%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP121-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 10:09:18 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.55s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 3
% Syntax : Number of clauses : 251 ( 251 unt; 0 nHn; 36 RR)
% Number of literals : 251 ( 250 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 374 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,identity) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_order3) ).
cnf(c2,axiom,
multiply(Y,multiply(multiply(Y,multiply(multiply(Y,Y),multiply(X,Z))),multiply(Z,multiply(Z,Z)))) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X3,identity),multiply(multiply(X3,identity),multiply(X3,identity))))),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(X3,identity),multiply(X3,identity)))))) = multiply(X3,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X3,identity) = multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X3,identity),multiply(multiply(X3,identity),multiply(X3,identity))))),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(X3,identity),multiply(X3,identity)))))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(identity,identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
multiply(multiply(identity,identity),multiply(identity,identity)) = multiply(multiply(identity,identity),identity),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(multiply(identity,identity),identity) = multiply(identity,identity),
inference(congruence,[status(thm)],[c5]) ).
cnf(c8,plain,
multiply(multiply(identity,identity),multiply(identity,identity)) = multiply(identity,identity),
inference(transitivity,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
multiply(identity,identity) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(identity,identity)) = multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(identity,identity) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c13,plain,
multiply(multiply(identity,identity),multiply(identity,identity)) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(identity,identity) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c19,plain,
multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(identity,identity) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c22,plain,
multiply(multiply(identity,identity),multiply(identity,identity)) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))) = X2,
inference(transitivity,[status(thm)],[c20,c26]) ).
cnf(c28,plain,
multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))) = X2,
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))) = multiply(X3,X2),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(X3,multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c33,plain,
multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(X3,multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(X3,multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(multiply(X3,X2),multiply(identity,identity)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c36,plain,
multiply(X3,multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(X3,multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),
inference(transitivity,[status(thm)],[c34,c36]) ).
cnf(c38,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),
inference(transitivity,[status(thm)],[c31,c37]) ).
cnf(c39,plain,
multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),
inference(transitivity,[status(thm)],[c17,c38]) ).
cnf(c40,plain,
multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))) = multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,multiply(identity,identity)))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c44,plain,
multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = X2,
inference(transitivity,[status(thm)],[c42,c43]) ).
cnf(c45,plain,
multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(multiply(identity,identity),multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c15,c44]) ).
cnf(c46,plain,
multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),multiply(identity,identity))) = X2,
inference(transitivity,[status(thm)],[c11,c45]) ).
cnf(c47,plain,
multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),multiply(identity,identity))),multiply(identity,identity))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),multiply(identity,identity)) = multiply(X2,multiply(identity,identity)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c50,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),multiply(identity,identity))) = multiply(X3,multiply(X2,multiply(identity,identity))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),multiply(identity,identity))),multiply(identity,identity)) = multiply(multiply(X3,multiply(X2,multiply(identity,identity))),multiply(identity,identity)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(X2,multiply(identity,identity))),multiply(identity,identity))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(X2,multiply(identity,identity))),multiply(identity,identity))),
inference(transitivity,[status(thm)],[c48,c52]) ).
cnf(c54,plain,
multiply(multiply(X3,X3),multiply(multiply(X3,multiply(X2,multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(X3,multiply(multiply(X3,X3),multiply(multiply(X3,multiply(X2,multiply(identity,identity))),multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(X3,multiply(multiply(X3,X3),multiply(multiply(X3,multiply(X2,multiply(identity,identity))),multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c55,c27]) ).
cnf(c57,plain,
multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),multiply(identity,identity))),multiply(identity,identity)))) = multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))) = multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),multiply(identity,identity))),multiply(identity,identity)))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(identity,identity)),multiply(X2,X4))),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(X3,multiply(identity,identity)),multiply(X2,X4)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c60,plain,
multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2)) = multiply(multiply(X4,X4),multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2))),multiply(identity,identity))),multiply(identity,identity))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = multiply(identity,multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c62,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))) = multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c63,plain,
multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))) = multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(identity,multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c66,plain,
multiply(identity,multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = X3,
inference(transitivity,[status(thm)],[c64,c65]) ).
cnf(c67,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = X3,
inference(transitivity,[status(thm)],[c61,c66]) ).
cnf(c68,plain,
X3 = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(multiply(multiply(X4,X4),multiply(X4,X4)),X3) = multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),X3)) = multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c72,plain,
multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))) = multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c74,plain,
multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))) = multiply(X4,X3),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(X4,X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))) = X2,
inference(substitution,[status(thm)],[c27]) ).
cnf(c78,plain,
X2 = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(multiply(identity,identity),X2) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity)) = multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))),multiply(identity,identity)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))),multiply(identity,identity))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))) = multiply(identity,multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c83,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))) = multiply(identity,multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c84,plain,
multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)) = multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(identity,multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))) = X2,
inference(substitution,[status(thm)],[c27]) ).
cnf(c87,plain,
multiply(identity,multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))) = X2,
inference(transitivity,[status(thm)],[c85,c86]) ).
cnf(c88,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))) = X2,
inference(transitivity,[status(thm)],[c82,c87]) ).
cnf(c89,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,multiply(identity,identity)))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c91,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)))),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),
inference(transitivity,[status(thm)],[c89,c91]) ).
cnf(c93,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),
inference(transitivity,[status(thm)],[c81,c92]) ).
cnf(c94,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity)),multiply(identity,identity)))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity)),multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity))),multiply(identity,identity))),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity))),multiply(identity,identity)) = multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity)),
inference(congruence,[status(thm)],[c93]) ).
cnf(c97,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity)))),multiply(identity,identity))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity))),multiply(identity,identity))) = X2,
inference(transitivity,[status(thm)],[c97,c88]) ).
cnf(c99,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),X2),multiply(identity,identity)),multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c95,c98]) ).
cnf(c100,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),multiply(identity,identity)),multiply(identity,identity)))) = multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),multiply(identity,identity)),multiply(identity,identity)))),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(identity,identity) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c103,plain,
multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c105,plain,
X3 = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(multiply(identity,identity),X3) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
multiply(multiply(multiply(identity,identity),X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c109,plain,
multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))) = multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),multiply(identity,identity))),multiply(identity,identity))),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),multiply(identity,identity)) = multiply(X3,multiply(identity,identity)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c111,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(X3,multiply(identity,identity))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),multiply(identity,identity))),multiply(identity,identity)) = multiply(multiply(multiply(identity,identity),multiply(X3,multiply(identity,identity))),multiply(identity,identity)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(multiply(identity,identity),multiply(X3,multiply(identity,identity))),multiply(identity,identity))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity))),multiply(identity,identity))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c115,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X2,multiply(identity,identity)),multiply(identity,identity)))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c116,plain,
multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(multiply(identity,identity),multiply(X2,multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X2,multiply(identity,identity)),multiply(identity,identity)))),
inference(transitivity,[status(thm)],[c114,c115]) ).
cnf(c117,plain,
multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X3,multiply(identity,identity)),multiply(identity,identity)))),
inference(transitivity,[status(thm)],[c113,c116]) ).
cnf(c118,plain,
multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X3,multiply(identity,identity)),multiply(identity,identity)))),
inference(transitivity,[status(thm)],[c109,c117]) ).
cnf(c119,plain,
multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2))),multiply(identity,identity)),multiply(identity,identity)))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2))),multiply(identity,identity)),multiply(identity,identity)))) = multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c99]) ).
cnf(c121,plain,
multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2)) = multiply(multiply(identity,identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c122,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2))),multiply(identity,identity)),multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c120,c121]) ).
cnf(c123,plain,
multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(identity,identity),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c119,c122]) ).
cnf(c124,plain,
multiply(multiply(multiply(identity,identity),X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(identity,identity),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c107,c123]) ).
cnf(c125,plain,
multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),X2)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),X2)),
inference(transitivity,[status(thm)],[c103,c125]) ).
cnf(c127,plain,
multiply(multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),multiply(identity,identity)) = multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),X2)),multiply(identity,identity)),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),multiply(identity,identity)),multiply(identity,identity)) = multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),X2)),multiply(identity,identity)),multiply(identity,identity)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),multiply(identity,identity)),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),X2)),multiply(identity,identity)),multiply(identity,identity))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),multiply(identity,identity)),multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),X2)),multiply(identity,identity)),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),X2)),multiply(identity,identity)),multiply(identity,identity)))) = multiply(multiply(identity,identity),X2),
inference(substitution,[status(thm)],[c99]) ).
cnf(c132,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),multiply(identity,identity)),multiply(identity,identity)))) = multiply(multiply(identity,identity),X2),
inference(transitivity,[status(thm)],[c130,c131]) ).
cnf(c133,plain,
multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))) = multiply(multiply(identity,identity),X2),
inference(transitivity,[status(thm)],[c101,c132]) ).
cnf(c134,plain,
multiply(multiply(X4,X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
multiply(X4,multiply(multiply(X4,X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2))),
inference(transitivity,[status(thm)],[c76,c135]) ).
cnf(c137,plain,
multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))) = multiply(X4,multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2))),
inference(transitivity,[status(thm)],[c72,c136]) ).
cnf(c138,plain,
multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(multiply(X4,multiply(identity,identity)),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))) = multiply(multiply(X4,multiply(identity,identity)),X3),
inference(congruence,[status(thm)],[c67]) ).
cnf(c140,plain,
multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,multiply(identity,identity)),X3)),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,multiply(identity,identity)),X3)),
inference(transitivity,[status(thm)],[c138,c140]) ).
cnf(c142,plain,
multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),X2)) = multiply(X3,multiply(multiply(X3,multiply(identity,identity)),X2)),
inference(transitivity,[status(thm)],[c70,c141]) ).
cnf(c143,plain,
multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))) = multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2))),
inference(substitution,[status(thm)],[c142]) ).
cnf(c144,plain,
multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2))) = multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2))) = multiply(X4,multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2))),
inference(transitivity,[status(thm)],[c144,c137]) ).
cnf(c146,plain,
multiply(multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2))),multiply(identity,identity)) = multiply(multiply(X4,multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2))),multiply(identity,identity)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(X4,multiply(multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2))),multiply(identity,identity))) = multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2))),multiply(identity,identity))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2))),multiply(identity,identity))),multiply(identity,identity)) = multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2))),multiply(identity,identity))),multiply(identity,identity)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(multiply(X4,X4),multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2))),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(X4,X4),multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2))),multiply(identity,identity))),multiply(identity,identity))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
multiply(multiply(X4,X4),multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2))),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c151,plain,
multiply(multiply(X4,X4),multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2))),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2)),
inference(transitivity,[status(thm)],[c149,c150]) ).
cnf(c152,plain,
multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2)) = multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2)),
inference(transitivity,[status(thm)],[c60,c151]) ).
cnf(c153,plain,
multiply(multiply(X3,multiply(identity,identity)),multiply(X2,multiply(identity,identity))) = multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(substitution,[status(thm)],[c152]) ).
cnf(c154,plain,
multiply(multiply(X3,X2),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(multiply(X3,X2),multiply(identity,identity)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c155,plain,
multiply(multiply(X3,multiply(identity,identity)),multiply(X2,multiply(identity,identity))) = multiply(multiply(X3,X2),multiply(identity,identity)),
inference(transitivity,[status(thm)],[c153,c154]) ).
cnf(c156,plain,
multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(identity,identity))) = multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),multiply(identity,identity)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),multiply(identity,identity)) = multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(identity,identity))),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),multiply(identity,identity))) = multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity))) = multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(identity,identity)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c160,plain,
multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(identity,identity)) = multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity))),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(identity,identity))) = multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(identity,identity)))) = multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity))))),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))),multiply(identity,identity)),multiply(identity,identity)))) = multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity))))),
inference(substitution,[status(thm)],[c99]) ).
cnf(c164,plain,
multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity))))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))),multiply(identity,identity)),multiply(identity,identity)))),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(X2,identity)),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X2,identity),multiply(identity,identity)))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c166,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X2,identity),multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(X2,identity)),multiply(identity,identity))),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X2,identity),multiply(identity,identity))))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(X2,identity)),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
multiply(identity,identity) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c169,plain,
multiply(multiply(identity,identity),multiply(X2,identity)) = multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,identity)),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(multiply(multiply(identity,identity),multiply(X2,identity)),multiply(identity,identity)) = multiply(multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,identity)),multiply(identity,identity)),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(X2,identity)),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,identity)),multiply(identity,identity))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(X2,identity)),multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,identity)),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,identity))),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,identity)),multiply(identity,identity)))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c174,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,identity)),multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,identity))),multiply(identity,identity))),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
multiply(identity,identity) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c176,plain,
multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,identity)) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,identity))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
multiply(identity,identity) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c179,plain,
multiply(multiply(identity,identity),multiply(identity,identity)) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c183,plain,
multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
multiply(multiply(identity,identity),multiply(identity,identity)) = multiply(identity,multiply(identity,identity)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c186,plain,
multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(identity,multiply(identity,multiply(identity,identity))),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,multiply(identity,identity)))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,multiply(identity,identity))))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
multiply(identity,multiply(identity,identity)) = multiply(identity,identity),
inference(congruence,[status(thm)],[c5]) ).
cnf(c190,plain,
multiply(identity,multiply(identity,multiply(identity,identity))) = multiply(identity,multiply(identity,identity)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,multiply(identity,identity)))) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,identity))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,multiply(identity,identity))))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,identity)))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,identity)))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c194,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,multiply(identity,identity))))) = X2,
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(multiply(identity,identity),multiply(identity,identity))))) = X2,
inference(transitivity,[status(thm)],[c188,c194]) ).
cnf(c196,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = X2,
inference(transitivity,[status(thm)],[c184,c195]) ).
cnf(c197,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(multiply(identity,identity),multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c181,c196]) ).
cnf(c198,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,identity))) = X2,
inference(transitivity,[status(thm)],[c177,c197]) ).
cnf(c199,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,identity))),multiply(identity,identity))) = X2,
inference(substitution,[status(thm)],[c198]) ).
cnf(c200,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X2,identity)),multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c174,c199]) ).
cnf(c201,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(X2,identity)),multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c172,c200]) ).
cnf(c202,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X2,identity),multiply(identity,identity))))) = X2,
inference(transitivity,[status(thm)],[c167,c201]) ).
cnf(c203,plain,
X2 = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X2,identity),multiply(identity,identity))))),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity))))) = multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X2,identity),multiply(identity,identity))))),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity))))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
multiply(multiply(identity,identity),multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))) = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X2,identity),multiply(identity,identity))))),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(X2,identity),multiply(identity,identity))))),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))) = multiply(identity,identity),
inference(substitution,[status(thm)],[c67]) ).
cnf(c207,plain,
multiply(multiply(identity,identity),multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))) = multiply(identity,identity),
inference(transitivity,[status(thm)],[c205,c206]) ).
cnf(c208,plain,
multiply(multiply(multiply(identity,identity),multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))),multiply(identity,identity)) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
multiply(multiply(multiply(multiply(identity,identity),multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))),multiply(identity,identity)),multiply(identity,identity)) = multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(identity,identity)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))),multiply(identity,identity)),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(identity,identity))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))),multiply(identity,identity)),multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c213,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c215,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c218,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c220,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(identity,identity),
inference(transitivity,[status(thm)],[c219,c8]) ).
cnf(c221,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(identity,identity),
inference(transitivity,[status(thm)],[c218,c220]) ).
cnf(c222,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))) = multiply(identity,identity),
inference(transitivity,[status(thm)],[c216,c221]) ).
cnf(c223,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(identity,identity)))) = multiply(identity,identity),
inference(transitivity,[status(thm)],[c213,c222]) ).
cnf(c224,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(multiply(multiply(multiply(identity,identity),multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity)))))),multiply(identity,identity)),multiply(identity,identity)))) = multiply(identity,identity),
inference(transitivity,[status(thm)],[c211,c223]) ).
cnf(c225,plain,
multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(X2,identity),multiply(identity,identity))))) = multiply(identity,identity),
inference(transitivity,[status(thm)],[c164,c224]) ).
cnf(c226,plain,
multiply(X2,multiply(multiply(multiply(X2,identity),multiply(identity,identity)),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(identity,identity)))) = multiply(identity,identity),
inference(transitivity,[status(thm)],[c162,c225]) ).
cnf(c227,plain,
multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),multiply(identity,identity))) = multiply(identity,identity),
inference(transitivity,[status(thm)],[c158,c226]) ).
cnf(c228,plain,
multiply(multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),multiply(identity,identity))),multiply(identity,identity)) = multiply(multiply(identity,identity),multiply(identity,identity)),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),multiply(identity,identity))),multiply(identity,identity))) = multiply(multiply(X2,X2),multiply(multiply(identity,identity),multiply(identity,identity))),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),multiply(identity,identity))),multiply(identity,identity)))) = multiply(X2,multiply(multiply(X2,X2),multiply(multiply(identity,identity),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2)) = multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c232,plain,
multiply(X2,multiply(identity,identity)) = multiply(X2,identity),
inference(congruence,[status(thm)],[c5]) ).
cnf(c233,plain,
multiply(multiply(X4,multiply(identity,identity)),multiply(X3,X2)) = multiply(multiply(X4,identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
multiply(multiply(X4,X3),multiply(multiply(identity,identity),X2)) = multiply(multiply(X4,identity),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c231,c233]) ).
cnf(c235,plain,
multiply(multiply(X2,X2),multiply(multiply(identity,identity),multiply(identity,identity))) = multiply(multiply(X2,identity),multiply(X2,multiply(identity,identity))),
inference(substitution,[status(thm)],[c234]) ).
cnf(c236,plain,
multiply(X2,multiply(multiply(X2,X2),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(X2,multiply(multiply(X2,identity),multiply(X2,multiply(identity,identity)))),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
multiply(X2,multiply(identity,identity)) = multiply(X2,identity),
inference(congruence,[status(thm)],[c5]) ).
cnf(c238,plain,
multiply(multiply(X2,identity),multiply(X2,multiply(identity,identity))) = multiply(multiply(X2,identity),multiply(X2,identity)),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
multiply(X2,multiply(multiply(X2,identity),multiply(X2,multiply(identity,identity)))) = multiply(X2,multiply(multiply(X2,identity),multiply(X2,identity))),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
multiply(X2,multiply(multiply(X2,X2),multiply(multiply(identity,identity),multiply(identity,identity)))) = multiply(X2,multiply(multiply(X2,identity),multiply(X2,identity))),
inference(transitivity,[status(thm)],[c236,c239]) ).
cnf(c241,plain,
multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),multiply(identity,identity))),multiply(identity,identity)))) = multiply(X2,multiply(multiply(X2,identity),multiply(X2,identity))),
inference(transitivity,[status(thm)],[c230,c240]) ).
cnf(c242,plain,
multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))) = multiply(X2,multiply(multiply(X2,identity),multiply(X2,identity))),
inference(transitivity,[status(thm)],[c58,c241]) ).
cnf(c243,plain,
multiply(multiply(X2,X2),multiply(multiply(X3,identity),multiply(multiply(X3,identity),multiply(X3,identity)))) = multiply(multiply(X2,X2),multiply(X3,multiply(multiply(X3,identity),multiply(X3,identity)))),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X3,identity),multiply(multiply(X3,identity),multiply(X3,identity))))) = multiply(X2,multiply(multiply(X2,X2),multiply(X3,multiply(multiply(X3,identity),multiply(X3,identity))))),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
multiply(multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X3,identity),multiply(multiply(X3,identity),multiply(X3,identity))))),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(X3,identity),multiply(X3,identity))))) = multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X3,multiply(multiply(X3,identity),multiply(X3,identity))))),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(X3,identity),multiply(X3,identity))))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X3,identity),multiply(multiply(X3,identity),multiply(X3,identity))))),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(X3,identity),multiply(X3,identity)))))) = multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X3,multiply(multiply(X3,identity),multiply(X3,identity))))),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(X3,identity),multiply(X3,identity)))))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X3,multiply(multiply(X3,identity),multiply(X3,identity))))),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(X3,identity),multiply(X3,identity)))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c248,plain,
multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X3,identity),multiply(multiply(X3,identity),multiply(X3,identity))))),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(X3,identity),multiply(X3,identity)))))) = X3,
inference(transitivity,[status(thm)],[c246,c247]) ).
cnf(c249,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c4,c248]) ).
cnf(c250,plain,
multiply(a,identity) = a,
inference(substitution,[status(thm)],[c249]) ).
cnf(c251,plain,
$false,
inference(resolution,[status(thm)],[c1,c250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP121-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n014.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:19:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.55 Command-line arguments: --flatten --complete-subsets
% 0.18/0.55
% 0.18/0.55 % SZS status Unsatisfiable
% 0.18/0.55
% 0.18/0.57 % SZS output start CNFRefutation
% See solution above
% 1.62/0.68
% 1.62/0.68 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------