refute_0_315,plain,
( add(X_40,X_41) != add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))
| add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))) != add(X_40,multiply(X_41,add(X_40,X_41)))
| add(X_40,X_41) = add(X_40,multiply(X_41,add(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_40,X_41),add(X_40,multiply(X_41,add(X_40,X_41)))) ),[0],$fot(add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))))]]) ).
cnf(refute_0_316,plain,
( add(X_40,X_41) != add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))
| add(X_40,X_41) = add(X_40,multiply(X_41,add(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41))),add(X_40,multiply(X_41,add(X_40,X_41)))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
( add(multiply(additive_identity,additive_identity),add(X_40,X_41)) != add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))
| add(X_40,X_41) = add(X_40,multiply(X_41,add(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(add(X_40,X_41),add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))) )],[refute_0_309,refute_0_316]) ).
cnf(refute_0_318,plain,
add(X_40,X_41) = add(X_40,multiply(X_41,add(X_40,X_41))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),add(X_40,X_41)),add(multiply(X_40,add(X_40,X_41)),multiply(X_41,add(X_40,X_41)))) )],[refute_0_299,refute_0_317]) ).
cnf(refute_0_319,plain,
( add(X_40,X_41) != add(X_40,multiply(X_41,add(X_40,X_41)))
| add(X_40,multiply(X_41,add(X_40,X_41))) = add(X_40,X_41) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X_40,X_41))),bind(Y0,$fot(add(X_40,multiply(X_41,add(X_40,X_41)))))]]) ).
cnf(refute_0_320,plain,
add(X_40,multiply(X_41,add(X_40,X_41))) = add(X_40,X_41),
inference(resolve,[$cnf( $equal(add(X_40,X_41),add(X_40,multiply(X_41,add(X_40,X_41)))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
add(X,multiply(Y,add(X,Y))) = add(X,Y),
inference(subst,[],[refute_0_320:[bind(X_40,$fot(X)),bind(X_41,$fot(Y))]]) ).
cnf(refute_0_322,plain,
( add(X,multiply(Y,add(X,Y))) != add(X,Y)
| add(X,multiply(Y,add(X,Y))) != add(multiply(X,additive_identity),add(X,Y))
| add(X,Y) = add(multiply(X,additive_identity),add(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,multiply(Y,add(X,Y))),add(multiply(X,additive_identity),add(X,Y))) ),[0],$fot(add(X,Y))]]) ).
cnf(refute_0_323,plain,
( add(X,multiply(Y,add(X,Y))) != add(multiply(X,additive_identity),add(X,Y))
| add(X,Y) = add(multiply(X,additive_identity),add(X,Y)) ),
inference(resolve,[$cnf( $equal(add(X,multiply(Y,add(X,Y))),add(X,Y)) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
add(X,Y) = add(multiply(X,additive_identity),add(X,Y)),
inference(resolve,[$cnf( $equal(add(X,multiply(Y,add(X,Y))),add(multiply(X,additive_identity),add(X,Y))) )],[refute_0_265,refute_0_323]) ).
cnf(refute_0_325,plain,
( add(X,Y) != add(multiply(X,additive_identity),add(X,Y))
| add(multiply(X,additive_identity),add(X,Y)) = add(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(multiply(X,additive_identity),add(X,Y))))]]) ).
cnf(refute_0_326,plain,
add(multiply(X,additive_identity),add(X,Y)) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(multiply(X,additive_identity),add(X,Y))) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
add(multiply(Y,additive_identity),add(Y,X_36)) = add(Y,X_36),
inference(subst,[],[refute_0_326:[bind(X,$fot(Y)),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_328,plain,
( add(Y,add(Y,X_36)) != add(multiply(Y,additive_identity),add(Y,X_36))
| add(multiply(Y,additive_identity),add(Y,X_36)) != add(Y,X_36)
| add(Y,add(Y,X_36)) = add(Y,X_36) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(Y,add(Y,X_36)),add(Y,X_36)) ),[0],$fot(add(multiply(Y,additive_identity),add(Y,X_36)))]]) ).
cnf(refute_0_329,plain,
( add(Y,add(Y,X_36)) != add(multiply(Y,additive_identity),add(Y,X_36))
| add(Y,add(Y,X_36)) = add(Y,X_36) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,additive_identity),add(Y,X_36)),add(Y,X_36)) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
( add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)) != add(multiply(Y,additive_identity),add(Y,X_36))
| add(Y,add(Y,X_36)) = add(Y,X_36) ),
inference(resolve,[$cnf( $equal(add(Y,add(Y,X_36)),add(multiply(Y,additive_identity),add(Y,X_36))) )],[refute_0_254,refute_0_329]) ).
cnf(refute_0_331,plain,
add(Y,add(Y,X_36)) = add(Y,X_36),
inference(resolve,[$cnf( $equal(add(add(Y,X_36),add(multiply(additive_identity,X_36),Y)),add(multiply(Y,additive_identity),add(Y,X_36))) )],[refute_0_231,refute_0_330]) ).
cnf(refute_0_332,plain,
add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = add(X_28,multiply(additive_identity,additive_identity)),
inference(subst,[],[refute_0_331:[bind(Y,$fot(X_28)),bind(X_36,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_333,plain,
( add(X_28,multiply(additive_identity,additive_identity)) != X_28
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != add(X_28,multiply(additive_identity,additive_identity))
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = X_28 ),
inference(subst,[],[refute_0_102:[bind(X0,$fot(add(X_28,add(X_28,multiply(additive_identity,additive_identity))))),bind(Y0,$fot(add(X_28,multiply(additive_identity,additive_identity)))),bind(Z0,$fot(X_28))]]) ).
cnf(refute_0_334,plain,
( add(X_28,multiply(additive_identity,additive_identity)) != X_28
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = X_28 ),
inference(resolve,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),add(X_28,multiply(additive_identity,additive_identity))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = X_28,
inference(resolve,[$cnf( $equal(add(X_28,multiply(additive_identity,additive_identity)),X_28) )],[refute_0_179,refute_0_334]) ).
cnf(refute_0_336,plain,
( add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != X_28
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != multiply(X_28,X_28)
| X_28 = multiply(X_28,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),multiply(X_28,X_28)) ),[0],$fot(X_28)]]) ).
cnf(refute_0_337,plain,
( add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != multiply(X_28,X_28)
| X_28 = multiply(X_28,X_28) ),
inference(resolve,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),X_28) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
X_28 = multiply(X_28,X_28),
inference(resolve,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),multiply(X_28,X_28)) )],[refute_0_64,refute_0_337]) ).
cnf(refute_0_339,plain,
( X_28 != multiply(X_28,X_28)
| multiply(X_28,X_28) = X_28 ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(X_28)),bind(Y0,$fot(multiply(X_28,X_28)))]]) ).
cnf(refute_0_340,plain,
multiply(X_28,X_28) = X_28,
inference(resolve,[$cnf( $equal(X_28,multiply(X_28,X_28)) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
multiply(a,a) = a,
inference(subst,[],[refute_0_340:[bind(X_28,$fot(a))]]) ).
cnf(refute_0_342,plain,
( multiply(a,a) != a
| a != a
| multiply(a,a) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,a),a) ),[0],$fot(a)]]) ).
cnf(refute_0_343,plain,
( a != a
| multiply(a,a) = a ),
inference(resolve,[$cnf( $equal(multiply(a,a),a) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
a != a,
inference(resolve,[$cnf( $equal(multiply(a,a),a) )],[refute_0_343,prove_a_times_a_is_a]) ).
cnf(refute_0_345,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_346,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_345,refute_0_344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO003-4 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 18:56:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.42/0.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.59
% 0.42/0.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.42/0.63
%------------------------------------------------------------------------------