%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP655-12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 10:11:34 AM UTC 2026
% Result : Unsatisfiable 3.80s 0.99s
% Output : CNFRefutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 90
% Number of leaves : 6
% Syntax : Number of clauses : 585 ( 585 unt; 0 nHn; 3 RR)
% Number of literals : 585 ( 584 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 1291 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
cnf(c3,plain,
ld(X,mult(X,rd(X2,X2))) = rd(X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
rd(X2,X2) = ld(X,mult(X,rd(X2,X2))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
mult(A2,mult(B2,mult(C,B2))) = mult(mult(mult(A2,B2),C),B2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
cnf(c6,plain,
mult(X2,mult(X,mult(X3,X))) = mult(mult(mult(X2,X),X3),X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
rd(mult(X3,mult(X2,mult(X,X2))),X2) = rd(mult(mult(mult(X3,X2),X),X2),X2),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
cnf(c9,plain,
rd(mult(mult(mult(X3,X2),X),X2),X2) = mult(mult(X3,X2),X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
rd(mult(X3,mult(X2,mult(X,X2))),X2) = mult(mult(X3,X2),X),
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
rd(mult(X3,mult(X2,mult(rd(X,X2),X2))),X2) = mult(mult(X3,X2),rd(X,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
mult(mult(X3,X2),rd(X,X2)) = rd(mult(X3,mult(X2,mult(rd(X,X2),X2))),X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
cnf(c14,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
mult(X2,mult(rd(X,X2),X2)) = mult(X2,X),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
mult(X3,mult(X2,mult(rd(X,X2),X2))) = mult(X3,mult(X2,X)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
rd(mult(X3,mult(X2,mult(rd(X,X2),X2))),X2) = rd(mult(X3,mult(X2,X)),X2),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
mult(mult(X3,X2),rd(X,X2)) = rd(mult(X3,mult(X2,X)),X2),
inference(transitivity,[status(thm)],[c12,c17]) ).
cnf(c19,plain,
mult(mult(rd(X3,X2),X2),rd(X,X2)) = rd(mult(rd(X3,X2),mult(X2,X)),X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
rd(mult(rd(X3,X2),mult(X2,X)),X2) = mult(mult(rd(X3,X2),X2),rd(X,X2)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c13]) ).
cnf(c22,plain,
mult(mult(rd(X3,X2),X2),rd(X,X2)) = mult(X3,rd(X,X2)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
rd(mult(rd(X3,X2),mult(X2,X)),X2) = mult(X3,rd(X,X2)),
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
rd(mult(rd(X2,X),mult(X,X)),X) = mult(X2,rd(X,X)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
mult(X2,rd(X,X)) = rd(mult(rd(X2,X),mult(X,X)),X),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
rd(mult(X2,X),X) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c27,plain,
X2 = rd(mult(X2,X),X),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
ld(mult(X2,X),X2) = ld(mult(X2,X),rd(mult(X2,X),X)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
rd(mult(ld(X,rd(X,X2)),X2),X2) = ld(X,rd(X,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c30,plain,
ld(X,rd(X,X2)) = rd(mult(ld(X,rd(X,X2)),X2),X2),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
mult(rd(X3,X2),mult(X2,mult(X,X2))) = mult(mult(mult(rd(X3,X2),X2),X),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c32,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c13]) ).
cnf(c33,plain,
mult(mult(rd(X3,X2),X2),X) = mult(X3,X),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
mult(mult(mult(rd(X3,X2),X2),X),X2) = mult(mult(X3,X),X2),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
mult(rd(X3,X2),mult(X2,mult(X,X2))) = mult(mult(X3,X),X2),
inference(transitivity,[status(thm)],[c31,c34]) ).
cnf(c36,plain,
mult(mult(X3,X),X2) = mult(rd(X3,X2),mult(X2,mult(X,X2))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
ld(rd(X3,X2),mult(mult(X3,X),X2)) = ld(rd(X3,X2),mult(rd(X3,X2),mult(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
ld(rd(X3,X2),mult(rd(X3,X2),mult(X2,mult(X,X2)))) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
ld(rd(X3,X2),mult(mult(X3,X),X2)) = mult(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c37,c38]) ).
cnf(c40,plain,
ld(rd(X2,X3),mult(mult(X2,ld(X2,X)),X3)) = mult(X3,mult(ld(X2,X),X3)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
mult(X3,mult(ld(X2,X),X3)) = ld(rd(X2,X3),mult(mult(X2,ld(X2,X)),X3)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
cnf(c43,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
mult(mult(X2,ld(X2,X)),X3) = mult(X,X3),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
ld(rd(X2,X3),mult(mult(X2,ld(X2,X)),X3)) = ld(rd(X2,X3),mult(X,X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
mult(X3,mult(ld(X2,X),X3)) = ld(rd(X2,X3),mult(X,X3)),
inference(transitivity,[status(thm)],[c41,c45]) ).
cnf(c47,plain,
ld(rd(X2,X3),mult(X,X3)) = mult(X3,mult(ld(X2,X),X3)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
ld(X3,ld(rd(X2,X3),mult(X,X3))) = ld(X3,mult(X3,mult(ld(X2,X),X3))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
ld(X3,mult(X3,mult(ld(X2,X),X3))) = mult(ld(X2,X),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c50,plain,
ld(X3,ld(rd(X2,X3),mult(X,X3))) = mult(ld(X2,X),X3),
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
ld(X,ld(rd(X2,X),mult(rd(X2,X),X))) = mult(ld(X2,rd(X2,X)),X),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
mult(ld(X2,rd(X2,X)),X) = ld(X,ld(rd(X2,X),mult(rd(X2,X),X))),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
ld(rd(X2,X),mult(rd(X2,X),X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c54,plain,
ld(X,ld(rd(X2,X),mult(rd(X2,X),X))) = ld(X,X),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
mult(ld(X2,rd(X2,X)),X) = ld(X,X),
inference(transitivity,[status(thm)],[c52,c54]) ).
cnf(c56,plain,
mult(ld(X,rd(X,X2)),X2) = ld(X2,X2),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
rd(mult(ld(X,rd(X,X2)),X2),X2) = rd(ld(X2,X2),X2),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
ld(X,X) = mult(ld(X2,rd(X2,X)),X),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c59,plain,
rd(ld(X,X),X) = rd(mult(ld(X2,rd(X2,X)),X),X),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
rd(mult(ld(X2,rd(X2,X)),X),X) = ld(X2,rd(X2,X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c61,plain,
rd(ld(X,X),X) = ld(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c59,c60]) ).
cnf(c62,plain,
rd(mult(ld(X,rd(X,X2)),X2),X2) = ld(X3,rd(X3,X2)),
inference(transitivity,[status(thm)],[c57,c61]) ).
cnf(c63,plain,
ld(X,rd(X,X2)) = ld(X3,rd(X3,X2)),
inference(transitivity,[status(thm)],[c30,c62]) ).
cnf(c64,plain,
ld(X,rd(X,X2)) = ld(mult(X3,X2),rd(mult(X3,X2),X2)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
ld(mult(X3,X2),rd(mult(X3,X2),X2)) = ld(X,rd(X,X2)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
ld(mult(X3,X2),X3) = ld(X,rd(X,X2)),
inference(transitivity,[status(thm)],[c28,c65]) ).
cnf(c67,plain,
ld(mult(X3,X),X3) = ld(X2,rd(X2,X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
ld(X2,rd(X2,X)) = ld(mult(X3,X),X3),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
rd(X3,ld(X2,rd(X2,X))) = rd(X3,ld(mult(X3,X),X3)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c42]) ).
cnf(c71,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
rd(X2,ld(X,X2)) = rd(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
rd(mult(X,ld(X,X2)),ld(X,X2)) = X,
inference(substitution,[status(thm)],[c8]) ).
cnf(c74,plain,
rd(X2,ld(X,X2)) = X,
inference(transitivity,[status(thm)],[c72,c73]) ).
cnf(c75,plain,
rd(X2,ld(mult(X2,X),X2)) = mult(X2,X),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
rd(X3,ld(X2,rd(X2,X))) = mult(X3,X),
inference(transitivity,[status(thm)],[c69,c75]) ).
cnf(c77,plain,
rd(rd(X2,ld(X,X)),ld(X2,rd(X2,X))) = mult(rd(X2,ld(X,X)),X),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
mult(rd(X2,ld(X,X)),X) = rd(rd(X2,ld(X,X)),ld(X2,rd(X2,X))),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
ld(X3,rd(X3,ld(X2,X))) = ld(X,rd(X,ld(X2,X))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c80,plain,
rd(X,ld(X2,X)) = X2,
inference(substitution,[status(thm)],[c74]) ).
cnf(c81,plain,
ld(X,rd(X,ld(X2,X))) = ld(X,X2),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
ld(X3,rd(X3,ld(X2,X))) = ld(X,X2),
inference(transitivity,[status(thm)],[c79,c81]) ).
cnf(c83,plain,
ld(X3,rd(X3,ld(X,X2))) = ld(X2,X),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
ld(X3,X2) = ld(X,rd(X,ld(X2,X3))),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
mult(X4,ld(X3,X2)) = mult(X4,ld(X,rd(X,ld(X2,X3)))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
mult(ld(X,rd(X,X2)),X2) = ld(X2,X2),
inference(substitution,[status(thm)],[c55]) ).
cnf(c87,plain,
ld(X2,X2) = mult(ld(X,rd(X,X2)),X2),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
rd(ld(X2,X2),X2) = rd(mult(ld(X,rd(X,X2)),X2),X2),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
rd(mult(ld(X,rd(X,X2)),X2),X2) = ld(X,rd(X,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c90,plain,
rd(ld(X2,X2),X2) = ld(X,rd(X,X2)),
inference(transitivity,[status(thm)],[c88,c89]) ).
cnf(c91,plain,
rd(ld(X,X),X) = ld(X2,rd(X2,X)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
ld(X2,rd(X2,X)) = rd(ld(X,X),X),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
mult(X3,ld(X2,rd(X2,X))) = mult(X3,rd(ld(X,X),X)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
rd(mult(rd(X3,X2),mult(X2,ld(X2,X))),X2) = mult(X3,rd(ld(X2,X),X2)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c95,plain,
mult(X3,rd(ld(X2,X),X2)) = rd(mult(rd(X3,X2),mult(X2,ld(X2,X))),X2),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c97,plain,
mult(rd(X3,X2),mult(X2,ld(X2,X))) = mult(rd(X3,X2),X),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
rd(mult(rd(X3,X2),mult(X2,ld(X2,X))),X2) = rd(mult(rd(X3,X2),X),X2),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
mult(X3,rd(ld(X2,X),X2)) = rd(mult(rd(X3,X2),X),X2),
inference(transitivity,[status(thm)],[c95,c98]) ).
cnf(c100,plain,
mult(X2,rd(ld(X,X),X)) = rd(mult(rd(X2,X),X),X),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
rd(mult(rd(X2,X),X),X) = rd(X2,X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c102,plain,
mult(X2,rd(ld(X,X),X)) = rd(X2,X),
inference(transitivity,[status(thm)],[c100,c101]) ).
cnf(c103,plain,
mult(X3,ld(X2,rd(X2,X))) = rd(X3,X),
inference(transitivity,[status(thm)],[c93,c102]) ).
cnf(c104,plain,
mult(X4,ld(X,rd(X,ld(X2,X3)))) = rd(X4,ld(X2,X3)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
mult(X3,ld(X2,X)) = rd(X3,ld(X,X2)),
inference(transitivity,[status(thm)],[c85,c104]) ).
cnf(c106,plain,
mult(X2,ld(X,X)) = rd(X2,ld(X,X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
rd(X2,ld(X,X)) = mult(X2,ld(X,X)),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
rd(rd(X2,ld(X,X)),ld(X2,rd(X2,X))) = rd(mult(X2,ld(X,X)),ld(X2,rd(X2,X))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
ld(X,X) = mult(ld(X2,rd(X2,X)),X),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c110,plain,
mult(X2,ld(X,X)) = mult(X2,mult(ld(X2,rd(X2,X)),X)),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
rd(mult(X2,ld(X,X)),ld(X2,rd(X2,X))) = rd(mult(X2,mult(ld(X2,rd(X2,X)),X)),ld(X2,rd(X2,X))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
mult(mult(X3,ld(X3,X2)),rd(X,ld(X3,X2))) = rd(mult(X3,mult(ld(X3,X2),X)),ld(X3,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c113,plain,
rd(mult(X3,mult(ld(X3,X2),X)),ld(X3,X2)) = mult(mult(X3,ld(X3,X2)),rd(X,ld(X3,X2))),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c115,plain,
mult(mult(X3,ld(X3,X2)),rd(X,ld(X3,X2))) = mult(X2,rd(X,ld(X3,X2))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
rd(mult(X3,mult(ld(X3,X2),X)),ld(X3,X2)) = mult(X2,rd(X,ld(X3,X2))),
inference(transitivity,[status(thm)],[c113,c115]) ).
cnf(c117,plain,
rd(mult(X2,mult(ld(X2,rd(X2,X)),X)),ld(X2,rd(X2,X))) = mult(rd(X2,X),rd(X,ld(X2,rd(X2,X)))),
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
ld(X3,rd(X3,X2)) = ld(X,rd(X,X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c119,plain,
rd(X2,ld(X3,rd(X3,X2))) = rd(X2,ld(X,rd(X,X2))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
mult(rd(X3,X2),rd(X2,ld(X3,rd(X3,X2)))) = mult(rd(X3,X2),rd(X2,ld(X,rd(X,X2)))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
rd(X2,ld(X,rd(X,X2))) = mult(X2,X2),
inference(substitution,[status(thm)],[c76]) ).
cnf(c122,plain,
mult(rd(X3,X2),rd(X2,ld(X,rd(X,X2)))) = mult(rd(X3,X2),mult(X2,X2)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
mult(rd(X2,X),rd(X,ld(X2,rd(X2,X)))) = mult(rd(X2,X),mult(X,X)),
inference(transitivity,[status(thm)],[c120,c122]) ).
cnf(c124,plain,
rd(mult(X2,mult(ld(X2,rd(X2,X)),X)),ld(X2,rd(X2,X))) = mult(rd(X2,X),mult(X,X)),
inference(transitivity,[status(thm)],[c117,c123]) ).
cnf(c125,plain,
rd(mult(X2,ld(X,X)),ld(X2,rd(X2,X))) = mult(rd(X2,X),mult(X,X)),
inference(transitivity,[status(thm)],[c111,c124]) ).
cnf(c126,plain,
rd(rd(X2,ld(X,X)),ld(X2,rd(X2,X))) = mult(rd(X2,X),mult(X,X)),
inference(transitivity,[status(thm)],[c108,c125]) ).
cnf(c127,plain,
mult(rd(X2,ld(X,X)),X) = mult(rd(X2,X),mult(X,X)),
inference(transitivity,[status(thm)],[c78,c126]) ).
cnf(c128,plain,
mult(rd(X2,X),mult(X,X)) = mult(rd(X2,ld(X,X)),X),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
rd(mult(rd(X2,X),mult(X,X)),X) = rd(mult(rd(X2,ld(X,X)),X),X),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
rd(mult(rd(X2,ld(X,X)),X),X) = rd(X2,ld(X,X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c131,plain,
rd(mult(rd(X2,X),mult(X,X)),X) = rd(X2,ld(X,X)),
inference(transitivity,[status(thm)],[c129,c130]) ).
cnf(c132,plain,
mult(X2,rd(X,X)) = rd(X2,ld(X,X)),
inference(transitivity,[status(thm)],[c25,c131]) ).
cnf(c133,plain,
mult(X,rd(X2,X2)) = rd(X,ld(X2,X2)),
inference(substitution,[status(thm)],[c132]) ).
cnf(c134,plain,
ld(X,mult(X,rd(X2,X2))) = ld(X,rd(X,ld(X2,X2))),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
ld(X,rd(X,ld(X2,X2))) = ld(X2,X2),
inference(substitution,[status(thm)],[c82]) ).
cnf(c136,plain,
ld(X,mult(X,rd(X2,X2))) = ld(X2,X2),
inference(transitivity,[status(thm)],[c134,c135]) ).
cnf(c137,plain,
rd(X,X) = ld(X,X),
inference(transitivity,[status(thm)],[c4,c136]) ).
cnf(c138,plain,
ld(X,X) = rd(X,X),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
mult(ld(X,X),X) = mult(rd(X,X),X),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
mult(rd(X,X),X) = X,
inference(substitution,[status(thm)],[c13]) ).
cnf(c141,plain,
mult(ld(X,X),X) = X,
inference(transitivity,[status(thm)],[c139,c140]) ).
cnf(c142,plain,
mult(ld(mult(rd(X,X),X2),mult(rd(X,X),X2)),mult(rd(X,X),X2)) = mult(rd(X,X),X2),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
mult(rd(X,X),X2) = mult(ld(mult(rd(X,X),X2),mult(rd(X,X),X2)),mult(rd(X,X),X2)),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
rd(mult(ld(mult(rd(X,X),X2),mult(rd(X,X),X2)),X2),X2) = ld(mult(rd(X,X),X2),mult(rd(X,X),X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c145,plain,
ld(mult(rd(X,X),X2),mult(rd(X,X),X2)) = rd(mult(ld(mult(rd(X,X),X2),mult(rd(X,X),X2)),X2),X2),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
rd(mult(rd(X2,X2),X),mult(rd(X2,X2),X)) = ld(mult(rd(X2,X2),X),mult(rd(X2,X2),X)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c147,plain,
ld(mult(rd(X2,X2),X),mult(rd(X2,X2),X)) = rd(mult(rd(X2,X2),X),mult(rd(X2,X2),X)),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
mult(ld(mult(rd(X2,X2),X),mult(rd(X2,X2),X)),X) = mult(rd(mult(rd(X2,X2),X),mult(rd(X2,X2),X)),X),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c13]) ).
cnf(c150,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
mult(X2,X) = mult(X2,mult(rd(X,X2),X2)),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
rd(X3,mult(X2,X)) = rd(X3,mult(X2,mult(rd(X,X2),X2))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
mult(rd(X3,mult(X2,X)),X2) = mult(rd(X3,mult(X2,mult(rd(X,X2),X2))),X2),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
rd(mult(mult(rd(X3,mult(X2,mult(X,X2))),X2),X),X) = mult(rd(X3,mult(X2,mult(X,X2))),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c155,plain,
mult(rd(X3,mult(X2,mult(X,X2))),X2) = rd(mult(mult(rd(X3,mult(X2,mult(X,X2))),X2),X),X),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
rd(mult(rd(X3,mult(X2,mult(X,X2))),mult(X2,mult(X,X2))),X2) = mult(mult(rd(X3,mult(X2,mult(X,X2))),X2),X),
inference(substitution,[status(thm)],[c10]) ).
cnf(c157,plain,
mult(mult(rd(X3,mult(X2,mult(X,X2))),X2),X) = rd(mult(rd(X3,mult(X2,mult(X,X2))),mult(X2,mult(X,X2))),X2),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
mult(rd(X3,mult(X2,mult(X,X2))),mult(X2,mult(X,X2))) = X3,
inference(substitution,[status(thm)],[c13]) ).
cnf(c159,plain,
rd(mult(rd(X3,mult(X2,mult(X,X2))),mult(X2,mult(X,X2))),X2) = rd(X3,X2),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
mult(mult(rd(X3,mult(X2,mult(X,X2))),X2),X) = rd(X3,X2),
inference(transitivity,[status(thm)],[c157,c159]) ).
cnf(c161,plain,
rd(mult(mult(rd(X3,mult(X2,mult(X,X2))),X2),X),X) = rd(rd(X3,X2),X),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
mult(rd(X3,mult(X2,mult(X,X2))),X2) = rd(rd(X3,X2),X),
inference(transitivity,[status(thm)],[c155,c161]) ).
cnf(c163,plain,
mult(rd(X3,mult(X2,mult(rd(X,X2),X2))),X2) = rd(rd(X3,X2),rd(X,X2)),
inference(substitution,[status(thm)],[c162]) ).
cnf(c164,plain,
mult(rd(X3,mult(X2,X)),X2) = rd(rd(X3,X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c153,c163]) ).
cnf(c165,plain,
mult(rd(X3,mult(X2,ld(X2,X))),X2) = rd(rd(X3,X2),rd(ld(X2,X),X2)),
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
rd(rd(X3,X2),rd(ld(X2,X),X2)) = mult(rd(X3,mult(X2,ld(X2,X))),X2),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c168,plain,
rd(X3,mult(X2,ld(X2,X))) = rd(X3,X),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
mult(rd(X3,mult(X2,ld(X2,X))),X2) = mult(rd(X3,X),X2),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
rd(rd(X3,X2),rd(ld(X2,X),X2)) = mult(rd(X3,X),X2),
inference(transitivity,[status(thm)],[c166,c169]) ).
cnf(c171,plain,
rd(rd(mult(X3,X2),X2),rd(ld(X2,X),X2)) = mult(rd(mult(X3,X2),X),X2),
inference(substitution,[status(thm)],[c170]) ).
cnf(c172,plain,
mult(rd(mult(X3,X2),X),X2) = rd(rd(mult(X3,X2),X2),rd(ld(X2,X),X2)),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
rd(mult(X2,X),X) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c174,plain,
rd(rd(mult(X3,X2),X2),rd(ld(X2,X),X2)) = rd(X3,rd(ld(X2,X),X2)),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
mult(rd(mult(X3,X2),X),X2) = rd(X3,rd(ld(X2,X),X2)),
inference(transitivity,[status(thm)],[c172,c174]) ).
cnf(c176,plain,
mult(rd(mult(rd(X2,X2),X),mult(rd(X2,X2),X)),X) = rd(rd(X2,X2),rd(ld(X,mult(rd(X2,X2),X)),X)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
rd(mult(X3,mult(X2,mult(ld(mult(X,X2),X),X2))),X2) = mult(mult(X3,X2),ld(mult(X,X2),X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c178,plain,
mult(mult(X3,X2),ld(mult(X,X2),X)) = rd(mult(X3,mult(X2,mult(ld(mult(X,X2),X),X2))),X2),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
ld(X3,mult(X3,mult(ld(mult(X2,X3),X),X3))) = mult(ld(mult(X2,X3),X),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c180,plain,
mult(ld(mult(X2,X3),X),X3) = ld(X3,mult(X3,mult(ld(mult(X2,X3),X),X3))),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
mult(X3,mult(X2,mult(X,X2))) = mult(mult(mult(X3,X2),X),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c182,plain,
mult(mult(mult(X3,X2),X),X2) = mult(X3,mult(X2,mult(X,X2))),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
ld(X3,mult(mult(mult(X3,X2),X),X2)) = ld(X3,mult(X3,mult(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
ld(X3,mult(X3,mult(X2,mult(X,X2)))) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c185,plain,
ld(X3,mult(mult(mult(X3,X2),X),X2)) = mult(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c183,c184]) ).
cnf(c186,plain,
ld(X2,mult(mult(mult(X2,X3),ld(mult(X2,X3),X)),X3)) = mult(X3,mult(ld(mult(X2,X3),X),X3)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
mult(X3,mult(ld(mult(X2,X3),X),X3)) = ld(X2,mult(mult(mult(X2,X3),ld(mult(X2,X3),X)),X3)),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
mult(mult(X2,X3),ld(mult(X2,X3),X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c189,plain,
mult(mult(mult(X2,X3),ld(mult(X2,X3),X)),X3) = mult(X,X3),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
ld(X2,mult(mult(mult(X2,X3),ld(mult(X2,X3),X)),X3)) = ld(X2,mult(X,X3)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
mult(X3,mult(ld(mult(X2,X3),X),X3)) = ld(X2,mult(X,X3)),
inference(transitivity,[status(thm)],[c187,c190]) ).
cnf(c192,plain,
ld(X3,mult(X3,mult(ld(mult(X2,X3),X),X3))) = ld(X3,ld(X2,mult(X,X3))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
mult(ld(mult(X2,X3),X),X3) = ld(X3,ld(X2,mult(X,X3))),
inference(transitivity,[status(thm)],[c180,c192]) ).
cnf(c194,plain,
mult(ld(mult(X2,X),X2),X) = ld(X,ld(X2,mult(X2,X))),
inference(substitution,[status(thm)],[c193]) ).
cnf(c195,plain,
ld(X2,mult(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c196,plain,
ld(X,ld(X2,mult(X2,X))) = ld(X,X),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
mult(ld(mult(X2,X),X2),X) = ld(X,X),
inference(transitivity,[status(thm)],[c194,c196]) ).
cnf(c198,plain,
mult(ld(mult(X,X2),X),X2) = ld(X2,X2),
inference(substitution,[status(thm)],[c197]) ).
cnf(c199,plain,
mult(X2,mult(ld(mult(X,X2),X),X2)) = mult(X2,ld(X2,X2)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
mult(X3,mult(X2,mult(ld(mult(X,X2),X),X2))) = mult(X3,mult(X2,ld(X2,X2))),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
rd(mult(X3,mult(X2,mult(ld(mult(X,X2),X),X2))),X2) = rd(mult(X3,mult(X2,ld(X2,X2))),X2),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
mult(X,ld(X,X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c203,plain,
mult(X2,mult(X,ld(X,X))) = mult(X2,X),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
rd(mult(X2,mult(X,ld(X,X))),X) = rd(mult(X2,X),X),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
rd(mult(X2,X),X) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c206,plain,
rd(mult(X2,mult(X,ld(X,X))),X) = X2,
inference(transitivity,[status(thm)],[c204,c205]) ).
cnf(c207,plain,
rd(mult(X3,mult(X2,mult(ld(mult(X,X2),X),X2))),X2) = X3,
inference(transitivity,[status(thm)],[c201,c206]) ).
cnf(c208,plain,
mult(mult(X3,X2),ld(mult(X,X2),X)) = X3,
inference(transitivity,[status(thm)],[c178,c207]) ).
cnf(c209,plain,
mult(mult(X2,X3),ld(mult(X,X3),X)) = X2,
inference(substitution,[status(thm)],[c208]) ).
cnf(c210,plain,
X2 = mult(mult(X2,X3),ld(mult(X,X3),X)),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
mult(ld(mult(X,X3),X),X2) = mult(ld(mult(X,X3),X),mult(mult(X2,X3),ld(mult(X,X3),X))),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
ld(X3,mult(X3,mult(ld(X3,X2),mult(X,ld(X3,X2))))) = mult(ld(X3,X2),mult(X,ld(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c213,plain,
mult(ld(X3,X2),mult(X,ld(X3,X2))) = ld(X3,mult(X3,mult(ld(X3,X2),mult(X,ld(X3,X2))))),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
mult(X3,mult(ld(X3,X2),mult(X,ld(X3,X2)))) = mult(mult(mult(X3,ld(X3,X2)),X),ld(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c215,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c216,plain,
mult(mult(X3,ld(X3,X2)),X) = mult(X2,X),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
mult(mult(mult(X3,ld(X3,X2)),X),ld(X3,X2)) = mult(mult(X2,X),ld(X3,X2)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
mult(X3,mult(ld(X3,X2),mult(X,ld(X3,X2)))) = mult(mult(X2,X),ld(X3,X2)),
inference(transitivity,[status(thm)],[c214,c217]) ).
cnf(c219,plain,
ld(X3,mult(X3,mult(ld(X3,X2),mult(X,ld(X3,X2))))) = ld(X3,mult(mult(X2,X),ld(X3,X2))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
mult(ld(X3,X2),mult(X,ld(X3,X2))) = ld(X3,mult(mult(X2,X),ld(X3,X2))),
inference(transitivity,[status(thm)],[c213,c219]) ).
cnf(c221,plain,
mult(ld(mult(X,X3),X),mult(mult(X2,X3),ld(mult(X,X3),X))) = ld(mult(X,X3),mult(mult(X,mult(X2,X3)),ld(mult(X,X3),X))),
inference(substitution,[status(thm)],[c220]) ).
cnf(c222,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c13]) ).
cnf(c223,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
mult(X3,ld(mult(X2,X),X2)) = mult(mult(rd(X3,X),X),ld(mult(X2,X),X2)),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
mult(mult(rd(X3,X),X),ld(mult(X2,X),X2)) = rd(X3,X),
inference(substitution,[status(thm)],[c208]) ).
cnf(c226,plain,
mult(X3,ld(mult(X2,X),X2)) = rd(X3,X),
inference(transitivity,[status(thm)],[c224,c225]) ).
cnf(c227,plain,
mult(mult(X,mult(X2,X3)),ld(mult(X,X3),X)) = rd(mult(X,mult(X2,X3)),X3),
inference(substitution,[status(thm)],[c226]) ).
cnf(c228,plain,
ld(mult(X,X3),mult(mult(X,mult(X2,X3)),ld(mult(X,X3),X))) = ld(mult(X,X3),rd(mult(X,mult(X2,X3)),X3)),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
mult(mult(X3,X2),rd(ld(X2,X),X2)) = rd(mult(X3,mult(X2,ld(X2,X))),X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c230,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c231,plain,
mult(X3,mult(X2,ld(X2,X))) = mult(X3,X),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
rd(mult(X3,mult(X2,ld(X2,X))),X2) = rd(mult(X3,X),X2),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
mult(mult(X3,X2),rd(ld(X2,X),X2)) = rd(mult(X3,X),X2),
inference(transitivity,[status(thm)],[c229,c232]) ).
cnf(c234,plain,
rd(mult(X3,X),X2) = mult(mult(X3,X2),rd(ld(X2,X),X2)),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
ld(mult(X3,X2),rd(mult(X3,X),X2)) = ld(mult(X3,X2),mult(mult(X3,X2),rd(ld(X2,X),X2))),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
ld(mult(X3,X2),mult(mult(X3,X2),rd(ld(X2,X),X2))) = rd(ld(X2,X),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c237,plain,
ld(mult(X3,X2),rd(mult(X3,X),X2)) = rd(ld(X2,X),X2),
inference(transitivity,[status(thm)],[c235,c236]) ).
cnf(c238,plain,
ld(mult(X,X3),rd(mult(X,mult(X2,X3)),X3)) = rd(ld(X3,mult(X2,X3)),X3),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
ld(mult(X,X3),mult(mult(X,mult(X2,X3)),ld(mult(X,X3),X))) = rd(ld(X3,mult(X2,X3)),X3),
inference(transitivity,[status(thm)],[c228,c238]) ).
cnf(c240,plain,
mult(ld(mult(X,X3),X),mult(mult(X2,X3),ld(mult(X,X3),X))) = rd(ld(X3,mult(X2,X3)),X3),
inference(transitivity,[status(thm)],[c221,c239]) ).
cnf(c241,plain,
mult(ld(mult(X,X3),X),X2) = rd(ld(X3,mult(X2,X3)),X3),
inference(transitivity,[status(thm)],[c211,c240]) ).
cnf(c242,plain,
mult(ld(mult(X,X3),X),rd(X2,X2)) = rd(ld(X3,mult(rd(X2,X2),X3)),X3),
inference(substitution,[status(thm)],[c241]) ).
cnf(c243,plain,
rd(ld(X3,mult(rd(X2,X2),X3)),X3) = mult(ld(mult(X,X3),X),rd(X2,X2)),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
rd(mult(mult(X2,rd(X,X)),rd(X,X)),rd(X,X)) = mult(X2,rd(X,X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c245,plain,
mult(X2,rd(X,X)) = rd(mult(mult(X2,rd(X,X)),rd(X,X)),rd(X,X)),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
rd(mult(X2,mult(rd(X,X),mult(rd(X,X),rd(X,X)))),rd(X,X)) = mult(mult(X2,rd(X,X)),rd(X,X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c247,plain,
mult(mult(X2,rd(X,X)),rd(X,X)) = rd(mult(X2,mult(rd(X,X),mult(rd(X,X),rd(X,X)))),rd(X,X)),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c249,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
ld(rd(rd(X2,X2),ld(X2,X)),X) = ld(rd(rd(X2,X2),ld(X2,X)),mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c13]) ).
cnf(c252,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c251]) ).
cnf(c253,plain,
mult(X3,X) = mult(mult(rd(X3,X2),X2),X),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
ld(rd(rd(X3,X2),X),mult(X3,X)) = ld(rd(rd(X3,X2),X),mult(mult(rd(X3,X2),X2),X)),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
ld(rd(rd(X3,X2),X),mult(mult(rd(X3,X2),X2),X)) = mult(X,mult(X2,X)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c256,plain,
ld(rd(rd(X3,X2),X),mult(X3,X)) = mult(X,mult(X2,X)),
inference(transitivity,[status(thm)],[c254,c255]) ).
cnf(c257,plain,
ld(rd(rd(X2,X2),ld(X2,X)),mult(X2,ld(X2,X))) = mult(ld(X2,X),mult(X2,ld(X2,X))),
inference(substitution,[status(thm)],[c256]) ).
cnf(c258,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c259,plain,
mult(ld(X2,X),mult(X2,ld(X2,X))) = mult(ld(X2,X),X),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
ld(rd(rd(X2,X2),ld(X2,X)),mult(X2,ld(X2,X))) = mult(ld(X2,X),X),
inference(transitivity,[status(thm)],[c257,c259]) ).
cnf(c261,plain,
ld(rd(rd(X2,X2),ld(X2,X)),X) = mult(ld(X2,X),X),
inference(transitivity,[status(thm)],[c250,c260]) ).
cnf(c262,plain,
ld(rd(rd(X,X),ld(X,rd(X,X))),rd(X,X)) = mult(ld(X,rd(X,X)),rd(X,X)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c263,plain,
mult(ld(X,rd(X,X)),rd(X,X)) = ld(rd(rd(X,X),ld(X,rd(X,X))),rd(X,X)),
inference(symmetry,[status(thm)],[c262]) ).
cnf(c264,plain,
rd(rd(X,X),ld(X,rd(X,X))) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c265,plain,
ld(rd(rd(X,X),ld(X,rd(X,X))),rd(X,X)) = ld(X,rd(X,X)),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
mult(ld(X,rd(X,X)),rd(X,X)) = ld(X,rd(X,X)),
inference(transitivity,[status(thm)],[c263,c265]) ).
cnf(c267,plain,
ld(X,rd(X,X)) = mult(ld(X,rd(X,X)),rd(X,X)),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
ld(ld(X,rd(X,X)),ld(X,rd(X,X))) = ld(ld(X,rd(X,X)),mult(ld(X,rd(X,X)),rd(X,X))),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
ld(ld(X,rd(X,X)),mult(ld(X,rd(X,X)),rd(X,X))) = rd(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c270,plain,
ld(ld(X,rd(X,X)),ld(X,rd(X,X))) = rd(X,X),
inference(transitivity,[status(thm)],[c268,c269]) ).
cnf(c271,plain,
rd(X,X) = ld(ld(X,rd(X,X)),ld(X,rd(X,X))),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
mult(rd(X,X),rd(X,X)) = mult(ld(ld(X,rd(X,X)),ld(X,rd(X,X))),rd(X,X)),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
ld(X,rd(X,X)) = mult(ld(X,rd(X,X)),rd(X,X)),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c274,plain,
rd(ld(X,rd(X,X)),rd(X,X)) = rd(mult(ld(X,rd(X,X)),rd(X,X)),rd(X,X)),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
rd(mult(ld(X,rd(X,X)),rd(X,X)),rd(X,X)) = ld(X,rd(X,X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c276,plain,
rd(ld(X,rd(X,X)),rd(X,X)) = ld(X,rd(X,X)),
inference(transitivity,[status(thm)],[c274,c275]) ).
cnf(c277,plain,
ld(X,rd(X,X)) = rd(ld(X,rd(X,X)),rd(X,X)),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
ld(ld(X,rd(X,X)),ld(X,rd(X,X))) = ld(ld(X,rd(X,X)),rd(ld(X,rd(X,X)),rd(X,X))),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
mult(ld(ld(X,rd(X,X)),ld(X,rd(X,X))),rd(X,X)) = mult(ld(ld(X,rd(X,X)),rd(ld(X,rd(X,X)),rd(X,X))),rd(X,X)),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
mult(ld(ld(X,rd(X,X)),rd(ld(X,rd(X,X)),rd(X,X))),rd(X,X)) = ld(rd(X,X),rd(X,X)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c281,plain,
mult(ld(ld(X,rd(X,X)),ld(X,rd(X,X))),rd(X,X)) = ld(rd(X,X),rd(X,X)),
inference(transitivity,[status(thm)],[c279,c280]) ).
cnf(c282,plain,
mult(rd(X,X),rd(X,X)) = ld(rd(X,X),rd(X,X)),
inference(transitivity,[status(thm)],[c272,c281]) ).
cnf(c283,plain,
mult(rd(X,X),mult(rd(X,X),rd(X,X))) = mult(rd(X,X),ld(rd(X,X),rd(X,X))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
mult(X2,mult(rd(X,X),mult(rd(X,X),rd(X,X)))) = mult(X2,mult(rd(X,X),ld(rd(X,X),rd(X,X)))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
rd(mult(X2,mult(rd(X,X),mult(rd(X,X),rd(X,X)))),rd(X,X)) = rd(mult(X2,mult(rd(X,X),ld(rd(X,X),rd(X,X)))),rd(X,X)),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
mult(rd(X,X),ld(rd(X,X),rd(X,X))) = rd(X,X),
inference(substitution,[status(thm)],[c42]) ).
cnf(c287,plain,
mult(X2,mult(rd(X,X),ld(rd(X,X),rd(X,X)))) = mult(X2,rd(X,X)),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
rd(mult(X2,mult(rd(X,X),ld(rd(X,X),rd(X,X)))),rd(X,X)) = rd(mult(X2,rd(X,X)),rd(X,X)),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
rd(mult(X2,rd(X,X)),rd(X,X)) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c290,plain,
rd(mult(X2,mult(rd(X,X),ld(rd(X,X),rd(X,X)))),rd(X,X)) = X2,
inference(transitivity,[status(thm)],[c288,c289]) ).
cnf(c291,plain,
rd(mult(X2,mult(rd(X,X),mult(rd(X,X),rd(X,X)))),rd(X,X)) = X2,
inference(transitivity,[status(thm)],[c285,c290]) ).
cnf(c292,plain,
mult(mult(X2,rd(X,X)),rd(X,X)) = X2,
inference(transitivity,[status(thm)],[c247,c291]) ).
cnf(c293,plain,
rd(mult(mult(X2,rd(X,X)),rd(X,X)),rd(X,X)) = rd(X2,rd(X,X)),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
mult(X2,rd(X,X)) = rd(X2,rd(X,X)),
inference(transitivity,[status(thm)],[c245,c293]) ).
cnf(c295,plain,
mult(ld(mult(X,X3),X),rd(X2,X2)) = rd(ld(mult(X,X3),X),rd(X2,X2)),
inference(substitution,[status(thm)],[c294]) ).
cnf(c296,plain,
rd(ld(X3,mult(rd(X2,X2),X3)),X3) = rd(ld(mult(X,X3),X),rd(X2,X2)),
inference(transitivity,[status(thm)],[c243,c295]) ).
cnf(c297,plain,
rd(ld(X,mult(rd(X3,X3),X)),X) = rd(ld(mult(X2,X),X2),rd(X3,X3)),
inference(substitution,[status(thm)],[c296]) ).
cnf(c298,plain,
rd(rd(X3,X3),rd(ld(X,mult(rd(X3,X3),X)),X)) = rd(rd(X3,X3),rd(ld(mult(X2,X),X2),rd(X3,X3))),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
mult(rd(mult(rd(X3,X3),X),mult(rd(X3,X3),X)),X) = rd(rd(X3,X3),rd(ld(mult(X2,X),X2),rd(X3,X3))),
inference(transitivity,[status(thm)],[c176,c298]) ).
cnf(c300,plain,
mult(ld(mult(rd(X3,X3),X),mult(rd(X3,X3),X)),X) = rd(rd(X3,X3),rd(ld(mult(X2,X),X2),rd(X3,X3))),
inference(transitivity,[status(thm)],[c148,c299]) ).
cnf(c301,plain,
mult(ld(mult(rd(X3,X3),X2),mult(rd(X3,X3),X2)),X2) = rd(rd(X3,X3),rd(ld(mult(X,X2),X),rd(X3,X3))),
inference(substitution,[status(thm)],[c300]) ).
cnf(c302,plain,
mult(ld(mult(X3,X2),X3),rd(X,X)) = rd(ld(mult(X3,X2),X3),rd(X,X)),
inference(substitution,[status(thm)],[c294]) ).
cnf(c303,plain,
rd(ld(mult(X3,X2),X3),rd(X,X)) = mult(ld(mult(X3,X2),X3),rd(X,X)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
rd(mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2),X2) = rd(ld(X2,rd(X,X)),rd(X,X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c305,plain,
rd(ld(X2,rd(X,X)),rd(X,X)) = rd(mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2),X2),
inference(symmetry,[status(thm)],[c304]) ).
cnf(c306,plain,
ld(X,rd(X,X)) = mult(ld(X,rd(X,X)),rd(X,X)),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c307,plain,
mult(ld(X2,rd(X2,X2)),X) = mult(mult(ld(X2,rd(X2,X2)),rd(X2,X2)),X),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
ld(rd(ld(X2,rd(X2,X2)),X),mult(ld(X2,rd(X2,X2)),X)) = ld(rd(ld(X2,rd(X2,X2)),X),mult(mult(ld(X2,rd(X2,X2)),rd(X2,X2)),X)),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
ld(rd(ld(X2,rd(X2,X2)),X),mult(mult(ld(X2,rd(X2,X2)),rd(X2,X2)),X)) = mult(X,mult(rd(X2,X2),X)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c310,plain,
ld(rd(ld(X2,rd(X2,X2)),X),mult(ld(X2,rd(X2,X2)),X)) = mult(X,mult(rd(X2,X2),X)),
inference(transitivity,[status(thm)],[c308,c309]) ).
cnf(c311,plain,
ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)) = mult(X2,mult(rd(X,X),X2)),
inference(substitution,[status(thm)],[c310]) ).
cnf(c312,plain,
mult(X2,mult(rd(X,X),X2)) = ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)),
inference(symmetry,[status(thm)],[c311]) ).
cnf(c313,plain,
ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2))) = ld(ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)),mult(X2,mult(rd(X,X),X2))),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)) = mult(X2,mult(rd(X,X),X2)),
inference(substitution,[status(thm)],[c310]) ).
cnf(c315,plain,
mult(X2,mult(rd(X,X),X2)) = ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)),
inference(symmetry,[status(thm)],[c314]) ).
cnf(c316,plain,
ld(ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)),mult(X2,mult(rd(X,X),X2))) = ld(ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
X = rd(X2,ld(X,X2)),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c318,plain,
ld(X2,X) = ld(X2,rd(X2,ld(X,X2))),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
mult(ld(X2,X),ld(X,X2)) = mult(ld(X2,rd(X2,ld(X,X2))),ld(X,X2)),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
mult(ld(X2,rd(X2,ld(X,X2))),ld(X,X2)) = ld(ld(X,X2),ld(X,X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c321,plain,
mult(ld(X2,X),ld(X,X2)) = ld(ld(X,X2),ld(X,X2)),
inference(transitivity,[status(thm)],[c319,c320]) ).
cnf(c322,plain,
mult(ld(mult(ld(X,rd(X,X)),X2),rd(ld(X,rd(X,X)),X2)),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))) = ld(ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))),
inference(substitution,[status(thm)],[c321]) ).
cnf(c323,plain,
ld(ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))) = mult(ld(mult(ld(X,rd(X,X)),X2),rd(ld(X,rd(X,X)),X2)),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c324,plain,
ld(X,rd(X,X)) = mult(ld(X,rd(X,X)),rd(X,X)),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c325,plain,
rd(ld(X2,rd(X2,X2)),X) = rd(mult(ld(X2,rd(X2,X2)),rd(X2,X2)),X),
inference(congruence,[status(thm)],[c324]) ).
cnf(c326,plain,
ld(mult(ld(X2,rd(X2,X2)),X),rd(ld(X2,rd(X2,X2)),X)) = ld(mult(ld(X2,rd(X2,X2)),X),rd(mult(ld(X2,rd(X2,X2)),rd(X2,X2)),X)),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
ld(mult(ld(X2,rd(X2,X2)),X),rd(mult(ld(X2,rd(X2,X2)),rd(X2,X2)),X)) = rd(ld(X,rd(X2,X2)),X),
inference(substitution,[status(thm)],[c237]) ).
cnf(c328,plain,
ld(mult(ld(X2,rd(X2,X2)),X),rd(ld(X2,rd(X2,X2)),X)) = rd(ld(X,rd(X2,X2)),X),
inference(transitivity,[status(thm)],[c326,c327]) ).
cnf(c329,plain,
ld(mult(ld(X,rd(X,X)),X2),rd(ld(X,rd(X,X)),X2)) = rd(ld(X2,rd(X,X)),X2),
inference(substitution,[status(thm)],[c328]) ).
cnf(c330,plain,
mult(ld(mult(ld(X,rd(X,X)),X2),rd(ld(X,rd(X,X)),X2)),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))) = mult(rd(ld(X2,rd(X,X)),X2),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
mult(rd(ld(X2,rd(X,X)),X2),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))) = rd(rd(ld(X2,rd(X,X)),X2),ld(mult(ld(X,rd(X,X)),X2),rd(ld(X,rd(X,X)),X2))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c332,plain,
ld(mult(ld(X,rd(X,X)),X2),rd(ld(X,rd(X,X)),X2)) = rd(ld(X2,rd(X,X)),X2),
inference(substitution,[status(thm)],[c328]) ).
cnf(c333,plain,
rd(rd(ld(X2,rd(X,X)),X2),ld(mult(ld(X,rd(X,X)),X2),rd(ld(X,rd(X,X)),X2))) = rd(rd(ld(X2,rd(X,X)),X2),rd(ld(X2,rd(X,X)),X2)),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
rd(rd(ld(X2,rd(X,X)),X2),rd(ld(X2,rd(X,X)),X2)) = mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2),
inference(substitution,[status(thm)],[c170]) ).
cnf(c335,plain,
rd(rd(ld(X2,rd(X,X)),X2),ld(mult(ld(X,rd(X,X)),X2),rd(ld(X,rd(X,X)),X2))) = mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2),
inference(transitivity,[status(thm)],[c333,c334]) ).
cnf(c336,plain,
mult(rd(ld(X2,rd(X,X)),X2),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))) = mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2),
inference(transitivity,[status(thm)],[c331,c335]) ).
cnf(c337,plain,
mult(ld(mult(ld(X,rd(X,X)),X2),rd(ld(X,rd(X,X)),X2)),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))) = mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2),
inference(transitivity,[status(thm)],[c330,c336]) ).
cnf(c338,plain,
ld(ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)),ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2))) = mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2),
inference(transitivity,[status(thm)],[c323,c337]) ).
cnf(c339,plain,
ld(ld(rd(ld(X,rd(X,X)),X2),mult(ld(X,rd(X,X)),X2)),mult(X2,mult(rd(X,X),X2))) = mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2),
inference(transitivity,[status(thm)],[c316,c338]) ).
cnf(c340,plain,
ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2))) = mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2),
inference(transitivity,[status(thm)],[c313,c339]) ).
cnf(c341,plain,
mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2) = ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2))),
inference(symmetry,[status(thm)],[c340]) ).
cnf(c342,plain,
mult(rd(X,X),ld(rd(X,X),ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2))))) = ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2))),
inference(substitution,[status(thm)],[c42]) ).
cnf(c343,plain,
ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2))) = mult(rd(X,X),ld(rd(X,X),ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2))))),
inference(symmetry,[status(thm)],[c342]) ).
cnf(c344,plain,
rd(X2,rd(X,X)) = mult(X2,rd(X,X)),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c345,plain,
rd(rd(X2,rd(X,X)),rd(X,X)) = rd(mult(X2,rd(X,X)),rd(X,X)),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
rd(mult(X2,rd(X,X)),rd(X,X)) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c347,plain,
rd(rd(X2,rd(X,X)),rd(X,X)) = X2,
inference(transitivity,[status(thm)],[c345,c346]) ).
cnf(c348,plain,
rd(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)) = mult(X,mult(rd(X2,X2),X)),
inference(substitution,[status(thm)],[c347]) ).
cnf(c349,plain,
mult(X,mult(rd(X2,X2),X)) = rd(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)),
inference(symmetry,[status(thm)],[c348]) ).
cnf(c350,plain,
ld(mult(X,mult(rd(X2,X2),X)),mult(X,mult(rd(X2,X2),X))) = ld(rd(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)),mult(X,mult(rd(X2,X2),X))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
ld(rd(X2,X2),ld(mult(X,mult(rd(X2,X2),X)),mult(X,mult(rd(X2,X2),X)))) = ld(rd(X2,X2),ld(rd(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)),mult(X,mult(rd(X2,X2),X)))),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
ld(X,ld(rd(X3,X),mult(rd(X2,X),X))) = mult(ld(X3,rd(X2,X)),X),
inference(substitution,[status(thm)],[c50]) ).
cnf(c353,plain,
mult(ld(X3,rd(X2,X)),X) = ld(X,ld(rd(X3,X),mult(rd(X2,X),X))),
inference(symmetry,[status(thm)],[c352]) ).
cnf(c354,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c13]) ).
cnf(c355,plain,
ld(rd(X3,X),mult(rd(X2,X),X)) = ld(rd(X3,X),X2),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
ld(X,ld(rd(X3,X),mult(rd(X2,X),X))) = ld(X,ld(rd(X3,X),X2)),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
mult(ld(X3,rd(X2,X)),X) = ld(X,ld(rd(X3,X),X2)),
inference(transitivity,[status(thm)],[c353,c356]) ).
cnf(c358,plain,
mult(ld(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2))),rd(X2,X2)) = ld(rd(X2,X2),ld(rd(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)),mult(X,mult(rd(X2,X2),X)))),
inference(substitution,[status(thm)],[c357]) ).
cnf(c359,plain,
ld(rd(X2,X2),ld(rd(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)),mult(X,mult(rd(X2,X2),X)))) = mult(ld(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2))),rd(X2,X2)),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c360,plain,
rd(mult(X3,mult(rd(X2,X2),X)),mult(rd(X2,X2),X)) = X3,
inference(substitution,[status(thm)],[c8]) ).
cnf(c361,plain,
X3 = rd(mult(X3,mult(rd(X2,X2),X)),mult(rd(X2,X2),X)),
inference(symmetry,[status(thm)],[c360]) ).
cnf(c362,plain,
rd(X3,rd(X2,X2)) = rd(rd(mult(X3,mult(rd(X2,X2),X)),mult(rd(X2,X2),X)),rd(X2,X2)),
inference(congruence,[status(thm)],[c361]) ).
cnf(c363,plain,
mult(rd(X3,rd(X2,X2)),rd(X,rd(X2,X2))) = mult(rd(rd(mult(X3,mult(rd(X2,X2),X)),mult(rd(X2,X2),X)),rd(X2,X2)),rd(X,rd(X2,X2))),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
mult(rd(X3,mult(rd(X2,X2),X)),rd(X2,X2)) = rd(rd(X3,mult(rd(X2,X2),X)),rd(X2,X2)),
inference(substitution,[status(thm)],[c294]) ).
cnf(c365,plain,
rd(rd(X3,mult(rd(X2,X2),X)),rd(X2,X2)) = mult(rd(X3,mult(rd(X2,X2),X)),rd(X2,X2)),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
mult(rd(X3,mult(rd(X2,X2),X)),rd(X2,X2)) = rd(rd(X3,rd(X2,X2)),rd(X,rd(X2,X2))),
inference(substitution,[status(thm)],[c164]) ).
cnf(c367,plain,
rd(rd(X3,mult(rd(X2,X2),X)),rd(X2,X2)) = rd(rd(X3,rd(X2,X2)),rd(X,rd(X2,X2))),
inference(transitivity,[status(thm)],[c365,c366]) ).
cnf(c368,plain,
mult(rd(rd(X3,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X,rd(X2,X2))) = mult(rd(rd(X3,rd(X2,X2)),rd(X,rd(X2,X2))),rd(X,rd(X2,X2))),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
mult(rd(rd(X3,rd(X2,X2)),rd(X,rd(X2,X2))),rd(X,rd(X2,X2))) = rd(X3,rd(X2,X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c370,plain,
mult(rd(rd(X3,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X,rd(X2,X2))) = rd(X3,rd(X2,X2)),
inference(transitivity,[status(thm)],[c368,c369]) ).
cnf(c371,plain,
mult(rd(rd(mult(X3,mult(rd(X2,X2),X)),mult(rd(X2,X2),X)),rd(X2,X2)),rd(X,rd(X2,X2))) = rd(mult(X3,mult(rd(X2,X2),X)),rd(X2,X2)),
inference(substitution,[status(thm)],[c370]) ).
cnf(c372,plain,
mult(rd(X3,rd(X2,X2)),rd(X,rd(X2,X2))) = rd(mult(X3,mult(rd(X2,X2),X)),rd(X2,X2)),
inference(transitivity,[status(thm)],[c363,c371]) ).
cnf(c373,plain,
mult(rd(X2,rd(X,X)),rd(X2,rd(X,X))) = rd(mult(X2,mult(rd(X,X),X2)),rd(X,X)),
inference(substitution,[status(thm)],[c372]) ).
cnf(c374,plain,
rd(mult(X2,mult(rd(X,X),X2)),rd(X,X)) = mult(rd(X2,rd(X,X)),rd(X2,rd(X,X))),
inference(symmetry,[status(thm)],[c373]) ).
cnf(c375,plain,
ld(rd(mult(X2,mult(rd(X,X),X2)),rd(X,X)),rd(mult(X2,mult(rd(X,X),X2)),rd(X,X))) = ld(rd(mult(X2,mult(rd(X,X),X2)),rd(X,X)),mult(rd(X2,rd(X,X)),rd(X2,rd(X,X)))),
inference(congruence,[status(thm)],[c374]) ).
cnf(c376,plain,
mult(rd(X2,rd(X,X)),rd(X2,rd(X,X))) = rd(mult(X2,mult(rd(X,X),X2)),rd(X,X)),
inference(substitution,[status(thm)],[c372]) ).
cnf(c377,plain,
rd(mult(X2,mult(rd(X,X),X2)),rd(X,X)) = mult(rd(X2,rd(X,X)),rd(X2,rd(X,X))),
inference(symmetry,[status(thm)],[c376]) ).
cnf(c378,plain,
ld(rd(mult(X2,mult(rd(X,X),X2)),rd(X,X)),mult(rd(X2,rd(X,X)),rd(X2,rd(X,X)))) = ld(mult(rd(X2,rd(X,X)),rd(X2,rd(X,X))),mult(rd(X2,rd(X,X)),rd(X2,rd(X,X)))),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
rd(mult(X,X),mult(X,X)) = ld(mult(X,X),mult(X,X)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c380,plain,
ld(mult(X,X),mult(X,X)) = rd(mult(X,X),mult(X,X)),
inference(symmetry,[status(thm)],[c379]) ).
cnf(c381,plain,
ld(X,X) = rd(X,X),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c382,plain,
mult(ld(X,X),mult(X,X)) = mult(rd(X,X),mult(X,X)),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
mult(rd(X,ld(X,X)),X) = mult(rd(X,X),mult(X,X)),
inference(substitution,[status(thm)],[c127]) ).
cnf(c384,plain,
mult(rd(X,X),mult(X,X)) = mult(rd(X,ld(X,X)),X),
inference(symmetry,[status(thm)],[c383]) ).
cnf(c385,plain,
rd(X,ld(X,X)) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c386,plain,
mult(rd(X,ld(X,X)),X) = mult(X,X),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
mult(rd(X,X),mult(X,X)) = mult(X,X),
inference(transitivity,[status(thm)],[c384,c386]) ).
cnf(c388,plain,
mult(ld(X,X),mult(X,X)) = mult(X,X),
inference(transitivity,[status(thm)],[c382,c387]) ).
cnf(c389,plain,
mult(X,X) = mult(ld(X,X),mult(X,X)),
inference(symmetry,[status(thm)],[c388]) ).
cnf(c390,plain,
rd(mult(X,X),mult(X,X)) = rd(mult(ld(X,X),mult(X,X)),mult(X,X)),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
rd(mult(ld(X,X),mult(X,X)),mult(X,X)) = ld(X,X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c392,plain,
rd(mult(X,X),mult(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c390,c391]) ).
cnf(c393,plain,
ld(mult(X,X),mult(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c380,c392]) ).
cnf(c394,plain,
ld(mult(rd(X2,rd(X,X)),rd(X2,rd(X,X))),mult(rd(X2,rd(X,X)),rd(X2,rd(X,X)))) = ld(rd(X2,rd(X,X)),rd(X2,rd(X,X))),
inference(substitution,[status(thm)],[c393]) ).
cnf(c395,plain,
rd(rd(X2,mult(rd(X,X),X2)),rd(X,X)) = rd(rd(X2,rd(X,X)),rd(X2,rd(X,X))),
inference(substitution,[status(thm)],[c367]) ).
cnf(c396,plain,
rd(rd(X2,rd(X,X)),rd(X2,rd(X,X))) = ld(rd(X2,rd(X,X)),rd(X2,rd(X,X))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c397,plain,
rd(rd(X2,mult(rd(X,X),X2)),rd(X,X)) = ld(rd(X2,rd(X,X)),rd(X2,rd(X,X))),
inference(transitivity,[status(thm)],[c395,c396]) ).
cnf(c398,plain,
ld(rd(X2,rd(X,X)),rd(X2,rd(X,X))) = rd(rd(X2,mult(rd(X,X),X2)),rd(X,X)),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
ld(mult(rd(X2,rd(X,X)),rd(X2,rd(X,X))),mult(rd(X2,rd(X,X)),rd(X2,rd(X,X)))) = rd(rd(X2,mult(rd(X,X),X2)),rd(X,X)),
inference(transitivity,[status(thm)],[c394,c398]) ).
cnf(c400,plain,
ld(rd(mult(X2,mult(rd(X,X),X2)),rd(X,X)),mult(rd(X2,rd(X,X)),rd(X2,rd(X,X)))) = rd(rd(X2,mult(rd(X,X),X2)),rd(X,X)),
inference(transitivity,[status(thm)],[c378,c399]) ).
cnf(c401,plain,
ld(rd(mult(X2,mult(rd(X,X),X2)),rd(X,X)),rd(mult(X2,mult(rd(X,X),X2)),rd(X,X))) = rd(rd(X2,mult(rd(X,X),X2)),rd(X,X)),
inference(transitivity,[status(thm)],[c375,c400]) ).
cnf(c402,plain,
ld(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2))) = rd(rd(X,mult(rd(X2,X2),X)),rd(X2,X2)),
inference(substitution,[status(thm)],[c401]) ).
cnf(c403,plain,
mult(ld(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2))),rd(X2,X2)) = mult(rd(rd(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)),
inference(congruence,[status(thm)],[c402]) ).
cnf(c404,plain,
mult(rd(rd(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)) = rd(X,mult(rd(X2,X2),X)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c405,plain,
mult(ld(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2))),rd(X2,X2)) = rd(X,mult(rd(X2,X2),X)),
inference(transitivity,[status(thm)],[c403,c404]) ).
cnf(c406,plain,
ld(rd(X2,X2),ld(rd(rd(mult(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)),mult(X,mult(rd(X2,X2),X)))) = rd(X,mult(rd(X2,X2),X)),
inference(transitivity,[status(thm)],[c359,c405]) ).
cnf(c407,plain,
ld(rd(X2,X2),ld(mult(X,mult(rd(X2,X2),X)),mult(X,mult(rd(X2,X2),X)))) = rd(X,mult(rd(X2,X2),X)),
inference(transitivity,[status(thm)],[c351,c406]) ).
cnf(c408,plain,
ld(rd(X,X),ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2)))) = rd(X2,mult(rd(X,X),X2)),
inference(substitution,[status(thm)],[c407]) ).
cnf(c409,plain,
mult(rd(X,X),ld(rd(X,X),ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2))))) = mult(rd(X,X),rd(X2,mult(rd(X,X),X2))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
mult(rd(rd(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)) = rd(X,mult(rd(X2,X2),X)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c411,plain,
rd(X,mult(rd(X2,X2),X)) = mult(rd(rd(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)),
inference(symmetry,[status(thm)],[c410]) ).
cnf(c412,plain,
rd(rd(X,mult(rd(X2,X2),X)),rd(X2,X2)) = ld(rd(X,rd(X2,X2)),rd(X,rd(X2,X2))),
inference(substitution,[status(thm)],[c397]) ).
cnf(c413,plain,
mult(rd(rd(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)) = mult(ld(rd(X,rd(X2,X2)),rd(X,rd(X2,X2))),rd(X2,X2)),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
mult(ld(rd(X,rd(X2,X2)),rd(X,rd(X2,X2))),rd(X2,X2)) = ld(rd(X2,X2),ld(rd(rd(X,rd(X2,X2)),rd(X2,X2)),X)),
inference(substitution,[status(thm)],[c357]) ).
cnf(c415,plain,
rd(rd(X,rd(X2,X2)),rd(X2,X2)) = X,
inference(substitution,[status(thm)],[c347]) ).
cnf(c416,plain,
ld(rd(rd(X,rd(X2,X2)),rd(X2,X2)),X) = ld(X,X),
inference(congruence,[status(thm)],[c415]) ).
cnf(c417,plain,
ld(rd(X2,X2),ld(rd(rd(X,rd(X2,X2)),rd(X2,X2)),X)) = ld(rd(X2,X2),ld(X,X)),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
mult(ld(rd(X,rd(X2,X2)),rd(X,rd(X2,X2))),rd(X2,X2)) = ld(rd(X2,X2),ld(X,X)),
inference(transitivity,[status(thm)],[c414,c417]) ).
cnf(c419,plain,
mult(rd(rd(X,mult(rd(X2,X2),X)),rd(X2,X2)),rd(X2,X2)) = ld(rd(X2,X2),ld(X,X)),
inference(transitivity,[status(thm)],[c413,c418]) ).
cnf(c420,plain,
rd(X,mult(rd(X2,X2),X)) = ld(rd(X2,X2),ld(X,X)),
inference(transitivity,[status(thm)],[c411,c419]) ).
cnf(c421,plain,
mult(rd(X2,X2),rd(X,mult(rd(X2,X2),X))) = mult(rd(X2,X2),ld(rd(X2,X2),ld(X,X))),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
mult(rd(X2,X2),ld(rd(X2,X2),ld(X,X))) = ld(X,X),
inference(substitution,[status(thm)],[c42]) ).
cnf(c423,plain,
mult(rd(X2,X2),rd(X,mult(rd(X2,X2),X))) = ld(X,X),
inference(transitivity,[status(thm)],[c421,c422]) ).
cnf(c424,plain,
mult(rd(X,X),rd(X2,mult(rd(X,X),X2))) = ld(X2,X2),
inference(substitution,[status(thm)],[c423]) ).
cnf(c425,plain,
mult(rd(X,X),ld(rd(X,X),ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2))))) = ld(X2,X2),
inference(transitivity,[status(thm)],[c409,c424]) ).
cnf(c426,plain,
ld(mult(X2,mult(rd(X,X),X2)),mult(X2,mult(rd(X,X),X2))) = ld(X2,X2),
inference(transitivity,[status(thm)],[c343,c425]) ).
cnf(c427,plain,
mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2) = ld(X2,X2),
inference(transitivity,[status(thm)],[c341,c426]) ).
cnf(c428,plain,
rd(mult(rd(ld(X2,rd(X,X)),rd(X,X)),X2),X2) = rd(ld(X2,X2),X2),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
mult(ld(mult(X,X2),X),X2) = ld(X2,X2),
inference(substitution,[status(thm)],[c197]) ).
cnf(c430,plain,
ld(X2,X2) = mult(ld(mult(X,X2),X),X2),
inference(symmetry,[status(thm)],[c429]) ).
cnf(c431,plain,
rd(ld(X2,X2),X2) = rd(mult(ld(mult(X,X2),X),X2),X2),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
rd(mult(ld(mult(X,X2),X),X2),X2) = ld(mult(X,X2),X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c433,plain,
rd(ld(X2,X2),X2) = ld(mult(X,X2),X),
inference(transitivity,[status(thm)],[c431,c432]) ).
cnf(c434,plain,
rd(mult(rd(ld(X3,rd(X2,X2)),rd(X2,X2)),X3),X3) = ld(mult(X,X3),X),
inference(transitivity,[status(thm)],[c428,c433]) ).
cnf(c435,plain,
rd(ld(X3,rd(X2,X2)),rd(X2,X2)) = ld(mult(X,X3),X),
inference(transitivity,[status(thm)],[c305,c434]) ).
cnf(c436,plain,
rd(ld(X2,rd(X,X)),rd(X,X)) = ld(mult(X3,X2),X3),
inference(substitution,[status(thm)],[c435]) ).
cnf(c437,plain,
ld(mult(X3,X2),X3) = rd(ld(X2,rd(X,X)),rd(X,X)),
inference(symmetry,[status(thm)],[c436]) ).
cnf(c438,plain,
mult(ld(mult(X3,X2),X3),rd(X,X)) = mult(rd(ld(X2,rd(X,X)),rd(X,X)),rd(X,X)),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
mult(rd(ld(X2,rd(X,X)),rd(X,X)),rd(X,X)) = ld(X2,rd(X,X)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c440,plain,
mult(ld(mult(X3,X2),X3),rd(X,X)) = ld(X2,rd(X,X)),
inference(transitivity,[status(thm)],[c438,c439]) ).
cnf(c441,plain,
rd(ld(mult(X3,X2),X3),rd(X,X)) = ld(X2,rd(X,X)),
inference(transitivity,[status(thm)],[c303,c440]) ).
cnf(c442,plain,
rd(ld(mult(X,X2),X),rd(X3,X3)) = ld(X2,rd(X3,X3)),
inference(substitution,[status(thm)],[c441]) ).
cnf(c443,plain,
rd(rd(X3,X3),rd(ld(mult(X,X2),X),rd(X3,X3))) = rd(rd(X3,X3),ld(X2,rd(X3,X3))),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
rd(rd(X2,X2),ld(X,rd(X2,X2))) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c445,plain,
rd(rd(X3,X3),rd(ld(mult(X,X2),X),rd(X3,X3))) = X2,
inference(transitivity,[status(thm)],[c443,c444]) ).
cnf(c446,plain,
mult(ld(mult(rd(X2,X2),X),mult(rd(X2,X2),X)),X) = X,
inference(transitivity,[status(thm)],[c301,c445]) ).
cnf(c447,plain,
mult(ld(mult(rd(X,X),X2),mult(rd(X,X),X2)),X2) = X2,
inference(substitution,[status(thm)],[c446]) ).
cnf(c448,plain,
rd(mult(ld(mult(rd(X,X),X2),mult(rd(X,X),X2)),X2),X2) = rd(X2,X2),
inference(congruence,[status(thm)],[c447]) ).
cnf(c449,plain,
rd(mult(ld(mult(rd(X,X),X2),mult(rd(X,X),X2)),X2),X2) = ld(X2,X2),
inference(transitivity,[status(thm)],[c448,c137]) ).
cnf(c450,plain,
ld(mult(rd(X,X),X2),mult(rd(X,X),X2)) = ld(X2,X2),
inference(transitivity,[status(thm)],[c145,c449]) ).
cnf(c451,plain,
rd(mult(rd(X2,X2),X),mult(rd(X2,X2),mult(rd(X2,X2),X))) = ld(rd(X2,X2),ld(mult(rd(X2,X2),X),mult(rd(X2,X2),X))),
inference(substitution,[status(thm)],[c420]) ).
cnf(c452,plain,
ld(rd(X2,X2),ld(mult(rd(X2,X2),X),mult(rd(X2,X2),X))) = rd(mult(rd(X2,X2),X),mult(rd(X2,X2),mult(rd(X2,X2),X))),
inference(symmetry,[status(thm)],[c451]) ).
cnf(c453,plain,
rd(rd(X,X),rd(X,X)) = ld(rd(X,X),rd(X,X)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c454,plain,
ld(rd(X,X),rd(X,X)) = rd(rd(X,X),rd(X,X)),
inference(symmetry,[status(thm)],[c453]) ).
cnf(c455,plain,
rd(rd(X,X),rd(X,X)) = rd(rd(X,X),ld(X,X)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c456,plain,
ld(rd(rd(X3,X),X2),mult(X3,X2)) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c256]) ).
cnf(c457,plain,
mult(X2,mult(X,X2)) = ld(rd(rd(X3,X),X2),mult(X3,X2)),
inference(symmetry,[status(thm)],[c456]) ).
cnf(c458,plain,
rd(mult(X3,X2),mult(X2,mult(X,X2))) = rd(mult(X3,X2),ld(rd(rd(X3,X),X2),mult(X3,X2))),
inference(congruence,[status(thm)],[c457]) ).
cnf(c459,plain,
rd(mult(X3,X2),ld(rd(rd(X3,X),X2),mult(X3,X2))) = rd(rd(X3,X),X2),
inference(substitution,[status(thm)],[c74]) ).
cnf(c460,plain,
rd(mult(X3,X2),mult(X2,mult(X,X2))) = rd(rd(X3,X),X2),
inference(transitivity,[status(thm)],[c458,c459]) ).
cnf(c461,plain,
rd(mult(X,ld(X,X2)),mult(ld(X,X2),mult(X,ld(X,X2)))) = rd(rd(X,X),ld(X,X2)),
inference(substitution,[status(thm)],[c460]) ).
cnf(c462,plain,
rd(rd(X,X),ld(X,X2)) = rd(mult(X,ld(X,X2)),mult(ld(X,X2),mult(X,ld(X,X2)))),
inference(symmetry,[status(thm)],[c461]) ).
cnf(c463,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c42]) ).
cnf(c464,plain,
rd(mult(X,ld(X,X2)),mult(ld(X,X2),mult(X,ld(X,X2)))) = rd(X2,mult(ld(X,X2),mult(X,ld(X,X2)))),
inference(congruence,[status(thm)],[c463]) ).
cnf(c465,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c42]) ).
cnf(c466,plain,
mult(ld(X,X2),mult(X,ld(X,X2))) = mult(ld(X,X2),X2),
inference(congruence,[status(thm)],[c465]) ).
cnf(c467,plain,
rd(X2,mult(ld(X,X2),mult(X,ld(X,X2)))) = rd(X2,mult(ld(X,X2),X2)),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
rd(mult(X,ld(X,X2)),mult(ld(X,X2),mult(X,ld(X,X2)))) = rd(X2,mult(ld(X,X2),X2)),
inference(transitivity,[status(thm)],[c464,c467]) ).
cnf(c469,plain,
rd(rd(X,X),ld(X,X2)) = rd(X2,mult(ld(X,X2),X2)),
inference(transitivity,[status(thm)],[c462,c468]) ).
cnf(c470,plain,
rd(rd(X,X),ld(X,X)) = rd(X,mult(ld(X,X),X)),
inference(substitution,[status(thm)],[c469]) ).
cnf(c471,plain,
ld(X,X) = rd(X,X),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c472,plain,
mult(ld(X,X),X) = mult(rd(X,X),X),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
rd(X,mult(ld(X,X),X)) = rd(X,mult(rd(X,X),X)),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
mult(rd(X,X),X) = X,
inference(substitution,[status(thm)],[c13]) ).
cnf(c475,plain,
rd(X,mult(rd(X,X),X)) = rd(X,X),
inference(congruence,[status(thm)],[c474]) ).
cnf(c476,plain,
rd(X,mult(ld(X,X),X)) = rd(X,X),
inference(transitivity,[status(thm)],[c473,c475]) ).
cnf(c477,plain,
rd(rd(X,X),ld(X,X)) = rd(X,X),
inference(transitivity,[status(thm)],[c470,c476]) ).
cnf(c478,plain,
rd(rd(X,X),rd(X,X)) = rd(X,X),
inference(transitivity,[status(thm)],[c455,c477]) ).
cnf(c479,plain,
ld(rd(X,X),rd(X,X)) = rd(X,X),
inference(transitivity,[status(thm)],[c454,c478]) ).
cnf(c480,plain,
rd(X,X) = ld(rd(X,X),rd(X,X)),
inference(symmetry,[status(thm)],[c479]) ).
cnf(c481,plain,
mult(rd(X2,X2),mult(rd(X2,X2),X)) = mult(ld(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X)),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
rd(rd(X,X),rd(X,X)) = ld(rd(X,X),rd(X,X)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c483,plain,
ld(rd(X,X),rd(X,X)) = rd(rd(X,X),rd(X,X)),
inference(symmetry,[status(thm)],[c482]) ).
cnf(c484,plain,
mult(ld(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X)) = mult(rd(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X)),
inference(congruence,[status(thm)],[c483]) ).
cnf(c485,plain,
mult(rd(X3,X),mult(X,mult(rd(X2,X),X))) = mult(mult(X3,rd(X2,X)),X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c486,plain,
mult(mult(X3,rd(X2,X)),X) = mult(rd(X3,X),mult(X,mult(rd(X2,X),X))),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c13]) ).
cnf(c488,plain,
mult(X,mult(rd(X2,X),X)) = mult(X,X2),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
mult(rd(X3,X),mult(X,mult(rd(X2,X),X))) = mult(rd(X3,X),mult(X,X2)),
inference(congruence,[status(thm)],[c488]) ).
cnf(c490,plain,
mult(mult(X3,rd(X2,X)),X) = mult(rd(X3,X),mult(X,X2)),
inference(transitivity,[status(thm)],[c486,c489]) ).
cnf(c491,plain,
mult(mult(rd(X2,X2),rd(X,rd(X2,X2))),rd(X2,X2)) = mult(rd(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X)),
inference(substitution,[status(thm)],[c490]) ).
cnf(c492,plain,
mult(rd(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X)) = mult(mult(rd(X2,X2),rd(X,rd(X2,X2))),rd(X2,X2)),
inference(symmetry,[status(thm)],[c491]) ).
cnf(c493,plain,
rd(X,X) = ld(rd(X,X),rd(X,X)),
inference(symmetry,[status(thm)],[c479]) ).
cnf(c494,plain,
rd(mult(rd(X2,X2),X),rd(X2,X2)) = rd(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2))),
inference(congruence,[status(thm)],[c493]) ).
cnf(c495,plain,
ld(rd(X2,X2),rd(mult(rd(X2,X2),X),rd(X2,X2))) = ld(rd(X2,X2),rd(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2)))),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
mult(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2))) = rd(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c497,plain,
rd(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2))) = mult(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2))),
inference(symmetry,[status(thm)],[c496]) ).
cnf(c498,plain,
ld(rd(X2,X2),rd(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2)))) = ld(rd(X2,X2),mult(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2)))),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,plain,
mult(ld(rd(X2,X2),rd(X2,X2)),mult(X,ld(rd(X2,X2),rd(X2,X2)))) = ld(rd(X2,X2),mult(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2)))),
inference(substitution,[status(thm)],[c220]) ).
cnf(c500,plain,
ld(rd(X2,X2),mult(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2)))) = mult(ld(rd(X2,X2),rd(X2,X2)),mult(X,ld(rd(X2,X2),rd(X2,X2)))),
inference(symmetry,[status(thm)],[c499]) ).
cnf(c501,plain,
mult(ld(rd(X2,X2),rd(X2,X2)),mult(X,ld(rd(X2,X2),rd(X2,X2)))) = mult(rd(X2,X2),mult(X,ld(rd(X2,X2),rd(X2,X2)))),
inference(congruence,[status(thm)],[c479]) ).
cnf(c502,plain,
mult(X,ld(rd(X2,X2),rd(X2,X2))) = rd(X,ld(rd(X2,X2),rd(X2,X2))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c503,plain,
mult(rd(X2,X2),mult(X,ld(rd(X2,X2),rd(X2,X2)))) = mult(rd(X2,X2),rd(X,ld(rd(X2,X2),rd(X2,X2)))),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
rd(X,ld(rd(X2,X2),rd(X2,X2))) = rd(X,rd(X2,X2)),
inference(congruence,[status(thm)],[c479]) ).
cnf(c505,plain,
mult(rd(X2,X2),rd(X,ld(rd(X2,X2),rd(X2,X2)))) = mult(rd(X2,X2),rd(X,rd(X2,X2))),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
mult(rd(X2,X2),mult(X,ld(rd(X2,X2),rd(X2,X2)))) = mult(rd(X2,X2),rd(X,rd(X2,X2))),
inference(transitivity,[status(thm)],[c503,c505]) ).
cnf(c507,plain,
mult(ld(rd(X2,X2),rd(X2,X2)),mult(X,ld(rd(X2,X2),rd(X2,X2)))) = mult(rd(X2,X2),rd(X,rd(X2,X2))),
inference(transitivity,[status(thm)],[c501,c506]) ).
cnf(c508,plain,
ld(rd(X2,X2),mult(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2)))) = mult(rd(X2,X2),rd(X,rd(X2,X2))),
inference(transitivity,[status(thm)],[c500,c507]) ).
cnf(c509,plain,
ld(rd(X2,X2),rd(mult(rd(X2,X2),X),ld(rd(X2,X2),rd(X2,X2)))) = mult(rd(X2,X2),rd(X,rd(X2,X2))),
inference(transitivity,[status(thm)],[c498,c508]) ).
cnf(c510,plain,
ld(rd(X2,X2),rd(mult(rd(X2,X2),X),rd(X2,X2))) = mult(rd(X2,X2),rd(X,rd(X2,X2))),
inference(transitivity,[status(thm)],[c495,c509]) ).
cnf(c511,plain,
mult(rd(X2,X2),rd(X,rd(X2,X2))) = ld(rd(X2,X2),rd(mult(rd(X2,X2),X),rd(X2,X2))),
inference(symmetry,[status(thm)],[c510]) ).
cnf(c512,plain,
mult(mult(rd(X2,X2),rd(X,rd(X2,X2))),rd(X2,X2)) = mult(ld(rd(X2,X2),rd(mult(rd(X2,X2),X),rd(X2,X2))),rd(X2,X2)),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
mult(ld(rd(X2,X2),rd(mult(rd(X2,X2),X),rd(X2,X2))),rd(X2,X2)) = ld(rd(X2,X2),ld(rd(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X))),
inference(substitution,[status(thm)],[c357]) ).
cnf(c514,plain,
rd(rd(X,X),rd(X,X)) = ld(rd(X,X),rd(X,X)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c515,plain,
ld(rd(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X)) = ld(ld(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X)),
inference(congruence,[status(thm)],[c514]) ).
cnf(c516,plain,
ld(rd(X2,X2),ld(rd(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X))) = ld(rd(X2,X2),ld(ld(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X))),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
ld(ld(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X)) = ld(rd(X2,X2),mult(rd(X2,X2),X)),
inference(congruence,[status(thm)],[c479]) ).
cnf(c518,plain,
ld(rd(X2,X2),ld(ld(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X))) = ld(rd(X2,X2),ld(rd(X2,X2),mult(rd(X2,X2),X))),
inference(congruence,[status(thm)],[c517]) ).
cnf(c519,plain,
ld(rd(X2,X2),mult(rd(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c520,plain,
ld(rd(X2,X2),ld(rd(X2,X2),mult(rd(X2,X2),X))) = ld(rd(X2,X2),X),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
ld(rd(X2,X2),ld(ld(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X))) = ld(rd(X2,X2),X),
inference(transitivity,[status(thm)],[c518,c520]) ).
cnf(c522,plain,
ld(rd(X2,X2),ld(rd(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X))) = ld(rd(X2,X2),X),
inference(transitivity,[status(thm)],[c516,c521]) ).
cnf(c523,plain,
mult(ld(rd(X2,X2),rd(mult(rd(X2,X2),X),rd(X2,X2))),rd(X2,X2)) = ld(rd(X2,X2),X),
inference(transitivity,[status(thm)],[c513,c522]) ).
cnf(c524,plain,
mult(mult(rd(X2,X2),rd(X,rd(X2,X2))),rd(X2,X2)) = ld(rd(X2,X2),X),
inference(transitivity,[status(thm)],[c512,c523]) ).
cnf(c525,plain,
mult(rd(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X)) = ld(rd(X2,X2),X),
inference(transitivity,[status(thm)],[c492,c524]) ).
cnf(c526,plain,
mult(ld(rd(X2,X2),rd(X2,X2)),mult(rd(X2,X2),X)) = ld(rd(X2,X2),X),
inference(transitivity,[status(thm)],[c484,c525]) ).
cnf(c527,plain,
mult(rd(X2,X2),mult(rd(X2,X2),X)) = ld(rd(X2,X2),X),
inference(transitivity,[status(thm)],[c481,c526]) ).
cnf(c528,plain,
rd(mult(rd(X2,X2),X),mult(rd(X2,X2),mult(rd(X2,X2),X))) = rd(mult(rd(X2,X2),X),ld(rd(X2,X2),X)),
inference(congruence,[status(thm)],[c527]) ).
cnf(c529,plain,
ld(rd(X2,X2),ld(mult(rd(X2,X2),X),mult(rd(X2,X2),X))) = rd(mult(rd(X2,X2),X),ld(rd(X2,X2),X)),
inference(transitivity,[status(thm)],[c452,c528]) ).
cnf(c530,plain,
ld(rd(X,X),mult(rd(X,X),X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c531,plain,
X2 = ld(rd(X,X),mult(rd(X,X),X2)),
inference(symmetry,[status(thm)],[c530]) ).
cnf(c532,plain,
ld(X2,rd(X,X)) = ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
rd(ld(X2,rd(X,X)),rd(X,X)) = rd(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X)),
inference(congruence,[status(thm)],[c532]) ).
cnf(c534,plain,
mult(X2,rd(ld(X2,rd(X,X)),rd(X,X))) = mult(X2,rd(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X))),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
mult(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X)) = rd(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X)),
inference(substitution,[status(thm)],[c294]) ).
cnf(c536,plain,
rd(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X)) = mult(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X)),
inference(symmetry,[status(thm)],[c535]) ).
cnf(c537,plain,
mult(X2,rd(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X))) = mult(X2,mult(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X))),
inference(congruence,[status(thm)],[c536]) ).
cnf(c538,plain,
ld(rd(X,X),mult(rd(X,X),X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c539,plain,
X2 = ld(rd(X,X),mult(rd(X,X),X2)),
inference(symmetry,[status(thm)],[c538]) ).
cnf(c540,plain,
mult(X2,mult(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X))) = mult(ld(rd(X,X),mult(rd(X,X),X2)),mult(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X))),
inference(congruence,[status(thm)],[c539]) ).
cnf(c541,plain,
mult(X,mult(ld(X,X2),mult(X,ld(X,X2)))) = mult(mult(X2,X),ld(X,X2)),
inference(substitution,[status(thm)],[c218]) ).
cnf(c542,plain,
mult(mult(X2,X),ld(X,X2)) = mult(X,mult(ld(X,X2),mult(X,ld(X,X2)))),
inference(symmetry,[status(thm)],[c541]) ).
cnf(c543,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c42]) ).
cnf(c544,plain,
mult(ld(X,X2),mult(X,ld(X,X2))) = mult(ld(X,X2),X2),
inference(congruence,[status(thm)],[c543]) ).
cnf(c545,plain,
mult(X,mult(ld(X,X2),mult(X,ld(X,X2)))) = mult(X,mult(ld(X,X2),X2)),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
mult(mult(X2,X),ld(X,X2)) = mult(X,mult(ld(X,X2),X2)),
inference(transitivity,[status(thm)],[c542,c545]) ).
cnf(c547,plain,
mult(mult(X2,ld(X2,X)),ld(ld(X2,X),X2)) = mult(ld(X2,X),mult(ld(ld(X2,X),X2),X2)),
inference(substitution,[status(thm)],[c546]) ).
cnf(c548,plain,
mult(ld(X2,X),mult(ld(ld(X2,X),X2),X2)) = mult(mult(X2,ld(X2,X)),ld(ld(X2,X),X2)),
inference(symmetry,[status(thm)],[c547]) ).
cnf(c549,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c550,plain,
mult(mult(X2,ld(X2,X)),ld(ld(X2,X),X2)) = mult(X,ld(ld(X2,X),X2)),
inference(congruence,[status(thm)],[c549]) ).
cnf(c551,plain,
mult(X,ld(ld(X2,X),X2)) = rd(X,ld(X2,ld(X2,X))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c552,plain,
mult(mult(X2,ld(X2,X)),ld(ld(X2,X),X2)) = rd(X,ld(X2,ld(X2,X))),
inference(transitivity,[status(thm)],[c550,c551]) ).
cnf(c553,plain,
mult(ld(X2,X),mult(ld(ld(X2,X),X2),X2)) = rd(X,ld(X2,ld(X2,X))),
inference(transitivity,[status(thm)],[c548,c552]) ).
cnf(c554,plain,
mult(ld(rd(X,X),mult(rd(X,X),X2)),mult(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X))) = rd(mult(rd(X,X),X2),ld(rd(X,X),ld(rd(X,X),mult(rd(X,X),X2)))),
inference(substitution,[status(thm)],[c553]) ).
cnf(c555,plain,
ld(rd(X,X),mult(rd(X,X),X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c556,plain,
ld(rd(X,X),ld(rd(X,X),mult(rd(X,X),X2))) = ld(rd(X,X),X2),
inference(congruence,[status(thm)],[c555]) ).
cnf(c557,plain,
rd(mult(rd(X,X),X2),ld(rd(X,X),ld(rd(X,X),mult(rd(X,X),X2)))) = rd(mult(rd(X,X),X2),ld(rd(X,X),X2)),
inference(congruence,[status(thm)],[c556]) ).
cnf(c558,plain,
mult(ld(rd(X,X),mult(rd(X,X),X2)),mult(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X))) = rd(mult(rd(X,X),X2),ld(rd(X,X),X2)),
inference(transitivity,[status(thm)],[c554,c557]) ).
cnf(c559,plain,
mult(X2,mult(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X))) = rd(mult(rd(X,X),X2),ld(rd(X,X),X2)),
inference(transitivity,[status(thm)],[c540,c558]) ).
cnf(c560,plain,
mult(X2,rd(ld(ld(rd(X,X),mult(rd(X,X),X2)),rd(X,X)),rd(X,X))) = rd(mult(rd(X,X),X2),ld(rd(X,X),X2)),
inference(transitivity,[status(thm)],[c537,c559]) ).
cnf(c561,plain,
mult(X2,rd(ld(X2,rd(X,X)),rd(X,X))) = rd(mult(rd(X,X),X2),ld(rd(X,X),X2)),
inference(transitivity,[status(thm)],[c534,c560]) ).
cnf(c562,plain,
mult(X,rd(ld(X,rd(X2,X2)),rd(X2,X2))) = rd(mult(rd(X2,X2),X),ld(rd(X2,X2),X)),
inference(substitution,[status(thm)],[c561]) ).
cnf(c563,plain,
rd(mult(rd(X2,X2),X),ld(rd(X2,X2),X)) = mult(X,rd(ld(X,rd(X2,X2)),rd(X2,X2))),
inference(symmetry,[status(thm)],[c562]) ).
cnf(c564,plain,
rd(ld(X2,rd(X3,X3)),rd(X3,X3)) = ld(mult(X,X2),X),
inference(substitution,[status(thm)],[c435]) ).
cnf(c565,plain,
mult(X2,rd(ld(X2,rd(X3,X3)),rd(X3,X3))) = mult(X2,ld(mult(X,X2),X)),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
mult(X2,ld(mult(X,X2),X)) = rd(X2,X2),
inference(substitution,[status(thm)],[c226]) ).
cnf(c567,plain,
mult(X2,ld(mult(X,X2),X)) = ld(X2,X2),
inference(transitivity,[status(thm)],[c566,c137]) ).
cnf(c568,plain,
mult(X,rd(ld(X,rd(X2,X2)),rd(X2,X2))) = ld(X,X),
inference(transitivity,[status(thm)],[c565,c567]) ).
cnf(c569,plain,
rd(mult(rd(X2,X2),X),ld(rd(X2,X2),X)) = ld(X,X),
inference(transitivity,[status(thm)],[c563,c568]) ).
cnf(c570,plain,
ld(rd(X2,X2),ld(mult(rd(X2,X2),X),mult(rd(X2,X2),X))) = ld(X,X),
inference(transitivity,[status(thm)],[c529,c569]) ).
cnf(c571,plain,
ld(rd(X,X),ld(mult(rd(X,X),X2),mult(rd(X,X),X2))) = ld(X2,X2),
inference(substitution,[status(thm)],[c570]) ).
cnf(c572,plain,
ld(X2,X2) = ld(rd(X,X),ld(mult(rd(X,X),X2),mult(rd(X,X),X2))),
inference(symmetry,[status(thm)],[c571]) ).
cnf(c573,plain,
ld(rd(X,X),ld(mult(rd(X,X),X2),mult(rd(X,X),X2))) = ld(rd(X,X),ld(X2,X2)),
inference(congruence,[status(thm)],[c450]) ).
cnf(c574,plain,
rd(X2,mult(rd(X,X),X2)) = ld(rd(X,X),ld(X2,X2)),
inference(substitution,[status(thm)],[c420]) ).
cnf(c575,plain,
ld(rd(X,X),ld(X2,X2)) = rd(X2,mult(rd(X,X),X2)),
inference(symmetry,[status(thm)],[c574]) ).
cnf(c576,plain,
ld(rd(X,X),ld(mult(rd(X,X),X2),mult(rd(X,X),X2))) = rd(X2,mult(rd(X,X),X2)),
inference(transitivity,[status(thm)],[c573,c575]) ).
cnf(c577,plain,
ld(X2,X2) = rd(X2,mult(rd(X,X),X2)),
inference(transitivity,[status(thm)],[c572,c576]) ).
cnf(c578,plain,
ld(mult(rd(X,X),X3),mult(rd(X,X),X3)) = rd(X3,mult(rd(X2,X2),X3)),
inference(transitivity,[status(thm)],[c450,c577]) ).
cnf(c579,plain,
ld(mult(rd(X,X),X2),mult(rd(X,X),X2)) = rd(X2,mult(rd(X,X),X2)),
inference(substitution,[status(thm)],[c578]) ).
cnf(c580,plain,
mult(ld(mult(rd(X,X),X2),mult(rd(X,X),X2)),mult(rd(X,X),X2)) = mult(rd(X2,mult(rd(X,X),X2)),mult(rd(X,X),X2)),
inference(congruence,[status(thm)],[c579]) ).
cnf(c581,plain,
mult(rd(X2,mult(rd(X,X),X2)),mult(rd(X,X),X2)) = X2,
inference(substitution,[status(thm)],[c13]) ).
cnf(c582,plain,
mult(ld(mult(rd(X,X),X2),mult(rd(X,X),X2)),mult(rd(X,X),X2)) = X2,
inference(transitivity,[status(thm)],[c580,c581]) ).
cnf(c583,plain,
mult(rd(X,X),X2) = X2,
inference(transitivity,[status(thm)],[c143,c582]) ).
cnf(c584,plain,
mult(rd(x1,x1),x0) = x0,
inference(substitution,[status(thm)],[c583]) ).
cnf(c585,plain,
$false,
inference(resolution,[status(thm)],[c1,c584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP655-12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 10:32:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.80/0.99 Command-line arguments: --flatten --complete-subsets
% 3.80/0.99
% 3.80/0.99 % SZS status Unsatisfiable
% 3.80/0.99
% 3.80/1.03 % SZS output start CNFRefutation
% See solution above
% 6.16/1.22
% 6.16/1.22 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------