%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG009-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:34:45 PM UTC 2026
% Result : Unsatisfiable 81.53s 10.70s
% Output : CNFRefutation 84.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 112
% Number of leaves : 9
% Syntax : Number of clauses : 694 ( 694 unt; 0 nHn; 7 RR)
% Number of literals : 694 ( 693 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 1620 ( 29 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutative_addition) ).
cnf(c3,plain,
add(additive_inverse(X3),X2) = add(X2,additive_inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
add(X2,additive_inverse(X3)) = add(additive_inverse(X3),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
add(X3,add(X2,additive_inverse(X3))) = add(X3,add(additive_inverse(X3),X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
add(add(X2,Y2),Z) = add(X2,add(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_addition) ).
cnf(c7,plain,
add(add(X3,additive_inverse(X3)),X2) = add(X3,add(additive_inverse(X3),X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
add(X3,add(additive_inverse(X3),X2)) = add(add(X3,additive_inverse(X3)),X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
add(X2,additive_inverse(X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c10,plain,
add(add(X3,additive_inverse(X3)),X2) = add(additive_identity,X2),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
add(X2,additive_identity) = add(additive_identity,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
add(additive_identity,X2) = add(X2,additive_identity),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
add(X2,additive_identity) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c14,plain,
add(additive_identity,X2) = X2,
inference(transitivity,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
add(add(X3,additive_inverse(X3)),X2) = X2,
inference(transitivity,[status(thm)],[c10,c14]) ).
cnf(c16,plain,
add(X3,add(additive_inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c8,c15]) ).
cnf(c17,plain,
add(X3,add(X2,additive_inverse(X3))) = X2,
inference(transitivity,[status(thm)],[c5,c16]) ).
cnf(c18,plain,
add(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))) = multiply(X2,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X2,X3) = add(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
add(additive_inverse(multiply(X2,X3)),multiply(X3,X2)) = add(multiply(X3,X2),additive_inverse(multiply(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
add(multiply(X3,X2),additive_inverse(multiply(X2,X3))) = add(additive_inverse(multiply(X2,X3)),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
add(X2,additive_inverse(X3)) = add(additive_inverse(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
add(additive_inverse(X3),X2) = add(X2,additive_inverse(X3)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
add(X3,add(additive_inverse(X3),X2)) = add(X3,add(X2,additive_inverse(X3))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
add(X3,add(additive_inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c24,c17]) ).
cnf(c26,plain,
add(multiply(X2,X3),add(additive_inverse(multiply(X2,X3)),multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))))) = multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))) = add(multiply(X2,X3),add(additive_inverse(multiply(X2,X3)),multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_multiplication) ).
cnf(c29,plain,
multiply(multiply(X3,X5),multiply(multiply(X5,X2),multiply(X5,X4))) = multiply(X3,multiply(X5,multiply(multiply(X5,X2),multiply(X5,X4)))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(multiply(multiply(X4,X3),X4),X2) = multiply(multiply(X4,X3),multiply(X4,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c31,plain,
multiply(multiply(X4,X3),multiply(X4,X2)) = multiply(multiply(multiply(X4,X3),X4),X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(X4,multiply(multiply(X4,X3),multiply(X4,X2))) = multiply(X4,multiply(multiply(multiply(X4,X3),X4),X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(multiply(X4,multiply(multiply(X4,X3),X4)),X2) = multiply(X4,multiply(multiply(multiply(X4,X3),X4),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c34,plain,
multiply(X4,multiply(multiply(multiply(X4,X3),X4),X2)) = multiply(multiply(X4,multiply(multiply(X4,X3),X4)),X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
add(multiply(X2,X3),add(additive_inverse(multiply(X2,X3)),multiply(X3,multiply(multiply(X3,X2),X3)))) = multiply(X3,multiply(multiply(X3,X2),X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c36,plain,
multiply(X3,multiply(multiply(X3,X2),X3)) = add(multiply(X2,X3),add(additive_inverse(multiply(X2,X3)),multiply(X3,multiply(multiply(X3,X2),X3)))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
add(X2,add(additive_inverse(X2),additive_inverse(additive_inverse(X2)))) = additive_inverse(additive_inverse(X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c38,plain,
additive_inverse(additive_inverse(X2)) = add(X2,add(additive_inverse(X2),additive_inverse(additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
add(additive_inverse(X2),additive_inverse(additive_inverse(X2))) = additive_identity,
inference(substitution,[status(thm)],[c9]) ).
cnf(c40,plain,
add(X2,add(additive_inverse(X2),additive_inverse(additive_inverse(X2)))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
add(X2,add(additive_inverse(X2),additive_inverse(additive_inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c40,c13]) ).
cnf(c42,plain,
additive_inverse(additive_inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c38,c41]) ).
cnf(c43,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(multiply(X2,X3),X2) = multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(X2,multiply(multiply(X2,X3),X2)) = multiply(X2,multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2)))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),X2))) = add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
add(additive_inverse(multiply(X3,X2)),additive_identity) = additive_inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c48,plain,
additive_inverse(multiply(X3,X2)) = add(additive_inverse(multiply(X3,X2)),additive_identity),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c50,plain,
multiply(X2,additive_identity) = multiply(additive_inverse(additive_inverse(X2)),additive_identity),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),additive_identity))) = multiply(additive_inverse(X2),additive_identity),
inference(substitution,[status(thm)],[c25]) ).
cnf(c52,plain,
multiply(additive_inverse(X2),additive_identity) = add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),additive_identity))),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
add(multiply(X3,X3),X2) = add(X2,multiply(X3,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c54,plain,
add(X2,multiply(X3,X3)) = add(multiply(X3,X3),X2),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(X3,add(X2,multiply(X3,X3))) = multiply(X3,add(multiply(X3,X3),X2)),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
cnf(c57,plain,
multiply(X3,add(multiply(X3,X3),X2)) = add(multiply(X3,multiply(X3,X3)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,axiom,
multiply(X2,multiply(X2,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c59,plain,
add(multiply(X3,multiply(X3,X3)),multiply(X3,X2)) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(X3,add(multiply(X3,X3),X2)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c57,c59]) ).
cnf(c61,plain,
multiply(X3,add(X2,multiply(X3,X3))) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c55,c60]) ).
cnf(c62,plain,
multiply(X2,add(additive_identity,multiply(X2,X2))) = add(X2,multiply(X2,additive_identity)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
add(X2,multiply(X2,additive_identity)) = multiply(X2,add(additive_identity,multiply(X2,X2))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
add(additive_identity,multiply(X2,X2)) = multiply(X2,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c65,plain,
multiply(X2,add(additive_identity,multiply(X2,X2))) = multiply(X2,multiply(X2,X2)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(X2,add(additive_identity,multiply(X2,X2))) = X2,
inference(transitivity,[status(thm)],[c65,c58]) ).
cnf(c67,plain,
add(X2,multiply(X2,additive_identity)) = X2,
inference(transitivity,[status(thm)],[c63,c66]) ).
cnf(c68,plain,
add(additive_inverse(X2),multiply(additive_inverse(X2),additive_identity)) = additive_inverse(X2),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),additive_identity))) = add(X2,additive_inverse(X2)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),additive_identity))) = additive_identity,
inference(transitivity,[status(thm)],[c69,c9]) ).
cnf(c71,plain,
multiply(additive_inverse(X2),additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c52,c70]) ).
cnf(c72,plain,
multiply(additive_inverse(additive_inverse(X2)),additive_identity) = additive_identity,
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(X2,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c50,c72]) ).
cnf(c74,plain,
additive_identity = multiply(X2,additive_identity),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
add(additive_inverse(multiply(X3,X2)),additive_identity) = add(additive_inverse(multiply(X3,X2)),multiply(X3,additive_identity)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
additive_identity = add(X2,additive_inverse(X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c77,plain,
multiply(X3,additive_identity) = multiply(X3,add(X2,additive_inverse(X2))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X3,additive_identity)) = add(additive_inverse(multiply(X3,X2)),multiply(X3,add(X2,additive_inverse(X2)))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
add(multiply(X4,X2),X3) = add(X3,multiply(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c80,plain,
add(X3,multiply(X4,X2)) = add(multiply(X4,X2),X3),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
add(multiply(X5,X4),add(X3,multiply(X5,X2))) = add(multiply(X5,X4),add(multiply(X5,X2),X3)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
add(add(X3,X2),X4) = add(X4,add(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c83,plain,
add(X4,add(X3,X2)) = add(add(X3,X2),X4),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
add(add(X3,X2),X4) = add(X3,add(X2,X4)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c85,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c86,plain,
add(X3,add(X2,X4)) = add(X3,add(X4,X2)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
add(add(X3,X2),X4) = add(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c84,c86]) ).
cnf(c88,plain,
add(X4,add(X3,X2)) = add(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c83,c87]) ).
cnf(c89,plain,
add(multiply(X5,X2),add(multiply(X5,X4),X3)) = add(multiply(X5,X4),add(multiply(X5,X2),X3)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
add(multiply(X5,X4),add(multiply(X5,X2),X3)) = add(multiply(X5,X2),add(multiply(X5,X4),X3)),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
add(add(multiply(X5,X2),multiply(X5,X4)),X3) = add(multiply(X5,X2),add(multiply(X5,X4),X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c92,plain,
add(multiply(X5,X2),add(multiply(X5,X4),X3)) = add(add(multiply(X5,X2),multiply(X5,X4)),X3),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(X4,add(X2,X3)) = add(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c94,plain,
add(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,add(X2,X3)),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
add(add(multiply(X5,X2),multiply(X5,X4)),X3) = add(multiply(X5,add(X2,X4)),X3),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
add(multiply(X5,add(X2,X4)),X3) = add(X3,multiply(X5,add(X2,X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c97,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c98,plain,
multiply(X4,add(X2,X3)) = multiply(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
add(X3,multiply(X5,add(X2,X4))) = add(X3,multiply(X5,add(X4,X2))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
add(multiply(X5,add(X2,X4)),X3) = add(X3,multiply(X5,add(X4,X2))),
inference(transitivity,[status(thm)],[c96,c99]) ).
cnf(c101,plain,
add(add(multiply(X5,X2),multiply(X5,X4)),X3) = add(X3,multiply(X5,add(X4,X2))),
inference(transitivity,[status(thm)],[c95,c100]) ).
cnf(c102,plain,
add(multiply(X5,X2),add(multiply(X5,X4),X3)) = add(X3,multiply(X5,add(X4,X2))),
inference(transitivity,[status(thm)],[c92,c101]) ).
cnf(c103,plain,
add(multiply(X5,X4),add(multiply(X5,X2),X3)) = add(X3,multiply(X5,add(X4,X2))),
inference(transitivity,[status(thm)],[c90,c102]) ).
cnf(c104,plain,
add(multiply(X5,X4),add(X3,multiply(X5,X2))) = add(X3,multiply(X5,add(X4,X2))),
inference(transitivity,[status(thm)],[c81,c103]) ).
cnf(c105,plain,
add(multiply(X4,X3),add(additive_inverse(multiply(X4,X3)),multiply(X4,X2))) = add(additive_inverse(multiply(X4,X3)),multiply(X4,add(X3,X2))),
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
add(additive_inverse(multiply(X4,X3)),multiply(X4,add(X3,X2))) = add(multiply(X4,X3),add(additive_inverse(multiply(X4,X3)),multiply(X4,X2))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
add(multiply(X4,X3),add(additive_inverse(multiply(X4,X3)),multiply(X4,X2))) = multiply(X4,X2),
inference(substitution,[status(thm)],[c25]) ).
cnf(c108,plain,
add(additive_inverse(multiply(X4,X3)),multiply(X4,add(X3,X2))) = multiply(X4,X2),
inference(transitivity,[status(thm)],[c106,c107]) ).
cnf(c109,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X3,add(X2,additive_inverse(X2)))) = multiply(X3,additive_inverse(X2)),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X3,additive_identity)) = multiply(X3,additive_inverse(X2)),
inference(transitivity,[status(thm)],[c78,c109]) ).
cnf(c111,plain,
add(additive_inverse(multiply(X3,X2)),additive_identity) = multiply(X3,additive_inverse(X2)),
inference(transitivity,[status(thm)],[c75,c110]) ).
cnf(c112,plain,
additive_inverse(multiply(X3,X2)) = multiply(X3,additive_inverse(X2)),
inference(transitivity,[status(thm)],[c48,c111]) ).
cnf(c113,plain,
additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2))) = multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))) = additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2))),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
multiply(X2,multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2)))) = multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2)))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))))) = add(additive_inverse(multiply(X3,X2)),multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2))))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2)))) = multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2)))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c118,plain,
multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2)))) = additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2))))) = add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c121,plain,
add(X3,X2) = add(X3,additive_inverse(additive_inverse(X2))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
additive_inverse(add(X3,X2)) = additive_inverse(add(X3,additive_inverse(additive_inverse(X2)))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c124,plain,
add(X3,X2) = add(X3,additive_inverse(additive_inverse(X2))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
additive_inverse(add(X3,X2)) = additive_inverse(add(X3,additive_inverse(additive_inverse(X2)))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
add(X3,additive_inverse(add(X3,X2))) = add(X3,additive_inverse(add(X3,additive_inverse(additive_inverse(X2))))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
add(additive_inverse(X2),X3) = add(X3,additive_inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c128,plain,
add(X3,additive_inverse(X2)) = add(additive_inverse(X2),X3),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
additive_inverse(add(X3,additive_inverse(X2))) = additive_inverse(add(additive_inverse(X2),X3)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
add(X3,additive_inverse(add(X3,additive_inverse(X2)))) = add(X3,additive_inverse(add(additive_inverse(X2),X3))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
add(X2,add(additive_inverse(X2),add(X3,additive_inverse(add(additive_inverse(X2),X3))))) = add(X3,additive_inverse(add(additive_inverse(X2),X3))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c132,plain,
add(X3,additive_inverse(add(additive_inverse(X2),X3))) = add(X2,add(additive_inverse(X2),add(X3,additive_inverse(add(additive_inverse(X2),X3))))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
add(add(X3,X2),additive_inverse(add(X3,X2))) = add(X3,add(X2,additive_inverse(add(X3,X2)))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c134,plain,
add(X3,add(X2,additive_inverse(add(X3,X2)))) = add(add(X3,X2),additive_inverse(add(X3,X2))),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
add(add(X3,X2),additive_inverse(add(X3,X2))) = additive_identity,
inference(substitution,[status(thm)],[c9]) ).
cnf(c136,plain,
add(X3,add(X2,additive_inverse(add(X3,X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c134,c135]) ).
cnf(c137,plain,
add(additive_inverse(X2),add(X3,additive_inverse(add(additive_inverse(X2),X3)))) = additive_identity,
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
add(X2,add(additive_inverse(X2),add(X3,additive_inverse(add(additive_inverse(X2),X3))))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
add(X2,add(additive_inverse(X2),add(X3,additive_inverse(add(additive_inverse(X2),X3))))) = X2,
inference(transitivity,[status(thm)],[c138,c13]) ).
cnf(c140,plain,
add(X3,additive_inverse(add(additive_inverse(X2),X3))) = X2,
inference(transitivity,[status(thm)],[c132,c139]) ).
cnf(c141,plain,
add(X3,additive_inverse(add(X3,additive_inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c130,c140]) ).
cnf(c142,plain,
add(X3,additive_inverse(add(X3,additive_inverse(additive_inverse(X2))))) = additive_inverse(X2),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
add(X3,additive_inverse(add(X3,X2))) = additive_inverse(X2),
inference(transitivity,[status(thm)],[c126,c142]) ).
cnf(c144,plain,
add(X2,additive_inverse(add(X2,add(X3,additive_inverse(X2))))) = additive_inverse(add(X3,additive_inverse(X2))),
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
additive_inverse(add(X3,additive_inverse(X2))) = add(X2,additive_inverse(add(X2,add(X3,additive_inverse(X2))))),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
add(X2,add(X3,additive_inverse(X2))) = X3,
inference(substitution,[status(thm)],[c17]) ).
cnf(c147,plain,
additive_inverse(add(X2,add(X3,additive_inverse(X2)))) = additive_inverse(X3),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
add(X2,additive_inverse(add(X2,add(X3,additive_inverse(X2))))) = add(X2,additive_inverse(X3)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
additive_inverse(add(X3,additive_inverse(X2))) = add(X2,additive_inverse(X3)),
inference(transitivity,[status(thm)],[c145,c148]) ).
cnf(c150,plain,
additive_inverse(add(X3,additive_inverse(additive_inverse(X2)))) = add(additive_inverse(X2),additive_inverse(X3)),
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
add(additive_inverse(X2),additive_inverse(X3)) = add(additive_inverse(X3),additive_inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c152,plain,
additive_inverse(add(X3,additive_inverse(additive_inverse(X2)))) = add(additive_inverse(X3),additive_inverse(X2)),
inference(transitivity,[status(thm)],[c150,c151]) ).
cnf(c153,plain,
additive_inverse(add(X3,X2)) = add(additive_inverse(X3),additive_inverse(X2)),
inference(transitivity,[status(thm)],[c122,c152]) ).
cnf(c154,plain,
additive_inverse(add(multiply(X3,X2),multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))) = add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))),
inference(substitution,[status(thm)],[c153]) ).
cnf(c155,plain,
add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))) = additive_inverse(add(multiply(X3,X2),multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(additive_inverse(multiply(X4,X3)),X2) = multiply(multiply(X4,additive_inverse(X3)),X2),
inference(congruence,[status(thm)],[c112]) ).
cnf(c157,plain,
multiply(multiply(X4,additive_inverse(X3)),X2) = multiply(X4,multiply(additive_inverse(X3),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c158,plain,
multiply(additive_inverse(multiply(X4,X3)),X2) = multiply(X4,multiply(additive_inverse(X3),X2)),
inference(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
add(multiply(X3,X2),additive_inverse(add(multiply(X3,X2),multiply(additive_inverse(X3),X2)))) = additive_inverse(multiply(additive_inverse(X3),X2)),
inference(substitution,[status(thm)],[c143]) ).
cnf(c160,plain,
additive_inverse(multiply(additive_inverse(X3),X2)) = add(multiply(X3,X2),additive_inverse(add(multiply(X3,X2),multiply(additive_inverse(X3),X2)))),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,axiom,
multiply(add(X2,Y2),Z2) = add(multiply(X2,Z2),multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).
cnf(c162,plain,
multiply(add(X3,additive_inverse(X3)),X2) = add(multiply(X3,X2),multiply(additive_inverse(X3),X2)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
add(multiply(X3,X2),multiply(additive_inverse(X3),X2)) = multiply(add(X3,additive_inverse(X3)),X2),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
multiply(add(X3,additive_inverse(X3)),X2) = multiply(additive_identity,X2),
inference(congruence,[status(thm)],[c9]) ).
cnf(c165,plain,
add(multiply(X2,X3),add(multiply(additive_identity,X3),additive_inverse(multiply(X2,X3)))) = multiply(additive_identity,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c166,plain,
multiply(additive_identity,X3) = add(multiply(X2,X3),add(multiply(additive_identity,X3),additive_inverse(multiply(X2,X3)))),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(add(X3,X4),X2) = add(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c168,plain,
add(multiply(X3,X2),multiply(X4,X2)) = multiply(add(X3,X4),X2),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c170,plain,
multiply(add(X3,X4),X2) = multiply(add(X4,X3),X2),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
add(multiply(X3,X2),multiply(X4,X2)) = multiply(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c168,c170]) ).
cnf(c172,plain,
add(multiply(X3,X2),multiply(additive_identity,X2)) = multiply(add(additive_identity,X3),X2),
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
multiply(add(additive_identity,X3),X2) = multiply(X3,X2),
inference(congruence,[status(thm)],[c14]) ).
cnf(c174,plain,
add(multiply(X3,X2),multiply(additive_identity,X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c172,c173]) ).
cnf(c175,plain,
add(multiply(X2,X3),multiply(additive_identity,X3)) = multiply(X2,X3),
inference(substitution,[status(thm)],[c174]) ).
cnf(c176,plain,
multiply(X2,X3) = add(multiply(X2,X3),multiply(additive_identity,X3)),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
additive_inverse(multiply(X2,X3)) = additive_inverse(add(multiply(X2,X3),multiply(additive_identity,X3))),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
add(multiply(additive_identity,X3),additive_inverse(multiply(X2,X3))) = add(multiply(additive_identity,X3),additive_inverse(add(multiply(X2,X3),multiply(additive_identity,X3)))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
add(multiply(X2,X3),add(multiply(additive_identity,X3),additive_inverse(multiply(X2,X3)))) = add(multiply(X2,X3),add(multiply(additive_identity,X3),additive_inverse(add(multiply(X2,X3),multiply(additive_identity,X3))))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
add(multiply(X2,X3),add(multiply(additive_identity,X3),additive_inverse(add(multiply(X2,X3),multiply(additive_identity,X3))))) = additive_identity,
inference(substitution,[status(thm)],[c136]) ).
cnf(c181,plain,
add(multiply(X2,X3),add(multiply(additive_identity,X3),additive_inverse(multiply(X2,X3)))) = additive_identity,
inference(transitivity,[status(thm)],[c179,c180]) ).
cnf(c182,plain,
multiply(additive_identity,X2) = additive_identity,
inference(transitivity,[status(thm)],[c166,c181]) ).
cnf(c183,plain,
multiply(add(X3,additive_inverse(X3)),X2) = additive_identity,
inference(transitivity,[status(thm)],[c164,c182]) ).
cnf(c184,plain,
add(multiply(X3,X2),multiply(additive_inverse(X3),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c163,c183]) ).
cnf(c185,plain,
additive_inverse(add(multiply(X3,X2),multiply(additive_inverse(X3),X2))) = additive_inverse(additive_identity),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
add(multiply(X3,X2),additive_inverse(add(multiply(X3,X2),multiply(additive_inverse(X3),X2)))) = add(multiply(X3,X2),additive_inverse(additive_identity)),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
add(additive_identity,additive_inverse(additive_identity)) = additive_inverse(additive_identity),
inference(substitution,[status(thm)],[c14]) ).
cnf(c188,plain,
additive_inverse(additive_identity) = add(additive_identity,additive_inverse(additive_identity)),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
add(additive_identity,additive_inverse(additive_identity)) = additive_identity,
inference(substitution,[status(thm)],[c9]) ).
cnf(c190,plain,
additive_inverse(additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c188,c189]) ).
cnf(c191,plain,
add(multiply(X3,X2),additive_inverse(additive_identity)) = add(multiply(X3,X2),additive_identity),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
add(multiply(X3,X2),additive_identity) = multiply(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c193,plain,
add(multiply(X3,X2),additive_inverse(additive_identity)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c191,c192]) ).
cnf(c194,plain,
add(multiply(X3,X2),additive_inverse(add(multiply(X3,X2),multiply(additive_inverse(X3),X2)))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c186,c193]) ).
cnf(c195,plain,
additive_inverse(multiply(additive_inverse(X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c160,c194]) ).
cnf(c196,plain,
multiply(X3,X2) = additive_inverse(multiply(additive_inverse(X3),X2)),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
additive_inverse(multiply(X3,X2)) = additive_inverse(additive_inverse(multiply(additive_inverse(X3),X2))),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
additive_inverse(additive_inverse(multiply(additive_inverse(X3),X2))) = multiply(additive_inverse(X3),X2),
inference(substitution,[status(thm)],[c42]) ).
cnf(c199,plain,
additive_inverse(multiply(X3,X2)) = multiply(additive_inverse(X3),X2),
inference(transitivity,[status(thm)],[c197,c198]) ).
cnf(c200,plain,
multiply(additive_inverse(X3),X2) = additive_inverse(multiply(X3,X2)),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
multiply(X4,multiply(additive_inverse(X3),X2)) = multiply(X4,additive_inverse(multiply(X3,X2))),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
multiply(multiply(X4,X3),additive_inverse(X2)) = multiply(X4,multiply(X3,additive_inverse(X2))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c203,plain,
multiply(X3,additive_inverse(X2)) = additive_inverse(multiply(X3,X2)),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c204,plain,
multiply(X4,multiply(X3,additive_inverse(X2))) = multiply(X4,additive_inverse(multiply(X3,X2))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
multiply(multiply(X4,X3),additive_inverse(X2)) = multiply(X4,additive_inverse(multiply(X3,X2))),
inference(transitivity,[status(thm)],[c202,c204]) ).
cnf(c206,plain,
multiply(X4,additive_inverse(multiply(X3,X2))) = multiply(multiply(X4,X3),additive_inverse(X2)),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
multiply(X4,multiply(additive_inverse(X3),X2)) = multiply(multiply(X4,X3),additive_inverse(X2)),
inference(transitivity,[status(thm)],[c201,c206]) ).
cnf(c208,plain,
multiply(additive_inverse(multiply(X4,X3)),X2) = multiply(multiply(X4,X3),additive_inverse(X2)),
inference(transitivity,[status(thm)],[c158,c207]) ).
cnf(c209,plain,
multiply(additive_inverse(multiply(X2,X3)),X2) = multiply(multiply(X2,X3),additive_inverse(X2)),
inference(substitution,[status(thm)],[c208]) ).
cnf(c210,plain,
multiply(multiply(X2,X3),additive_inverse(X2)) = multiply(additive_inverse(multiply(X2,X3)),X2),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))) = multiply(X2,multiply(additive_inverse(multiply(X2,X3)),X2)),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
add(multiply(X3,X2),multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2)))) = add(multiply(X3,X2),multiply(X2,multiply(additive_inverse(multiply(X2,X3)),X2))),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
multiply(multiply(X2,additive_inverse(multiply(X2,X3))),X2) = multiply(X2,multiply(additive_inverse(multiply(X2,X3)),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c214,plain,
multiply(X2,multiply(additive_inverse(multiply(X2,X3)),X2)) = multiply(multiply(X2,additive_inverse(multiply(X2,X3))),X2),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
add(multiply(X3,X2),multiply(X2,multiply(additive_inverse(multiply(X2,X3)),X2))) = add(multiply(X3,X2),multiply(multiply(X2,additive_inverse(multiply(X2,X3))),X2)),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),X2) = add(multiply(X3,X2),multiply(multiply(X2,additive_inverse(multiply(X2,X3))),X2)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c217,plain,
add(multiply(X3,X2),multiply(multiply(X2,additive_inverse(multiply(X2,X3))),X2)) = multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),X2),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
multiply(multiply(X3,X2),multiply(X3,X2)) = multiply(X3,multiply(X2,multiply(X3,X2))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c219,plain,
multiply(X3,multiply(X2,multiply(X3,X2))) = multiply(multiply(X3,X2),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
multiply(X2,multiply(X3,multiply(X2,multiply(X3,X2)))) = multiply(X2,multiply(multiply(X3,X2),multiply(X3,X2))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
multiply(X3,multiply(X2,multiply(X3,multiply(X2,multiply(X3,X2))))) = multiply(X3,multiply(X2,multiply(multiply(X3,X2),multiply(X3,X2)))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(X3,X2))) = multiply(X3,multiply(X2,multiply(multiply(X3,X2),multiply(X3,X2)))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c223,plain,
multiply(X3,multiply(X2,multiply(multiply(X3,X2),multiply(X3,X2)))) = multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c58]) ).
cnf(c225,plain,
multiply(X3,multiply(X2,multiply(multiply(X3,X2),multiply(X3,X2)))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c223,c224]) ).
cnf(c226,plain,
multiply(X3,multiply(X2,multiply(X3,multiply(X2,multiply(X3,X2))))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c221,c225]) ).
cnf(c227,plain,
multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),multiply(X2,multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),multiply(X2,multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),X2))))) = multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),X2),
inference(substitution,[status(thm)],[c226]) ).
cnf(c228,plain,
multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),X2) = multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),multiply(X2,multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),multiply(X2,multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),X2))))),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
add(multiply(X3,additive_inverse(multiply(X3,X2))),X2) = add(X2,multiply(X3,additive_inverse(multiply(X3,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c230,plain,
add(X2,multiply(X3,additive_inverse(multiply(X3,X2)))) = add(multiply(X3,additive_inverse(multiply(X3,X2))),X2),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
multiply(add(X3,multiply(X4,additive_inverse(multiply(X4,X3)))),X2) = multiply(add(multiply(X4,additive_inverse(multiply(X4,X3))),X3),X2),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
multiply(X4,multiply(add(X3,multiply(X4,additive_inverse(multiply(X4,X3)))),X2)) = multiply(X4,multiply(add(multiply(X4,additive_inverse(multiply(X4,X3))),X3),X2)),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
multiply(X4,add(X2,X3)) = add(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c234,plain,
add(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,add(X2,X3)),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c236,plain,
multiply(X4,add(X2,X3)) = multiply(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
add(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c234,c236]) ).
cnf(c238,plain,
add(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,add(X2,X3)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
multiply(add(multiply(X5,X4),multiply(X5,X3)),X2) = multiply(multiply(X5,add(X3,X4)),X2),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
multiply(multiply(X5,add(X3,X4)),X2) = multiply(X5,multiply(add(X3,X4),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c241,plain,
multiply(add(multiply(X5,X4),multiply(X5,X3)),X2) = multiply(X5,multiply(add(X3,X4),X2)),
inference(transitivity,[status(thm)],[c239,c240]) ).
cnf(c242,plain,
multiply(add(multiply(X4,X3),multiply(X4,multiply(X4,additive_inverse(multiply(X4,X3))))),X2) = multiply(X4,multiply(add(multiply(X4,additive_inverse(multiply(X4,X3))),X3),X2)),
inference(substitution,[status(thm)],[c241]) ).
cnf(c243,plain,
multiply(X4,multiply(add(multiply(X4,additive_inverse(multiply(X4,X3))),X3),X2)) = multiply(add(multiply(X4,X3),multiply(X4,multiply(X4,additive_inverse(multiply(X4,X3))))),X2),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c245,plain,
multiply(X2,X2) = multiply(X2,additive_inverse(additive_inverse(X2))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
multiply(additive_inverse(X2),multiply(X2,X2)) = multiply(additive_inverse(X2),multiply(X2,additive_inverse(additive_inverse(X2)))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c248,plain,
multiply(X2,additive_inverse(additive_inverse(X2))) = multiply(additive_inverse(additive_inverse(X2)),additive_inverse(additive_inverse(X2))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
multiply(additive_inverse(X2),multiply(X2,additive_inverse(additive_inverse(X2)))) = multiply(additive_inverse(X2),multiply(additive_inverse(additive_inverse(X2)),additive_inverse(additive_inverse(X2)))),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
add(X2,add(additive_inverse(X2),multiply(X2,multiply(additive_inverse(X2),additive_inverse(X2))))) = multiply(X2,multiply(additive_inverse(X2),additive_inverse(X2))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c251,plain,
multiply(X2,multiply(additive_inverse(X2),additive_inverse(X2))) = add(X2,add(additive_inverse(X2),multiply(X2,multiply(additive_inverse(X2),additive_inverse(X2))))),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c253,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
multiply(add(X3,X2),multiply(X2,X2)) = multiply(add(X2,X3),multiply(X2,X2)),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
multiply(add(X3,X2),multiply(X3,X3)) = add(multiply(X3,multiply(X3,X3)),multiply(X2,multiply(X3,X3))),
inference(substitution,[status(thm)],[c161]) ).
cnf(c256,plain,
add(multiply(X3,multiply(X3,X3)),multiply(X2,multiply(X3,X3))) = add(X3,multiply(X2,multiply(X3,X3))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c257,plain,
multiply(add(X3,X2),multiply(X3,X3)) = add(X3,multiply(X2,multiply(X3,X3))),
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
multiply(add(X2,X3),multiply(X2,X2)) = add(X2,multiply(X3,multiply(X2,X2))),
inference(substitution,[status(thm)],[c257]) ).
cnf(c259,plain,
multiply(add(X3,X2),multiply(X2,X2)) = add(X2,multiply(X3,multiply(X2,X2))),
inference(transitivity,[status(thm)],[c254,c258]) ).
cnf(c260,plain,
multiply(add(X2,additive_inverse(X2)),multiply(additive_inverse(X2),additive_inverse(X2))) = add(additive_inverse(X2),multiply(X2,multiply(additive_inverse(X2),additive_inverse(X2)))),
inference(substitution,[status(thm)],[c259]) ).
cnf(c261,plain,
add(additive_inverse(X2),multiply(X2,multiply(additive_inverse(X2),additive_inverse(X2)))) = multiply(add(X2,additive_inverse(X2)),multiply(additive_inverse(X2),additive_inverse(X2))),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c262,plain,
multiply(add(X2,additive_inverse(X2)),multiply(additive_inverse(X2),additive_inverse(X2))) = multiply(additive_identity,multiply(additive_inverse(X2),additive_inverse(X2))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c263,plain,
multiply(additive_identity,multiply(additive_inverse(X2),additive_inverse(X2))) = additive_identity,
inference(substitution,[status(thm)],[c182]) ).
cnf(c264,plain,
multiply(add(X2,additive_inverse(X2)),multiply(additive_inverse(X2),additive_inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c262,c263]) ).
cnf(c265,plain,
add(additive_inverse(X2),multiply(X2,multiply(additive_inverse(X2),additive_inverse(X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c261,c264]) ).
cnf(c266,plain,
add(X2,add(additive_inverse(X2),multiply(X2,multiply(additive_inverse(X2),additive_inverse(X2))))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
add(X2,add(additive_inverse(X2),multiply(X2,multiply(additive_inverse(X2),additive_inverse(X2))))) = X2,
inference(transitivity,[status(thm)],[c266,c13]) ).
cnf(c268,plain,
multiply(X2,multiply(additive_inverse(X2),additive_inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c251,c267]) ).
cnf(c269,plain,
multiply(additive_inverse(X2),multiply(additive_inverse(additive_inverse(X2)),additive_inverse(additive_inverse(X2)))) = additive_inverse(X2),
inference(substitution,[status(thm)],[c268]) ).
cnf(c270,plain,
multiply(additive_inverse(X2),multiply(X2,additive_inverse(additive_inverse(X2)))) = additive_inverse(X2),
inference(transitivity,[status(thm)],[c249,c269]) ).
cnf(c271,plain,
multiply(additive_inverse(X2),multiply(X2,X2)) = additive_inverse(X2),
inference(transitivity,[status(thm)],[c246,c270]) ).
cnf(c272,plain,
additive_inverse(X2) = multiply(additive_inverse(X2),multiply(X2,X2)),
inference(symmetry,[status(thm)],[c271]) ).
cnf(c273,plain,
multiply(additive_inverse(X2),additive_inverse(X2)) = multiply(additive_inverse(X2),multiply(additive_inverse(X2),multiply(X2,X2))),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
multiply(multiply(additive_inverse(X3),X3),X2) = multiply(additive_inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c275,plain,
multiply(additive_inverse(X3),multiply(X3,X2)) = multiply(multiply(additive_inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c274]) ).
cnf(c276,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X3),multiply(X3,X2))) = multiply(additive_inverse(X3),multiply(multiply(additive_inverse(X3),X3),X2)),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
multiply(multiply(additive_inverse(X3),multiply(additive_inverse(X3),X3)),X2) = multiply(additive_inverse(X3),multiply(multiply(additive_inverse(X3),X3),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c278,plain,
multiply(additive_inverse(X3),multiply(multiply(additive_inverse(X3),X3),X2)) = multiply(multiply(additive_inverse(X3),multiply(additive_inverse(X3),X3)),X2),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c280,plain,
multiply(additive_inverse(X2),X2) = multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
multiply(additive_inverse(X2),multiply(additive_inverse(X2),X2)) = multiply(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))))) = multiply(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c283,plain,
multiply(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))) = add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))))),
inference(symmetry,[status(thm)],[c282]) ).
cnf(c284,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c285,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
multiply(X3,add(X3,X2)) = multiply(X3,add(X2,X3)),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
multiply(X3,multiply(X3,add(X3,X2))) = multiply(X3,multiply(X3,add(X2,X3))),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
multiply(X3,add(X2,X3)) = add(multiply(X3,X2),multiply(X3,X3)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c289,plain,
multiply(X3,multiply(X3,add(X2,X3))) = multiply(X3,add(multiply(X3,X2),multiply(X3,X3))),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
multiply(X3,add(multiply(X3,X2),multiply(X3,X3))) = add(X3,multiply(X3,multiply(X3,X2))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c291,plain,
multiply(X3,multiply(X3,add(X2,X3))) = add(X3,multiply(X3,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c289,c290]) ).
cnf(c292,plain,
multiply(X3,multiply(X3,add(X3,X2))) = add(X3,multiply(X3,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c287,c291]) ).
cnf(c293,plain,
multiply(X2,multiply(X2,add(X2,additive_inverse(X2)))) = add(X2,multiply(X2,multiply(X2,additive_inverse(X2)))),
inference(substitution,[status(thm)],[c292]) ).
cnf(c294,plain,
add(X2,multiply(X2,multiply(X2,additive_inverse(X2)))) = multiply(X2,multiply(X2,add(X2,additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
multiply(X2,add(X2,additive_inverse(X2))) = multiply(X2,additive_identity),
inference(congruence,[status(thm)],[c9]) ).
cnf(c296,plain,
multiply(X2,multiply(X2,add(X2,additive_inverse(X2)))) = multiply(X2,multiply(X2,additive_identity)),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
multiply(X2,multiply(X2,additive_identity)) = multiply(X2,additive_identity),
inference(congruence,[status(thm)],[c73]) ).
cnf(c298,plain,
multiply(X2,multiply(X2,additive_identity)) = additive_identity,
inference(transitivity,[status(thm)],[c297,c73]) ).
cnf(c299,plain,
multiply(X2,multiply(X2,add(X2,additive_inverse(X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c296,c298]) ).
cnf(c300,plain,
add(X2,multiply(X2,multiply(X2,additive_inverse(X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c294,c299]) ).
cnf(c301,plain,
add(additive_inverse(X2),multiply(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))))) = additive_identity,
inference(substitution,[status(thm)],[c300]) ).
cnf(c302,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))))) = X2,
inference(transitivity,[status(thm)],[c302,c13]) ).
cnf(c304,plain,
multiply(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c283,c303]) ).
cnf(c305,plain,
multiply(additive_inverse(X2),multiply(additive_inverse(X2),X2)) = X2,
inference(transitivity,[status(thm)],[c281,c304]) ).
cnf(c306,plain,
multiply(multiply(additive_inverse(X3),multiply(additive_inverse(X3),X3)),X2) = multiply(X3,X2),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
multiply(additive_inverse(X3),multiply(multiply(additive_inverse(X3),X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c278,c306]) ).
cnf(c308,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c276,c307]) ).
cnf(c309,plain,
multiply(additive_inverse(X2),multiply(additive_inverse(X2),multiply(X2,X2))) = multiply(X2,X2),
inference(substitution,[status(thm)],[c308]) ).
cnf(c310,plain,
multiply(additive_inverse(X2),additive_inverse(X2)) = multiply(X2,X2),
inference(transitivity,[status(thm)],[c273,c309]) ).
cnf(c311,plain,
multiply(X2,X2) = multiply(additive_inverse(X2),additive_inverse(X2)),
inference(symmetry,[status(thm)],[c310]) ).
cnf(c312,plain,
multiply(multiply(X3,X3),X2) = multiply(multiply(additive_inverse(X3),additive_inverse(X3)),X2),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
multiply(multiply(additive_inverse(X3),additive_inverse(X3)),X2) = multiply(additive_inverse(X3),multiply(additive_inverse(X3),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c314,plain,
multiply(multiply(X3,X3),X2) = multiply(additive_inverse(X3),multiply(additive_inverse(X3),X2)),
inference(transitivity,[status(thm)],[c312,c313]) ).
cnf(c315,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X3),X2)) = multiply(multiply(X3,X3),X2),
inference(symmetry,[status(thm)],[c314]) ).
cnf(c316,plain,
multiply(multiply(X3,X3),X2) = multiply(X3,multiply(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c317,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X3),X2)) = multiply(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c315,c316]) ).
cnf(c318,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X3),additive_inverse(multiply(X3,X2)))) = multiply(X3,multiply(X3,additive_inverse(multiply(X3,X2)))),
inference(substitution,[status(thm)],[c317]) ).
cnf(c319,plain,
multiply(X3,multiply(X3,additive_inverse(multiply(X3,X2)))) = multiply(additive_inverse(X3),multiply(additive_inverse(X3),additive_inverse(multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
add(multiply(X3,X2),multiply(X3,multiply(X3,additive_inverse(multiply(X3,X2))))) = add(multiply(X3,X2),multiply(additive_inverse(X3),multiply(additive_inverse(X3),additive_inverse(multiply(X3,X2))))),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
multiply(add(multiply(X4,X3),multiply(X4,multiply(X4,additive_inverse(multiply(X4,X3))))),X2) = multiply(add(multiply(X4,X3),multiply(additive_inverse(X4),multiply(additive_inverse(X4),additive_inverse(multiply(X4,X3))))),X2),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
multiply(multiply(X3,X3),additive_inverse(multiply(X3,X2))) = multiply(additive_inverse(X3),multiply(additive_inverse(X3),additive_inverse(multiply(X3,X2)))),
inference(substitution,[status(thm)],[c314]) ).
cnf(c323,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X3),additive_inverse(multiply(X3,X2)))) = multiply(multiply(X3,X3),additive_inverse(multiply(X3,X2))),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c324,plain,
add(multiply(X3,X2),multiply(additive_inverse(X3),multiply(additive_inverse(X3),additive_inverse(multiply(X3,X2))))) = add(multiply(X3,X2),multiply(multiply(X3,X3),additive_inverse(multiply(X3,X2)))),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
multiply(add(multiply(X4,X3),multiply(additive_inverse(X4),multiply(additive_inverse(X4),additive_inverse(multiply(X4,X3))))),X2) = multiply(add(multiply(X4,X3),multiply(multiply(X4,X4),additive_inverse(multiply(X4,X3)))),X2),
inference(congruence,[status(thm)],[c324]) ).
cnf(c326,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c327,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c326]) ).
cnf(c328,plain,
multiply(add(X4,X2),X3) = multiply(add(X2,X4),X3),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
add(multiply(X4,additive_inverse(X3)),multiply(add(X4,X2),X3)) = add(multiply(X4,additive_inverse(X3)),multiply(add(X2,X4),X3)),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
multiply(X3,additive_inverse(X2)) = additive_inverse(multiply(X3,X2)),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c331,plain,
add(multiply(X4,additive_inverse(X3)),multiply(add(X2,X4),X3)) = add(additive_inverse(multiply(X4,X3)),multiply(add(X2,X4),X3)),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
add(X2,multiply(X3,X4)) = add(multiply(X3,X4),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c333,plain,
add(multiply(X3,X4),X2) = add(X2,multiply(X3,X4)),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
add(multiply(X5,X4),add(multiply(X3,X4),X2)) = add(multiply(X5,X4),add(X2,multiply(X3,X4))),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
add(multiply(X2,X4),X3) = add(X3,multiply(X2,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c336,plain,
add(X3,multiply(X2,X4)) = add(multiply(X2,X4),X3),
inference(symmetry,[status(thm)],[c335]) ).
cnf(c337,plain,
add(multiply(X5,X4),add(X3,multiply(X2,X4))) = add(multiply(X5,X4),add(multiply(X2,X4),X3)),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
add(multiply(X2,X4),add(multiply(X5,X4),X3)) = add(multiply(X5,X4),add(multiply(X2,X4),X3)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c339,plain,
add(multiply(X5,X4),add(multiply(X2,X4),X3)) = add(multiply(X2,X4),add(multiply(X5,X4),X3)),
inference(symmetry,[status(thm)],[c338]) ).
cnf(c340,plain,
add(add(multiply(X2,X4),multiply(X5,X4)),X3) = add(multiply(X2,X4),add(multiply(X5,X4),X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c341,plain,
add(multiply(X2,X4),add(multiply(X5,X4),X3)) = add(add(multiply(X2,X4),multiply(X5,X4)),X3),
inference(symmetry,[status(thm)],[c340]) ).
cnf(c342,plain,
multiply(add(X2,X4),X3) = add(multiply(X2,X3),multiply(X4,X3)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c343,plain,
add(multiply(X2,X3),multiply(X4,X3)) = multiply(add(X2,X4),X3),
inference(symmetry,[status(thm)],[c342]) ).
cnf(c344,plain,
add(add(multiply(X2,X4),multiply(X5,X4)),X3) = add(multiply(add(X2,X5),X4),X3),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
add(multiply(add(X2,X5),X4),X3) = add(X3,multiply(add(X2,X5),X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c346,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c347,plain,
multiply(add(X2,X4),X3) = multiply(add(X4,X2),X3),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
add(X3,multiply(add(X2,X5),X4)) = add(X3,multiply(add(X5,X2),X4)),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
add(multiply(add(X2,X5),X4),X3) = add(X3,multiply(add(X5,X2),X4)),
inference(transitivity,[status(thm)],[c345,c348]) ).
cnf(c350,plain,
add(add(multiply(X2,X4),multiply(X5,X4)),X3) = add(X3,multiply(add(X5,X2),X4)),
inference(transitivity,[status(thm)],[c344,c349]) ).
cnf(c351,plain,
add(multiply(X2,X4),add(multiply(X5,X4),X3)) = add(X3,multiply(add(X5,X2),X4)),
inference(transitivity,[status(thm)],[c341,c350]) ).
cnf(c352,plain,
add(multiply(X5,X4),add(multiply(X2,X4),X3)) = add(X3,multiply(add(X5,X2),X4)),
inference(transitivity,[status(thm)],[c339,c351]) ).
cnf(c353,plain,
add(multiply(X5,X4),add(X3,multiply(X2,X4))) = add(X3,multiply(add(X5,X2),X4)),
inference(transitivity,[status(thm)],[c337,c352]) ).
cnf(c354,plain,
add(multiply(X5,X4),add(X2,multiply(X3,X4))) = add(X2,multiply(add(X5,X3),X4)),
inference(substitution,[status(thm)],[c353]) ).
cnf(c355,plain,
add(multiply(X5,X4),add(multiply(X3,X4),X2)) = add(X2,multiply(add(X5,X3),X4)),
inference(transitivity,[status(thm)],[c334,c354]) ).
cnf(c356,plain,
add(multiply(X2,X3),add(multiply(X4,X3),additive_inverse(multiply(X4,X3)))) = add(additive_inverse(multiply(X4,X3)),multiply(add(X2,X4),X3)),
inference(substitution,[status(thm)],[c355]) ).
cnf(c357,plain,
add(additive_inverse(multiply(X4,X3)),multiply(add(X2,X4),X3)) = add(multiply(X2,X3),add(multiply(X4,X3),additive_inverse(multiply(X4,X3)))),
inference(symmetry,[status(thm)],[c356]) ).
cnf(c358,plain,
add(multiply(X3,X2),additive_inverse(multiply(X3,X2))) = additive_identity,
inference(substitution,[status(thm)],[c9]) ).
cnf(c359,plain,
add(multiply(X2,X3),add(multiply(X4,X3),additive_inverse(multiply(X4,X3)))) = add(multiply(X2,X3),additive_identity),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
add(multiply(X2,X3),additive_identity) = multiply(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c361,plain,
add(multiply(X2,X3),add(multiply(X4,X3),additive_inverse(multiply(X4,X3)))) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c359,c360]) ).
cnf(c362,plain,
add(additive_inverse(multiply(X4,X3)),multiply(add(X2,X4),X3)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c357,c361]) ).
cnf(c363,plain,
add(multiply(X4,additive_inverse(X3)),multiply(add(X2,X4),X3)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c331,c362]) ).
cnf(c364,plain,
add(multiply(X4,additive_inverse(X3)),multiply(add(X4,X2),X3)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c329,c363]) ).
cnf(c365,plain,
add(multiply(X3,additive_inverse(X2)),multiply(add(X3,additive_inverse(X3)),X2)) = multiply(additive_inverse(X3),X2),
inference(substitution,[status(thm)],[c364]) ).
cnf(c366,plain,
multiply(additive_inverse(X3),X2) = add(multiply(X3,additive_inverse(X2)),multiply(add(X3,additive_inverse(X3)),X2)),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c367,plain,
multiply(add(X3,additive_inverse(X3)),X2) = multiply(additive_identity,X2),
inference(congruence,[status(thm)],[c9]) ).
cnf(c368,plain,
add(multiply(X3,additive_inverse(X2)),multiply(add(X3,additive_inverse(X3)),X2)) = add(multiply(X3,additive_inverse(X2)),multiply(additive_identity,X2)),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
add(multiply(X3,additive_inverse(X2)),multiply(additive_identity,X2)) = add(multiply(X3,additive_inverse(X2)),additive_identity),
inference(congruence,[status(thm)],[c182]) ).
cnf(c370,plain,
add(multiply(X3,additive_inverse(X2)),additive_identity) = multiply(X3,additive_inverse(X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c371,plain,
add(multiply(X3,additive_inverse(X2)),multiply(additive_identity,X2)) = multiply(X3,additive_inverse(X2)),
inference(transitivity,[status(thm)],[c369,c370]) ).
cnf(c372,plain,
add(multiply(X3,additive_inverse(X2)),multiply(add(X3,additive_inverse(X3)),X2)) = multiply(X3,additive_inverse(X2)),
inference(transitivity,[status(thm)],[c368,c371]) ).
cnf(c373,plain,
multiply(additive_inverse(X3),X2) = multiply(X3,additive_inverse(X2)),
inference(transitivity,[status(thm)],[c366,c372]) ).
cnf(c374,plain,
multiply(additive_inverse(multiply(X3,X3)),multiply(X3,X2)) = multiply(multiply(X3,X3),additive_inverse(multiply(X3,X2))),
inference(substitution,[status(thm)],[c373]) ).
cnf(c375,plain,
multiply(multiply(X3,X3),additive_inverse(multiply(X3,X2))) = multiply(additive_inverse(multiply(X3,X3)),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c374]) ).
cnf(c376,plain,
add(multiply(X3,X2),multiply(multiply(X3,X3),additive_inverse(multiply(X3,X2)))) = add(multiply(X3,X2),multiply(additive_inverse(multiply(X3,X3)),multiply(X3,X2))),
inference(congruence,[status(thm)],[c375]) ).
cnf(c377,plain,
multiply(add(multiply(X4,X3),multiply(multiply(X4,X4),additive_inverse(multiply(X4,X3)))),X2) = multiply(add(multiply(X4,X3),multiply(additive_inverse(multiply(X4,X4)),multiply(X4,X3))),X2),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
multiply(multiply(X3,X2),X4) = multiply(X3,multiply(X2,X4)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c379,plain,
multiply(X3,multiply(X2,X4)) = multiply(multiply(X3,X2),X4),
inference(symmetry,[status(thm)],[c378]) ).
cnf(c380,plain,
add(multiply(X5,X4),multiply(X3,multiply(X2,X4))) = add(multiply(X5,X4),multiply(multiply(X3,X2),X4)),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
multiply(add(X5,multiply(X3,X2)),X4) = add(multiply(X5,X4),multiply(multiply(X3,X2),X4)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c382,plain,
add(multiply(X5,X4),multiply(multiply(X3,X2),X4)) = multiply(add(X5,multiply(X3,X2)),X4),
inference(symmetry,[status(thm)],[c381]) ).
cnf(c383,plain,
add(multiply(X5,X4),multiply(X3,multiply(X2,X4))) = multiply(add(X5,multiply(X3,X2)),X4),
inference(transitivity,[status(thm)],[c380,c382]) ).
cnf(c384,plain,
add(multiply(multiply(X4,X3),X2),multiply(X5,multiply(multiply(X4,X3),X2))) = multiply(add(multiply(X4,X3),multiply(X5,multiply(X4,X3))),X2),
inference(substitution,[status(thm)],[c383]) ).
cnf(c385,plain,
multiply(add(multiply(X4,X3),multiply(X5,multiply(X4,X3))),X2) = add(multiply(multiply(X4,X3),X2),multiply(X5,multiply(multiply(X4,X3),X2))),
inference(symmetry,[status(thm)],[c384]) ).
cnf(c386,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c387,plain,
multiply(X4,multiply(multiply(X4,X3),X2)) = multiply(X4,multiply(X4,multiply(X3,X2))),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
multiply(X4,multiply(X4,multiply(multiply(X4,X3),X2))) = multiply(X4,multiply(X4,multiply(X4,multiply(X3,X2)))),
inference(congruence,[status(thm)],[c387]) ).
cnf(c389,plain,
multiply(multiply(X3,X3),X2) = multiply(X3,multiply(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c390,plain,
multiply(X3,multiply(X3,X2)) = multiply(multiply(X3,X3),X2),
inference(symmetry,[status(thm)],[c389]) ).
cnf(c391,plain,
multiply(X3,multiply(X3,multiply(X3,X2))) = multiply(X3,multiply(multiply(X3,X3),X2)),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
multiply(multiply(X3,multiply(X3,X3)),X2) = multiply(X3,multiply(multiply(X3,X3),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c393,plain,
multiply(X3,multiply(multiply(X3,X3),X2)) = multiply(multiply(X3,multiply(X3,X3)),X2),
inference(symmetry,[status(thm)],[c392]) ).
cnf(c394,plain,
multiply(multiply(X3,multiply(X3,X3)),X2) = multiply(X3,X2),
inference(congruence,[status(thm)],[c58]) ).
cnf(c395,plain,
multiply(X3,multiply(multiply(X3,X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c393,c394]) ).
cnf(c396,plain,
multiply(X3,multiply(X3,multiply(X3,X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c391,c395]) ).
cnf(c397,plain,
multiply(X4,multiply(X4,multiply(X4,multiply(X3,X2)))) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c396]) ).
cnf(c398,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c399,plain,
multiply(X4,multiply(X3,X2)) = multiply(multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c398]) ).
cnf(c400,plain,
multiply(X4,multiply(X4,multiply(X4,multiply(X3,X2)))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c397,c399]) ).
cnf(c401,plain,
multiply(X4,multiply(X4,multiply(multiply(X4,X3),X2))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c388,c400]) ).
cnf(c402,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X4,multiply(multiply(X4,X3),X2))),
inference(symmetry,[status(thm)],[c401]) ).
cnf(c403,plain,
add(multiply(multiply(X4,X3),X2),multiply(X5,multiply(multiply(X4,X3),X2))) = add(multiply(X4,multiply(X4,multiply(multiply(X4,X3),X2))),multiply(X5,multiply(multiply(X4,X3),X2))),
inference(congruence,[status(thm)],[c402]) ).
cnf(c404,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c405,plain,
multiply(X4,multiply(X3,X2)) = multiply(multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c404]) ).
cnf(c406,plain,
add(multiply(X5,multiply(X4,X3)),multiply(X2,X3)) = add(multiply(multiply(X5,X4),X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c405]) ).
cnf(c407,plain,
multiply(add(multiply(X5,X4),X2),X3) = add(multiply(multiply(X5,X4),X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c408,plain,
add(multiply(multiply(X5,X4),X3),multiply(X2,X3)) = multiply(add(multiply(X5,X4),X2),X3),
inference(symmetry,[status(thm)],[c407]) ).
cnf(c409,plain,
add(multiply(X4,X3),X2) = add(X2,multiply(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c410,plain,
multiply(add(multiply(X5,X4),X2),X3) = multiply(add(X2,multiply(X5,X4)),X3),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
add(multiply(multiply(X5,X4),X3),multiply(X2,X3)) = multiply(add(X2,multiply(X5,X4)),X3),
inference(transitivity,[status(thm)],[c408,c410]) ).
cnf(c412,plain,
add(multiply(X5,multiply(X4,X3)),multiply(X2,X3)) = multiply(add(X2,multiply(X5,X4)),X3),
inference(transitivity,[status(thm)],[c406,c411]) ).
cnf(c413,plain,
add(multiply(X4,multiply(X4,multiply(multiply(X4,X3),X2))),multiply(X5,multiply(multiply(X4,X3),X2))) = multiply(add(X5,multiply(X4,X4)),multiply(multiply(X4,X3),X2)),
inference(substitution,[status(thm)],[c412]) ).
cnf(c414,plain,
add(multiply(multiply(X4,X3),X2),multiply(X5,multiply(multiply(X4,X3),X2))) = multiply(add(X5,multiply(X4,X4)),multiply(multiply(X4,X3),X2)),
inference(transitivity,[status(thm)],[c403,c413]) ).
cnf(c415,plain,
multiply(add(multiply(X4,X3),multiply(X5,multiply(X4,X3))),X2) = multiply(add(X5,multiply(X4,X4)),multiply(multiply(X4,X3),X2)),
inference(transitivity,[status(thm)],[c385,c414]) ).
cnf(c416,plain,
multiply(add(multiply(X5,X3),multiply(X4,multiply(X5,X3))),X2) = multiply(add(X4,multiply(X5,X5)),multiply(multiply(X5,X3),X2)),
inference(substitution,[status(thm)],[c415]) ).
cnf(c417,plain,
add(X2,multiply(X3,X3)) = add(multiply(X3,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c418,plain,
multiply(add(X4,multiply(X5,X5)),multiply(multiply(X5,X3),X2)) = multiply(add(multiply(X5,X5),X4),multiply(multiply(X5,X3),X2)),
inference(congruence,[status(thm)],[c417]) ).
cnf(c419,plain,
multiply(add(multiply(X5,X3),multiply(X4,multiply(X5,X3))),X2) = multiply(add(multiply(X5,X5),X4),multiply(multiply(X5,X3),X2)),
inference(transitivity,[status(thm)],[c416,c418]) ).
cnf(c420,plain,
multiply(add(multiply(X4,X3),multiply(additive_inverse(multiply(X4,X4)),multiply(X4,X3))),X2) = multiply(add(multiply(X4,X4),additive_inverse(multiply(X4,X4))),multiply(multiply(X4,X3),X2)),
inference(substitution,[status(thm)],[c419]) ).
cnf(c421,plain,
add(multiply(X2,X2),additive_inverse(multiply(X2,X2))) = additive_identity,
inference(substitution,[status(thm)],[c9]) ).
cnf(c422,plain,
multiply(add(multiply(X4,X4),additive_inverse(multiply(X4,X4))),multiply(multiply(X4,X3),X2)) = multiply(additive_identity,multiply(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c421]) ).
cnf(c423,plain,
multiply(multiply(additive_identity,X3),X2) = multiply(additive_identity,multiply(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c424,plain,
multiply(additive_identity,multiply(X3,X2)) = multiply(multiply(additive_identity,X3),X2),
inference(symmetry,[status(thm)],[c423]) ).
cnf(c425,plain,
multiply(multiply(additive_identity,X3),X2) = multiply(additive_identity,X2),
inference(congruence,[status(thm)],[c182]) ).
cnf(c426,plain,
multiply(additive_identity,multiply(X3,X2)) = multiply(additive_identity,X2),
inference(transitivity,[status(thm)],[c424,c425]) ).
cnf(c427,plain,
multiply(additive_identity,multiply(multiply(X4,X3),X2)) = multiply(additive_identity,X2),
inference(substitution,[status(thm)],[c426]) ).
cnf(c428,plain,
multiply(additive_identity,multiply(multiply(X4,X3),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c427,c182]) ).
cnf(c429,plain,
multiply(add(multiply(X4,X4),additive_inverse(multiply(X4,X4))),multiply(multiply(X4,X3),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c422,c428]) ).
cnf(c430,plain,
multiply(add(multiply(X4,X3),multiply(additive_inverse(multiply(X4,X4)),multiply(X4,X3))),X2) = additive_identity,
inference(transitivity,[status(thm)],[c420,c429]) ).
cnf(c431,plain,
multiply(add(multiply(X4,X3),multiply(multiply(X4,X4),additive_inverse(multiply(X4,X3)))),X2) = additive_identity,
inference(transitivity,[status(thm)],[c377,c430]) ).
cnf(c432,plain,
multiply(add(multiply(X4,X3),multiply(additive_inverse(X4),multiply(additive_inverse(X4),additive_inverse(multiply(X4,X3))))),X2) = additive_identity,
inference(transitivity,[status(thm)],[c325,c431]) ).
cnf(c433,plain,
multiply(add(multiply(X4,X3),multiply(X4,multiply(X4,additive_inverse(multiply(X4,X3))))),X2) = additive_identity,
inference(transitivity,[status(thm)],[c321,c432]) ).
cnf(c434,plain,
multiply(X4,multiply(add(multiply(X4,additive_inverse(multiply(X4,X3))),X3),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c243,c433]) ).
cnf(c435,plain,
multiply(X4,multiply(add(X3,multiply(X4,additive_inverse(multiply(X4,X3)))),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c232,c434]) ).
cnf(c436,plain,
multiply(X2,multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),multiply(X2,multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),X2)))) = additive_identity,
inference(substitution,[status(thm)],[c435]) ).
cnf(c437,plain,
multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),multiply(X2,multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),multiply(X2,multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),X2))))) = multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),additive_identity),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),additive_identity) = additive_identity,
inference(substitution,[status(thm)],[c73]) ).
cnf(c439,plain,
multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),multiply(X2,multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),multiply(X2,multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),X2))))) = additive_identity,
inference(transitivity,[status(thm)],[c437,c438]) ).
cnf(c440,plain,
multiply(add(X3,multiply(X2,additive_inverse(multiply(X2,X3)))),X2) = additive_identity,
inference(transitivity,[status(thm)],[c228,c439]) ).
cnf(c441,plain,
add(multiply(X3,X2),multiply(multiply(X2,additive_inverse(multiply(X2,X3))),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c217,c440]) ).
cnf(c442,plain,
add(multiply(X3,X2),multiply(X2,multiply(additive_inverse(multiply(X2,X3)),X2))) = additive_identity,
inference(transitivity,[status(thm)],[c215,c441]) ).
cnf(c443,plain,
add(multiply(X3,X2),multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c212,c442]) ).
cnf(c444,plain,
additive_inverse(add(multiply(X3,X2),multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))) = additive_inverse(additive_identity),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
additive_inverse(add(multiply(X3,X2),multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))) = additive_identity,
inference(transitivity,[status(thm)],[c444,c190]) ).
cnf(c446,plain,
add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))) = additive_identity,
inference(transitivity,[status(thm)],[c155,c445]) ).
cnf(c447,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2))))) = additive_identity,
inference(transitivity,[status(thm)],[c119,c446]) ).
cnf(c448,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))))) = additive_identity,
inference(transitivity,[status(thm)],[c116,c447]) ).
cnf(c449,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),X2))) = additive_identity,
inference(transitivity,[status(thm)],[c46,c448]) ).
cnf(c450,plain,
add(additive_inverse(multiply(X2,X3)),multiply(X3,multiply(multiply(X3,X2),X3))) = additive_identity,
inference(substitution,[status(thm)],[c449]) ).
cnf(c451,plain,
add(multiply(X2,X3),add(additive_inverse(multiply(X2,X3)),multiply(X3,multiply(multiply(X3,X2),X3)))) = add(multiply(X2,X3),additive_identity),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
add(multiply(X2,X3),additive_identity) = multiply(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c453,plain,
add(multiply(X2,X3),add(additive_inverse(multiply(X2,X3)),multiply(X3,multiply(multiply(X3,X2),X3)))) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c451,c452]) ).
cnf(c454,plain,
multiply(X3,multiply(multiply(X3,X2),X3)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c36,c453]) ).
cnf(c455,plain,
multiply(multiply(X4,multiply(multiply(X4,X3),X4)),X2) = multiply(multiply(X3,X4),X2),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
multiply(X4,multiply(multiply(multiply(X4,X3),X4),X2)) = multiply(multiply(X3,X4),X2),
inference(transitivity,[status(thm)],[c34,c455]) ).
cnf(c457,plain,
multiply(X4,multiply(multiply(X4,X3),multiply(X4,X2))) = multiply(multiply(X3,X4),X2),
inference(transitivity,[status(thm)],[c32,c456]) ).
cnf(c458,plain,
multiply(X3,multiply(multiply(X3,X4),multiply(X3,X2))) = multiply(multiply(X4,X3),X2),
inference(substitution,[status(thm)],[c457]) ).
cnf(c459,plain,
multiply(X5,multiply(X3,multiply(multiply(X3,X4),multiply(X3,X2)))) = multiply(X5,multiply(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c458]) ).
cnf(c460,plain,
multiply(multiply(X5,X3),multiply(multiply(X3,X4),multiply(X3,X2))) = multiply(X5,multiply(multiply(X4,X3),X2)),
inference(transitivity,[status(thm)],[c29,c459]) ).
cnf(c461,plain,
multiply(multiply(X2,X3),multiply(multiply(X3,X2),multiply(X3,X2))) = multiply(X2,multiply(multiply(X2,X3),X2)),
inference(substitution,[status(thm)],[c460]) ).
cnf(c462,plain,
add(additive_inverse(multiply(X3,X2)),multiply(multiply(X2,X3),multiply(multiply(X3,X2),multiply(X3,X2)))) = add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),X2))),
inference(congruence,[status(thm)],[c461]) ).
cnf(c463,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c464,plain,
multiply(multiply(X2,X3),X2) = multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))),
inference(congruence,[status(thm)],[c463]) ).
cnf(c465,plain,
multiply(X2,multiply(multiply(X2,X3),X2)) = multiply(X2,multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2)))),
inference(congruence,[status(thm)],[c464]) ).
cnf(c466,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),X2))) = add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))))),
inference(congruence,[status(thm)],[c465]) ).
cnf(c467,plain,
additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2))) = multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c468,plain,
multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))) = additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2))),
inference(symmetry,[status(thm)],[c467]) ).
cnf(c469,plain,
multiply(X2,multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2)))) = multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2)))),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))))) = add(additive_inverse(multiply(X3,X2)),multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2))))),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,plain,
additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2)))) = multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2)))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c472,plain,
multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2)))) = additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c471]) ).
cnf(c473,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2))))) = add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
additive_inverse(add(multiply(X3,X2),multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))) = add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))),
inference(substitution,[status(thm)],[c153]) ).
cnf(c475,plain,
add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))) = additive_inverse(add(multiply(X3,X2),multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))),
inference(symmetry,[status(thm)],[c474]) ).
cnf(c476,plain,
additive_inverse(add(multiply(X3,X2),multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))) = additive_inverse(additive_identity),
inference(congruence,[status(thm)],[c443]) ).
cnf(c477,plain,
additive_inverse(add(multiply(X3,X2),multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))) = additive_identity,
inference(transitivity,[status(thm)],[c476,c190]) ).
cnf(c478,plain,
add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(X2,multiply(multiply(X2,X3),additive_inverse(X2))))) = additive_identity,
inference(transitivity,[status(thm)],[c475,c477]) ).
cnf(c479,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,additive_inverse(multiply(multiply(X2,X3),additive_inverse(X2))))) = additive_identity,
inference(transitivity,[status(thm)],[c473,c478]) ).
cnf(c480,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),additive_inverse(additive_inverse(X2))))) = additive_identity,
inference(transitivity,[status(thm)],[c470,c479]) ).
cnf(c481,plain,
add(additive_inverse(multiply(X3,X2)),multiply(X2,multiply(multiply(X2,X3),X2))) = additive_identity,
inference(transitivity,[status(thm)],[c466,c480]) ).
cnf(c482,plain,
add(additive_inverse(multiply(X3,X2)),multiply(multiply(X2,X3),multiply(multiply(X3,X2),multiply(X3,X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c462,c481]) ).
cnf(c483,plain,
add(additive_inverse(multiply(X2,X3)),multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3)))) = additive_identity,
inference(substitution,[status(thm)],[c482]) ).
cnf(c484,plain,
add(multiply(X2,X3),add(additive_inverse(multiply(X2,X3)),multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))))) = add(multiply(X2,X3),additive_identity),
inference(congruence,[status(thm)],[c483]) ).
cnf(c485,plain,
add(multiply(X2,X3),additive_identity) = multiply(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c486,plain,
add(multiply(X2,X3),add(additive_inverse(multiply(X2,X3)),multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))))) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c484,c485]) ).
cnf(c487,plain,
multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c27,c486]) ).
cnf(c488,plain,
multiply(X2,X3) = multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))),
inference(symmetry,[status(thm)],[c487]) ).
cnf(c489,plain,
multiply(multiply(X3,X2),multiply(X2,X3)) = multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3)))),
inference(congruence,[status(thm)],[c488]) ).
cnf(c490,plain,
multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(X2,X3))) = multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))))),
inference(congruence,[status(thm)],[c489]) ).
cnf(c491,plain,
multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))))) = multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))),
inference(substitution,[status(thm)],[c396]) ).
cnf(c492,plain,
multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))))) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c491,c487]) ).
cnf(c493,plain,
multiply(multiply(X3,X2),multiply(multiply(X3,X2),multiply(X2,X3))) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c490,c492]) ).
cnf(c494,plain,
multiply(multiply(X2,X3),multiply(multiply(X2,X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c493]) ).
cnf(c495,plain,
multiply(X3,X2) = multiply(multiply(X2,X3),multiply(multiply(X2,X3),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c494]) ).
cnf(c496,plain,
add(additive_inverse(multiply(X2,X3)),multiply(X3,X2)) = add(additive_inverse(multiply(X2,X3)),multiply(multiply(X2,X3),multiply(multiply(X2,X3),multiply(X3,X2)))),
inference(congruence,[status(thm)],[c495]) ).
cnf(c497,plain,
additive_inverse(additive_inverse(add(X2,additive_inverse(X3)))) = add(X2,additive_inverse(X3)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c498,plain,
add(X2,additive_inverse(X3)) = additive_inverse(additive_inverse(add(X2,additive_inverse(X3)))),
inference(symmetry,[status(thm)],[c497]) ).
cnf(c499,plain,
multiply(X3,add(X2,additive_inverse(X3))) = multiply(X3,additive_inverse(additive_inverse(add(X2,additive_inverse(X3))))),
inference(congruence,[status(thm)],[c498]) ).
cnf(c500,plain,
multiply(X3,multiply(X3,add(X2,additive_inverse(X3)))) = multiply(X3,multiply(X3,additive_inverse(additive_inverse(add(X2,additive_inverse(X3)))))),
inference(congruence,[status(thm)],[c499]) ).
cnf(c501,plain,
multiply(additive_inverse(X3),additive_inverse(add(X2,additive_inverse(X3)))) = multiply(X3,additive_inverse(additive_inverse(add(X2,additive_inverse(X3))))),
inference(substitution,[status(thm)],[c373]) ).
cnf(c502,plain,
multiply(X3,additive_inverse(additive_inverse(add(X2,additive_inverse(X3))))) = multiply(additive_inverse(X3),additive_inverse(add(X2,additive_inverse(X3)))),
inference(symmetry,[status(thm)],[c501]) ).
cnf(c503,plain,
multiply(X3,multiply(X3,additive_inverse(additive_inverse(add(X2,additive_inverse(X3)))))) = multiply(X3,multiply(additive_inverse(X3),additive_inverse(add(X2,additive_inverse(X3))))),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
additive_inverse(multiply(additive_inverse(X3),add(X2,additive_inverse(X3)))) = multiply(additive_inverse(X3),additive_inverse(add(X2,additive_inverse(X3)))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c505,plain,
multiply(additive_inverse(X3),additive_inverse(add(X2,additive_inverse(X3)))) = additive_inverse(multiply(additive_inverse(X3),add(X2,additive_inverse(X3)))),
inference(symmetry,[status(thm)],[c504]) ).
cnf(c506,plain,
multiply(X3,multiply(additive_inverse(X3),additive_inverse(add(X2,additive_inverse(X3))))) = multiply(X3,additive_inverse(multiply(additive_inverse(X3),add(X2,additive_inverse(X3))))),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X3),add(X2,additive_inverse(X3)))) = multiply(X3,additive_inverse(multiply(additive_inverse(X3),add(X2,additive_inverse(X3))))),
inference(substitution,[status(thm)],[c373]) ).
cnf(c508,plain,
multiply(X3,additive_inverse(multiply(additive_inverse(X3),add(X2,additive_inverse(X3))))) = multiply(additive_inverse(X3),multiply(additive_inverse(X3),add(X2,additive_inverse(X3)))),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c509,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c510,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c509]) ).
cnf(c511,plain,
multiply(X3,add(X2,X3)) = multiply(X3,add(X3,X2)),
inference(congruence,[status(thm)],[c510]) ).
cnf(c512,plain,
multiply(X3,multiply(X3,add(X2,X3))) = multiply(X3,multiply(X3,add(X3,X2))),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
multiply(X3,multiply(X3,add(X2,X3))) = add(X3,multiply(X3,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c512,c292]) ).
cnf(c514,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X3),add(X2,additive_inverse(X3)))) = add(additive_inverse(X3),multiply(additive_inverse(X3),multiply(additive_inverse(X3),X2))),
inference(substitution,[status(thm)],[c513]) ).
cnf(c515,plain,
add(additive_inverse(X3),multiply(additive_inverse(X3),multiply(additive_inverse(X3),X2))) = add(additive_inverse(X3),multiply(X3,multiply(X3,X2))),
inference(congruence,[status(thm)],[c317]) ).
cnf(c516,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X3),add(X2,additive_inverse(X3)))) = add(additive_inverse(X3),multiply(X3,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c514,c515]) ).
cnf(c517,plain,
multiply(X3,additive_inverse(multiply(additive_inverse(X3),add(X2,additive_inverse(X3))))) = add(additive_inverse(X3),multiply(X3,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c508,c516]) ).
cnf(c518,plain,
multiply(X3,multiply(additive_inverse(X3),additive_inverse(add(X2,additive_inverse(X3))))) = add(additive_inverse(X3),multiply(X3,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c506,c517]) ).
cnf(c519,plain,
multiply(X3,multiply(X3,additive_inverse(additive_inverse(add(X2,additive_inverse(X3)))))) = add(additive_inverse(X3),multiply(X3,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c503,c518]) ).
cnf(c520,plain,
multiply(X3,multiply(X3,add(X2,additive_inverse(X3)))) = add(additive_inverse(X3),multiply(X3,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c500,c519]) ).
cnf(c521,plain,
multiply(multiply(X2,X3),multiply(multiply(X2,X3),add(multiply(X3,X2),additive_inverse(multiply(X2,X3))))) = add(additive_inverse(multiply(X2,X3)),multiply(multiply(X2,X3),multiply(multiply(X2,X3),multiply(X3,X2)))),
inference(substitution,[status(thm)],[c520]) ).
cnf(c522,plain,
add(additive_inverse(multiply(X2,X3)),multiply(multiply(X2,X3),multiply(multiply(X2,X3),multiply(X3,X2)))) = multiply(multiply(X2,X3),multiply(multiply(X2,X3),add(multiply(X3,X2),additive_inverse(multiply(X2,X3))))),
inference(symmetry,[status(thm)],[c521]) ).
cnf(c523,plain,
multiply(multiply(X3,X2),multiply(add(multiply(X2,X3),additive_inverse(multiply(X3,X2))),multiply(multiply(X3,X2),multiply(add(multiply(X2,X3),additive_inverse(multiply(X3,X2))),multiply(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))))))) = multiply(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))),
inference(substitution,[status(thm)],[c226]) ).
cnf(c524,plain,
multiply(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))) = multiply(multiply(X3,X2),multiply(add(multiply(X2,X3),additive_inverse(multiply(X3,X2))),multiply(multiply(X3,X2),multiply(add(multiply(X2,X3),additive_inverse(multiply(X3,X2))),multiply(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))))))),
inference(symmetry,[status(thm)],[c523]) ).
cnf(c525,plain,
multiply(multiply(add(multiply(X4,X3),additive_inverse(multiply(X3,X4))),multiply(X3,X4)),X2) = multiply(add(multiply(X4,X3),additive_inverse(multiply(X3,X4))),multiply(multiply(X3,X4),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c526,plain,
multiply(add(multiply(X4,X3),additive_inverse(multiply(X3,X4))),multiply(multiply(X3,X4),X2)) = multiply(multiply(add(multiply(X4,X3),additive_inverse(multiply(X3,X4))),multiply(X3,X4)),X2),
inference(symmetry,[status(thm)],[c525]) ).
cnf(c527,plain,
add(multiply(X2,additive_inverse(X3)),multiply(X4,X3)) = add(multiply(X4,X3),multiply(X2,additive_inverse(X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c528,plain,
add(multiply(X4,X3),multiply(X2,additive_inverse(X3))) = add(multiply(X2,additive_inverse(X3)),multiply(X4,X3)),
inference(symmetry,[status(thm)],[c527]) ).
cnf(c529,plain,
add(X2,add(X3,additive_inverse(X2))) = X3,
inference(substitution,[status(thm)],[c17]) ).
cnf(c530,plain,
X3 = add(X2,add(X3,additive_inverse(X2))),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c531,plain,
multiply(X4,X3) = multiply(add(X2,add(X4,additive_inverse(X2))),X3),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
add(multiply(X2,additive_inverse(X3)),multiply(X4,X3)) = add(multiply(X2,additive_inverse(X3)),multiply(add(X2,add(X4,additive_inverse(X2))),X3)),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
add(multiply(X2,additive_inverse(X3)),multiply(add(X2,add(X4,additive_inverse(X2))),X3)) = multiply(add(X4,additive_inverse(X2)),X3),
inference(substitution,[status(thm)],[c364]) ).
cnf(c534,plain,
add(multiply(X2,additive_inverse(X3)),multiply(X4,X3)) = multiply(add(X4,additive_inverse(X2)),X3),
inference(transitivity,[status(thm)],[c532,c533]) ).
cnf(c535,plain,
add(multiply(X4,X3),multiply(X2,additive_inverse(X3))) = multiply(add(X4,additive_inverse(X2)),X3),
inference(transitivity,[status(thm)],[c528,c534]) ).
cnf(c536,plain,
add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(multiply(X2,X3),additive_inverse(multiply(X2,X3)))) = multiply(add(multiply(X3,X2),additive_inverse(multiply(X2,X3))),multiply(X2,X3)),
inference(substitution,[status(thm)],[c535]) ).
cnf(c537,plain,
multiply(add(multiply(X3,X2),additive_inverse(multiply(X2,X3))),multiply(X2,X3)) = add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(multiply(X2,X3),additive_inverse(multiply(X2,X3)))),
inference(symmetry,[status(thm)],[c536]) ).
cnf(c538,plain,
additive_inverse(multiply(X2,X3)) = multiply(X2,additive_inverse(X3)),
inference(substitution,[status(thm)],[c112]) ).
cnf(c539,plain,
multiply(multiply(X2,X3),additive_inverse(multiply(X2,X3))) = multiply(multiply(X2,X3),multiply(X2,additive_inverse(X3))),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(multiply(X2,X3),additive_inverse(multiply(X2,X3)))) = add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(multiply(X2,X3),multiply(X2,additive_inverse(X3)))),
inference(congruence,[status(thm)],[c539]) ).
cnf(c541,plain,
multiply(multiply(X5,X4),multiply(X3,X2)) = multiply(X5,multiply(X4,multiply(X3,X2))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c542,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c543,plain,
multiply(X4,multiply(X3,X2)) = multiply(multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c542]) ).
cnf(c544,plain,
multiply(X5,multiply(X4,multiply(X3,X2))) = multiply(X5,multiply(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c543]) ).
cnf(c545,plain,
multiply(multiply(X5,X4),multiply(X3,X2)) = multiply(X5,multiply(multiply(X4,X3),X2)),
inference(transitivity,[status(thm)],[c541,c544]) ).
cnf(c546,plain,
multiply(multiply(X2,X3),multiply(X2,additive_inverse(X3))) = multiply(X2,multiply(multiply(X3,X2),additive_inverse(X3))),
inference(substitution,[status(thm)],[c545]) ).
cnf(c547,plain,
add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(multiply(X2,X3),multiply(X2,additive_inverse(X3)))) = add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(X2,multiply(multiply(X3,X2),additive_inverse(X3)))),
inference(congruence,[status(thm)],[c546]) ).
cnf(c548,plain,
additive_inverse(multiply(multiply(X3,X2),X3)) = multiply(multiply(X3,X2),additive_inverse(X3)),
inference(substitution,[status(thm)],[c112]) ).
cnf(c549,plain,
multiply(multiply(X3,X2),additive_inverse(X3)) = additive_inverse(multiply(multiply(X3,X2),X3)),
inference(symmetry,[status(thm)],[c548]) ).
cnf(c550,plain,
multiply(X2,multiply(multiply(X3,X2),additive_inverse(X3))) = multiply(X2,additive_inverse(multiply(multiply(X3,X2),X3))),
inference(congruence,[status(thm)],[c549]) ).
cnf(c551,plain,
add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(X2,multiply(multiply(X3,X2),additive_inverse(X3)))) = add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(X2,additive_inverse(multiply(multiply(X3,X2),X3)))),
inference(congruence,[status(thm)],[c550]) ).
cnf(c552,plain,
add(additive_identity,multiply(X2,X3)) = multiply(X2,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c553,plain,
multiply(X2,X3) = add(additive_identity,multiply(X2,X3)),
inference(symmetry,[status(thm)],[c552]) ).
cnf(c554,plain,
multiply(multiply(X2,X3),multiply(X2,X3)) = multiply(add(additive_identity,multiply(X2,X3)),multiply(X2,X3)),
inference(congruence,[status(thm)],[c553]) ).
cnf(c555,plain,
multiply(X2,X3) = multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3))),
inference(symmetry,[status(thm)],[c487]) ).
cnf(c556,plain,
add(X4,multiply(X2,X3)) = add(X4,multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3)))),
inference(congruence,[status(thm)],[c555]) ).
cnf(c557,plain,
multiply(add(X4,multiply(X2,X3)),multiply(X2,X3)) = multiply(add(X4,multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3)))),multiply(X2,X3)),
inference(congruence,[status(thm)],[c556]) ).
cnf(c558,plain,
multiply(multiply(X3,X2),X2) = multiply(X3,multiply(X2,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c559,plain,
multiply(X3,multiply(X2,X2)) = multiply(multiply(X3,X2),X2),
inference(symmetry,[status(thm)],[c558]) ).
cnf(c560,plain,
add(X4,multiply(X3,multiply(X2,X2))) = add(X4,multiply(multiply(X3,X2),X2)),
inference(congruence,[status(thm)],[c559]) ).
cnf(c561,plain,
multiply(add(X4,multiply(X3,multiply(X2,X2))),X2) = multiply(add(X4,multiply(multiply(X3,X2),X2)),X2),
inference(congruence,[status(thm)],[c560]) ).
cnf(c562,plain,
add(multiply(X4,multiply(X2,X2)),multiply(X3,multiply(X2,multiply(X2,X2)))) = multiply(add(X4,multiply(X3,X2)),multiply(X2,X2)),
inference(substitution,[status(thm)],[c383]) ).
cnf(c563,plain,
multiply(add(X4,multiply(X3,X2)),multiply(X2,X2)) = add(multiply(X4,multiply(X2,X2)),multiply(X3,multiply(X2,multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c562]) ).
cnf(c564,plain,
multiply(X3,multiply(X2,multiply(X2,X2))) = multiply(X3,X2),
inference(congruence,[status(thm)],[c58]) ).
cnf(c565,plain,
add(multiply(X4,multiply(X2,X2)),multiply(X3,multiply(X2,multiply(X2,X2)))) = add(multiply(X4,multiply(X2,X2)),multiply(X3,X2)),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
add(multiply(X4,multiply(X2,X2)),multiply(X3,X2)) = multiply(add(X3,multiply(X4,X2)),X2),
inference(substitution,[status(thm)],[c412]) ).
cnf(c567,plain,
add(multiply(X4,multiply(X2,X2)),multiply(X3,multiply(X2,multiply(X2,X2)))) = multiply(add(X3,multiply(X4,X2)),X2),
inference(transitivity,[status(thm)],[c565,c566]) ).
cnf(c568,plain,
multiply(add(X4,multiply(X3,X2)),multiply(X2,X2)) = multiply(add(X3,multiply(X4,X2)),X2),
inference(transitivity,[status(thm)],[c563,c567]) ).
cnf(c569,plain,
multiply(add(multiply(X3,X2),multiply(X4,X2)),multiply(X2,X2)) = multiply(add(X4,multiply(multiply(X3,X2),X2)),X2),
inference(substitution,[status(thm)],[c568]) ).
cnf(c570,plain,
multiply(add(X4,multiply(multiply(X3,X2),X2)),X2) = multiply(add(multiply(X3,X2),multiply(X4,X2)),multiply(X2,X2)),
inference(symmetry,[status(thm)],[c569]) ).
cnf(c571,plain,
multiply(add(X3,X4),X2) = add(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c572,plain,
add(multiply(X3,X2),multiply(X4,X2)) = multiply(add(X3,X4),X2),
inference(symmetry,[status(thm)],[c571]) ).
cnf(c573,plain,
multiply(add(multiply(X3,X2),multiply(X4,X2)),multiply(X2,X2)) = multiply(multiply(add(X3,X4),X2),multiply(X2,X2)),
inference(congruence,[status(thm)],[c572]) ).
cnf(c574,plain,
multiply(multiply(add(X3,X4),X2),multiply(X2,X2)) = multiply(add(X3,X4),multiply(X2,multiply(X2,X2))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c575,plain,
multiply(add(X3,X4),multiply(X2,multiply(X2,X2))) = multiply(add(X3,X4),X2),
inference(congruence,[status(thm)],[c58]) ).
cnf(c576,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c577,plain,
multiply(add(X3,X4),X2) = multiply(add(X4,X3),X2),
inference(congruence,[status(thm)],[c576]) ).
cnf(c578,plain,
multiply(add(X3,X4),multiply(X2,multiply(X2,X2))) = multiply(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c575,c577]) ).
cnf(c579,plain,
multiply(multiply(add(X3,X4),X2),multiply(X2,X2)) = multiply(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c574,c578]) ).
cnf(c580,plain,
multiply(add(multiply(X3,X2),multiply(X4,X2)),multiply(X2,X2)) = multiply(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c573,c579]) ).
cnf(c581,plain,
multiply(add(X4,multiply(multiply(X3,X2),X2)),X2) = multiply(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c570,c580]) ).
cnf(c582,plain,
multiply(add(X4,multiply(X3,multiply(X2,X2))),X2) = multiply(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c561,c581]) ).
cnf(c583,plain,
multiply(add(X4,multiply(multiply(X3,X2),multiply(multiply(X2,X3),multiply(X2,X3)))),multiply(X2,X3)) = multiply(add(X4,multiply(X3,X2)),multiply(X2,X3)),
inference(substitution,[status(thm)],[c582]) ).
cnf(c584,plain,
multiply(add(X4,multiply(X2,X3)),multiply(X2,X3)) = multiply(add(X4,multiply(X3,X2)),multiply(X2,X3)),
inference(transitivity,[status(thm)],[c557,c583]) ).
cnf(c585,plain,
multiply(add(additive_identity,multiply(X2,X3)),multiply(X2,X3)) = multiply(add(additive_identity,multiply(X3,X2)),multiply(X2,X3)),
inference(substitution,[status(thm)],[c584]) ).
cnf(c586,plain,
add(additive_identity,multiply(X3,X2)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c587,plain,
multiply(add(additive_identity,multiply(X3,X2)),multiply(X2,X3)) = multiply(multiply(X3,X2),multiply(X2,X3)),
inference(congruence,[status(thm)],[c586]) ).
cnf(c588,plain,
multiply(add(additive_identity,multiply(X2,X3)),multiply(X2,X3)) = multiply(multiply(X3,X2),multiply(X2,X3)),
inference(transitivity,[status(thm)],[c585,c587]) ).
cnf(c589,plain,
multiply(multiply(X2,X3),multiply(X2,X3)) = multiply(multiply(X3,X2),multiply(X2,X3)),
inference(transitivity,[status(thm)],[c554,c588]) ).
cnf(c590,plain,
multiply(multiply(X3,X2),multiply(X2,X3)) = multiply(multiply(X2,X3),multiply(X2,X3)),
inference(symmetry,[status(thm)],[c589]) ).
cnf(c591,plain,
add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(X2,additive_inverse(multiply(multiply(X3,X2),X3)))) = add(multiply(multiply(X2,X3),multiply(X2,X3)),multiply(X2,additive_inverse(multiply(multiply(X3,X2),X3)))),
inference(congruence,[status(thm)],[c590]) ).
cnf(c592,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c593,plain,
add(multiply(multiply(X5,X3),X2),multiply(X5,X4)) = add(multiply(X5,multiply(X3,X2)),multiply(X5,X4)),
inference(congruence,[status(thm)],[c592]) ).
cnf(c594,plain,
multiply(X5,add(multiply(X3,X2),X4)) = add(multiply(X5,multiply(X3,X2)),multiply(X5,X4)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c595,plain,
add(multiply(X5,multiply(X3,X2)),multiply(X5,X4)) = multiply(X5,add(multiply(X3,X2),X4)),
inference(symmetry,[status(thm)],[c594]) ).
cnf(c596,plain,
add(multiply(X3,X2),X4) = add(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c597,plain,
multiply(X5,add(multiply(X3,X2),X4)) = multiply(X5,add(X4,multiply(X3,X2))),
inference(congruence,[status(thm)],[c596]) ).
cnf(c598,plain,
add(multiply(X5,multiply(X3,X2)),multiply(X5,X4)) = multiply(X5,add(X4,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c595,c597]) ).
cnf(c599,plain,
add(multiply(multiply(X5,X3),X2),multiply(X5,X4)) = multiply(X5,add(X4,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c593,c598]) ).
cnf(c600,plain,
add(multiply(multiply(X5,X4),X3),multiply(X5,X2)) = multiply(X5,add(X2,multiply(X4,X3))),
inference(substitution,[status(thm)],[c599]) ).
cnf(c601,plain,
add(X2,multiply(X4,X3)) = add(multiply(X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c602,plain,
multiply(X5,add(X2,multiply(X4,X3))) = multiply(X5,add(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c601]) ).
cnf(c603,plain,
add(multiply(multiply(X5,X4),X3),multiply(X5,X2)) = multiply(X5,add(multiply(X4,X3),X2)),
inference(transitivity,[status(thm)],[c600,c602]) ).
cnf(c604,plain,
add(multiply(multiply(X5,X4),multiply(X3,X2)),multiply(X5,X6)) = multiply(X5,add(multiply(X4,multiply(X3,X2)),X6)),
inference(substitution,[status(thm)],[c603]) ).
cnf(c605,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c606,plain,
multiply(X4,multiply(X3,X2)) = multiply(multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c605]) ).
cnf(c607,plain,
add(multiply(X5,multiply(X4,X3)),X2) = add(multiply(multiply(X5,X4),X3),X2),
inference(congruence,[status(thm)],[c606]) ).
cnf(c608,plain,
multiply(X6,add(multiply(X5,multiply(X4,X3)),X2)) = multiply(X6,add(multiply(multiply(X5,X4),X3),X2)),
inference(congruence,[status(thm)],[c607]) ).
cnf(c609,plain,
add(multiply(multiply(X6,X5),multiply(X4,X3)),multiply(X6,X2)) = multiply(X6,add(multiply(multiply(X5,X4),X3),X2)),
inference(transitivity,[status(thm)],[c604,c608]) ).
cnf(c610,plain,
add(multiply(multiply(X2,X3),multiply(X2,X3)),multiply(X2,additive_inverse(multiply(multiply(X3,X2),X3)))) = multiply(X2,add(multiply(multiply(X3,X2),X3),additive_inverse(multiply(multiply(X3,X2),X3)))),
inference(substitution,[status(thm)],[c609]) ).
cnf(c611,plain,
add(multiply(multiply(X3,X2),X3),additive_inverse(multiply(multiply(X3,X2),X3))) = additive_identity,
inference(substitution,[status(thm)],[c9]) ).
cnf(c612,plain,
multiply(X2,add(multiply(multiply(X3,X2),X3),additive_inverse(multiply(multiply(X3,X2),X3)))) = multiply(X2,additive_identity),
inference(congruence,[status(thm)],[c611]) ).
cnf(c613,plain,
multiply(X2,add(multiply(multiply(X3,X2),X3),additive_inverse(multiply(multiply(X3,X2),X3)))) = additive_identity,
inference(transitivity,[status(thm)],[c612,c73]) ).
cnf(c614,plain,
add(multiply(multiply(X2,X3),multiply(X2,X3)),multiply(X2,additive_inverse(multiply(multiply(X3,X2),X3)))) = additive_identity,
inference(transitivity,[status(thm)],[c610,c613]) ).
cnf(c615,plain,
add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(X2,additive_inverse(multiply(multiply(X3,X2),X3)))) = additive_identity,
inference(transitivity,[status(thm)],[c591,c614]) ).
cnf(c616,plain,
add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(X2,multiply(multiply(X3,X2),additive_inverse(X3)))) = additive_identity,
inference(transitivity,[status(thm)],[c551,c615]) ).
cnf(c617,plain,
add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(multiply(X2,X3),multiply(X2,additive_inverse(X3)))) = additive_identity,
inference(transitivity,[status(thm)],[c547,c616]) ).
cnf(c618,plain,
add(multiply(multiply(X3,X2),multiply(X2,X3)),multiply(multiply(X2,X3),additive_inverse(multiply(X2,X3)))) = additive_identity,
inference(transitivity,[status(thm)],[c540,c617]) ).
cnf(c619,plain,
multiply(add(multiply(X3,X2),additive_inverse(multiply(X2,X3))),multiply(X2,X3)) = additive_identity,
inference(transitivity,[status(thm)],[c537,c618]) ).
cnf(c620,plain,
multiply(multiply(add(multiply(X4,X3),additive_inverse(multiply(X3,X4))),multiply(X3,X4)),X2) = multiply(additive_identity,X2),
inference(congruence,[status(thm)],[c619]) ).
cnf(c621,plain,
multiply(multiply(add(multiply(X4,X3),additive_inverse(multiply(X3,X4))),multiply(X3,X4)),X2) = additive_identity,
inference(transitivity,[status(thm)],[c620,c182]) ).
cnf(c622,plain,
multiply(add(multiply(X4,X3),additive_inverse(multiply(X3,X4))),multiply(multiply(X3,X4),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c526,c621]) ).
cnf(c623,plain,
multiply(add(multiply(X2,X3),additive_inverse(multiply(X3,X2))),multiply(multiply(X3,X2),multiply(add(multiply(X2,X3),additive_inverse(multiply(X3,X2))),multiply(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2))))))) = additive_identity,
inference(substitution,[status(thm)],[c622]) ).
cnf(c624,plain,
multiply(multiply(X3,X2),multiply(add(multiply(X2,X3),additive_inverse(multiply(X3,X2))),multiply(multiply(X3,X2),multiply(add(multiply(X2,X3),additive_inverse(multiply(X3,X2))),multiply(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))))))) = multiply(multiply(X3,X2),additive_identity),
inference(congruence,[status(thm)],[c623]) ).
cnf(c625,plain,
multiply(multiply(X3,X2),additive_identity) = additive_identity,
inference(substitution,[status(thm)],[c73]) ).
cnf(c626,plain,
multiply(multiply(X3,X2),multiply(add(multiply(X2,X3),additive_inverse(multiply(X3,X2))),multiply(multiply(X3,X2),multiply(add(multiply(X2,X3),additive_inverse(multiply(X3,X2))),multiply(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))))))) = additive_identity,
inference(transitivity,[status(thm)],[c624,c625]) ).
cnf(c627,plain,
multiply(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c524,c626]) ).
cnf(c628,plain,
multiply(multiply(X2,X3),add(multiply(X3,X2),additive_inverse(multiply(X2,X3)))) = additive_identity,
inference(substitution,[status(thm)],[c627]) ).
cnf(c629,plain,
multiply(multiply(X2,X3),multiply(multiply(X2,X3),add(multiply(X3,X2),additive_inverse(multiply(X2,X3))))) = multiply(multiply(X2,X3),additive_identity),
inference(congruence,[status(thm)],[c628]) ).
cnf(c630,plain,
multiply(multiply(X3,X4),multiply(multiply(X3,X4),multiply(multiply(X3,X4),X2))) = multiply(multiply(X3,X4),X2),
inference(substitution,[status(thm)],[c396]) ).
cnf(c631,plain,
multiply(multiply(X3,X4),X2) = multiply(multiply(X3,X4),multiply(multiply(X3,X4),multiply(multiply(X3,X4),X2))),
inference(symmetry,[status(thm)],[c630]) ).
cnf(c632,plain,
multiply(additive_inverse(multiply(X3,X4)),multiply(additive_inverse(multiply(X3,X4)),X2)) = multiply(multiply(X3,X4),multiply(multiply(X3,X4),X2)),
inference(substitution,[status(thm)],[c317]) ).
cnf(c633,plain,
multiply(multiply(X3,X4),multiply(multiply(X3,X4),X2)) = multiply(additive_inverse(multiply(X3,X4)),multiply(additive_inverse(multiply(X3,X4)),X2)),
inference(symmetry,[status(thm)],[c632]) ).
cnf(c634,plain,
multiply(multiply(multiply(X3,X4),multiply(X3,X4)),X2) = multiply(additive_inverse(multiply(X3,X4)),multiply(additive_inverse(multiply(X3,X4)),X2)),
inference(substitution,[status(thm)],[c314]) ).
cnf(c635,plain,
multiply(additive_inverse(multiply(X3,X4)),multiply(additive_inverse(multiply(X3,X4)),X2)) = multiply(multiply(multiply(X3,X4),multiply(X3,X4)),X2),
inference(symmetry,[status(thm)],[c634]) ).
cnf(c636,plain,
multiply(multiply(multiply(X3,X4),multiply(X3,X4)),X2) = multiply(multiply(multiply(X4,X3),multiply(X3,X4)),X2),
inference(congruence,[status(thm)],[c589]) ).
cnf(c637,plain,
multiply(multiply(multiply(X4,X3),multiply(X3,X4)),X2) = multiply(multiply(X4,X3),multiply(multiply(X3,X4),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c638,plain,
multiply(multiply(multiply(X3,X4),multiply(X3,X4)),X2) = multiply(multiply(X4,X3),multiply(multiply(X3,X4),X2)),
inference(transitivity,[status(thm)],[c636,c637]) ).
cnf(c639,plain,
multiply(additive_inverse(multiply(X3,X4)),multiply(additive_inverse(multiply(X3,X4)),X2)) = multiply(multiply(X4,X3),multiply(multiply(X3,X4),X2)),
inference(transitivity,[status(thm)],[c635,c638]) ).
cnf(c640,plain,
multiply(multiply(X3,X4),multiply(multiply(X3,X4),X2)) = multiply(multiply(X4,X3),multiply(multiply(X3,X4),X2)),
inference(transitivity,[status(thm)],[c633,c639]) ).
cnf(c641,plain,
multiply(multiply(X3,X4),multiply(multiply(X3,X4),multiply(multiply(X3,X4),X2))) = multiply(multiply(X4,X3),multiply(multiply(X3,X4),multiply(multiply(X3,X4),X2))),
inference(substitution,[status(thm)],[c640]) ).
cnf(c642,plain,
multiply(multiply(X4,X3),multiply(multiply(X3,X4),multiply(multiply(X3,X4),X2))) = multiply(multiply(X4,X3),multiply(multiply(X4,X3),multiply(multiply(X3,X4),X2))),
inference(congruence,[status(thm)],[c640]) ).
cnf(c643,plain,
add(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))) = multiply(X2,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c644,plain,
multiply(X2,X3) = add(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c643]) ).
cnf(c645,plain,
multiply(multiply(X3,X4),X2) = multiply(add(multiply(X4,X3),add(multiply(X3,X4),additive_inverse(multiply(X4,X3)))),X2),
inference(congruence,[status(thm)],[c644]) ).
cnf(c646,plain,
multiply(multiply(X4,X3),multiply(multiply(X3,X4),X2)) = multiply(multiply(X4,X3),multiply(add(multiply(X4,X3),add(multiply(X3,X4),additive_inverse(multiply(X4,X3)))),X2)),
inference(congruence,[status(thm)],[c645]) ).
cnf(c647,plain,
multiply(multiply(X4,X3),multiply(multiply(X4,X3),multiply(multiply(X3,X4),X2))) = multiply(multiply(X4,X3),multiply(multiply(X4,X3),multiply(add(multiply(X4,X3),add(multiply(X3,X4),additive_inverse(multiply(X4,X3)))),X2))),
inference(congruence,[status(thm)],[c646]) ).
cnf(c648,plain,
multiply(multiply(X4,add(X3,multiply(X4,X4))),X2) = multiply(X4,multiply(add(X3,multiply(X4,X4)),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c649,plain,
multiply(X4,multiply(add(X3,multiply(X4,X4)),X2)) = multiply(multiply(X4,add(X3,multiply(X4,X4))),X2),
inference(symmetry,[status(thm)],[c648]) ).
cnf(c650,plain,
multiply(multiply(X4,add(X3,multiply(X4,X4))),X2) = multiply(add(X4,multiply(X4,X3)),X2),
inference(congruence,[status(thm)],[c61]) ).
cnf(c651,plain,
multiply(X4,multiply(add(X3,multiply(X4,X4)),X2)) = multiply(add(X4,multiply(X4,X3)),X2),
inference(transitivity,[status(thm)],[c649,c650]) ).
cnf(c652,plain,
multiply(X4,multiply(add(multiply(X4,X3),multiply(X4,X4)),X2)) = multiply(add(X4,multiply(X4,multiply(X4,X3))),X2),
inference(substitution,[status(thm)],[c651]) ).
cnf(c653,plain,
multiply(add(X4,multiply(X4,multiply(X4,X3))),X2) = multiply(X4,multiply(add(multiply(X4,X3),multiply(X4,X4)),X2)),
inference(symmetry,[status(thm)],[c652]) ).
cnf(c654,plain,
multiply(X3,add(X2,X3)) = add(multiply(X3,X2),multiply(X3,X3)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c655,plain,
add(multiply(X3,X2),multiply(X3,X3)) = multiply(X3,add(X2,X3)),
inference(symmetry,[status(thm)],[c654]) ).
cnf(c656,plain,
multiply(add(multiply(X4,X3),multiply(X4,X4)),X2) = multiply(multiply(X4,add(X3,X4)),X2),
inference(congruence,[status(thm)],[c655]) ).
cnf(c657,plain,
multiply(X4,multiply(add(multiply(X4,X3),multiply(X4,X4)),X2)) = multiply(X4,multiply(multiply(X4,add(X3,X4)),X2)),
inference(congruence,[status(thm)],[c656]) ).
cnf(c658,plain,
multiply(multiply(X4,add(X3,X4)),X2) = multiply(X4,multiply(add(X3,X4),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c659,plain,
multiply(X4,multiply(multiply(X4,add(X3,X4)),X2)) = multiply(X4,multiply(X4,multiply(add(X3,X4),X2))),
inference(congruence,[status(thm)],[c658]) ).
cnf(c660,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c661,plain,
multiply(add(X3,X4),X2) = multiply(add(X4,X3),X2),
inference(congruence,[status(thm)],[c660]) ).
cnf(c662,plain,
multiply(X4,multiply(add(X3,X4),X2)) = multiply(X4,multiply(add(X4,X3),X2)),
inference(congruence,[status(thm)],[c661]) ).
cnf(c663,plain,
multiply(X4,multiply(X4,multiply(add(X3,X4),X2))) = multiply(X4,multiply(X4,multiply(add(X4,X3),X2))),
inference(congruence,[status(thm)],[c662]) ).
cnf(c664,plain,
multiply(X4,multiply(multiply(X4,add(X3,X4)),X2)) = multiply(X4,multiply(X4,multiply(add(X4,X3),X2))),
inference(transitivity,[status(thm)],[c659,c663]) ).
cnf(c665,plain,
multiply(X4,multiply(add(multiply(X4,X3),multiply(X4,X4)),X2)) = multiply(X4,multiply(X4,multiply(add(X4,X3),X2))),
inference(transitivity,[status(thm)],[c657,c664]) ).
cnf(c666,plain,
multiply(add(X4,multiply(X4,multiply(X4,X3))),X2) = multiply(X4,multiply(X4,multiply(add(X4,X3),X2))),
inference(transitivity,[status(thm)],[c653,c665]) ).
cnf(c667,plain,
multiply(add(multiply(X4,X3),multiply(multiply(X4,X3),multiply(multiply(X4,X3),add(multiply(X3,X4),additive_inverse(multiply(X4,X3)))))),X2) = multiply(multiply(X4,X3),multiply(multiply(X4,X3),multiply(add(multiply(X4,X3),add(multiply(X3,X4),additive_inverse(multiply(X4,X3)))),X2))),
inference(substitution,[status(thm)],[c666]) ).
cnf(c668,plain,
multiply(multiply(X4,X3),multiply(multiply(X4,X3),multiply(add(multiply(X4,X3),add(multiply(X3,X4),additive_inverse(multiply(X4,X3)))),X2))) = multiply(add(multiply(X4,X3),multiply(multiply(X4,X3),multiply(multiply(X4,X3),add(multiply(X3,X4),additive_inverse(multiply(X4,X3)))))),X2),
inference(symmetry,[status(thm)],[c667]) ).
cnf(c669,plain,
multiply(multiply(X3,X2),multiply(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2))))) = multiply(multiply(X3,X2),additive_identity),
inference(congruence,[status(thm)],[c627]) ).
cnf(c670,plain,
add(multiply(X3,X2),multiply(multiply(X3,X2),multiply(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))))) = add(multiply(X3,X2),multiply(multiply(X3,X2),additive_identity)),
inference(congruence,[status(thm)],[c669]) ).
cnf(c671,plain,
multiply(add(multiply(X4,X3),multiply(multiply(X4,X3),multiply(multiply(X4,X3),add(multiply(X3,X4),additive_inverse(multiply(X4,X3)))))),X2) = multiply(add(multiply(X4,X3),multiply(multiply(X4,X3),additive_identity)),X2),
inference(congruence,[status(thm)],[c670]) ).
cnf(c672,plain,
add(multiply(X3,X2),multiply(multiply(X3,X2),additive_identity)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c67]) ).
cnf(c673,plain,
multiply(add(multiply(X4,X3),multiply(multiply(X4,X3),additive_identity)),X2) = multiply(multiply(X4,X3),X2),
inference(congruence,[status(thm)],[c672]) ).
cnf(c674,plain,
multiply(add(multiply(X4,X3),multiply(multiply(X4,X3),multiply(multiply(X4,X3),add(multiply(X3,X4),additive_inverse(multiply(X4,X3)))))),X2) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c671,c673]) ).
cnf(c675,plain,
multiply(multiply(X4,X3),multiply(multiply(X4,X3),multiply(add(multiply(X4,X3),add(multiply(X3,X4),additive_inverse(multiply(X4,X3)))),X2))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c668,c674]) ).
cnf(c676,plain,
multiply(multiply(X4,X3),multiply(multiply(X4,X3),multiply(multiply(X3,X4),X2))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c647,c675]) ).
cnf(c677,plain,
multiply(multiply(X4,X3),multiply(multiply(X3,X4),multiply(multiply(X3,X4),X2))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c642,c676]) ).
cnf(c678,plain,
multiply(multiply(X3,X4),multiply(multiply(X3,X4),multiply(multiply(X3,X4),X2))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c641,c677]) ).
cnf(c679,plain,
multiply(multiply(X3,X4),X2) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c631,c678]) ).
cnf(c680,plain,
multiply(multiply(X3,X2),additive_identity) = multiply(multiply(X2,X3),additive_identity),
inference(substitution,[status(thm)],[c679]) ).
cnf(c681,plain,
multiply(multiply(X2,X3),additive_identity) = multiply(multiply(X3,X2),additive_identity),
inference(symmetry,[status(thm)],[c680]) ).
cnf(c682,plain,
multiply(multiply(X3,X2),additive_identity) = additive_identity,
inference(substitution,[status(thm)],[c73]) ).
cnf(c683,plain,
multiply(multiply(X2,X3),additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c681,c682]) ).
cnf(c684,plain,
multiply(multiply(X2,X3),multiply(multiply(X2,X3),add(multiply(X3,X2),additive_inverse(multiply(X2,X3))))) = additive_identity,
inference(transitivity,[status(thm)],[c629,c683]) ).
cnf(c685,plain,
add(additive_inverse(multiply(X2,X3)),multiply(multiply(X2,X3),multiply(multiply(X2,X3),multiply(X3,X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c522,c684]) ).
cnf(c686,plain,
add(additive_inverse(multiply(X2,X3)),multiply(X3,X2)) = additive_identity,
inference(transitivity,[status(thm)],[c496,c685]) ).
cnf(c687,plain,
add(multiply(X3,X2),additive_inverse(multiply(X2,X3))) = additive_identity,
inference(transitivity,[status(thm)],[c21,c686]) ).
cnf(c688,plain,
add(multiply(X2,X3),additive_inverse(multiply(X3,X2))) = additive_identity,
inference(substitution,[status(thm)],[c687]) ).
cnf(c689,plain,
add(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))) = add(multiply(X3,X2),additive_identity),
inference(congruence,[status(thm)],[c688]) ).
cnf(c690,plain,
add(multiply(X3,X2),additive_identity) = multiply(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c691,plain,
add(multiply(X3,X2),add(multiply(X2,X3),additive_inverse(multiply(X3,X2)))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c689,c690]) ).
cnf(c692,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c19,c691]) ).
cnf(c693,plain,
multiply(a,b) = multiply(b,a),
inference(substitution,[status(thm)],[c692]) ).
cnf(c694,plain,
$false,
inference(resolution,[status(thm)],[c1,c693]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG009-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 23:00:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.53/10.70 Command-line arguments: --flatten --complete-subsets
% 81.53/10.70
% 81.53/10.70 % SZS status Unsatisfiable
% 81.53/10.70
% 81.53/10.75 % SZS output start CNFRefutation
% See solution above
% 84.61/11.12
% 84.61/11.12 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------