%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP691-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 10:11:45 AM UTC 2026
% Result : Unsatisfiable 198.25s 25.49s
% Output : CNFRefutation 207.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 126
% Number of leaves : 12
% Syntax : Number of clauses : 1441 (1441 unt; 0 nHn; 13 RR)
% Number of literals : 1441 (1440 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 2630 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(op_d,i(mult(a,op_d))) != i(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
mult(op_c,mult(op_c,op_c)) = op_d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
op_d = mult(op_c,mult(op_c,op_c)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
mult(X,op_d) = mult(X,mult(op_c,mult(op_c,op_c))),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
i(mult(X,op_d)) = i(mult(X,mult(op_c,mult(op_c,op_c)))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))) = mult(mult(op_c,mult(op_c,op_c)),i(mult(X,mult(op_c,mult(op_c,op_c))))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
mult(mult(op_c,mult(op_c,op_c)),i(mult(X,mult(op_c,mult(op_c,op_c))))) = mult(op_d,i(mult(X,mult(op_c,mult(op_c,op_c))))),
inference(congruence,[status(thm)],[c2]) ).
cnf(c8,plain,
mult(X,mult(op_c,mult(op_c,op_c))) = mult(X,op_d),
inference(congruence,[status(thm)],[c2]) ).
cnf(c9,plain,
i(mult(X,mult(op_c,mult(op_c,op_c)))) = i(mult(X,op_d)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
mult(op_d,i(mult(X,mult(op_c,mult(op_c,op_c))))) = mult(op_d,i(mult(X,op_d))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
mult(mult(op_c,mult(op_c,op_c)),i(mult(X,mult(op_c,mult(op_c,op_c))))) = mult(op_d,i(mult(X,op_d))),
inference(transitivity,[status(thm)],[c7,c10]) ).
cnf(c12,plain,
mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))) = mult(op_d,i(mult(X,op_d))),
inference(transitivity,[status(thm)],[c6,c11]) ).
cnf(c13,plain,
mult(op_d,i(mult(X,op_d))) = mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
mult(A,i(A)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
cnf(c15,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
unit = mult(X,i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
ld(X,unit) = ld(X,mult(X,i(X))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,axiom,
ld(A2,mult(A2,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c19,plain,
ld(X,mult(X,i(X))) = i(X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
ld(X,unit) = i(X),
inference(transitivity,[status(thm)],[c17,c19]) ).
cnf(c21,plain,
i(X) = ld(X,unit),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
ld(mult(op_c,mult(op_c,op_c)),i(X)) = ld(mult(op_c,mult(op_c,op_c)),ld(X,unit)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,axiom,
mult(i(A2),A2) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
cnf(c24,plain,
mult(i(mult(X,op_d)),mult(X,op_d)) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
unit = mult(i(mult(X,op_d)),mult(X,op_d)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
ld(X,unit) = ld(X,mult(i(mult(X,op_d)),mult(X,op_d))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
ld(mult(op_c,mult(op_c,op_c)),ld(X,unit)) = ld(mult(op_c,mult(op_c,op_c)),ld(X,mult(i(mult(X,op_d)),mult(X,op_d)))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
op_d = mult(op_c,mult(op_c,op_c)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c29,plain,
mult(X,op_d) = mult(X,mult(op_c,mult(op_c,op_c))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
mult(X2,mult(X,op_d)) = mult(X2,mult(X,mult(op_c,mult(op_c,op_c)))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
ld(X2,mult(X,mult(X2,op_d))) = ld(X2,mult(X,mult(X2,mult(op_c,mult(op_c,op_c))))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
ld(mult(op_c,mult(op_c,op_c)),ld(X2,mult(X,mult(X2,op_d)))) = ld(mult(op_c,mult(op_c,op_c)),ld(X2,mult(X,mult(X2,mult(op_c,mult(op_c,op_c)))))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
ld(X2,mult(X2,mult(ld(X2,mult(X,X2)),X3))) = mult(ld(X2,mult(X,X2)),X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c34,plain,
mult(ld(X3,mult(X2,X3)),X) = ld(X3,mult(X3,mult(ld(X3,mult(X2,X3)),X))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
cnf(c36,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
rd(X2,X) = rd(mult(X,ld(X,X2)),X),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
mult(rd(X3,X2),mult(X2,X)) = mult(rd(mult(X2,ld(X2,X3)),X2),mult(X2,X)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,axiom,
mult(A2,mult(B2,C)) = mult(rd(mult(A2,B2),A2),mult(A2,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
cnf(c41,plain,
mult(X2,mult(ld(X2,X3),X)) = mult(rd(mult(X2,ld(X2,X3)),X2),mult(X2,X)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
mult(rd(mult(X2,ld(X2,X3)),X2),mult(X2,X)) = mult(X2,mult(ld(X2,X3),X)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
mult(rd(X3,X2),mult(X2,X)) = mult(X2,mult(ld(X2,X3),X)),
inference(transitivity,[status(thm)],[c39,c42]) ).
cnf(c44,plain,
mult(rd(mult(X2,X3),X3),mult(X3,X)) = mult(X3,mult(ld(X3,mult(X2,X3)),X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
mult(X3,mult(ld(X3,mult(X2,X3)),X)) = mult(rd(mult(X2,X3),X3),mult(X3,X)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(c47,plain,
rd(mult(X,X2),X2) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
mult(rd(mult(X2,X3),X3),mult(X3,X)) = mult(X2,mult(X3,X)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
mult(X3,mult(ld(X3,mult(X2,X3)),X)) = mult(X2,mult(X3,X)),
inference(transitivity,[status(thm)],[c45,c48]) ).
cnf(c50,plain,
ld(X3,mult(X3,mult(ld(X3,mult(X2,X3)),X))) = ld(X3,mult(X2,mult(X3,X))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
mult(ld(X3,mult(X2,X3)),X) = ld(X3,mult(X2,mult(X3,X))),
inference(transitivity,[status(thm)],[c34,c50]) ).
cnf(c52,plain,
mult(ld(X2,mult(X,X2)),mult(op_c,mult(op_c,op_c))) = ld(X2,mult(X,mult(X2,mult(op_c,mult(op_c,op_c))))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
ld(X2,mult(X,mult(X2,mult(op_c,mult(op_c,op_c))))) = mult(ld(X2,mult(X,X2)),mult(op_c,mult(op_c,op_c))),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
ld(mult(op_c,mult(op_c,op_c)),ld(X2,mult(X,mult(X2,mult(op_c,mult(op_c,op_c)))))) = ld(mult(op_c,mult(op_c,op_c)),mult(ld(X2,mult(X,X2)),mult(op_c,mult(op_c,op_c)))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
ld(mult(X2,op_d),mult(mult(X2,op_d),ld(mult(op_c,mult(op_c,op_c)),mult(X,mult(op_c,mult(op_c,op_c)))))) = ld(mult(op_c,mult(op_c,op_c)),mult(X,mult(op_c,mult(op_c,op_c)))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c56,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(X,mult(op_c,mult(op_c,op_c)))) = ld(mult(X2,op_d),mult(mult(X2,op_d),ld(mult(op_c,mult(op_c,op_c)),mult(X,mult(op_c,mult(op_c,op_c)))))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(X,mult(op_c,mult(op_c,op_c)))) = ld(op_d,mult(X,mult(op_c,mult(op_c,op_c)))),
inference(congruence,[status(thm)],[c2]) ).
cnf(c58,plain,
mult(mult(X2,op_d),ld(mult(op_c,mult(op_c,op_c)),mult(X,mult(op_c,mult(op_c,op_c))))) = mult(mult(X2,op_d),ld(op_d,mult(X,mult(op_c,mult(op_c,op_c))))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
mult(X,mult(op_c,mult(op_c,op_c))) = mult(X,op_d),
inference(congruence,[status(thm)],[c2]) ).
cnf(c60,plain,
ld(op_d,mult(X,mult(op_c,mult(op_c,op_c)))) = ld(op_d,mult(X,op_d)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
mult(mult(X2,op_d),ld(op_d,mult(X,mult(op_c,mult(op_c,op_c))))) = mult(mult(X2,op_d),ld(op_d,mult(X,op_d))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,axiom,
mult(mult(A2,B2),C2) = mult(mult(A2,C2),ld(C2,mult(B2,C2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
cnf(c63,plain,
mult(mult(X2,X),op_d) = mult(mult(X2,op_d),ld(op_d,mult(X,op_d))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
mult(mult(X2,op_d),ld(op_d,mult(X,op_d))) = mult(mult(X2,X),op_d),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
op_d = mult(op_c,mult(op_c,op_c)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c66,plain,
mult(mult(X2,X),op_d) = mult(mult(X2,X),mult(op_c,mult(op_c,op_c))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
mult(mult(X2,op_d),ld(op_d,mult(X,op_d))) = mult(mult(X2,X),mult(op_c,mult(op_c,op_c))),
inference(transitivity,[status(thm)],[c64,c66]) ).
cnf(c68,plain,
mult(mult(X2,op_d),ld(op_d,mult(X,mult(op_c,mult(op_c,op_c))))) = mult(mult(X2,X),mult(op_c,mult(op_c,op_c))),
inference(transitivity,[status(thm)],[c61,c67]) ).
cnf(c69,plain,
mult(mult(X2,op_d),ld(mult(op_c,mult(op_c,op_c)),mult(X,mult(op_c,mult(op_c,op_c))))) = mult(mult(X2,X),mult(op_c,mult(op_c,op_c))),
inference(transitivity,[status(thm)],[c58,c68]) ).
cnf(c70,plain,
ld(mult(X2,op_d),mult(mult(X2,op_d),ld(mult(op_c,mult(op_c,op_c)),mult(X,mult(op_c,mult(op_c,op_c)))))) = ld(mult(X2,op_d),mult(mult(X2,X),mult(op_c,mult(op_c,op_c)))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(X,mult(op_c,mult(op_c,op_c)))) = ld(mult(X2,op_d),mult(mult(X2,X),mult(op_c,mult(op_c,op_c)))),
inference(transitivity,[status(thm)],[c56,c70]) ).
cnf(c72,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(ld(X2,X),mult(op_c,mult(op_c,op_c)))) = ld(mult(X2,op_d),mult(mult(X2,ld(X2,X)),mult(op_c,mult(op_c,op_c)))),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c74,plain,
mult(mult(X2,ld(X2,X)),mult(op_c,mult(op_c,op_c))) = mult(X,mult(op_c,mult(op_c,op_c))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
ld(mult(X2,op_d),mult(mult(X2,ld(X2,X)),mult(op_c,mult(op_c,op_c)))) = ld(mult(X2,op_d),mult(X,mult(op_c,mult(op_c,op_c)))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(ld(X2,X),mult(op_c,mult(op_c,op_c)))) = ld(mult(X2,op_d),mult(X,mult(op_c,mult(op_c,op_c)))),
inference(transitivity,[status(thm)],[c72,c75]) ).
cnf(c77,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(ld(X2,mult(X,X2)),mult(op_c,mult(op_c,op_c)))) = ld(mult(X2,op_d),mult(mult(X,X2),mult(op_c,mult(op_c,op_c)))),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
ld(mult(op_c,mult(op_c,op_c)),ld(X2,mult(X,mult(X2,mult(op_c,mult(op_c,op_c)))))) = ld(mult(X2,op_d),mult(mult(X,X2),mult(op_c,mult(op_c,op_c)))),
inference(transitivity,[status(thm)],[c54,c77]) ).
cnf(c79,plain,
ld(mult(op_c,mult(op_c,op_c)),ld(X2,mult(X,mult(X2,op_d)))) = ld(mult(X2,op_d),mult(mult(X,X2),mult(op_c,mult(op_c,op_c)))),
inference(transitivity,[status(thm)],[c32,c78]) ).
cnf(c80,plain,
ld(mult(op_c,mult(op_c,op_c)),ld(X,mult(i(mult(X,op_d)),mult(X,op_d)))) = ld(mult(X,op_d),mult(mult(i(mult(X,op_d)),X),mult(op_c,mult(op_c,op_c)))),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
ld(X,mult(X,i(mult(X,mult(X,X))))) = i(mult(X,mult(X,X))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c82,plain,
i(mult(X,mult(X,X))) = ld(X,mult(X,i(mult(X,mult(X,X))))),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
mult(X2,mult(X,i(X2))) = mult(rd(mult(X2,X),X2),mult(X2,i(X2))),
inference(substitution,[status(thm)],[c40]) ).
cnf(c84,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c85,plain,
mult(rd(mult(X2,X),X2),mult(X2,i(X2))) = mult(rd(mult(X2,X),X2),unit),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(c87,plain,
mult(rd(mult(X2,X),X2),unit) = rd(mult(X2,X),X2),
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
mult(rd(mult(X2,X),X2),mult(X2,i(X2))) = rd(mult(X2,X),X2),
inference(transitivity,[status(thm)],[c85,c87]) ).
cnf(c89,plain,
mult(X2,mult(X,i(X2))) = rd(mult(X2,X),X2),
inference(transitivity,[status(thm)],[c83,c88]) ).
cnf(c90,plain,
rd(mult(X2,X),X2) = mult(X2,mult(X,i(X2))),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
ld(X2,rd(mult(X2,X),X2)) = ld(X2,mult(X2,mult(X,i(X2)))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
ld(X2,mult(X2,mult(X,i(X2)))) = mult(X,i(X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c93,plain,
ld(X2,rd(mult(X2,X),X2)) = mult(X,i(X2)),
inference(transitivity,[status(thm)],[c91,c92]) ).
cnf(c94,plain,
ld(mult(X,mult(X,X)),rd(mult(mult(X,mult(X,X)),X),mult(X,mult(X,X)))) = mult(X,i(mult(X,mult(X,X)))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
mult(X,i(mult(X,mult(X,X)))) = ld(mult(X,mult(X,X)),rd(mult(mult(X,mult(X,X)),X),mult(X,mult(X,X)))),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
mult(X,mult(mult(X,mult(X,X)),i(X))) = rd(mult(X,mult(X,mult(X,X))),X),
inference(substitution,[status(thm)],[c89]) ).
cnf(c97,plain,
rd(mult(X,mult(X,mult(X,X))),X) = mult(X,mult(mult(X,mult(X,X)),i(X))),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
mult(mult(X2,X),i(X2)) = mult(mult(X2,i(X2)),ld(i(X2),mult(X,i(X2)))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c99,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c100,plain,
mult(mult(X2,i(X2)),ld(i(X2),mult(X,i(X2)))) = mult(unit,ld(i(X2),mult(X,i(X2)))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,axiom,
mult(unit,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c102,plain,
mult(unit,ld(i(X2),mult(X,i(X2)))) = ld(i(X2),mult(X,i(X2))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
mult(mult(X2,i(X2)),ld(i(X2),mult(X,i(X2)))) = ld(i(X2),mult(X,i(X2))),
inference(transitivity,[status(thm)],[c100,c102]) ).
cnf(c104,plain,
mult(mult(X2,X),i(X2)) = ld(i(X2),mult(X,i(X2))),
inference(transitivity,[status(thm)],[c98,c103]) ).
cnf(c105,plain,
mult(mult(X,mult(X,X)),i(X)) = ld(i(X),mult(mult(X,X),i(X))),
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
mult(mult(X,X),i(X)) = ld(i(X),mult(X,i(X))),
inference(substitution,[status(thm)],[c104]) ).
cnf(c107,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c108,plain,
ld(i(X),mult(X,i(X))) = ld(i(X),unit),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
ld(i(X),unit) = i(i(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c110,plain,
ld(i(X),unit) = i(i(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c111,plain,
i(i(X)) = ld(i(X),unit),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c113,plain,
unit = mult(i(X),X),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
ld(i(X),unit) = ld(i(X),mult(i(X),X)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
ld(i(X),mult(i(X),X)) = X,
inference(substitution,[status(thm)],[c18]) ).
cnf(c116,plain,
ld(i(X),unit) = X,
inference(transitivity,[status(thm)],[c114,c115]) ).
cnf(c117,plain,
i(i(X)) = X,
inference(transitivity,[status(thm)],[c111,c116]) ).
cnf(c118,plain,
ld(i(X),unit) = X,
inference(transitivity,[status(thm)],[c109,c117]) ).
cnf(c119,plain,
ld(i(X),mult(X,i(X))) = X,
inference(transitivity,[status(thm)],[c108,c118]) ).
cnf(c120,plain,
mult(mult(X,X),i(X)) = X,
inference(transitivity,[status(thm)],[c106,c119]) ).
cnf(c121,plain,
ld(i(X),mult(mult(X,X),i(X))) = ld(i(X),X),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
ld(i(X),mult(i(X),mult(X,X))) = mult(X,X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c123,plain,
mult(X,X) = ld(i(X),mult(i(X),mult(X,X))),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
mult(i(X2),mult(X,X2)) = mult(rd(mult(i(X2),X),i(X2)),mult(i(X2),X2)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c125,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c126,plain,
mult(rd(mult(i(X2),X),i(X2)),mult(i(X2),X2)) = mult(rd(mult(i(X2),X),i(X2)),unit),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
mult(rd(mult(i(X2),X),i(X2)),unit) = rd(mult(i(X2),X),i(X2)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c128,plain,
mult(rd(mult(i(X2),X),i(X2)),mult(i(X2),X2)) = rd(mult(i(X2),X),i(X2)),
inference(transitivity,[status(thm)],[c126,c127]) ).
cnf(c129,plain,
mult(i(X2),mult(X,X2)) = rd(mult(i(X2),X),i(X2)),
inference(transitivity,[status(thm)],[c124,c128]) ).
cnf(c130,plain,
mult(i(X),mult(X,X)) = rd(mult(i(X),X),i(X)),
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c132,plain,
rd(mult(i(X),X),i(X)) = rd(unit,i(X)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c134,plain,
unit = mult(i(X),X),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
rd(unit,X) = rd(mult(i(X),X),X),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
rd(mult(i(X),X),X) = i(X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c137,plain,
rd(unit,X) = i(X),
inference(transitivity,[status(thm)],[c135,c136]) ).
cnf(c138,plain,
rd(unit,i(X)) = i(i(X)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
rd(unit,i(X)) = X,
inference(transitivity,[status(thm)],[c138,c117]) ).
cnf(c140,plain,
rd(mult(i(X),X),i(X)) = X,
inference(transitivity,[status(thm)],[c132,c139]) ).
cnf(c141,plain,
mult(i(X),mult(X,X)) = X,
inference(transitivity,[status(thm)],[c130,c140]) ).
cnf(c142,plain,
ld(i(X),mult(i(X),mult(X,X))) = ld(i(X),X),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
mult(X,X) = ld(i(X),X),
inference(transitivity,[status(thm)],[c123,c142]) ).
cnf(c144,plain,
ld(i(X),X) = mult(X,X),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
ld(i(X),mult(mult(X,X),i(X))) = mult(X,X),
inference(transitivity,[status(thm)],[c121,c144]) ).
cnf(c146,plain,
mult(mult(X,mult(X,X)),i(X)) = mult(X,X),
inference(transitivity,[status(thm)],[c105,c145]) ).
cnf(c147,plain,
mult(X,mult(mult(X,mult(X,X)),i(X))) = mult(X,mult(X,X)),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
rd(mult(X,mult(X,mult(X,X))),X) = mult(X,mult(X,X)),
inference(transitivity,[status(thm)],[c97,c147]) ).
cnf(c149,plain,
mult(X,mult(X,X)) = rd(mult(X,mult(X,mult(X,X))),X),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
mult(mult(X,mult(X,X)),X) = mult(rd(mult(X,mult(X,mult(X,X))),X),X),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(c152,plain,
mult(rd(mult(X,mult(X,mult(X,X))),X),X) = mult(X,mult(X,mult(X,X))),
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
mult(mult(X,mult(X,X)),X) = mult(X,mult(X,mult(X,X))),
inference(transitivity,[status(thm)],[c150,c152]) ).
cnf(c154,plain,
rd(mult(mult(X,mult(X,X)),X),mult(X,mult(X,X))) = rd(mult(X,mult(X,mult(X,X))),mult(X,mult(X,X))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
rd(mult(X,mult(X,mult(X,X))),mult(X,mult(X,X))) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c156,plain,
rd(mult(mult(X,mult(X,X)),X),mult(X,mult(X,X))) = X,
inference(transitivity,[status(thm)],[c154,c155]) ).
cnf(c157,plain,
ld(mult(X,mult(X,X)),rd(mult(mult(X,mult(X,X)),X),mult(X,mult(X,X)))) = ld(mult(X,mult(X,X)),X),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
mult(X,mult(mult(X,X),i(X))) = rd(mult(X,mult(X,X)),X),
inference(substitution,[status(thm)],[c89]) ).
cnf(c159,plain,
rd(mult(X,mult(X,X)),X) = mult(X,mult(mult(X,X),i(X))),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
mult(X,mult(mult(X,X),i(X))) = mult(X,X),
inference(congruence,[status(thm)],[c120]) ).
cnf(c161,plain,
rd(mult(X,mult(X,X)),X) = mult(X,X),
inference(transitivity,[status(thm)],[c159,c160]) ).
cnf(c162,plain,
mult(X,X) = rd(mult(X,mult(X,X)),X),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
mult(mult(X,X),X) = mult(rd(mult(X,mult(X,X)),X),X),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
mult(rd(mult(X,mult(X,X)),X),X) = mult(X,mult(X,X)),
inference(substitution,[status(thm)],[c151]) ).
cnf(c165,plain,
mult(mult(X,X),X) = mult(X,mult(X,X)),
inference(transitivity,[status(thm)],[c163,c164]) ).
cnf(c166,plain,
mult(X,mult(X,X)) = mult(mult(X,X),X),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
i(i(mult(X,X))) = mult(X,X),
inference(substitution,[status(thm)],[c117]) ).
cnf(c168,plain,
mult(X,X) = i(i(mult(X,X))),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
mult(mult(X,X),X) = mult(i(i(mult(X,X))),X),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
mult(mult(i(X2),X),X2) = mult(mult(i(X2),X2),ld(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c171,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c172,plain,
mult(mult(i(X2),X2),ld(X2,mult(X,X2))) = mult(unit,ld(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
mult(unit,ld(X2,mult(X,X2))) = ld(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c101]) ).
cnf(c174,plain,
mult(mult(i(X2),X2),ld(X2,mult(X,X2))) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c172,c173]) ).
cnf(c175,plain,
mult(mult(i(X2),X),X2) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c170,c174]) ).
cnf(c176,plain,
ld(X2,mult(X,X2)) = mult(mult(i(X2),X),X2),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
rd(ld(X2,mult(X,X2)),X2) = rd(mult(mult(i(X2),X),X2),X2),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
rd(mult(mult(i(X2),X),X2),X2) = mult(i(X2),X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c179,plain,
rd(ld(X2,mult(X,X2)),X2) = mult(i(X2),X),
inference(transitivity,[status(thm)],[c177,c178]) ).
cnf(c180,plain,
rd(ld(i(mult(X,X)),mult(X,i(mult(X,X)))),i(mult(X,X))) = mult(i(i(mult(X,X))),X),
inference(substitution,[status(thm)],[c179]) ).
cnf(c181,plain,
mult(i(i(mult(X,X))),X) = rd(ld(i(mult(X,X)),mult(X,i(mult(X,X)))),i(mult(X,X))),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
ld(mult(X,X),rd(mult(mult(X,X),X),mult(X,X))) = mult(X,i(mult(X,X))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c183,plain,
mult(X,i(mult(X,X))) = ld(mult(X,X),rd(mult(mult(X,X),X),mult(X,X))),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
rd(mult(mult(X,X),X),mult(X,X)) = rd(mult(X,mult(X,X)),mult(X,X)),
inference(congruence,[status(thm)],[c165]) ).
cnf(c185,plain,
ld(mult(X,X),rd(mult(mult(X,X),X),mult(X,X))) = ld(mult(X,X),rd(mult(X,mult(X,X)),mult(X,X))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
rd(mult(X,mult(X,X)),mult(X,X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c187,plain,
ld(mult(X,X),rd(mult(X,mult(X,X)),mult(X,X))) = ld(mult(X,X),X),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
X = mult(mult(X,X),i(X)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c189,plain,
ld(mult(X,X),X) = ld(mult(X,X),mult(mult(X,X),i(X))),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
ld(mult(X,X),mult(mult(X,X),i(X))) = i(X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c191,plain,
ld(mult(X,X),X) = i(X),
inference(transitivity,[status(thm)],[c189,c190]) ).
cnf(c192,plain,
ld(mult(X,X),rd(mult(X,mult(X,X)),mult(X,X))) = i(X),
inference(transitivity,[status(thm)],[c187,c191]) ).
cnf(c193,plain,
ld(mult(X,X),rd(mult(mult(X,X),X),mult(X,X))) = i(X),
inference(transitivity,[status(thm)],[c185,c192]) ).
cnf(c194,plain,
mult(X,i(mult(X,X))) = i(X),
inference(transitivity,[status(thm)],[c183,c193]) ).
cnf(c195,plain,
ld(i(mult(X,X)),mult(X,i(mult(X,X)))) = ld(i(mult(X,X)),i(X)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
rd(ld(i(mult(X,X)),mult(X,i(mult(X,X)))),i(mult(X,X))) = rd(ld(i(mult(X,X)),i(X)),i(mult(X,X))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
rd(ld(mult(X,X),mult(X,mult(X,X))),mult(X,X)) = mult(i(mult(X,X)),X),
inference(substitution,[status(thm)],[c179]) ).
cnf(c198,plain,
mult(i(mult(X,X)),X) = rd(ld(mult(X,X),mult(X,mult(X,X))),mult(X,X)),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
mult(X,X) = rd(mult(X,mult(X,X)),X),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c200,plain,
ld(mult(X,X),mult(X,mult(X,X))) = ld(rd(mult(X,mult(X,X)),X),mult(X,mult(X,X))),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c151]) ).
cnf(c202,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
ld(rd(X2,X),X2) = ld(rd(X2,X),mult(rd(X2,X),X)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
ld(rd(X2,X),mult(rd(X2,X),X)) = X,
inference(substitution,[status(thm)],[c18]) ).
cnf(c205,plain,
ld(rd(X2,X),X2) = X,
inference(transitivity,[status(thm)],[c203,c204]) ).
cnf(c206,plain,
ld(rd(mult(X,mult(X,X)),X),mult(X,mult(X,X))) = X,
inference(substitution,[status(thm)],[c205]) ).
cnf(c207,plain,
ld(mult(X,X),mult(X,mult(X,X))) = X,
inference(transitivity,[status(thm)],[c200,c206]) ).
cnf(c208,plain,
rd(ld(mult(X,X),mult(X,mult(X,X))),mult(X,X)) = rd(X,mult(X,X)),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
X = mult(i(X),mult(X,X)),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c210,plain,
rd(X,mult(X,X)) = rd(mult(i(X),mult(X,X)),mult(X,X)),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
rd(mult(i(X),mult(X,X)),mult(X,X)) = i(X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c212,plain,
rd(X,mult(X,X)) = i(X),
inference(transitivity,[status(thm)],[c210,c211]) ).
cnf(c213,plain,
rd(ld(mult(X,X),mult(X,mult(X,X))),mult(X,X)) = i(X),
inference(transitivity,[status(thm)],[c208,c212]) ).
cnf(c214,plain,
mult(i(mult(X,X)),X) = i(X),
inference(transitivity,[status(thm)],[c198,c213]) ).
cnf(c215,plain,
i(X) = mult(i(mult(X,X)),X),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
ld(i(mult(X,X)),i(X)) = ld(i(mult(X,X)),mult(i(mult(X,X)),X)),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
ld(i(mult(X,X)),mult(i(mult(X,X)),X)) = X,
inference(substitution,[status(thm)],[c18]) ).
cnf(c218,plain,
ld(i(mult(X,X)),i(X)) = X,
inference(transitivity,[status(thm)],[c216,c217]) ).
cnf(c219,plain,
rd(ld(i(mult(X,X)),i(X)),i(mult(X,X))) = rd(X,i(mult(X,X))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
rd(ld(i(mult(X,X)),mult(X,i(mult(X,X)))),i(mult(X,X))) = rd(X,i(mult(X,X))),
inference(transitivity,[status(thm)],[c196,c219]) ).
cnf(c221,plain,
mult(i(i(mult(X,X))),X) = rd(X,i(mult(X,X))),
inference(transitivity,[status(thm)],[c181,c220]) ).
cnf(c222,plain,
mult(mult(X,X),X) = rd(X,i(mult(X,X))),
inference(transitivity,[status(thm)],[c169,c221]) ).
cnf(c223,plain,
mult(X,mult(X,X)) = rd(X,i(mult(X,X))),
inference(transitivity,[status(thm)],[c166,c222]) ).
cnf(c224,plain,
ld(mult(X,mult(X,X)),X) = ld(rd(X,i(mult(X,X))),X),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
ld(rd(X,i(mult(X,X))),X) = i(mult(X,X)),
inference(substitution,[status(thm)],[c205]) ).
cnf(c226,plain,
ld(mult(X,mult(X,X)),X) = i(mult(X,X)),
inference(transitivity,[status(thm)],[c224,c225]) ).
cnf(c227,plain,
ld(mult(X,mult(X,X)),rd(mult(mult(X,mult(X,X)),X),mult(X,mult(X,X)))) = i(mult(X,X)),
inference(transitivity,[status(thm)],[c157,c226]) ).
cnf(c228,plain,
mult(X,i(mult(X,mult(X,X)))) = i(mult(X,X)),
inference(transitivity,[status(thm)],[c95,c227]) ).
cnf(c229,plain,
ld(X,mult(X,i(mult(X,mult(X,X))))) = ld(X,i(mult(X,X))),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
i(mult(X,mult(X,X))) = ld(X,i(mult(X,X))),
inference(transitivity,[status(thm)],[c82,c229]) ).
cnf(c231,plain,
i(mult(op_c,mult(op_c,op_c))) = ld(op_c,i(mult(op_c,op_c))),
inference(substitution,[status(thm)],[c230]) ).
cnf(c232,plain,
rd(ld(mult(X,X),mult(i(X),mult(X,X))),mult(X,X)) = mult(i(mult(X,X)),i(X)),
inference(substitution,[status(thm)],[c179]) ).
cnf(c233,plain,
mult(i(mult(X,X)),i(X)) = rd(ld(mult(X,X),mult(i(X),mult(X,X))),mult(X,X)),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
ld(mult(X,X),mult(i(X),mult(X,X))) = ld(mult(X,X),X),
inference(congruence,[status(thm)],[c141]) ).
cnf(c235,plain,
rd(ld(mult(X,X),mult(i(X),mult(X,X))),mult(X,X)) = rd(ld(mult(X,X),X),mult(X,X)),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
rd(ld(mult(X,X),X),mult(X,X)) = rd(i(X),mult(X,X)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c237,plain,
rd(ld(mult(X,X),mult(i(X),mult(X,X))),mult(X,X)) = rd(i(X),mult(X,X)),
inference(transitivity,[status(thm)],[c235,c236]) ).
cnf(c238,plain,
mult(i(mult(X,X)),i(X)) = rd(i(X),mult(X,X)),
inference(transitivity,[status(thm)],[c233,c237]) ).
cnf(c239,plain,
rd(i(X),mult(X,X)) = mult(i(mult(X,X)),i(X)),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
ld(X,rd(mult(X,i(mult(X,X))),X)) = mult(i(mult(X,X)),i(X)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c241,plain,
mult(i(mult(X,X)),i(X)) = ld(X,rd(mult(X,i(mult(X,X))),X)),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
rd(mult(X,i(mult(X,X))),X) = rd(i(X),X),
inference(congruence,[status(thm)],[c194]) ).
cnf(c243,plain,
ld(X,rd(mult(X,i(mult(X,X))),X)) = ld(X,rd(i(X),X)),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
rd(mult(i(mult(X,X)),X),X) = i(mult(X,X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c245,plain,
i(mult(X,X)) = rd(mult(i(mult(X,X)),X),X),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
rd(mult(i(mult(X,X)),X),X) = rd(i(X),X),
inference(congruence,[status(thm)],[c214]) ).
cnf(c247,plain,
i(mult(X,X)) = rd(i(X),X),
inference(transitivity,[status(thm)],[c245,c246]) ).
cnf(c248,plain,
rd(i(X),X) = i(mult(X,X)),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
ld(X,rd(i(X),X)) = ld(X,i(mult(X,X))),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
ld(X,rd(mult(X,i(mult(X,X))),X)) = ld(X,i(mult(X,X))),
inference(transitivity,[status(thm)],[c243,c249]) ).
cnf(c251,plain,
mult(i(mult(X,X)),i(X)) = ld(X,i(mult(X,X))),
inference(transitivity,[status(thm)],[c241,c250]) ).
cnf(c252,plain,
rd(i(X),mult(X,X)) = ld(X,i(mult(X,X))),
inference(transitivity,[status(thm)],[c239,c251]) ).
cnf(c253,plain,
rd(i(op_c),mult(op_c,op_c)) = ld(op_c,i(mult(op_c,op_c))),
inference(substitution,[status(thm)],[c252]) ).
cnf(c254,plain,
ld(op_c,i(mult(op_c,op_c))) = rd(i(op_c),mult(op_c,op_c)),
inference(symmetry,[status(thm)],[c253]) ).
cnf(c255,plain,
mult(mult(i(mult(X,op_d)),X),mult(op_c,op_c)) = mult(mult(i(mult(X,op_d)),mult(op_c,op_c)),ld(mult(op_c,op_c),mult(X,mult(op_c,op_c)))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c256,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c101]) ).
cnf(c257,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
ld(mult(i(X2),X),X) = ld(mult(i(X2),X),mult(unit,X)),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c260,plain,
unit = mult(i(X),X),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
mult(unit,X) = mult(mult(i(X2),X2),X),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
ld(mult(i(X2),X),mult(unit,X)) = ld(mult(i(X2),X),mult(mult(i(X2),X2),X)),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
mult(mult(X3,X),X2) = mult(mult(X3,X2),ld(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c264,plain,
ld(mult(X3,X2),mult(mult(X3,X),X2)) = ld(mult(X3,X2),mult(mult(X3,X2),ld(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c263]) ).
cnf(c265,plain,
ld(mult(X3,X2),mult(mult(X3,X2),ld(X2,mult(X,X2)))) = ld(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c266,plain,
ld(mult(X3,X2),mult(mult(X3,X),X2)) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c264,c265]) ).
cnf(c267,plain,
ld(mult(i(X2),X),mult(mult(i(X2),X2),X)) = ld(X,mult(X2,X)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c268,plain,
ld(mult(i(X2),X),mult(unit,X)) = ld(X,mult(X2,X)),
inference(transitivity,[status(thm)],[c262,c267]) ).
cnf(c269,plain,
ld(mult(i(X2),X),X) = ld(X,mult(X2,X)),
inference(transitivity,[status(thm)],[c258,c268]) ).
cnf(c270,plain,
ld(mult(i(X),mult(op_c,op_c)),mult(op_c,op_c)) = ld(mult(op_c,op_c),mult(X,mult(op_c,op_c))),
inference(substitution,[status(thm)],[c269]) ).
cnf(c271,plain,
ld(mult(op_c,op_c),mult(X,mult(op_c,op_c))) = ld(mult(i(X),mult(op_c,op_c)),mult(op_c,op_c)),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
mult(mult(i(mult(X,op_d)),mult(op_c,op_c)),ld(mult(op_c,op_c),mult(X,mult(op_c,op_c)))) = mult(mult(i(mult(X,op_d)),mult(op_c,op_c)),ld(mult(i(X),mult(op_c,op_c)),mult(op_c,op_c))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
mult(ld(mult(op_c,mult(op_c,op_c)),mult(i(X2),mult(op_c,mult(op_c,op_c)))),X) = ld(mult(op_c,mult(op_c,op_c)),mult(i(X2),mult(mult(op_c,mult(op_c,op_c)),X))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c274,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(i(X2),mult(mult(op_c,mult(op_c,op_c)),X))) = mult(ld(mult(op_c,mult(op_c,op_c)),mult(i(X2),mult(op_c,mult(op_c,op_c)))),X),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(op_c,mult(op_c,op_c)))) = ld(mult(X,op_d),mult(mult(X,i(X)),mult(op_c,mult(op_c,op_c)))),
inference(substitution,[status(thm)],[c71]) ).
cnf(c276,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c277,plain,
mult(mult(X,i(X)),mult(op_c,mult(op_c,op_c))) = mult(unit,mult(op_c,mult(op_c,op_c))),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
ld(mult(X,op_d),mult(mult(X,i(X)),mult(op_c,mult(op_c,op_c)))) = ld(mult(X,op_d),mult(unit,mult(op_c,mult(op_c,op_c)))),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
mult(unit,mult(op_c,mult(op_c,op_c))) = mult(op_c,mult(op_c,op_c)),
inference(substitution,[status(thm)],[c101]) ).
cnf(c280,plain,
ld(mult(X,op_d),mult(unit,mult(op_c,mult(op_c,op_c)))) = ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
ld(mult(X,op_d),mult(mult(X,i(X)),mult(op_c,mult(op_c,op_c)))) = ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),
inference(transitivity,[status(thm)],[c278,c280]) ).
cnf(c282,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(op_c,mult(op_c,op_c)))) = ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),
inference(transitivity,[status(thm)],[c275,c281]) ).
cnf(c283,plain,
mult(ld(mult(op_c,mult(op_c,op_c)),mult(i(X2),mult(op_c,mult(op_c,op_c)))),X) = mult(ld(mult(X2,op_d),mult(op_c,mult(op_c,op_c))),X),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(i(X2),mult(mult(op_c,mult(op_c,op_c)),X))) = mult(ld(mult(X2,op_d),mult(op_c,mult(op_c,op_c))),X),
inference(transitivity,[status(thm)],[c274,c283]) ).
cnf(c285,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(mult(op_c,mult(op_c,op_c)),i(op_c)))) = mult(ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),i(op_c)),
inference(substitution,[status(thm)],[c284]) ).
cnf(c286,plain,
mult(ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),i(op_c)) = ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(mult(op_c,mult(op_c,op_c)),i(op_c)))),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
mult(mult(op_c,mult(op_c,op_c)),i(op_c)) = mult(op_c,op_c),
inference(substitution,[status(thm)],[c146]) ).
cnf(c288,plain,
mult(i(X),mult(mult(op_c,mult(op_c,op_c)),i(op_c))) = mult(i(X),mult(op_c,op_c)),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(mult(op_c,mult(op_c,op_c)),i(op_c)))) = ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(op_c,op_c))),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
mult(ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),i(op_c)) = ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(op_c,op_c))),
inference(transitivity,[status(thm)],[c286,c289]) ).
cnf(c291,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(op_c,op_c))) = mult(ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),i(op_c)),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
rd(mult(X2,X),X2) = mult(X2,mult(X,i(X2))),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c293,plain,
i(X) = rd(unit,X),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c294,plain,
mult(i(X2),mult(X2,X)) = mult(rd(unit,X2),mult(X2,X)),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c296,plain,
unit = mult(X,i(X)),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
rd(unit,X) = rd(mult(X,i(X)),X),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
mult(rd(unit,X2),mult(X2,X)) = mult(rd(mult(X2,i(X2)),X2),mult(X2,X)),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
mult(X2,mult(i(X2),X)) = mult(rd(mult(X2,i(X2)),X2),mult(X2,X)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c300,plain,
mult(rd(mult(X2,i(X2)),X2),mult(X2,X)) = mult(X2,mult(i(X2),X)),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
mult(rd(unit,X2),mult(X2,X)) = mult(X2,mult(i(X2),X)),
inference(transitivity,[status(thm)],[c298,c300]) ).
cnf(c302,plain,
mult(i(X2),mult(X2,X)) = mult(X2,mult(i(X2),X)),
inference(transitivity,[status(thm)],[c294,c301]) ).
cnf(c303,plain,
mult(X2,mult(i(X2),X)) = mult(i(X2),mult(X2,X)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
mult(X2,mult(rd(X,i(X2)),i(X2))) = rd(mult(X2,rd(X,i(X2))),X2),
inference(substitution,[status(thm)],[c89]) ).
cnf(c305,plain,
rd(mult(X2,rd(X,i(X2))),X2) = mult(X2,mult(rd(X,i(X2)),i(X2))),
inference(symmetry,[status(thm)],[c304]) ).
cnf(c306,plain,
mult(rd(X,i(X2)),i(X2)) = X,
inference(substitution,[status(thm)],[c151]) ).
cnf(c307,plain,
mult(X2,mult(rd(X,i(X2)),i(X2))) = mult(X2,X),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
rd(mult(X2,rd(X,i(X2))),X2) = mult(X2,X),
inference(transitivity,[status(thm)],[c305,c307]) ).
cnf(c309,plain,
mult(X2,X) = rd(mult(X2,rd(X,i(X2))),X2),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c310,plain,
mult(i(X2),mult(X2,X)) = mult(i(X2),rd(mult(X2,rd(X,i(X2))),X2)),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
rd(ld(X2,mult(rd(X,X2),X2)),X2) = mult(i(X2),rd(X,X2)),
inference(substitution,[status(thm)],[c179]) ).
cnf(c312,plain,
mult(i(X2),rd(X,X2)) = rd(ld(X2,mult(rd(X,X2),X2)),X2),
inference(symmetry,[status(thm)],[c311]) ).
cnf(c313,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c151]) ).
cnf(c314,plain,
ld(X2,mult(rd(X,X2),X2)) = ld(X2,X),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
rd(ld(X2,mult(rd(X,X2),X2)),X2) = rd(ld(X2,X),X2),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
mult(i(X2),rd(X,X2)) = rd(ld(X2,X),X2),
inference(transitivity,[status(thm)],[c312,c315]) ).
cnf(c317,plain,
mult(i(X2),rd(mult(X2,rd(X,i(X2))),X2)) = rd(ld(X2,mult(X2,rd(X,i(X2)))),X2),
inference(substitution,[status(thm)],[c316]) ).
cnf(c318,plain,
ld(X2,mult(X2,rd(X,i(X2)))) = rd(X,i(X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c319,plain,
rd(ld(X2,mult(X2,rd(X,i(X2)))),X2) = rd(rd(X,i(X2)),X2),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
mult(i(X2),rd(mult(X2,rd(X,i(X2))),X2)) = rd(rd(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c317,c319]) ).
cnf(c321,plain,
mult(i(X2),mult(X2,X)) = rd(rd(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c310,c320]) ).
cnf(c322,plain,
mult(X2,mult(i(X2),X)) = rd(rd(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c303,c321]) ).
cnf(c323,plain,
rd(rd(X,i(X2)),X2) = mult(X2,mult(i(X2),X)),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c324,plain,
ld(i(X2),rd(rd(X,i(X2)),X2)) = ld(i(X2),mult(X2,mult(i(X2),X))),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
mult(X2,mult(i(X2),X)) = mult(i(X2),mult(X2,X)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c326,plain,
ld(i(X2),mult(X2,mult(i(X2),X))) = ld(i(X2),mult(i(X2),mult(X2,X))),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
ld(i(X2),mult(i(X2),mult(X2,X))) = mult(X2,X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c328,plain,
ld(i(X2),mult(X2,mult(i(X2),X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c326,c327]) ).
cnf(c329,plain,
ld(i(X2),rd(rd(X,i(X2)),X2)) = mult(X2,X),
inference(transitivity,[status(thm)],[c324,c328]) ).
cnf(c330,plain,
ld(i(X2),rd(rd(mult(X,i(X2)),i(X2)),X2)) = mult(X2,mult(X,i(X2))),
inference(substitution,[status(thm)],[c329]) ).
cnf(c331,plain,
mult(X2,mult(X,i(X2))) = ld(i(X2),rd(rd(mult(X,i(X2)),i(X2)),X2)),
inference(symmetry,[status(thm)],[c330]) ).
cnf(c332,plain,
rd(mult(X,i(X2)),i(X2)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c333,plain,
rd(rd(mult(X,i(X2)),i(X2)),X2) = rd(X,X2),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
ld(i(X2),rd(rd(mult(X,i(X2)),i(X2)),X2)) = ld(i(X2),rd(X,X2)),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
mult(X2,mult(X,i(X2))) = ld(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c331,c334]) ).
cnf(c336,plain,
rd(mult(X2,X),X2) = ld(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c292,c335]) ).
cnf(c337,plain,
ld(i(X2),rd(X,X2)) = rd(mult(X2,X),X2),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
mult(ld(i(X3),rd(X2,X3)),X) = mult(rd(mult(X3,X2),X3),X),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c340,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c339]) ).
cnf(c341,plain,
mult(rd(mult(X3,X2),X3),X) = mult(rd(mult(X3,X2),X3),mult(X3,ld(X3,X))),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
mult(X3,mult(X2,ld(X3,X))) = mult(rd(mult(X3,X2),X3),mult(X3,ld(X3,X))),
inference(substitution,[status(thm)],[c40]) ).
cnf(c343,plain,
mult(rd(mult(X3,X2),X3),mult(X3,ld(X3,X))) = mult(X3,mult(X2,ld(X3,X))),
inference(symmetry,[status(thm)],[c342]) ).
cnf(c344,plain,
mult(rd(mult(X3,X2),X3),X) = mult(X3,mult(X2,ld(X3,X))),
inference(transitivity,[status(thm)],[c341,c343]) ).
cnf(c345,plain,
mult(ld(i(X3),rd(X2,X3)),X) = mult(X3,mult(X2,ld(X3,X))),
inference(transitivity,[status(thm)],[c338,c344]) ).
cnf(c346,plain,
mult(ld(i(i(mult(X2,op_d))),rd(mult(op_d,i(mult(X2,op_d))),i(mult(X2,op_d)))),X) = mult(i(mult(X2,op_d)),mult(mult(op_d,i(mult(X2,op_d))),ld(i(mult(X2,op_d)),X))),
inference(substitution,[status(thm)],[c345]) ).
cnf(c347,plain,
mult(i(mult(X2,op_d)),mult(mult(op_d,i(mult(X2,op_d))),ld(i(mult(X2,op_d)),X))) = mult(ld(i(i(mult(X2,op_d))),rd(mult(op_d,i(mult(X2,op_d))),i(mult(X2,op_d)))),X),
inference(symmetry,[status(thm)],[c346]) ).
cnf(c348,plain,
mult(op_d,i(mult(X,op_d))) = mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c349,plain,
rd(mult(op_d,i(mult(X,op_d))),i(mult(X,op_d))) = rd(mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))),i(mult(X,op_d))),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
rd(mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))),i(mult(X,op_d))) = mult(op_c,mult(op_c,op_c)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c351,plain,
rd(mult(op_d,i(mult(X,op_d))),i(mult(X,op_d))) = mult(op_c,mult(op_c,op_c)),
inference(transitivity,[status(thm)],[c349,c350]) ).
cnf(c352,plain,
ld(i(i(mult(X,op_d))),rd(mult(op_d,i(mult(X,op_d))),i(mult(X,op_d)))) = ld(i(i(mult(X,op_d))),mult(op_c,mult(op_c,op_c))),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
mult(ld(i(i(mult(X2,op_d))),rd(mult(op_d,i(mult(X2,op_d))),i(mult(X2,op_d)))),X) = mult(ld(i(i(mult(X2,op_d))),mult(op_c,mult(op_c,op_c))),X),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
i(i(mult(X,op_d))) = mult(X,op_d),
inference(substitution,[status(thm)],[c117]) ).
cnf(c355,plain,
ld(i(i(mult(X,op_d))),mult(op_c,mult(op_c,op_c))) = ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
mult(ld(i(i(mult(X2,op_d))),mult(op_c,mult(op_c,op_c))),X) = mult(ld(mult(X2,op_d),mult(op_c,mult(op_c,op_c))),X),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
mult(ld(i(i(mult(X2,op_d))),rd(mult(op_d,i(mult(X2,op_d))),i(mult(X2,op_d)))),X) = mult(ld(mult(X2,op_d),mult(op_c,mult(op_c,op_c))),X),
inference(transitivity,[status(thm)],[c353,c356]) ).
cnf(c358,plain,
mult(i(mult(X2,op_d)),mult(mult(op_d,i(mult(X2,op_d))),ld(i(mult(X2,op_d)),X))) = mult(ld(mult(X2,op_d),mult(op_c,mult(op_c,op_c))),X),
inference(transitivity,[status(thm)],[c347,c357]) ).
cnf(c359,plain,
mult(i(mult(X,op_d)),mult(mult(op_d,i(mult(X,op_d))),ld(i(mult(X,op_d)),i(op_c)))) = mult(ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),i(op_c)),
inference(substitution,[status(thm)],[c358]) ).
cnf(c360,plain,
mult(ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),i(op_c)) = mult(i(mult(X,op_d)),mult(mult(op_d,i(mult(X,op_d))),ld(i(mult(X,op_d)),i(op_c)))),
inference(symmetry,[status(thm)],[c359]) ).
cnf(c361,plain,
X = ld(mult(X,X),mult(X,mult(X,X))),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c362,plain,
mult(X2,X) = mult(ld(mult(X2,X2),mult(X2,mult(X2,X2))),X),
inference(congruence,[status(thm)],[c361]) ).
cnf(c363,plain,
mult(mult(X2,X2),mult(X2,X)) = mult(mult(X2,X2),mult(ld(mult(X2,X2),mult(X2,mult(X2,X2))),X)),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
mult(rd(mult(X2,mult(X2,X2)),mult(X2,X2)),mult(mult(X2,X2),X)) = mult(mult(X2,X2),mult(ld(mult(X2,X2),mult(X2,mult(X2,X2))),X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c365,plain,
mult(mult(X2,X2),mult(ld(mult(X2,X2),mult(X2,mult(X2,X2))),X)) = mult(rd(mult(X2,mult(X2,X2)),mult(X2,X2)),mult(mult(X2,X2),X)),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
rd(mult(X,mult(X,X)),mult(X,X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c367,plain,
mult(rd(mult(X2,mult(X2,X2)),mult(X2,X2)),mult(mult(X2,X2),X)) = mult(X2,mult(mult(X2,X2),X)),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
mult(mult(X2,X2),mult(ld(mult(X2,X2),mult(X2,mult(X2,X2))),X)) = mult(X2,mult(mult(X2,X2),X)),
inference(transitivity,[status(thm)],[c365,c367]) ).
cnf(c369,plain,
mult(mult(X2,X2),mult(X2,X)) = mult(X2,mult(mult(X2,X2),X)),
inference(transitivity,[status(thm)],[c363,c368]) ).
cnf(c370,plain,
ld(X2,mult(mult(X2,X2),mult(X2,X))) = ld(X2,mult(X2,mult(mult(X2,X2),X))),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
ld(X2,mult(X2,mult(mult(X2,X2),X))) = mult(mult(X2,X2),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c372,plain,
ld(X2,mult(mult(X2,X2),mult(X2,X))) = mult(mult(X2,X2),X),
inference(transitivity,[status(thm)],[c370,c371]) ).
cnf(c373,plain,
ld(X2,mult(mult(X2,X2),mult(X2,i(mult(X,X2))))) = mult(mult(X2,X2),i(mult(X,X2))),
inference(substitution,[status(thm)],[c372]) ).
cnf(c374,plain,
mult(mult(X2,X2),i(mult(X,X2))) = ld(X2,mult(mult(X2,X2),mult(X2,i(mult(X,X2))))),
inference(symmetry,[status(thm)],[c373]) ).
cnf(c375,plain,
mult(X,ld(X,mult(ld(X2,i(X)),X))) = mult(ld(X2,i(X)),X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c376,plain,
mult(ld(X2,i(X)),X) = mult(X,ld(X,mult(ld(X2,i(X)),X))),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c378,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c377]) ).
cnf(c379,plain,
mult(X,X2) = mult(mult(X3,ld(X3,X)),X2),
inference(congruence,[status(thm)],[c378]) ).
cnf(c380,plain,
ld(mult(X3,X2),mult(X,X2)) = ld(mult(X3,X2),mult(mult(X3,ld(X3,X)),X2)),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
ld(mult(X3,X2),mult(mult(X3,ld(X3,X)),X2)) = ld(X2,mult(ld(X3,X),X2)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c382,plain,
ld(mult(X3,X2),mult(X,X2)) = ld(X2,mult(ld(X3,X),X2)),
inference(transitivity,[status(thm)],[c380,c381]) ).
cnf(c383,plain,
ld(mult(X,X2),mult(i(X2),X2)) = ld(X2,mult(ld(X,i(X2)),X2)),
inference(substitution,[status(thm)],[c382]) ).
cnf(c384,plain,
ld(X2,mult(ld(X,i(X2)),X2)) = ld(mult(X,X2),mult(i(X2),X2)),
inference(symmetry,[status(thm)],[c383]) ).
cnf(c385,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c386,plain,
ld(mult(X,X2),mult(i(X2),X2)) = ld(mult(X,X2),unit),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
ld(mult(X,X2),unit) = i(mult(X,X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c388,plain,
ld(mult(X,X2),mult(i(X2),X2)) = i(mult(X,X2)),
inference(transitivity,[status(thm)],[c386,c387]) ).
cnf(c389,plain,
ld(X2,mult(ld(X,i(X2)),X2)) = i(mult(X,X2)),
inference(transitivity,[status(thm)],[c384,c388]) ).
cnf(c390,plain,
ld(X,mult(ld(X2,i(X)),X)) = i(mult(X2,X)),
inference(substitution,[status(thm)],[c389]) ).
cnf(c391,plain,
mult(X,ld(X,mult(ld(X2,i(X)),X))) = mult(X,i(mult(X2,X))),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
mult(ld(X2,i(X)),X) = mult(X,i(mult(X2,X))),
inference(transitivity,[status(thm)],[c376,c391]) ).
cnf(c393,plain,
mult(ld(X,i(X2)),X2) = mult(X2,i(mult(X,X2))),
inference(substitution,[status(thm)],[c392]) ).
cnf(c394,plain,
mult(X2,i(mult(X,X2))) = mult(ld(X,i(X2)),X2),
inference(symmetry,[status(thm)],[c393]) ).
cnf(c395,plain,
mult(mult(X2,X2),mult(X2,i(mult(X,X2)))) = mult(mult(X2,X2),mult(ld(X,i(X2)),X2)),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
ld(X2,mult(mult(X2,X2),mult(X2,i(mult(X,X2))))) = ld(X2,mult(mult(X2,X2),mult(ld(X,i(X2)),X2))),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
ld(X2,mult(mult(X2,X2),mult(X2,ld(X2,X)))) = mult(mult(X2,X2),ld(X2,X)),
inference(substitution,[status(thm)],[c372]) ).
cnf(c398,plain,
mult(mult(X2,X2),ld(X2,X)) = ld(X2,mult(mult(X2,X2),mult(X2,ld(X2,X)))),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c400,plain,
mult(mult(X2,X2),mult(X2,ld(X2,X))) = mult(mult(X2,X2),X),
inference(congruence,[status(thm)],[c399]) ).
cnf(c401,plain,
ld(X2,mult(mult(X2,X2),mult(X2,ld(X2,X)))) = ld(X2,mult(mult(X2,X2),X)),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
mult(mult(X2,X2),ld(X2,X)) = ld(X2,mult(mult(X2,X2),X)),
inference(transitivity,[status(thm)],[c398,c401]) ).
cnf(c403,plain,
mult(mult(X2,X2),ld(X2,mult(X,X2))) = ld(X2,mult(mult(X2,X2),mult(X,X2))),
inference(substitution,[status(thm)],[c402]) ).
cnf(c404,plain,
ld(X2,mult(mult(X2,X2),mult(X,X2))) = mult(mult(X2,X2),ld(X2,mult(X,X2))),
inference(symmetry,[status(thm)],[c403]) ).
cnf(c405,plain,
mult(mult(X2,X),X2) = mult(mult(X2,X2),ld(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c406,plain,
mult(mult(X2,X2),ld(X2,mult(X,X2))) = mult(mult(X2,X),X2),
inference(symmetry,[status(thm)],[c405]) ).
cnf(c407,plain,
mult(X2,X) = rd(mult(X2,rd(X,i(X2))),X2),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c408,plain,
mult(mult(X2,X),X2) = mult(rd(mult(X2,rd(X,i(X2))),X2),X2),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
mult(rd(mult(X2,rd(X,i(X2))),X2),X2) = mult(X2,rd(X,i(X2))),
inference(substitution,[status(thm)],[c151]) ).
cnf(c410,plain,
mult(mult(X2,X),X2) = mult(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c408,c409]) ).
cnf(c411,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c412,plain,
mult(X2,rd(X,i(X2))) = mult(i(i(X2)),rd(X,i(X2))),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
mult(i(i(X2)),rd(X,i(X2))) = rd(ld(i(X2),X),i(X2)),
inference(substitution,[status(thm)],[c316]) ).
cnf(c414,plain,
mult(X2,rd(X,i(X2))) = rd(ld(i(X2),X),i(X2)),
inference(transitivity,[status(thm)],[c412,c413]) ).
cnf(c415,plain,
mult(mult(X2,X),X2) = rd(ld(i(X2),X),i(X2)),
inference(transitivity,[status(thm)],[c410,c414]) ).
cnf(c416,plain,
mult(mult(X2,X2),ld(X2,mult(X,X2))) = rd(ld(i(X2),X),i(X2)),
inference(transitivity,[status(thm)],[c406,c415]) ).
cnf(c417,plain,
ld(X2,mult(mult(X2,X2),mult(X,X2))) = rd(ld(i(X2),X),i(X2)),
inference(transitivity,[status(thm)],[c404,c416]) ).
cnf(c418,plain,
ld(X2,mult(mult(X2,X2),mult(ld(X,i(X2)),X2))) = rd(ld(i(X2),ld(X,i(X2))),i(X2)),
inference(substitution,[status(thm)],[c417]) ).
cnf(c419,plain,
rd(ld(X2,X),X2) = mult(i(X2),rd(X,X2)),
inference(symmetry,[status(thm)],[c316]) ).
cnf(c420,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c421,plain,
rd(X2,ld(X2,rd(X2,X))) = rd(i(i(X2)),ld(X2,rd(X2,X))),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c423,plain,
ld(X2,rd(X2,X)) = ld(i(i(X2)),rd(X2,X)),
inference(congruence,[status(thm)],[c422]) ).
cnf(c424,plain,
rd(i(i(X2)),ld(X2,rd(X2,X))) = rd(i(i(X2)),ld(i(i(X2)),rd(X2,X))),
inference(congruence,[status(thm)],[c423]) ).
cnf(c425,plain,
ld(X,mult(ld(X2,i(X)),X)) = i(mult(X2,X)),
inference(substitution,[status(thm)],[c389]) ).
cnf(c426,plain,
i(mult(X2,X)) = ld(X,mult(ld(X2,i(X)),X)),
inference(symmetry,[status(thm)],[c425]) ).
cnf(c427,plain,
rd(i(mult(X2,X)),X) = rd(ld(X,mult(ld(X2,i(X)),X)),X),
inference(congruence,[status(thm)],[c426]) ).
cnf(c428,plain,
rd(ld(X,mult(ld(X2,i(X)),X)),X) = mult(i(X),ld(X2,i(X))),
inference(substitution,[status(thm)],[c179]) ).
cnf(c429,plain,
mult(X,ld(X,mult(i(rd(X2,X)),X))) = mult(i(rd(X2,X)),X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c430,plain,
mult(i(rd(X2,X)),X) = mult(X,ld(X,mult(i(rd(X2,X)),X))),
inference(symmetry,[status(thm)],[c429]) ).
cnf(c431,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c101]) ).
cnf(c432,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c431]) ).
cnf(c433,plain,
ld(mult(X2,X),X) = ld(mult(X2,X),mult(unit,X)),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c435,plain,
unit = mult(X,i(X)),
inference(symmetry,[status(thm)],[c434]) ).
cnf(c436,plain,
mult(unit,X) = mult(mult(X2,i(X2)),X),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
ld(mult(X2,X),mult(unit,X)) = ld(mult(X2,X),mult(mult(X2,i(X2)),X)),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
ld(mult(X2,X),mult(mult(X2,i(X2)),X)) = ld(X,mult(i(X2),X)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c439,plain,
ld(mult(X2,X),mult(unit,X)) = ld(X,mult(i(X2),X)),
inference(transitivity,[status(thm)],[c437,c438]) ).
cnf(c440,plain,
ld(mult(X2,X),X) = ld(X,mult(i(X2),X)),
inference(transitivity,[status(thm)],[c433,c439]) ).
cnf(c441,plain,
ld(mult(rd(X,X2),X2),X2) = ld(X2,mult(i(rd(X,X2)),X2)),
inference(substitution,[status(thm)],[c440]) ).
cnf(c442,plain,
ld(X2,mult(i(rd(X,X2)),X2)) = ld(mult(rd(X,X2),X2),X2),
inference(symmetry,[status(thm)],[c441]) ).
cnf(c443,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c151]) ).
cnf(c444,plain,
ld(mult(rd(X,X2),X2),X2) = ld(X,X2),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
ld(X2,mult(i(rd(X,X2)),X2)) = ld(X,X2),
inference(transitivity,[status(thm)],[c442,c444]) ).
cnf(c446,plain,
ld(X,mult(i(rd(X2,X)),X)) = ld(X2,X),
inference(substitution,[status(thm)],[c445]) ).
cnf(c447,plain,
mult(X,ld(X,mult(i(rd(X2,X)),X))) = mult(X,ld(X2,X)),
inference(congruence,[status(thm)],[c446]) ).
cnf(c448,plain,
mult(i(rd(X2,X)),X) = mult(X,ld(X2,X)),
inference(transitivity,[status(thm)],[c430,c447]) ).
cnf(c449,plain,
mult(i(rd(X,X2)),X2) = mult(X2,ld(X,X2)),
inference(substitution,[status(thm)],[c448]) ).
cnf(c450,plain,
mult(X2,ld(X,X2)) = mult(i(rd(X,X2)),X2),
inference(symmetry,[status(thm)],[c449]) ).
cnf(c451,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c452,plain,
mult(X,X2) = mult(i(i(X)),X2),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
ld(X2,mult(X,X2)) = ld(X2,mult(i(i(X)),X2)),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
rd(X2,ld(X2,mult(X,X2))) = rd(X2,ld(X2,mult(i(i(X)),X2))),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
ld(mult(X,X2),X2) = ld(X2,mult(i(X),X2)),
inference(substitution,[status(thm)],[c440]) ).
cnf(c456,plain,
ld(X2,mult(i(X),X2)) = ld(mult(X,X2),X2),
inference(symmetry,[status(thm)],[c455]) ).
cnf(c457,plain,
rd(X2,ld(X2,mult(i(X),X2))) = rd(X2,ld(mult(X,X2),X2)),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c35]) ).
cnf(c459,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c458]) ).
cnf(c460,plain,
rd(X2,ld(X,X2)) = rd(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
rd(mult(X,ld(X,X2)),ld(X,X2)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c462,plain,
rd(X2,ld(X,X2)) = X,
inference(transitivity,[status(thm)],[c460,c461]) ).
cnf(c463,plain,
rd(X2,ld(mult(X,X2),X2)) = mult(X,X2),
inference(substitution,[status(thm)],[c462]) ).
cnf(c464,plain,
rd(X2,ld(X2,mult(i(X),X2))) = mult(X,X2),
inference(transitivity,[status(thm)],[c457,c463]) ).
cnf(c465,plain,
rd(X2,ld(X2,mult(i(i(X)),X2))) = mult(i(X),X2),
inference(substitution,[status(thm)],[c464]) ).
cnf(c466,plain,
rd(X2,ld(X2,mult(X,X2))) = mult(i(X),X2),
inference(transitivity,[status(thm)],[c454,c465]) ).
cnf(c467,plain,
rd(X,ld(X,mult(rd(X2,X),X))) = mult(i(rd(X2,X)),X),
inference(substitution,[status(thm)],[c466]) ).
cnf(c468,plain,
mult(i(rd(X2,X)),X) = rd(X,ld(X,mult(rd(X2,X),X))),
inference(symmetry,[status(thm)],[c467]) ).
cnf(c469,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c151]) ).
cnf(c470,plain,
ld(X,mult(rd(X2,X),X)) = ld(X,X2),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,plain,
rd(X,ld(X,mult(rd(X2,X),X))) = rd(X,ld(X,X2)),
inference(congruence,[status(thm)],[c470]) ).
cnf(c472,plain,
mult(i(rd(X2,X)),X) = rd(X,ld(X,X2)),
inference(transitivity,[status(thm)],[c468,c471]) ).
cnf(c473,plain,
mult(i(rd(X,X2)),X2) = rd(X2,ld(X2,X)),
inference(substitution,[status(thm)],[c472]) ).
cnf(c474,plain,
mult(X2,ld(X,X2)) = rd(X2,ld(X2,X)),
inference(transitivity,[status(thm)],[c450,c473]) ).
cnf(c475,plain,
mult(i(X),ld(X2,i(X))) = rd(i(X),ld(i(X),X2)),
inference(substitution,[status(thm)],[c474]) ).
cnf(c476,plain,
rd(ld(X,mult(ld(X2,i(X)),X)),X) = rd(i(X),ld(i(X),X2)),
inference(transitivity,[status(thm)],[c428,c475]) ).
cnf(c477,plain,
rd(i(mult(X2,X)),X) = rd(i(X),ld(i(X),X2)),
inference(transitivity,[status(thm)],[c427,c476]) ).
cnf(c478,plain,
rd(i(mult(rd(X2,X),i(X2))),i(X2)) = rd(i(i(X2)),ld(i(i(X2)),rd(X2,X))),
inference(substitution,[status(thm)],[c477]) ).
cnf(c479,plain,
rd(i(i(X2)),ld(i(i(X2)),rd(X2,X))) = rd(i(mult(rd(X2,X),i(X2))),i(X2)),
inference(symmetry,[status(thm)],[c478]) ).
cnf(c480,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c151]) ).
cnf(c481,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c480]) ).
cnf(c482,plain,
i(X2) = i(mult(rd(X2,X),X)),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
mult(rd(X2,X),i(X2)) = mult(rd(X2,X),i(mult(rd(X2,X),X))),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
i(mult(rd(X2,X),i(X2))) = i(mult(rd(X2,X),i(mult(rd(X2,X),X)))),
inference(congruence,[status(thm)],[c483]) ).
cnf(c485,plain,
ld(mult(X2,i(mult(X2,X))),mult(mult(X2,X),i(mult(X2,X)))) = ld(i(mult(X2,X)),mult(X,i(mult(X2,X)))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c486,plain,
ld(i(mult(X2,X)),mult(X,i(mult(X2,X)))) = ld(mult(X2,i(mult(X2,X))),mult(mult(X2,X),i(mult(X2,X)))),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
mult(mult(X2,X),i(mult(X2,X))) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c488,plain,
ld(mult(X2,i(mult(X2,X))),mult(mult(X2,X),i(mult(X2,X)))) = ld(mult(X2,i(mult(X2,X))),unit),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
ld(mult(X2,i(mult(X2,X))),unit) = i(mult(X2,i(mult(X2,X)))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c490,plain,
ld(mult(X2,i(mult(X2,X))),mult(mult(X2,X),i(mult(X2,X)))) = i(mult(X2,i(mult(X2,X)))),
inference(transitivity,[status(thm)],[c488,c489]) ).
cnf(c491,plain,
ld(i(mult(X2,X)),mult(X,i(mult(X2,X)))) = i(mult(X2,i(mult(X2,X)))),
inference(transitivity,[status(thm)],[c486,c490]) ).
cnf(c492,plain,
ld(i(mult(rd(X2,X),X)),mult(X,i(mult(rd(X2,X),X)))) = i(mult(rd(X2,X),i(mult(rd(X2,X),X)))),
inference(substitution,[status(thm)],[c491]) ).
cnf(c493,plain,
i(mult(rd(X2,X),i(mult(rd(X2,X),X)))) = ld(i(mult(rd(X2,X),X)),mult(X,i(mult(rd(X2,X),X)))),
inference(symmetry,[status(thm)],[c492]) ).
cnf(c494,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c151]) ).
cnf(c495,plain,
i(mult(rd(X2,X),X)) = i(X2),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
ld(i(mult(rd(X2,X),X)),mult(X,i(mult(rd(X2,X),X)))) = ld(i(X2),mult(X,i(mult(rd(X2,X),X)))),
inference(congruence,[status(thm)],[c495]) ).
cnf(c497,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c151]) ).
cnf(c498,plain,
i(mult(rd(X2,X),X)) = i(X2),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,plain,
mult(X,i(mult(rd(X2,X),X))) = mult(X,i(X2)),
inference(congruence,[status(thm)],[c498]) ).
cnf(c500,plain,
ld(i(X2),mult(X,i(mult(rd(X2,X),X)))) = ld(i(X2),mult(X,i(X2))),
inference(congruence,[status(thm)],[c499]) ).
cnf(c501,plain,
ld(i(mult(rd(X2,X),X)),mult(X,i(mult(rd(X2,X),X)))) = ld(i(X2),mult(X,i(X2))),
inference(transitivity,[status(thm)],[c496,c500]) ).
cnf(c502,plain,
i(mult(rd(X2,X),i(mult(rd(X2,X),X)))) = ld(i(X2),mult(X,i(X2))),
inference(transitivity,[status(thm)],[c493,c501]) ).
cnf(c503,plain,
i(mult(rd(X2,X),i(X2))) = ld(i(X2),mult(X,i(X2))),
inference(transitivity,[status(thm)],[c484,c502]) ).
cnf(c504,plain,
rd(i(mult(rd(X2,X),i(X2))),i(X2)) = rd(ld(i(X2),mult(X,i(X2))),i(X2)),
inference(congruence,[status(thm)],[c503]) ).
cnf(c505,plain,
rd(ld(i(X2),mult(X,i(X2))),i(X2)) = mult(i(i(X2)),X),
inference(substitution,[status(thm)],[c179]) ).
cnf(c506,plain,
mult(i(i(X2)),X) = mult(X2,X),
inference(congruence,[status(thm)],[c117]) ).
cnf(c507,plain,
rd(ld(i(X2),mult(X,i(X2))),i(X2)) = mult(X2,X),
inference(transitivity,[status(thm)],[c505,c506]) ).
cnf(c508,plain,
rd(i(mult(rd(X2,X),i(X2))),i(X2)) = mult(X2,X),
inference(transitivity,[status(thm)],[c504,c507]) ).
cnf(c509,plain,
rd(i(i(X2)),ld(i(i(X2)),rd(X2,X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c479,c508]) ).
cnf(c510,plain,
rd(i(i(X2)),ld(X2,rd(X2,X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c424,c509]) ).
cnf(c511,plain,
rd(X2,ld(X2,rd(X2,X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c421,c510]) ).
cnf(c512,plain,
rd(i(X2),ld(i(X2),rd(i(X2),rd(X,X2)))) = mult(i(X2),rd(X,X2)),
inference(substitution,[status(thm)],[c511]) ).
cnf(c513,plain,
mult(i(X2),rd(X,X2)) = rd(i(X2),ld(i(X2),rd(i(X2),rd(X,X2)))),
inference(symmetry,[status(thm)],[c512]) ).
cnf(c514,plain,
rd(mult(X,X2),X2) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c515,plain,
X = rd(mult(X,X2),X2),
inference(symmetry,[status(thm)],[c514]) ).
cnf(c516,plain,
ld(X2,X) = ld(X2,rd(mult(X,X2),X2)),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
i(ld(X2,X)) = i(ld(X2,rd(mult(X,X2),X2))),
inference(congruence,[status(thm)],[c516]) ).
cnf(c518,plain,
rd(i(ld(X2,X)),X2) = rd(i(ld(X2,rd(mult(X,X2),X2))),X2),
inference(congruence,[status(thm)],[c517]) ).
cnf(c519,plain,
ld(X2,rd(mult(X2,ld(X2,X)),X2)) = mult(ld(X2,X),i(X2)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c520,plain,
mult(ld(X2,X),i(X2)) = ld(X2,rd(mult(X2,ld(X2,X)),X2)),
inference(symmetry,[status(thm)],[c519]) ).
cnf(c521,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c522,plain,
rd(mult(X2,ld(X2,X)),X2) = rd(X,X2),
inference(congruence,[status(thm)],[c521]) ).
cnf(c523,plain,
ld(X2,rd(mult(X2,ld(X2,X)),X2)) = ld(X2,rd(X,X2)),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
mult(ld(X2,X),i(X2)) = ld(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c520,c523]) ).
cnf(c525,plain,
mult(ld(X2,mult(X,X2)),i(X2)) = ld(X2,rd(mult(X,X2),X2)),
inference(substitution,[status(thm)],[c524]) ).
cnf(c526,plain,
ld(X2,rd(mult(X,X2),X2)) = mult(ld(X2,mult(X,X2)),i(X2)),
inference(symmetry,[status(thm)],[c525]) ).
cnf(c527,plain,
i(ld(X2,rd(mult(X,X2),X2))) = i(mult(ld(X2,mult(X,X2)),i(X2))),
inference(congruence,[status(thm)],[c526]) ).
cnf(c528,plain,
rd(i(ld(X2,rd(mult(X,X2),X2))),X2) = rd(i(mult(ld(X2,mult(X,X2)),i(X2))),X2),
inference(congruence,[status(thm)],[c527]) ).
cnf(c529,plain,
mult(mult(i(X2),ld(i(X2),X)),X2) = ld(X2,mult(ld(i(X2),X),X2)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c530,plain,
ld(X2,mult(ld(i(X2),X),X2)) = mult(mult(i(X2),ld(i(X2),X)),X2),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c531,plain,
mult(i(X2),ld(i(X2),X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c532,plain,
mult(mult(i(X2),ld(i(X2),X)),X2) = mult(X,X2),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
ld(X2,mult(ld(i(X2),X),X2)) = mult(X,X2),
inference(transitivity,[status(thm)],[c530,c532]) ).
cnf(c534,plain,
ld(X,mult(ld(i(X),X2),X)) = mult(X2,X),
inference(substitution,[status(thm)],[c533]) ).
cnf(c535,plain,
mult(X2,X) = ld(X,mult(ld(i(X),X2),X)),
inference(symmetry,[status(thm)],[c534]) ).
cnf(c536,plain,
mult(mult(X2,X),i(X)) = mult(ld(X,mult(ld(i(X),X2),X)),i(X)),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
mult(ld(X,mult(ld(i(X),X2),X)),i(X)) = ld(X,rd(mult(ld(i(X),X2),X),X)),
inference(substitution,[status(thm)],[c524]) ).
cnf(c538,plain,
rd(mult(ld(i(X),X2),X),X) = ld(i(X),X2),
inference(substitution,[status(thm)],[c46]) ).
cnf(c539,plain,
ld(X,rd(mult(ld(i(X),X2),X),X)) = ld(X,ld(i(X),X2)),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
mult(ld(X,mult(ld(i(X),X2),X)),i(X)) = ld(X,ld(i(X),X2)),
inference(transitivity,[status(thm)],[c537,c539]) ).
cnf(c541,plain,
mult(mult(X2,X),i(X)) = ld(X,ld(i(X),X2)),
inference(transitivity,[status(thm)],[c536,c540]) ).
cnf(c542,plain,
mult(mult(X,X2),i(X2)) = ld(X2,ld(i(X2),X)),
inference(substitution,[status(thm)],[c541]) ).
cnf(c543,plain,
ld(X2,ld(i(X2),X)) = mult(mult(X,X2),i(X2)),
inference(symmetry,[status(thm)],[c542]) ).
cnf(c544,plain,
rd(ld(X2,ld(i(X2),X)),X2) = rd(mult(mult(X,X2),i(X2)),X2),
inference(congruence,[status(thm)],[c543]) ).
cnf(c545,plain,
mult(mult(X2,i(X)),X) = mult(mult(X2,X),ld(X,mult(i(X),X))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c546,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c547,plain,
ld(X,mult(i(X),X)) = ld(X,unit),
inference(congruence,[status(thm)],[c546]) ).
cnf(c548,plain,
mult(mult(X2,X),ld(X,mult(i(X),X))) = mult(mult(X2,X),ld(X,unit)),
inference(congruence,[status(thm)],[c547]) ).
cnf(c549,plain,
mult(mult(X2,X),ld(X,unit)) = mult(mult(X2,X),i(X)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c550,plain,
mult(mult(X2,X),ld(X,mult(i(X),X))) = mult(mult(X2,X),i(X)),
inference(transitivity,[status(thm)],[c548,c549]) ).
cnf(c551,plain,
mult(mult(X2,i(X)),X) = mult(mult(X2,X),i(X)),
inference(transitivity,[status(thm)],[c545,c550]) ).
cnf(c552,plain,
mult(mult(X,i(X2)),X2) = mult(mult(X,X2),i(X2)),
inference(substitution,[status(thm)],[c551]) ).
cnf(c553,plain,
mult(mult(X,X2),i(X2)) = mult(mult(X,i(X2)),X2),
inference(symmetry,[status(thm)],[c552]) ).
cnf(c554,plain,
rd(mult(mult(X,X2),i(X2)),X2) = rd(mult(mult(X,i(X2)),X2),X2),
inference(congruence,[status(thm)],[c553]) ).
cnf(c555,plain,
rd(mult(mult(X,i(X2)),X2),X2) = mult(X,i(X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c556,plain,
rd(mult(mult(X,X2),i(X2)),X2) = mult(X,i(X2)),
inference(transitivity,[status(thm)],[c554,c555]) ).
cnf(c557,plain,
rd(ld(X2,ld(i(X2),X)),X2) = mult(X,i(X2)),
inference(transitivity,[status(thm)],[c544,c556]) ).
cnf(c558,plain,
rd(ld(X,ld(i(X),i(rd(X2,X)))),X) = mult(i(rd(X2,X)),i(X)),
inference(substitution,[status(thm)],[c557]) ).
cnf(c559,plain,
mult(i(rd(X2,X)),i(X)) = rd(ld(X,ld(i(X),i(rd(X2,X)))),X),
inference(symmetry,[status(thm)],[c558]) ).
cnf(c560,plain,
rd(mult(X,X2),X2) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c561,plain,
X = rd(mult(X,X2),X2),
inference(symmetry,[status(thm)],[c560]) ).
cnf(c562,plain,
ld(X2,X) = ld(X2,rd(mult(X,X2),X2)),
inference(congruence,[status(thm)],[c561]) ).
cnf(c563,plain,
ld(i(X2),ld(X2,X)) = ld(i(X2),ld(X2,rd(mult(X,X2),X2))),
inference(congruence,[status(thm)],[c562]) ).
cnf(c564,plain,
ld(X2,rd(X,X2)) = mult(ld(X2,X),i(X2)),
inference(symmetry,[status(thm)],[c524]) ).
cnf(c565,plain,
ld(i(X2),ld(X2,rd(X,X2))) = ld(i(X2),mult(ld(X2,X),i(X2))),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
mult(mult(X2,ld(X2,X)),i(X2)) = ld(i(X2),mult(ld(X2,X),i(X2))),
inference(substitution,[status(thm)],[c104]) ).
cnf(c567,plain,
ld(i(X2),mult(ld(X2,X),i(X2))) = mult(mult(X2,ld(X2,X)),i(X2)),
inference(symmetry,[status(thm)],[c566]) ).
cnf(c568,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c569,plain,
mult(mult(X2,ld(X2,X)),i(X2)) = mult(X,i(X2)),
inference(congruence,[status(thm)],[c568]) ).
cnf(c570,plain,
ld(i(X2),mult(ld(X2,X),i(X2))) = mult(X,i(X2)),
inference(transitivity,[status(thm)],[c567,c569]) ).
cnf(c571,plain,
ld(i(X2),ld(X2,rd(X,X2))) = mult(X,i(X2)),
inference(transitivity,[status(thm)],[c565,c570]) ).
cnf(c572,plain,
ld(i(X2),ld(X2,rd(mult(X,X2),X2))) = mult(mult(X,X2),i(X2)),
inference(substitution,[status(thm)],[c571]) ).
cnf(c573,plain,
mult(mult(X,X2),i(X2)) = ld(X2,ld(i(X2),X)),
inference(substitution,[status(thm)],[c541]) ).
cnf(c574,plain,
ld(i(X2),ld(X2,rd(mult(X,X2),X2))) = ld(X2,ld(i(X2),X)),
inference(transitivity,[status(thm)],[c572,c573]) ).
cnf(c575,plain,
ld(i(X2),ld(X2,X)) = ld(X2,ld(i(X2),X)),
inference(transitivity,[status(thm)],[c563,c574]) ).
cnf(c576,plain,
ld(i(X2),ld(X2,i(rd(X,X2)))) = ld(X2,ld(i(X2),i(rd(X,X2)))),
inference(substitution,[status(thm)],[c575]) ).
cnf(c577,plain,
ld(X2,ld(i(X2),i(rd(X,X2)))) = ld(i(X2),ld(X2,i(rd(X,X2)))),
inference(symmetry,[status(thm)],[c576]) ).
cnf(c578,plain,
ld(X,mult(i(rd(X2,X)),X)) = ld(X2,X),
inference(substitution,[status(thm)],[c445]) ).
cnf(c579,plain,
ld(X2,X) = ld(X,mult(i(rd(X2,X)),X)),
inference(symmetry,[status(thm)],[c578]) ).
cnf(c580,plain,
mult(ld(X2,X),i(X)) = mult(ld(X,mult(i(rd(X2,X)),X)),i(X)),
inference(congruence,[status(thm)],[c579]) ).
cnf(c581,plain,
mult(ld(X,mult(i(rd(X2,X)),X)),i(X)) = ld(X,rd(mult(i(rd(X2,X)),X),X)),
inference(substitution,[status(thm)],[c524]) ).
cnf(c582,plain,
rd(mult(i(rd(X2,X)),X),X) = i(rd(X2,X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c583,plain,
ld(X,rd(mult(i(rd(X2,X)),X),X)) = ld(X,i(rd(X2,X))),
inference(congruence,[status(thm)],[c582]) ).
cnf(c584,plain,
mult(ld(X,mult(i(rd(X2,X)),X)),i(X)) = ld(X,i(rd(X2,X))),
inference(transitivity,[status(thm)],[c581,c583]) ).
cnf(c585,plain,
mult(ld(X2,X),i(X)) = ld(X,i(rd(X2,X))),
inference(transitivity,[status(thm)],[c580,c584]) ).
cnf(c586,plain,
mult(ld(X,X2),i(X2)) = ld(X2,i(rd(X,X2))),
inference(substitution,[status(thm)],[c585]) ).
cnf(c587,plain,
ld(X2,i(rd(X,X2))) = mult(ld(X,X2),i(X2)),
inference(symmetry,[status(thm)],[c586]) ).
cnf(c588,plain,
ld(i(X2),ld(X2,i(rd(X,X2)))) = ld(i(X2),mult(ld(X,X2),i(X2))),
inference(congruence,[status(thm)],[c587]) ).
cnf(c589,plain,
ld(mult(X,i(X2)),mult(X2,i(X2))) = ld(i(X2),mult(ld(X,X2),i(X2))),
inference(substitution,[status(thm)],[c382]) ).
cnf(c590,plain,
ld(i(X2),mult(ld(X,X2),i(X2))) = ld(mult(X,i(X2)),mult(X2,i(X2))),
inference(symmetry,[status(thm)],[c589]) ).
cnf(c591,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c592,plain,
ld(mult(X,i(X2)),mult(X2,i(X2))) = ld(mult(X,i(X2)),unit),
inference(congruence,[status(thm)],[c591]) ).
cnf(c593,plain,
ld(mult(X,i(X2)),unit) = i(mult(X,i(X2))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c594,plain,
ld(mult(X,i(X2)),mult(X2,i(X2))) = i(mult(X,i(X2))),
inference(transitivity,[status(thm)],[c592,c593]) ).
cnf(c595,plain,
ld(i(X2),mult(ld(X,X2),i(X2))) = i(mult(X,i(X2))),
inference(transitivity,[status(thm)],[c590,c594]) ).
cnf(c596,plain,
ld(i(X2),ld(X2,i(rd(X,X2)))) = i(mult(X,i(X2))),
inference(transitivity,[status(thm)],[c588,c595]) ).
cnf(c597,plain,
ld(X2,ld(i(X2),i(rd(X,X2)))) = i(mult(X,i(X2))),
inference(transitivity,[status(thm)],[c577,c596]) ).
cnf(c598,plain,
ld(X,ld(i(X),i(rd(X2,X)))) = i(mult(X2,i(X))),
inference(substitution,[status(thm)],[c597]) ).
cnf(c599,plain,
rd(ld(X,ld(i(X),i(rd(X2,X)))),X) = rd(i(mult(X2,i(X))),X),
inference(congruence,[status(thm)],[c598]) ).
cnf(c600,plain,
mult(i(rd(X2,X)),i(X)) = rd(i(mult(X2,i(X))),X),
inference(transitivity,[status(thm)],[c559,c599]) ).
cnf(c601,plain,
mult(i(rd(ld(X2,mult(X,X2)),X2)),i(X2)) = rd(i(mult(ld(X2,mult(X,X2)),i(X2))),X2),
inference(substitution,[status(thm)],[c600]) ).
cnf(c602,plain,
rd(i(mult(ld(X2,mult(X,X2)),i(X2))),X2) = mult(i(rd(ld(X2,mult(X,X2)),X2)),i(X2)),
inference(symmetry,[status(thm)],[c601]) ).
cnf(c603,plain,
i(rd(ld(X2,mult(X,X2)),X2)) = i(mult(i(X2),X)),
inference(congruence,[status(thm)],[c179]) ).
cnf(c604,plain,
mult(i(rd(ld(X2,mult(X,X2)),X2)),i(X2)) = mult(i(mult(i(X2),X)),i(X2)),
inference(congruence,[status(thm)],[c603]) ).
cnf(c605,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c606,plain,
mult(X2,X) = mult(i(i(X2)),X),
inference(congruence,[status(thm)],[c605]) ).
cnf(c607,plain,
i(mult(X2,X)) = i(mult(i(i(X2)),X)),
inference(congruence,[status(thm)],[c606]) ).
cnf(c608,plain,
mult(i(mult(X2,X)),X2) = mult(i(mult(i(i(X2)),X)),X2),
inference(congruence,[status(thm)],[c607]) ).
cnf(c609,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c610,plain,
ld(X2,rd(rd(X,X2),i(X2))) = ld(i(i(X2)),rd(rd(X,X2),i(X2))),
inference(congruence,[status(thm)],[c609]) ).
cnf(c611,plain,
rd(mult(i(X2),rd(X,X2)),i(X2)) = ld(i(i(X2)),rd(rd(X,X2),i(X2))),
inference(substitution,[status(thm)],[c336]) ).
cnf(c612,plain,
ld(i(i(X2)),rd(rd(X,X2),i(X2))) = rd(mult(i(X2),rd(X,X2)),i(X2)),
inference(symmetry,[status(thm)],[c611]) ).
cnf(c613,plain,
mult(i(X2),mult(rd(X,X2),X2)) = rd(mult(i(X2),rd(X,X2)),i(X2)),
inference(substitution,[status(thm)],[c129]) ).
cnf(c614,plain,
rd(mult(i(X2),rd(X,X2)),i(X2)) = mult(i(X2),mult(rd(X,X2),X2)),
inference(symmetry,[status(thm)],[c613]) ).
cnf(c615,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c151]) ).
cnf(c616,plain,
mult(i(X2),mult(rd(X,X2),X2)) = mult(i(X2),X),
inference(congruence,[status(thm)],[c615]) ).
cnf(c617,plain,
rd(mult(i(X2),rd(X,X2)),i(X2)) = mult(i(X2),X),
inference(transitivity,[status(thm)],[c614,c616]) ).
cnf(c618,plain,
ld(i(i(X2)),rd(rd(X,X2),i(X2))) = mult(i(X2),X),
inference(transitivity,[status(thm)],[c612,c617]) ).
cnf(c619,plain,
ld(X2,rd(rd(X,X2),i(X2))) = mult(i(X2),X),
inference(transitivity,[status(thm)],[c610,c618]) ).
cnf(c620,plain,
ld(i(X2),rd(rd(X,i(X2)),i(i(X2)))) = mult(i(i(X2)),X),
inference(substitution,[status(thm)],[c619]) ).
cnf(c621,plain,
mult(i(i(X2)),X) = ld(i(X2),rd(rd(X,i(X2)),i(i(X2)))),
inference(symmetry,[status(thm)],[c620]) ).
cnf(c622,plain,
i(mult(i(i(X2)),X)) = i(ld(i(X2),rd(rd(X,i(X2)),i(i(X2))))),
inference(congruence,[status(thm)],[c621]) ).
cnf(c623,plain,
mult(i(mult(i(i(X2)),X)),X2) = mult(i(ld(i(X2),rd(rd(X,i(X2)),i(i(X2))))),X2),
inference(congruence,[status(thm)],[c622]) ).
cnf(c624,plain,
rd(X2,ld(X2,mult(ld(i(X2),X),X2))) = mult(i(ld(i(X2),X)),X2),
inference(substitution,[status(thm)],[c466]) ).
cnf(c625,plain,
mult(i(ld(i(X2),X)),X2) = rd(X2,ld(X2,mult(ld(i(X2),X),X2))),
inference(symmetry,[status(thm)],[c624]) ).
cnf(c626,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c627,plain,
mult(ld(i(X2),X),X2) = mult(ld(i(X2),X),i(i(X2))),
inference(congruence,[status(thm)],[c626]) ).
cnf(c628,plain,
mult(ld(i(X2),X),i(i(X2))) = ld(i(X2),rd(X,i(X2))),
inference(substitution,[status(thm)],[c524]) ).
cnf(c629,plain,
mult(ld(i(X2),X),X2) = ld(i(X2),rd(X,i(X2))),
inference(transitivity,[status(thm)],[c627,c628]) ).
cnf(c630,plain,
ld(X2,mult(ld(i(X2),X),X2)) = ld(X2,ld(i(X2),rd(X,i(X2)))),
inference(congruence,[status(thm)],[c629]) ).
cnf(c631,plain,
rd(X2,ld(X2,mult(ld(i(X2),X),X2))) = rd(X2,ld(X2,ld(i(X2),rd(X,i(X2))))),
inference(congruence,[status(thm)],[c630]) ).
cnf(c632,plain,
ld(i(X2),rd(X,i(X2))) = mult(ld(i(X2),X),X2),
inference(symmetry,[status(thm)],[c629]) ).
cnf(c633,plain,
ld(X2,ld(i(X2),rd(X,i(X2)))) = ld(X2,mult(ld(i(X2),X),X2)),
inference(congruence,[status(thm)],[c632]) ).
cnf(c634,plain,
mult(mult(i(X2),ld(i(X2),X)),X2) = ld(X2,mult(ld(i(X2),X),X2)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c635,plain,
ld(X2,mult(ld(i(X2),X),X2)) = mult(mult(i(X2),ld(i(X2),X)),X2),
inference(symmetry,[status(thm)],[c634]) ).
cnf(c636,plain,
mult(i(X2),ld(i(X2),X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c637,plain,
mult(mult(i(X2),ld(i(X2),X)),X2) = mult(X,X2),
inference(congruence,[status(thm)],[c636]) ).
cnf(c638,plain,
ld(X2,mult(ld(i(X2),X),X2)) = mult(X,X2),
inference(transitivity,[status(thm)],[c635,c637]) ).
cnf(c639,plain,
ld(X2,ld(i(X2),rd(X,i(X2)))) = mult(X,X2),
inference(transitivity,[status(thm)],[c633,c638]) ).
cnf(c640,plain,
rd(X2,ld(X2,ld(i(X2),rd(X,i(X2))))) = rd(X2,mult(X,X2)),
inference(congruence,[status(thm)],[c639]) ).
cnf(c641,plain,
rd(X2,ld(X2,mult(ld(i(X2),X),X2))) = rd(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c631,c640]) ).
cnf(c642,plain,
mult(i(ld(i(X2),X)),X2) = rd(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c625,c641]) ).
cnf(c643,plain,
mult(i(ld(i(X2),rd(rd(X,i(X2)),i(i(X2))))),X2) = rd(X2,mult(rd(rd(X,i(X2)),i(i(X2))),X2)),
inference(substitution,[status(thm)],[c642]) ).
cnf(c644,plain,
rd(rd(X,i(X2)),i(i(X2))) = rd(rd(X,i(X2)),X2),
inference(congruence,[status(thm)],[c117]) ).
cnf(c645,plain,
mult(rd(rd(X,i(X2)),i(i(X2))),X2) = mult(rd(rd(X,i(X2)),X2),X2),
inference(congruence,[status(thm)],[c644]) ).
cnf(c646,plain,
rd(X2,mult(rd(rd(X,i(X2)),i(i(X2))),X2)) = rd(X2,mult(rd(rd(X,i(X2)),X2),X2)),
inference(congruence,[status(thm)],[c645]) ).
cnf(c647,plain,
mult(rd(rd(X,i(X2)),X2),X2) = rd(X,i(X2)),
inference(substitution,[status(thm)],[c151]) ).
cnf(c648,plain,
rd(X2,mult(rd(rd(X,i(X2)),X2),X2)) = rd(X2,rd(X,i(X2))),
inference(congruence,[status(thm)],[c647]) ).
cnf(c649,plain,
rd(X2,mult(rd(rd(X,i(X2)),i(i(X2))),X2)) = rd(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c646,c648]) ).
cnf(c650,plain,
mult(i(ld(i(X2),rd(rd(X,i(X2)),i(i(X2))))),X2) = rd(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c643,c649]) ).
cnf(c651,plain,
mult(i(mult(i(i(X2)),X)),X2) = rd(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c623,c650]) ).
cnf(c652,plain,
mult(i(mult(X2,X)),X2) = rd(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c608,c651]) ).
cnf(c653,plain,
mult(i(mult(i(X2),X)),i(X2)) = rd(i(X2),rd(X,i(i(X2)))),
inference(substitution,[status(thm)],[c652]) ).
cnf(c654,plain,
rd(X,i(i(X2))) = rd(X,X2),
inference(congruence,[status(thm)],[c117]) ).
cnf(c655,plain,
rd(i(X2),rd(X,i(i(X2)))) = rd(i(X2),rd(X,X2)),
inference(congruence,[status(thm)],[c654]) ).
cnf(c656,plain,
mult(i(mult(i(X2),X)),i(X2)) = rd(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c653,c655]) ).
cnf(c657,plain,
mult(i(rd(ld(X2,mult(X,X2)),X2)),i(X2)) = rd(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c604,c656]) ).
cnf(c658,plain,
rd(i(mult(ld(X2,mult(X,X2)),i(X2))),X2) = rd(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c602,c657]) ).
cnf(c659,plain,
rd(i(ld(X2,rd(mult(X,X2),X2))),X2) = rd(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c528,c658]) ).
cnf(c660,plain,
rd(i(ld(X2,X)),X2) = rd(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c518,c659]) ).
cnf(c661,plain,
rd(i(X2),rd(X,X2)) = rd(i(ld(X2,X)),X2),
inference(symmetry,[status(thm)],[c660]) ).
cnf(c662,plain,
ld(i(X2),rd(i(X2),rd(X,X2))) = ld(i(X2),rd(i(ld(X2,X)),X2)),
inference(congruence,[status(thm)],[c661]) ).
cnf(c663,plain,
mult(X3,mult(X2,ld(X3,X))) = mult(ld(i(X3),rd(X2,X3)),X),
inference(symmetry,[status(thm)],[c345]) ).
cnf(c664,plain,
rd(mult(X3,mult(X2,ld(X3,X))),X) = rd(mult(ld(i(X3),rd(X2,X3)),X),X),
inference(congruence,[status(thm)],[c663]) ).
cnf(c665,plain,
rd(mult(ld(i(X3),rd(X2,X3)),X),X) = ld(i(X3),rd(X2,X3)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c666,plain,
rd(mult(X3,mult(X2,ld(X3,X))),X) = ld(i(X3),rd(X2,X3)),
inference(transitivity,[status(thm)],[c664,c665]) ).
cnf(c667,plain,
rd(mult(X2,mult(i(ld(X2,X)),ld(X2,X))),X) = ld(i(X2),rd(i(ld(X2,X)),X2)),
inference(substitution,[status(thm)],[c666]) ).
cnf(c668,plain,
ld(i(X2),rd(i(ld(X2,X)),X2)) = rd(mult(X2,mult(i(ld(X2,X)),ld(X2,X))),X),
inference(symmetry,[status(thm)],[c667]) ).
cnf(c669,plain,
mult(i(ld(X2,X)),ld(X2,X)) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c670,plain,
mult(X2,mult(i(ld(X2,X)),ld(X2,X))) = mult(X2,unit),
inference(congruence,[status(thm)],[c669]) ).
cnf(c671,plain,
rd(mult(X2,mult(i(ld(X2,X)),ld(X2,X))),X) = rd(mult(X2,unit),X),
inference(congruence,[status(thm)],[c670]) ).
cnf(c672,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c86]) ).
cnf(c673,plain,
rd(mult(X2,unit),X) = rd(X2,X),
inference(congruence,[status(thm)],[c672]) ).
cnf(c674,plain,
rd(mult(X2,mult(i(ld(X2,X)),ld(X2,X))),X) = rd(X2,X),
inference(transitivity,[status(thm)],[c671,c673]) ).
cnf(c675,plain,
ld(i(X2),rd(i(ld(X2,X)),X2)) = rd(X2,X),
inference(transitivity,[status(thm)],[c668,c674]) ).
cnf(c676,plain,
ld(i(X2),rd(i(X2),rd(X,X2))) = rd(X2,X),
inference(transitivity,[status(thm)],[c662,c675]) ).
cnf(c677,plain,
rd(i(X2),ld(i(X2),rd(i(X2),rd(X,X2)))) = rd(i(X2),rd(X2,X)),
inference(congruence,[status(thm)],[c676]) ).
cnf(c678,plain,
mult(i(X2),rd(X,X2)) = rd(i(X2),rd(X2,X)),
inference(transitivity,[status(thm)],[c513,c677]) ).
cnf(c679,plain,
rd(ld(X2,X),X2) = rd(i(X2),rd(X2,X)),
inference(transitivity,[status(thm)],[c419,c678]) ).
cnf(c680,plain,
rd(ld(i(X2),ld(X,i(X2))),i(X2)) = rd(i(i(X2)),rd(i(X2),ld(X,i(X2)))),
inference(substitution,[status(thm)],[c679]) ).
cnf(c681,plain,
rd(i(i(X2)),rd(i(X2),ld(X,i(X2)))) = rd(X2,rd(i(X2),ld(X,i(X2)))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c682,plain,
rd(i(X2),ld(X,i(X2))) = X,
inference(substitution,[status(thm)],[c462]) ).
cnf(c683,plain,
rd(X2,rd(i(X2),ld(X,i(X2)))) = rd(X2,X),
inference(congruence,[status(thm)],[c682]) ).
cnf(c684,plain,
rd(i(i(X2)),rd(i(X2),ld(X,i(X2)))) = rd(X2,X),
inference(transitivity,[status(thm)],[c681,c683]) ).
cnf(c685,plain,
rd(ld(i(X2),ld(X,i(X2))),i(X2)) = rd(X2,X),
inference(transitivity,[status(thm)],[c680,c684]) ).
cnf(c686,plain,
ld(X2,mult(mult(X2,X2),mult(ld(X,i(X2)),X2))) = rd(X2,X),
inference(transitivity,[status(thm)],[c418,c685]) ).
cnf(c687,plain,
ld(X2,mult(mult(X2,X2),mult(X2,i(mult(X,X2))))) = rd(X2,X),
inference(transitivity,[status(thm)],[c396,c686]) ).
cnf(c688,plain,
mult(mult(X2,X2),i(mult(X,X2))) = rd(X2,X),
inference(transitivity,[status(thm)],[c374,c687]) ).
cnf(c689,plain,
rd(X2,X) = mult(mult(X2,X2),i(mult(X,X2))),
inference(symmetry,[status(thm)],[c688]) ).
cnf(c690,plain,
ld(mult(X2,X2),rd(X2,X)) = ld(mult(X2,X2),mult(mult(X2,X2),i(mult(X,X2)))),
inference(congruence,[status(thm)],[c689]) ).
cnf(c691,plain,
ld(mult(X2,X2),mult(mult(X2,X2),i(mult(X,X2)))) = i(mult(X,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c692,plain,
ld(mult(X2,X2),rd(X2,X)) = i(mult(X,X2)),
inference(transitivity,[status(thm)],[c690,c691]) ).
cnf(c693,plain,
ld(mult(X,X),rd(X,ld(X2,X))) = i(mult(ld(X2,X),X)),
inference(substitution,[status(thm)],[c692]) ).
cnf(c694,plain,
i(mult(ld(X2,X),X)) = ld(mult(X,X),rd(X,ld(X2,X))),
inference(symmetry,[status(thm)],[c693]) ).
cnf(c695,plain,
rd(X,ld(X2,X)) = X2,
inference(substitution,[status(thm)],[c462]) ).
cnf(c696,plain,
ld(mult(X,X),rd(X,ld(X2,X))) = ld(mult(X,X),X2),
inference(congruence,[status(thm)],[c695]) ).
cnf(c697,plain,
i(mult(ld(X2,X),X)) = ld(mult(X,X),X2),
inference(transitivity,[status(thm)],[c694,c696]) ).
cnf(c698,plain,
ld(mult(X,X),X2) = i(mult(ld(X2,X),X)),
inference(symmetry,[status(thm)],[c697]) ).
cnf(c699,plain,
i(ld(mult(X,X),X2)) = i(i(mult(ld(X2,X),X))),
inference(congruence,[status(thm)],[c698]) ).
cnf(c700,plain,
i(i(mult(ld(X2,X),X))) = mult(ld(X2,X),X),
inference(substitution,[status(thm)],[c117]) ).
cnf(c701,plain,
i(ld(mult(X,X),X2)) = mult(ld(X2,X),X),
inference(transitivity,[status(thm)],[c699,c700]) ).
cnf(c702,plain,
i(ld(mult(X2,X2),rd(X,X2))) = mult(ld(rd(X,X2),X2),X2),
inference(substitution,[status(thm)],[c701]) ).
cnf(c703,plain,
ld(X2,i(ld(mult(X2,X2),rd(X,X2)))) = ld(X2,mult(ld(rd(X,X2),X2),X2)),
inference(congruence,[status(thm)],[c702]) ).
cnf(c704,plain,
mult(rd(rd(ld(X2,X),i(X2)),X2),X2) = rd(ld(X2,X),i(X2)),
inference(substitution,[status(thm)],[c151]) ).
cnf(c705,plain,
rd(ld(X2,X),i(X2)) = mult(rd(rd(ld(X2,X),i(X2)),X2),X2),
inference(symmetry,[status(thm)],[c704]) ).
cnf(c706,plain,
mult(X2,mult(i(X2),ld(X2,X))) = rd(rd(ld(X2,X),i(X2)),X2),
inference(substitution,[status(thm)],[c322]) ).
cnf(c707,plain,
rd(rd(ld(X2,X),i(X2)),X2) = mult(X2,mult(i(X2),ld(X2,X))),
inference(symmetry,[status(thm)],[c706]) ).
cnf(c708,plain,
mult(i(X2),mult(X2,ld(X2,X))) = mult(X2,mult(i(X2),ld(X2,X))),
inference(substitution,[status(thm)],[c302]) ).
cnf(c709,plain,
mult(X2,mult(i(X2),ld(X2,X))) = mult(i(X2),mult(X2,ld(X2,X))),
inference(symmetry,[status(thm)],[c708]) ).
cnf(c710,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c711,plain,
mult(i(X2),mult(X2,ld(X2,X))) = mult(i(X2),X),
inference(congruence,[status(thm)],[c710]) ).
cnf(c712,plain,
mult(X2,mult(i(X2),ld(X2,X))) = mult(i(X2),X),
inference(transitivity,[status(thm)],[c709,c711]) ).
cnf(c713,plain,
rd(rd(ld(X2,X),i(X2)),X2) = mult(i(X2),X),
inference(transitivity,[status(thm)],[c707,c712]) ).
cnf(c714,plain,
mult(rd(rd(ld(X2,X),i(X2)),X2),X2) = mult(mult(i(X2),X),X2),
inference(congruence,[status(thm)],[c713]) ).
cnf(c715,plain,
mult(rd(rd(ld(X2,X),i(X2)),X2),X2) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c714,c175]) ).
cnf(c716,plain,
rd(ld(X2,X),i(X2)) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c705,c715]) ).
cnf(c717,plain,
rd(ld(X2,ld(rd(X,X2),X2)),i(X2)) = ld(X2,mult(ld(rd(X,X2),X2),X2)),
inference(substitution,[status(thm)],[c716]) ).
cnf(c718,plain,
ld(X2,mult(ld(rd(X,X2),X2),X2)) = rd(ld(X2,ld(rd(X,X2),X2)),i(X2)),
inference(symmetry,[status(thm)],[c717]) ).
cnf(c719,plain,
ld(X2,mult(ld(rd(i(X2),X),i(X2)),X2)) = i(mult(rd(i(X2),X),X2)),
inference(substitution,[status(thm)],[c389]) ).
cnf(c720,plain,
i(mult(rd(i(X2),X),X2)) = ld(X2,mult(ld(rd(i(X2),X),i(X2)),X2)),
inference(symmetry,[status(thm)],[c719]) ).
cnf(c721,plain,
ld(rd(i(X2),X),i(X2)) = X,
inference(substitution,[status(thm)],[c205]) ).
cnf(c722,plain,
mult(ld(rd(i(X2),X),i(X2)),X2) = mult(X,X2),
inference(congruence,[status(thm)],[c721]) ).
cnf(c723,plain,
ld(X2,mult(ld(rd(i(X2),X),i(X2)),X2)) = ld(X2,mult(X,X2)),
inference(congruence,[status(thm)],[c722]) ).
cnf(c724,plain,
i(mult(rd(i(X2),X),X2)) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c720,c723]) ).
cnf(c725,plain,
ld(X2,mult(X,X2)) = i(mult(rd(i(X2),X),X2)),
inference(symmetry,[status(thm)],[c724]) ).
cnf(c726,plain,
i(ld(X2,mult(X,X2))) = i(i(mult(rd(i(X2),X),X2))),
inference(congruence,[status(thm)],[c725]) ).
cnf(c727,plain,
i(i(mult(rd(i(X2),X),X2))) = mult(rd(i(X2),X),X2),
inference(substitution,[status(thm)],[c117]) ).
cnf(c728,plain,
i(ld(X2,mult(X,X2))) = mult(rd(i(X2),X),X2),
inference(transitivity,[status(thm)],[c726,c727]) ).
cnf(c729,plain,
mult(rd(i(X2),X),X2) = i(ld(X2,mult(X,X2))),
inference(symmetry,[status(thm)],[c728]) ).
cnf(c730,plain,
ld(X2,mult(X,X2)) = rd(ld(X2,X),i(X2)),
inference(symmetry,[status(thm)],[c716]) ).
cnf(c731,plain,
i(ld(X2,mult(X,X2))) = i(rd(ld(X2,X),i(X2))),
inference(congruence,[status(thm)],[c730]) ).
cnf(c732,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c733,plain,
rd(X2,X) = rd(i(i(X2)),X),
inference(congruence,[status(thm)],[c732]) ).
cnf(c734,plain,
ld(X2,rd(X2,X)) = ld(X2,rd(i(i(X2)),X)),
inference(congruence,[status(thm)],[c733]) ).
cnf(c735,plain,
ld(X2,ld(X2,rd(X2,X))) = ld(X2,ld(X2,rd(i(i(X2)),X))),
inference(congruence,[status(thm)],[c734]) ).
cnf(c736,plain,
rd(X2,rd(X,i(X2))) = mult(i(mult(X2,X)),X2),
inference(symmetry,[status(thm)],[c652]) ).
cnf(c737,plain,
ld(X2,rd(X2,rd(X,i(X2)))) = ld(X2,mult(i(mult(X2,X)),X2)),
inference(congruence,[status(thm)],[c736]) ).
cnf(c738,plain,
ld(mult(mult(X2,X),X2),X2) = ld(X2,mult(i(mult(X2,X)),X2)),
inference(substitution,[status(thm)],[c440]) ).
cnf(c739,plain,
ld(X2,mult(i(mult(X2,X)),X2)) = ld(mult(mult(X2,X),X2),X2),
inference(symmetry,[status(thm)],[c738]) ).
cnf(c740,plain,
mult(X2,X) = rd(mult(X2,rd(X,i(X2))),X2),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c741,plain,
mult(mult(X2,X),X2) = mult(rd(mult(X2,rd(X,i(X2))),X2),X2),
inference(congruence,[status(thm)],[c740]) ).
cnf(c742,plain,
mult(rd(mult(X2,rd(X,i(X2))),X2),X2) = mult(X2,rd(X,i(X2))),
inference(substitution,[status(thm)],[c151]) ).
cnf(c743,plain,
mult(rd(mult(X2,rd(X,i(X2))),X2),X2) = rd(ld(i(X2),X),i(X2)),
inference(transitivity,[status(thm)],[c742,c414]) ).
cnf(c744,plain,
mult(mult(X2,X),X2) = rd(ld(i(X2),X),i(X2)),
inference(transitivity,[status(thm)],[c741,c743]) ).
cnf(c745,plain,
ld(mult(mult(X2,X),X2),X2) = ld(rd(ld(i(X2),X),i(X2)),X2),
inference(congruence,[status(thm)],[c744]) ).
cnf(c746,plain,
rd(ld(i(X2),X),i(X2)) = rd(i(i(X2)),rd(i(X2),X)),
inference(substitution,[status(thm)],[c679]) ).
cnf(c747,plain,
ld(rd(ld(i(X2),X),i(X2)),X2) = ld(rd(i(i(X2)),rd(i(X2),X)),X2),
inference(congruence,[status(thm)],[c746]) ).
cnf(c748,plain,
rd(i(i(X2)),rd(i(X2),X)) = rd(X2,rd(i(X2),X)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c749,plain,
ld(rd(i(i(X2)),rd(i(X2),X)),X2) = ld(rd(X2,rd(i(X2),X)),X2),
inference(congruence,[status(thm)],[c748]) ).
cnf(c750,plain,
ld(rd(X2,rd(i(X2),X)),X2) = rd(i(X2),X),
inference(substitution,[status(thm)],[c205]) ).
cnf(c751,plain,
ld(rd(i(i(X2)),rd(i(X2),X)),X2) = rd(i(X2),X),
inference(transitivity,[status(thm)],[c749,c750]) ).
cnf(c752,plain,
ld(rd(ld(i(X2),X),i(X2)),X2) = rd(i(X2),X),
inference(transitivity,[status(thm)],[c747,c751]) ).
cnf(c753,plain,
ld(mult(mult(X2,X),X2),X2) = rd(i(X2),X),
inference(transitivity,[status(thm)],[c745,c752]) ).
cnf(c754,plain,
ld(X2,mult(i(mult(X2,X)),X2)) = rd(i(X2),X),
inference(transitivity,[status(thm)],[c739,c753]) ).
cnf(c755,plain,
ld(X2,rd(X2,rd(X,i(X2)))) = rd(i(X2),X),
inference(transitivity,[status(thm)],[c737,c754]) ).
cnf(c756,plain,
ld(i(X2),rd(i(X2),rd(X,i(i(X2))))) = rd(i(i(X2)),X),
inference(substitution,[status(thm)],[c755]) ).
cnf(c757,plain,
rd(i(i(X2)),X) = ld(i(X2),rd(i(X2),rd(X,i(i(X2))))),
inference(symmetry,[status(thm)],[c756]) ).
cnf(c758,plain,
ld(X2,rd(i(i(X2)),X)) = ld(X2,ld(i(X2),rd(i(X2),rd(X,i(i(X2)))))),
inference(congruence,[status(thm)],[c757]) ).
cnf(c759,plain,
ld(X2,ld(X2,rd(i(i(X2)),X))) = ld(X2,ld(X2,ld(i(X2),rd(i(X2),rd(X,i(i(X2))))))),
inference(congruence,[status(thm)],[c758]) ).
cnf(c760,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c761,plain,
mult(X2,X) = mult(i(i(X2)),X),
inference(congruence,[status(thm)],[c760]) ).
cnf(c762,plain,
ld(mult(X2,X2),mult(X2,X)) = ld(mult(X2,X2),mult(i(i(X2)),X)),
inference(congruence,[status(thm)],[c761]) ).
cnf(c763,plain,
rd(ld(i(X2),mult(X,i(X2))),i(X2)) = mult(i(i(X2)),X),
inference(substitution,[status(thm)],[c179]) ).
cnf(c764,plain,
mult(i(i(X2)),X) = rd(ld(i(X2),mult(X,i(X2))),i(X2)),
inference(symmetry,[status(thm)],[c763]) ).
cnf(c765,plain,
ld(mult(X2,X2),mult(i(i(X2)),X)) = ld(mult(X2,X2),rd(ld(i(X2),mult(X,i(X2))),i(X2))),
inference(congruence,[status(thm)],[c764]) ).
cnf(c766,plain,
rd(ld(i(X2),X),i(X2)) = mult(X2,rd(X,i(X2))),
inference(symmetry,[status(thm)],[c414]) ).
cnf(c767,plain,
ld(mult(X2,X2),rd(ld(i(X2),X),i(X2))) = ld(mult(X2,X2),mult(X2,rd(X,i(X2)))),
inference(congruence,[status(thm)],[c766]) ).
cnf(c768,plain,
mult(X2,rd(X,i(X2))) = mult(mult(X2,X),X2),
inference(symmetry,[status(thm)],[c410]) ).
cnf(c769,plain,
ld(mult(X2,X2),mult(X2,rd(X,i(X2)))) = ld(mult(X2,X2),mult(mult(X2,X),X2)),
inference(congruence,[status(thm)],[c768]) ).
cnf(c770,plain,
mult(mult(X2,X),X2) = mult(mult(X2,X2),ld(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c771,plain,
ld(mult(X2,X2),mult(mult(X2,X),X2)) = ld(mult(X2,X2),mult(mult(X2,X2),ld(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c770]) ).
cnf(c772,plain,
ld(mult(X2,X2),mult(mult(X2,X2),ld(X2,mult(X,X2)))) = ld(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c773,plain,
ld(mult(X2,X2),mult(mult(X2,X),X2)) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c771,c772]) ).
cnf(c774,plain,
ld(mult(X2,X2),mult(X2,rd(X,i(X2)))) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c769,c773]) ).
cnf(c775,plain,
ld(mult(X2,X2),rd(ld(i(X2),X),i(X2))) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c767,c774]) ).
cnf(c776,plain,
ld(mult(X2,X2),rd(ld(i(X2),mult(X,i(X2))),i(X2))) = ld(X2,mult(mult(X,i(X2)),X2)),
inference(substitution,[status(thm)],[c775]) ).
cnf(c777,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c778,plain,
mult(mult(X2,i(X)),X) = mult(mult(X2,i(X)),i(i(X))),
inference(congruence,[status(thm)],[c777]) ).
cnf(c779,plain,
mult(mult(X2,i(X)),i(i(X))) = ld(i(X),ld(i(i(X)),X2)),
inference(substitution,[status(thm)],[c541]) ).
cnf(c780,plain,
ld(i(i(X)),X2) = ld(X,X2),
inference(congruence,[status(thm)],[c117]) ).
cnf(c781,plain,
ld(i(X),ld(i(i(X)),X2)) = ld(i(X),ld(X,X2)),
inference(congruence,[status(thm)],[c780]) ).
cnf(c782,plain,
mult(mult(X2,i(X)),i(i(X))) = ld(i(X),ld(X,X2)),
inference(transitivity,[status(thm)],[c779,c781]) ).
cnf(c783,plain,
mult(mult(X2,i(X)),X) = ld(i(X),ld(X,X2)),
inference(transitivity,[status(thm)],[c778,c782]) ).
cnf(c784,plain,
mult(mult(X,i(X2)),X2) = ld(i(X2),ld(X2,X)),
inference(substitution,[status(thm)],[c783]) ).
cnf(c785,plain,
ld(X2,mult(mult(X,i(X2)),X2)) = ld(X2,ld(i(X2),ld(X2,X))),
inference(congruence,[status(thm)],[c784]) ).
cnf(c786,plain,
ld(X2,ld(i(X2),ld(X2,X))) = ld(X2,ld(X2,ld(i(X2),X))),
inference(congruence,[status(thm)],[c575]) ).
cnf(c787,plain,
ld(X2,mult(mult(X,i(X2)),X2)) = ld(X2,ld(X2,ld(i(X2),X))),
inference(transitivity,[status(thm)],[c785,c786]) ).
cnf(c788,plain,
ld(mult(X2,X2),rd(ld(i(X2),mult(X,i(X2))),i(X2))) = ld(X2,ld(X2,ld(i(X2),X))),
inference(transitivity,[status(thm)],[c776,c787]) ).
cnf(c789,plain,
ld(mult(X2,X2),mult(i(i(X2)),X)) = ld(X2,ld(X2,ld(i(X2),X))),
inference(transitivity,[status(thm)],[c765,c788]) ).
cnf(c790,plain,
ld(mult(X2,X2),mult(X2,X)) = ld(X2,ld(X2,ld(i(X2),X))),
inference(transitivity,[status(thm)],[c762,c789]) ).
cnf(c791,plain,
ld(mult(X2,X2),mult(X2,rd(i(X2),rd(X,i(i(X2)))))) = ld(X2,ld(X2,ld(i(X2),rd(i(X2),rd(X,i(i(X2))))))),
inference(substitution,[status(thm)],[c790]) ).
cnf(c792,plain,
ld(X2,ld(X2,ld(i(X2),rd(i(X2),rd(X,i(i(X2))))))) = ld(mult(X2,X2),mult(X2,rd(i(X2),rd(X,i(i(X2)))))),
inference(symmetry,[status(thm)],[c791]) ).
cnf(c793,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c794,plain,
mult(X2,rd(i(X2),X)) = mult(i(i(X2)),rd(i(X2),X)),
inference(congruence,[status(thm)],[c793]) ).
cnf(c795,plain,
rd(X2,X) = ld(i(X2),rd(i(X2),rd(X,X2))),
inference(symmetry,[status(thm)],[c676]) ).
cnf(c796,plain,
mult(i(X2),rd(X2,X)) = mult(i(X2),ld(i(X2),rd(i(X2),rd(X,X2)))),
inference(congruence,[status(thm)],[c795]) ).
cnf(c797,plain,
mult(i(X2),ld(i(X2),rd(i(X2),rd(X,X2)))) = rd(i(X2),rd(X,X2)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c798,plain,
mult(i(X2),rd(X2,X)) = rd(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c796,c797]) ).
cnf(c799,plain,
mult(i(i(X2)),rd(i(X2),X)) = rd(i(i(X2)),rd(X,i(X2))),
inference(substitution,[status(thm)],[c798]) ).
cnf(c800,plain,
rd(i(i(X2)),rd(X,i(X2))) = rd(X2,rd(X,i(X2))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c801,plain,
mult(i(i(X2)),rd(i(X2),X)) = rd(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c799,c800]) ).
cnf(c802,plain,
mult(X2,rd(i(X2),X)) = rd(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c794,c801]) ).
cnf(c803,plain,
mult(X2,rd(i(X2),rd(X,i(i(X2))))) = rd(X2,rd(rd(X,i(i(X2))),i(X2))),
inference(substitution,[status(thm)],[c802]) ).
cnf(c804,plain,
ld(mult(X2,X2),mult(X2,rd(i(X2),rd(X,i(i(X2)))))) = ld(mult(X2,X2),rd(X2,rd(rd(X,i(i(X2))),i(X2)))),
inference(congruence,[status(thm)],[c803]) ).
cnf(c805,plain,
ld(mult(X2,X2),rd(X2,rd(rd(X,i(i(X2))),i(X2)))) = i(mult(rd(rd(X,i(i(X2))),i(X2)),X2)),
inference(substitution,[status(thm)],[c692]) ).
cnf(c806,plain,
ld(X,mult(ld(i(X),rd(X2,i(X))),X)) = mult(rd(X2,i(X)),X),
inference(substitution,[status(thm)],[c533]) ).
cnf(c807,plain,
mult(rd(X2,i(X)),X) = ld(X,mult(ld(i(X),rd(X2,i(X))),X)),
inference(symmetry,[status(thm)],[c806]) ).
cnf(c808,plain,
mult(ld(i(X),X2),X) = ld(i(X),rd(X2,i(X))),
inference(substitution,[status(thm)],[c629]) ).
cnf(c809,plain,
ld(i(X),rd(X2,i(X))) = mult(ld(i(X),X2),X),
inference(symmetry,[status(thm)],[c808]) ).
cnf(c810,plain,
mult(ld(i(X),rd(X2,i(X))),X) = mult(mult(ld(i(X),X2),X),X),
inference(congruence,[status(thm)],[c809]) ).
cnf(c811,plain,
ld(X,mult(ld(i(X),rd(X2,i(X))),X)) = ld(X,mult(mult(ld(i(X),X2),X),X)),
inference(congruence,[status(thm)],[c810]) ).
cnf(c812,plain,
rd(ld(X,mult(ld(i(X),X2),X)),i(X)) = ld(X,mult(mult(ld(i(X),X2),X),X)),
inference(substitution,[status(thm)],[c716]) ).
cnf(c813,plain,
ld(X,mult(mult(ld(i(X),X2),X),X)) = rd(ld(X,mult(ld(i(X),X2),X)),i(X)),
inference(symmetry,[status(thm)],[c812]) ).
cnf(c814,plain,
ld(X,mult(ld(i(X),X2),X)) = mult(X2,X),
inference(substitution,[status(thm)],[c533]) ).
cnf(c815,plain,
rd(ld(X,mult(ld(i(X),X2),X)),i(X)) = rd(mult(X2,X),i(X)),
inference(congruence,[status(thm)],[c814]) ).
cnf(c816,plain,
ld(X,mult(mult(ld(i(X),X2),X),X)) = rd(mult(X2,X),i(X)),
inference(transitivity,[status(thm)],[c813,c815]) ).
cnf(c817,plain,
ld(X,mult(ld(i(X),rd(X2,i(X))),X)) = rd(mult(X2,X),i(X)),
inference(transitivity,[status(thm)],[c811,c816]) ).
cnf(c818,plain,
mult(rd(X2,i(X)),X) = rd(mult(X2,X),i(X)),
inference(transitivity,[status(thm)],[c807,c817]) ).
cnf(c819,plain,
mult(rd(rd(X,i(i(X2))),i(X2)),X2) = rd(mult(rd(X,i(i(X2))),X2),i(X2)),
inference(substitution,[status(thm)],[c818]) ).
cnf(c820,plain,
i(mult(rd(rd(X,i(i(X2))),i(X2)),X2)) = i(rd(mult(rd(X,i(i(X2))),X2),i(X2))),
inference(congruence,[status(thm)],[c819]) ).
cnf(c821,plain,
rd(X,i(i(X2))) = rd(X,X2),
inference(congruence,[status(thm)],[c117]) ).
cnf(c822,plain,
mult(rd(X,i(i(X2))),X2) = mult(rd(X,X2),X2),
inference(congruence,[status(thm)],[c821]) ).
cnf(c823,plain,
rd(mult(rd(X,i(i(X2))),X2),i(X2)) = rd(mult(rd(X,X2),X2),i(X2)),
inference(congruence,[status(thm)],[c822]) ).
cnf(c824,plain,
i(rd(mult(rd(X,i(i(X2))),X2),i(X2))) = i(rd(mult(rd(X,X2),X2),i(X2))),
inference(congruence,[status(thm)],[c823]) ).
cnf(c825,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c151]) ).
cnf(c826,plain,
rd(mult(rd(X,X2),X2),i(X2)) = rd(X,i(X2)),
inference(congruence,[status(thm)],[c825]) ).
cnf(c827,plain,
i(rd(mult(rd(X,X2),X2),i(X2))) = i(rd(X,i(X2))),
inference(congruence,[status(thm)],[c826]) ).
cnf(c828,plain,
i(rd(mult(rd(X,i(i(X2))),X2),i(X2))) = i(rd(X,i(X2))),
inference(transitivity,[status(thm)],[c824,c827]) ).
cnf(c829,plain,
i(mult(rd(rd(X,i(i(X2))),i(X2)),X2)) = i(rd(X,i(X2))),
inference(transitivity,[status(thm)],[c820,c828]) ).
cnf(c830,plain,
ld(mult(X2,X2),rd(X2,rd(rd(X,i(i(X2))),i(X2)))) = i(rd(X,i(X2))),
inference(transitivity,[status(thm)],[c805,c829]) ).
cnf(c831,plain,
ld(mult(X2,X2),mult(X2,rd(i(X2),rd(X,i(i(X2)))))) = i(rd(X,i(X2))),
inference(transitivity,[status(thm)],[c804,c830]) ).
cnf(c832,plain,
ld(X2,ld(X2,ld(i(X2),rd(i(X2),rd(X,i(i(X2))))))) = i(rd(X,i(X2))),
inference(transitivity,[status(thm)],[c792,c831]) ).
cnf(c833,plain,
ld(X2,ld(X2,rd(i(i(X2)),X))) = i(rd(X,i(X2))),
inference(transitivity,[status(thm)],[c759,c832]) ).
cnf(c834,plain,
ld(X2,ld(X2,rd(X2,X))) = i(rd(X,i(X2))),
inference(transitivity,[status(thm)],[c735,c833]) ).
cnf(c835,plain,
ld(X2,ld(X2,rd(X2,ld(X2,X)))) = i(rd(ld(X2,X),i(X2))),
inference(substitution,[status(thm)],[c834]) ).
cnf(c836,plain,
i(rd(ld(X2,X),i(X2))) = ld(X2,ld(X2,rd(X2,ld(X2,X)))),
inference(symmetry,[status(thm)],[c835]) ).
cnf(c837,plain,
mult(i(rd(X,X2)),X2) = rd(X2,ld(X2,X)),
inference(substitution,[status(thm)],[c472]) ).
cnf(c838,plain,
rd(X2,ld(X2,X)) = mult(i(rd(X,X2)),X2),
inference(symmetry,[status(thm)],[c837]) ).
cnf(c839,plain,
ld(X2,rd(X2,ld(X2,X))) = ld(X2,mult(i(rd(X,X2)),X2)),
inference(congruence,[status(thm)],[c838]) ).
cnf(c840,plain,
ld(X2,rd(X2,ld(X2,X))) = ld(X,X2),
inference(transitivity,[status(thm)],[c839,c445]) ).
cnf(c841,plain,
ld(X2,ld(X2,rd(X2,ld(X2,X)))) = ld(X2,ld(X,X2)),
inference(congruence,[status(thm)],[c840]) ).
cnf(c842,plain,
i(rd(ld(X2,X),i(X2))) = ld(X2,ld(X,X2)),
inference(transitivity,[status(thm)],[c836,c841]) ).
cnf(c843,plain,
i(ld(X2,mult(X,X2))) = ld(X2,ld(X,X2)),
inference(transitivity,[status(thm)],[c731,c842]) ).
cnf(c844,plain,
mult(rd(i(X2),X),X2) = ld(X2,ld(X,X2)),
inference(transitivity,[status(thm)],[c729,c843]) ).
cnf(c845,plain,
mult(rd(i(X2),rd(X,X2)),X2) = ld(X2,ld(rd(X,X2),X2)),
inference(substitution,[status(thm)],[c844]) ).
cnf(c846,plain,
ld(X2,ld(rd(X,X2),X2)) = mult(rd(i(X2),rd(X,X2)),X2),
inference(symmetry,[status(thm)],[c845]) ).
cnf(c847,plain,
rd(ld(X2,ld(rd(X,X2),X2)),i(X2)) = rd(mult(rd(i(X2),rd(X,X2)),X2),i(X2)),
inference(congruence,[status(thm)],[c846]) ).
cnf(c848,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c849,plain,
mult(X2,X) = mult(i(i(X2)),X),
inference(congruence,[status(thm)],[c848]) ).
cnf(c850,plain,
mult(mult(X2,X),mult(X2,X2)) = mult(mult(i(i(X2)),X),mult(X2,X2)),
inference(congruence,[status(thm)],[c849]) ).
cnf(c851,plain,
ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2))) = ld(mult(X2,X2),mult(mult(i(i(X2)),X),mult(X2,X2))),
inference(congruence,[status(thm)],[c850]) ).
cnf(c852,plain,
ld(i(X2),rd(rd(X,i(X2)),i(i(X2)))) = mult(i(i(X2)),X),
inference(substitution,[status(thm)],[c619]) ).
cnf(c853,plain,
mult(i(i(X2)),X) = ld(i(X2),rd(rd(X,i(X2)),i(i(X2)))),
inference(symmetry,[status(thm)],[c852]) ).
cnf(c854,plain,
mult(mult(i(i(X2)),X),mult(X2,X2)) = mult(ld(i(X2),rd(rd(X,i(X2)),i(i(X2)))),mult(X2,X2)),
inference(congruence,[status(thm)],[c853]) ).
cnf(c855,plain,
ld(mult(X2,X2),mult(mult(i(i(X2)),X),mult(X2,X2))) = ld(mult(X2,X2),mult(ld(i(X2),rd(rd(X,i(X2)),i(i(X2)))),mult(X2,X2))),
inference(congruence,[status(thm)],[c854]) ).
cnf(c856,plain,
ld(mult(i(X2),mult(X2,X2)),mult(X,mult(X2,X2))) = ld(mult(X2,X2),mult(ld(i(X2),X),mult(X2,X2))),
inference(substitution,[status(thm)],[c382]) ).
cnf(c857,plain,
ld(mult(X2,X2),mult(ld(i(X2),X),mult(X2,X2))) = ld(mult(i(X2),mult(X2,X2)),mult(X,mult(X2,X2))),
inference(symmetry,[status(thm)],[c856]) ).
cnf(c858,plain,
ld(mult(i(X2),mult(X2,X2)),mult(X,mult(X2,X2))) = ld(X2,mult(X,mult(X2,X2))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c859,plain,
ld(mult(X2,X2),mult(ld(i(X2),X),mult(X2,X2))) = ld(X2,mult(X,mult(X2,X2))),
inference(transitivity,[status(thm)],[c857,c858]) ).
cnf(c860,plain,
ld(mult(X2,X2),mult(ld(i(X2),rd(rd(X,i(X2)),i(i(X2)))),mult(X2,X2))) = ld(X2,mult(rd(rd(X,i(X2)),i(i(X2))),mult(X2,X2))),
inference(substitution,[status(thm)],[c859]) ).
cnf(c861,plain,
rd(rd(X,i(X2)),i(i(X2))) = rd(rd(X,i(X2)),X2),
inference(congruence,[status(thm)],[c117]) ).
cnf(c862,plain,
mult(rd(rd(X,i(X2)),i(i(X2))),mult(X2,X2)) = mult(rd(rd(X,i(X2)),X2),mult(X2,X2)),
inference(congruence,[status(thm)],[c861]) ).
cnf(c863,plain,
ld(X2,mult(rd(rd(X,i(X2)),i(i(X2))),mult(X2,X2))) = ld(X2,mult(rd(rd(X,i(X2)),X2),mult(X2,X2))),
inference(congruence,[status(thm)],[c862]) ).
cnf(c864,plain,
mult(rd(X2,X3),mult(X3,X)) = mult(X3,mult(ld(X3,X2),X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c865,plain,
ld(X3,mult(rd(X2,X3),mult(X3,X))) = ld(X3,mult(X3,mult(ld(X3,X2),X))),
inference(congruence,[status(thm)],[c864]) ).
cnf(c866,plain,
ld(X3,mult(X3,mult(ld(X3,X2),X))) = mult(ld(X3,X2),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c867,plain,
ld(X3,mult(rd(X2,X3),mult(X3,X))) = mult(ld(X3,X2),X),
inference(transitivity,[status(thm)],[c865,c866]) ).
cnf(c868,plain,
ld(X2,mult(rd(rd(X,i(X2)),X2),mult(X2,X2))) = mult(ld(X2,rd(X,i(X2))),X2),
inference(substitution,[status(thm)],[c867]) ).
cnf(c869,plain,
mult(i(X2),mult(X,X2)) = mult(rd(mult(i(X2),X),i(X2)),mult(i(X2),X2)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c870,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c871,plain,
mult(rd(mult(i(X2),X),i(X2)),mult(i(X2),X2)) = mult(rd(mult(i(X2),X),i(X2)),unit),
inference(congruence,[status(thm)],[c870]) ).
cnf(c872,plain,
mult(rd(mult(i(X2),X),i(X2)),unit) = rd(mult(i(X2),X),i(X2)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c873,plain,
rd(mult(i(X2),X),i(X2)) = ld(i(i(X2)),rd(X,i(X2))),
inference(substitution,[status(thm)],[c336]) ).
cnf(c874,plain,
ld(i(i(X2)),rd(X,i(X2))) = ld(X2,rd(X,i(X2))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c875,plain,
rd(mult(i(X2),X),i(X2)) = ld(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c873,c874]) ).
cnf(c876,plain,
mult(rd(mult(i(X2),X),i(X2)),unit) = ld(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c872,c875]) ).
cnf(c877,plain,
mult(rd(mult(i(X2),X),i(X2)),mult(i(X2),X2)) = ld(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c871,c876]) ).
cnf(c878,plain,
mult(i(X2),mult(X,X2)) = ld(X2,rd(X,i(X2))),
inference(transitivity,[status(thm)],[c869,c877]) ).
cnf(c879,plain,
ld(X2,rd(X,i(X2))) = mult(i(X2),mult(X,X2)),
inference(symmetry,[status(thm)],[c878]) ).
cnf(c880,plain,
mult(ld(X2,rd(X,i(X2))),X2) = mult(mult(i(X2),mult(X,X2)),X2),
inference(congruence,[status(thm)],[c879]) ).
cnf(c881,plain,
mult(mult(i(X2),mult(X,X2)),X2) = ld(X2,mult(mult(X,X2),X2)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c882,plain,
mult(ld(X2,rd(X,i(X2))),X2) = ld(X2,mult(mult(X,X2),X2)),
inference(transitivity,[status(thm)],[c880,c881]) ).
cnf(c883,plain,
ld(X2,rd(rd(mult(X,mult(X2,X2)),X2),i(X2))) = mult(i(X2),mult(X,mult(X2,X2))),
inference(substitution,[status(thm)],[c619]) ).
cnf(c884,plain,
mult(i(X2),mult(X,mult(X2,X2))) = ld(X2,rd(rd(mult(X,mult(X2,X2)),X2),i(X2))),
inference(symmetry,[status(thm)],[c883]) ).
cnf(c885,plain,
mult(X,mult(i(X),X2)) = rd(rd(X2,i(X)),X),
inference(substitution,[status(thm)],[c322]) ).
cnf(c886,plain,
rd(rd(X2,i(X)),X) = mult(X,mult(i(X),X2)),
inference(symmetry,[status(thm)],[c885]) ).
cnf(c887,plain,
rd(mult(i(X),rd(X2,i(i(X)))),i(X)) = mult(i(X),X2),
inference(substitution,[status(thm)],[c308]) ).
cnf(c888,plain,
mult(i(X),X2) = rd(mult(i(X),rd(X2,i(i(X)))),i(X)),
inference(symmetry,[status(thm)],[c887]) ).
cnf(c889,plain,
mult(X,mult(i(X),X2)) = mult(X,rd(mult(i(X),rd(X2,i(i(X)))),i(X))),
inference(congruence,[status(thm)],[c888]) ).
cnf(c890,plain,
mult(X,rd(mult(i(X),rd(X2,i(i(X)))),i(X))) = rd(ld(i(X),mult(i(X),rd(X2,i(i(X))))),i(X)),
inference(substitution,[status(thm)],[c414]) ).
cnf(c891,plain,
ld(i(X),mult(i(X),rd(X2,i(i(X))))) = rd(X2,i(i(X))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c892,plain,
rd(ld(i(X),mult(i(X),rd(X2,i(i(X))))),i(X)) = rd(rd(X2,i(i(X))),i(X)),
inference(congruence,[status(thm)],[c891]) ).
cnf(c893,plain,
rd(X2,i(i(X))) = rd(X2,X),
inference(congruence,[status(thm)],[c117]) ).
cnf(c894,plain,
rd(rd(X2,i(i(X))),i(X)) = rd(rd(X2,X),i(X)),
inference(congruence,[status(thm)],[c893]) ).
cnf(c895,plain,
rd(ld(i(X),mult(i(X),rd(X2,i(i(X))))),i(X)) = rd(rd(X2,X),i(X)),
inference(transitivity,[status(thm)],[c892,c894]) ).
cnf(c896,plain,
mult(X,rd(mult(i(X),rd(X2,i(i(X)))),i(X))) = rd(rd(X2,X),i(X)),
inference(transitivity,[status(thm)],[c890,c895]) ).
cnf(c897,plain,
mult(X,mult(i(X),X2)) = rd(rd(X2,X),i(X)),
inference(transitivity,[status(thm)],[c889,c896]) ).
cnf(c898,plain,
rd(rd(X2,i(X)),X) = rd(rd(X2,X),i(X)),
inference(transitivity,[status(thm)],[c886,c897]) ).
cnf(c899,plain,
rd(rd(mult(X,mult(X2,X2)),i(X2)),X2) = rd(rd(mult(X,mult(X2,X2)),X2),i(X2)),
inference(substitution,[status(thm)],[c898]) ).
cnf(c900,plain,
rd(rd(mult(X,mult(X2,X2)),X2),i(X2)) = rd(rd(mult(X,mult(X2,X2)),i(X2)),X2),
inference(symmetry,[status(thm)],[c899]) ).
cnf(c901,plain,
ld(X2,rd(rd(mult(X,mult(X2,X2)),X2),i(X2))) = ld(X2,rd(rd(mult(X,mult(X2,X2)),i(X2)),X2)),
inference(congruence,[status(thm)],[c900]) ).
cnf(c902,plain,
mult(mult(rd(X3,X2),X),X2) = mult(mult(rd(X3,X2),X2),ld(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c903,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c151]) ).
cnf(c904,plain,
mult(mult(rd(X3,X2),X2),ld(X2,mult(X,X2))) = mult(X3,ld(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c903]) ).
cnf(c905,plain,
mult(mult(rd(X3,X2),X),X2) = mult(X3,ld(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c902,c904]) ).
cnf(c906,plain,
mult(X3,ld(X2,mult(X,X2))) = mult(mult(rd(X3,X2),X),X2),
inference(symmetry,[status(thm)],[c905]) ).
cnf(c907,plain,
rd(mult(X3,ld(X2,mult(X,X2))),X2) = rd(mult(mult(rd(X3,X2),X),X2),X2),
inference(congruence,[status(thm)],[c906]) ).
cnf(c908,plain,
rd(mult(mult(rd(X3,X2),X),X2),X2) = mult(rd(X3,X2),X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c909,plain,
rd(mult(X3,ld(X2,mult(X,X2))),X2) = mult(rd(X3,X2),X),
inference(transitivity,[status(thm)],[c907,c908]) ).
cnf(c910,plain,
rd(mult(X2,ld(i(X),mult(mult(X,X),i(X)))),i(X)) = mult(rd(X2,i(X)),mult(X,X)),
inference(substitution,[status(thm)],[c909]) ).
cnf(c911,plain,
mult(rd(X2,i(X)),mult(X,X)) = rd(mult(X2,ld(i(X),mult(mult(X,X),i(X)))),i(X)),
inference(symmetry,[status(thm)],[c910]) ).
cnf(c912,plain,
ld(i(X),mult(mult(X,X),i(X))) = ld(i(X),X),
inference(congruence,[status(thm)],[c120]) ).
cnf(c913,plain,
mult(X2,ld(i(X),mult(mult(X,X),i(X)))) = mult(X2,ld(i(X),X)),
inference(congruence,[status(thm)],[c912]) ).
cnf(c914,plain,
rd(mult(X2,ld(i(X),mult(mult(X,X),i(X)))),i(X)) = rd(mult(X2,ld(i(X),X)),i(X)),
inference(congruence,[status(thm)],[c913]) ).
cnf(c915,plain,
ld(i(X),X) = mult(X,X),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c916,plain,
mult(X2,ld(i(X),X)) = mult(X2,mult(X,X)),
inference(congruence,[status(thm)],[c915]) ).
cnf(c917,plain,
rd(mult(X2,ld(i(X),X)),i(X)) = rd(mult(X2,mult(X,X)),i(X)),
inference(congruence,[status(thm)],[c916]) ).
cnf(c918,plain,
rd(mult(X2,ld(i(X),mult(mult(X,X),i(X)))),i(X)) = rd(mult(X2,mult(X,X)),i(X)),
inference(transitivity,[status(thm)],[c914,c917]) ).
cnf(c919,plain,
mult(rd(X2,i(X)),mult(X,X)) = rd(mult(X2,mult(X,X)),i(X)),
inference(transitivity,[status(thm)],[c911,c918]) ).
cnf(c920,plain,
mult(rd(X,i(X2)),mult(X2,X2)) = rd(mult(X,mult(X2,X2)),i(X2)),
inference(substitution,[status(thm)],[c919]) ).
cnf(c921,plain,
rd(mult(X,mult(X2,X2)),i(X2)) = mult(rd(X,i(X2)),mult(X2,X2)),
inference(symmetry,[status(thm)],[c920]) ).
cnf(c922,plain,
rd(rd(mult(X,mult(X2,X2)),i(X2)),X2) = rd(mult(rd(X,i(X2)),mult(X2,X2)),X2),
inference(congruence,[status(thm)],[c921]) ).
cnf(c923,plain,
ld(X2,rd(rd(mult(X,mult(X2,X2)),i(X2)),X2)) = ld(X2,rd(mult(rd(X,i(X2)),mult(X2,X2)),X2)),
inference(congruence,[status(thm)],[c922]) ).
cnf(c924,plain,
mult(rd(X,X2),mult(X2,X2)) = mult(X2,mult(ld(X2,X),X2)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c925,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c926,plain,
mult(X,X2) = mult(X,i(i(X2))),
inference(congruence,[status(thm)],[c925]) ).
cnf(c927,plain,
mult(X2,mult(X,X2)) = mult(X2,mult(X,i(i(X2)))),
inference(congruence,[status(thm)],[c926]) ).
cnf(c928,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c929,plain,
mult(X2,mult(X,i(i(X2)))) = mult(i(i(X2)),mult(X,i(i(X2)))),
inference(congruence,[status(thm)],[c928]) ).
cnf(c930,plain,
mult(X2,ld(X2,mult(ld(i(X2),X),X2))) = mult(ld(i(X2),X),X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c931,plain,
mult(ld(i(X2),X),X2) = mult(X2,ld(X2,mult(ld(i(X2),X),X2))),
inference(symmetry,[status(thm)],[c930]) ).
cnf(c932,plain,
mult(X2,ld(X2,mult(ld(i(X2),X),X2))) = mult(X2,mult(X,X2)),
inference(congruence,[status(thm)],[c533]) ).
cnf(c933,plain,
mult(ld(i(X2),X),X2) = mult(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c931,c932]) ).
cnf(c934,plain,
mult(ld(i(i(X2)),X),i(X2)) = mult(i(X2),mult(X,i(X2))),
inference(substitution,[status(thm)],[c933]) ).
cnf(c935,plain,
mult(i(X2),mult(X,i(X2))) = mult(ld(i(i(X2)),X),i(X2)),
inference(symmetry,[status(thm)],[c934]) ).
cnf(c936,plain,
ld(i(i(X2)),X) = ld(X2,X),
inference(congruence,[status(thm)],[c117]) ).
cnf(c937,plain,
mult(ld(i(i(X2)),X),i(X2)) = mult(ld(X2,X),i(X2)),
inference(congruence,[status(thm)],[c936]) ).
cnf(c938,plain,
mult(ld(i(i(X2)),X),i(X2)) = ld(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c937,c524]) ).
cnf(c939,plain,
mult(i(X2),mult(X,i(X2))) = ld(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c935,c938]) ).
cnf(c940,plain,
mult(i(i(X2)),mult(X,i(i(X2)))) = ld(i(X2),rd(X,i(X2))),
inference(substitution,[status(thm)],[c939]) ).
cnf(c941,plain,
mult(X2,mult(X,i(i(X2)))) = ld(i(X2),rd(X,i(X2))),
inference(transitivity,[status(thm)],[c929,c940]) ).
cnf(c942,plain,
mult(X2,mult(X,X2)) = ld(i(X2),rd(X,i(X2))),
inference(transitivity,[status(thm)],[c927,c941]) ).
cnf(c943,plain,
mult(X2,mult(ld(X2,X),X2)) = ld(i(X2),rd(ld(X2,X),i(X2))),
inference(substitution,[status(thm)],[c942]) ).
cnf(c944,plain,
ld(i(X2),rd(ld(X2,X),i(X2))) = ld(i(X2),ld(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c716]) ).
cnf(c945,plain,
ld(i(X2),ld(X2,mult(X,X2))) = ld(X2,ld(i(X2),mult(X,X2))),
inference(substitution,[status(thm)],[c575]) ).
cnf(c946,plain,
ld(i(X2),rd(ld(X2,X),i(X2))) = ld(X2,ld(i(X2),mult(X,X2))),
inference(transitivity,[status(thm)],[c944,c945]) ).
cnf(c947,plain,
mult(X2,mult(ld(X2,X),X2)) = ld(X2,ld(i(X2),mult(X,X2))),
inference(transitivity,[status(thm)],[c943,c946]) ).
cnf(c948,plain,
mult(rd(X,X2),mult(X2,X2)) = ld(X2,ld(i(X2),mult(X,X2))),
inference(transitivity,[status(thm)],[c924,c947]) ).
cnf(c949,plain,
mult(rd(X2,X),mult(X,X)) = ld(X,ld(i(X),mult(X2,X))),
inference(substitution,[status(thm)],[c948]) ).
cnf(c950,plain,
rd(mult(X,X2),X2) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c951,plain,
X = rd(mult(X,X2),X2),
inference(symmetry,[status(thm)],[c950]) ).
cnf(c952,plain,
mult(X,mult(X2,X2)) = mult(rd(mult(X,X2),X2),mult(X2,X2)),
inference(congruence,[status(thm)],[c951]) ).
cnf(c953,plain,
rd(mult(X,mult(X2,X2)),X2) = rd(mult(rd(mult(X,X2),X2),mult(X2,X2)),X2),
inference(congruence,[status(thm)],[c952]) ).
cnf(c954,plain,
mult(rd(X2,X),mult(X,X)) = ld(X,ld(i(X),mult(X2,X))),
inference(substitution,[status(thm)],[c948]) ).
cnf(c955,plain,
rd(mult(rd(X2,X),mult(X,X)),X) = rd(ld(X,ld(i(X),mult(X2,X))),X),
inference(congruence,[status(thm)],[c954]) ).
cnf(c956,plain,
rd(ld(X,ld(i(X),mult(X2,X))),X) = mult(mult(X2,X),i(X)),
inference(substitution,[status(thm)],[c557]) ).
cnf(c957,plain,
rd(ld(X,ld(i(X),mult(X2,X))),X) = ld(X,ld(i(X),X2)),
inference(transitivity,[status(thm)],[c956,c541]) ).
cnf(c958,plain,
rd(mult(rd(X2,X),mult(X,X)),X) = ld(X,ld(i(X),X2)),
inference(transitivity,[status(thm)],[c955,c957]) ).
cnf(c959,plain,
rd(mult(rd(mult(X,X2),X2),mult(X2,X2)),X2) = ld(X2,ld(i(X2),mult(X,X2))),
inference(substitution,[status(thm)],[c958]) ).
cnf(c960,plain,
rd(mult(X,mult(X2,X2)),X2) = ld(X2,ld(i(X2),mult(X,X2))),
inference(transitivity,[status(thm)],[c953,c959]) ).
cnf(c961,plain,
rd(mult(X2,mult(X,X)),X) = ld(X,ld(i(X),mult(X2,X))),
inference(substitution,[status(thm)],[c960]) ).
cnf(c962,plain,
ld(X,ld(i(X),mult(X2,X))) = rd(mult(X2,mult(X,X)),X),
inference(symmetry,[status(thm)],[c961]) ).
cnf(c963,plain,
mult(rd(X2,X),mult(X,X)) = rd(mult(X2,mult(X,X)),X),
inference(transitivity,[status(thm)],[c949,c962]) ).
cnf(c964,plain,
mult(rd(X,X2),mult(X2,X2)) = rd(mult(X,mult(X2,X2)),X2),
inference(substitution,[status(thm)],[c963]) ).
cnf(c965,plain,
rd(mult(X,mult(X2,X2)),X2) = mult(rd(X,X2),mult(X2,X2)),
inference(symmetry,[status(thm)],[c964]) ).
cnf(c966,plain,
ld(X2,rd(mult(X,mult(X2,X2)),X2)) = ld(X2,mult(rd(X,X2),mult(X2,X2))),
inference(congruence,[status(thm)],[c965]) ).
cnf(c967,plain,
mult(rd(X,X2),mult(X2,X2)) = mult(X2,mult(ld(X2,X),X2)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c968,plain,
ld(X2,mult(rd(X,X2),mult(X2,X2))) = ld(X2,mult(X2,mult(ld(X2,X),X2))),
inference(congruence,[status(thm)],[c967]) ).
cnf(c969,plain,
ld(X2,mult(X2,mult(ld(X2,X),X2))) = mult(ld(X2,X),X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c970,plain,
ld(X2,mult(rd(X,X2),mult(X2,X2))) = mult(ld(X2,X),X2),
inference(transitivity,[status(thm)],[c968,c969]) ).
cnf(c971,plain,
ld(X2,rd(mult(X,mult(X2,X2)),X2)) = mult(ld(X2,X),X2),
inference(transitivity,[status(thm)],[c966,c970]) ).
cnf(c972,plain,
ld(X2,rd(mult(rd(X,i(X2)),mult(X2,X2)),X2)) = mult(ld(X2,rd(X,i(X2))),X2),
inference(substitution,[status(thm)],[c971]) ).
cnf(c973,plain,
ld(X2,rd(mult(rd(X,i(X2)),mult(X2,X2)),X2)) = ld(X2,mult(mult(X,X2),X2)),
inference(transitivity,[status(thm)],[c972,c882]) ).
cnf(c974,plain,
ld(X2,rd(rd(mult(X,mult(X2,X2)),i(X2)),X2)) = ld(X2,mult(mult(X,X2),X2)),
inference(transitivity,[status(thm)],[c923,c973]) ).
cnf(c975,plain,
ld(X2,rd(rd(mult(X,mult(X2,X2)),X2),i(X2))) = ld(X2,mult(mult(X,X2),X2)),
inference(transitivity,[status(thm)],[c901,c974]) ).
cnf(c976,plain,
mult(i(X2),mult(X,mult(X2,X2))) = ld(X2,mult(mult(X,X2),X2)),
inference(transitivity,[status(thm)],[c884,c975]) ).
cnf(c977,plain,
ld(X2,mult(mult(X,X2),X2)) = mult(i(X2),mult(X,mult(X2,X2))),
inference(symmetry,[status(thm)],[c976]) ).
cnf(c978,plain,
mult(ld(X2,rd(X,i(X2))),X2) = mult(i(X2),mult(X,mult(X2,X2))),
inference(transitivity,[status(thm)],[c882,c977]) ).
cnf(c979,plain,
ld(X2,mult(rd(rd(X,i(X2)),X2),mult(X2,X2))) = mult(i(X2),mult(X,mult(X2,X2))),
inference(transitivity,[status(thm)],[c868,c978]) ).
cnf(c980,plain,
ld(X2,mult(rd(rd(X,i(X2)),i(i(X2))),mult(X2,X2))) = mult(i(X2),mult(X,mult(X2,X2))),
inference(transitivity,[status(thm)],[c863,c979]) ).
cnf(c981,plain,
ld(mult(X2,X2),mult(ld(i(X2),rd(rd(X,i(X2)),i(i(X2)))),mult(X2,X2))) = mult(i(X2),mult(X,mult(X2,X2))),
inference(transitivity,[status(thm)],[c860,c980]) ).
cnf(c982,plain,
ld(mult(X2,X2),mult(mult(i(i(X2)),X),mult(X2,X2))) = mult(i(X2),mult(X,mult(X2,X2))),
inference(transitivity,[status(thm)],[c855,c981]) ).
cnf(c983,plain,
ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2))) = mult(i(X2),mult(X,mult(X2,X2))),
inference(transitivity,[status(thm)],[c851,c982]) ).
cnf(c984,plain,
mult(i(X2),mult(X,mult(X2,X2))) = ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2))),
inference(symmetry,[status(thm)],[c983]) ).
cnf(c985,plain,
i(i(mult(X2,X))) = mult(X2,X),
inference(substitution,[status(thm)],[c117]) ).
cnf(c986,plain,
mult(X2,X) = i(i(mult(X2,X))),
inference(symmetry,[status(thm)],[c985]) ).
cnf(c987,plain,
mult(mult(X2,X),mult(X2,X2)) = mult(i(i(mult(X2,X))),mult(X2,X2)),
inference(congruence,[status(thm)],[c986]) ).
cnf(c988,plain,
ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2))) = ld(mult(X2,X2),mult(i(i(mult(X2,X))),mult(X2,X2))),
inference(congruence,[status(thm)],[c987]) ).
cnf(c989,plain,
ld(mult(i(mult(X2,X)),mult(X2,X2)),mult(X2,X2)) = ld(mult(X2,X2),mult(i(i(mult(X2,X))),mult(X2,X2))),
inference(substitution,[status(thm)],[c440]) ).
cnf(c990,plain,
ld(mult(X2,X2),mult(i(i(mult(X2,X))),mult(X2,X2))) = ld(mult(i(mult(X2,X)),mult(X2,X2)),mult(X2,X2)),
inference(symmetry,[status(thm)],[c989]) ).
cnf(c991,plain,
rd(mult(X2,X2),ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2)))) = mult(i(mult(X2,X)),mult(X2,X2)),
inference(substitution,[status(thm)],[c466]) ).
cnf(c992,plain,
mult(i(mult(X2,X)),mult(X2,X2)) = rd(mult(X2,X2),ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2)))),
inference(symmetry,[status(thm)],[c991]) ).
cnf(c993,plain,
rd(ld(mult(X2,X2),mult(X2,X)),i(mult(X2,X2))) = ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2))),
inference(substitution,[status(thm)],[c716]) ).
cnf(c994,plain,
ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2))) = rd(ld(mult(X2,X2),mult(X2,X)),i(mult(X2,X2))),
inference(symmetry,[status(thm)],[c993]) ).
cnf(c995,plain,
rd(mult(X2,X2),ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2)))) = rd(mult(X2,X2),rd(ld(mult(X2,X2),mult(X2,X)),i(mult(X2,X2)))),
inference(congruence,[status(thm)],[c994]) ).
cnf(c996,plain,
mult(i(mult(mult(X2,X2),X)),mult(X2,X2)) = rd(mult(X2,X2),rd(X,i(mult(X2,X2)))),
inference(substitution,[status(thm)],[c652]) ).
cnf(c997,plain,
rd(mult(X2,X2),rd(X,i(mult(X2,X2)))) = mult(i(mult(mult(X2,X2),X)),mult(X2,X2)),
inference(symmetry,[status(thm)],[c996]) ).
cnf(c998,plain,
ld(rd(X2,mult(X,mult(X2,X2))),X2) = mult(X,mult(X2,X2)),
inference(substitution,[status(thm)],[c205]) ).
cnf(c999,plain,
mult(X,mult(X2,X2)) = ld(rd(X2,mult(X,mult(X2,X2))),X2),
inference(symmetry,[status(thm)],[c998]) ).
cnf(c1000,plain,
ld(i(X2),rd(i(X2),rd(mult(X,mult(X2,X2)),X2))) = rd(X2,mult(X,mult(X2,X2))),
inference(substitution,[status(thm)],[c676]) ).
cnf(c1001,plain,
rd(X2,mult(X,mult(X2,X2))) = ld(i(X2),rd(i(X2),rd(mult(X,mult(X2,X2)),X2))),
inference(symmetry,[status(thm)],[c1000]) ).
cnf(c1002,plain,
rd(ld(X2,mult(i(rd(X,X2)),X2)),X2) = mult(i(X2),i(rd(X,X2))),
inference(substitution,[status(thm)],[c179]) ).
cnf(c1003,plain,
mult(i(X2),i(rd(X,X2))) = rd(ld(X2,mult(i(rd(X,X2)),X2)),X2),
inference(symmetry,[status(thm)],[c1002]) ).
cnf(c1004,plain,
rd(ld(X2,mult(i(rd(X,X2)),X2)),X2) = rd(ld(X,X2),X2),
inference(congruence,[status(thm)],[c445]) ).
cnf(c1005,plain,
mult(rd(rd(ld(X2,X),X),X),X) = rd(ld(X2,X),X),
inference(substitution,[status(thm)],[c151]) ).
cnf(c1006,plain,
rd(ld(X2,X),X) = mult(rd(rd(ld(X2,X),X),X),X),
inference(symmetry,[status(thm)],[c1005]) ).
cnf(c1007,plain,
ld(i(X2),mult(i(X2),i(ld(i(X2),rd(X2,X))))) = i(ld(i(X2),rd(X2,X))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c1008,plain,
i(ld(i(X2),rd(X2,X))) = ld(i(X2),mult(i(X2),i(ld(i(X2),rd(X2,X))))),
inference(symmetry,[status(thm)],[c1007]) ).
cnf(c1009,plain,
rd(X2,ld(X2,mult(i(rd(X2,X)),X2))) = mult(rd(X2,X),X2),
inference(substitution,[status(thm)],[c464]) ).
cnf(c1010,plain,
mult(rd(X2,X),X2) = rd(X2,ld(X2,mult(i(rd(X2,X)),X2))),
inference(symmetry,[status(thm)],[c1009]) ).
cnf(c1011,plain,
ld(i(i(X2)),rd(i(i(X2)),rd(ld(X2,X),i(X2)))) = rd(i(X2),ld(X2,X)),
inference(substitution,[status(thm)],[c676]) ).
cnf(c1012,plain,
rd(i(X2),ld(X2,X)) = ld(i(i(X2)),rd(i(i(X2)),rd(ld(X2,X),i(X2)))),
inference(symmetry,[status(thm)],[c1011]) ).
cnf(c1013,plain,
rd(i(i(X2)),rd(ld(X2,X),i(X2))) = rd(i(i(X2)),ld(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c716]) ).
cnf(c1014,plain,
ld(i(i(X2)),rd(i(i(X2)),rd(ld(X2,X),i(X2)))) = ld(i(i(X2)),rd(i(i(X2)),ld(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c1013]) ).
cnf(c1015,plain,
ld(i(i(X2)),rd(i(i(X2)),ld(X2,mult(X,X2)))) = ld(X2,rd(i(i(X2)),ld(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1016,plain,
rd(i(i(X2)),ld(X2,mult(X,X2))) = rd(X2,ld(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1017,plain,
ld(X2,rd(i(i(X2)),ld(X2,mult(X,X2)))) = ld(X2,rd(X2,ld(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c1016]) ).
cnf(c1018,plain,
ld(X2,rd(X2,ld(X2,mult(X,X2)))) = ld(mult(X,X2),X2),
inference(substitution,[status(thm)],[c840]) ).
cnf(c1019,plain,
ld(mult(X,X2),X2) = ld(X2,mult(i(X),X2)),
inference(substitution,[status(thm)],[c440]) ).
cnf(c1020,plain,
ld(X2,rd(X2,ld(X2,mult(X,X2)))) = ld(X2,mult(i(X),X2)),
inference(transitivity,[status(thm)],[c1018,c1019]) ).
cnf(c1021,plain,
ld(X2,rd(i(i(X2)),ld(X2,mult(X,X2)))) = ld(X2,mult(i(X),X2)),
inference(transitivity,[status(thm)],[c1017,c1020]) ).
cnf(c1022,plain,
ld(i(i(X2)),rd(i(i(X2)),ld(X2,mult(X,X2)))) = ld(X2,mult(i(X),X2)),
inference(transitivity,[status(thm)],[c1015,c1021]) ).
cnf(c1023,plain,
ld(i(i(X2)),rd(i(i(X2)),rd(ld(X2,X),i(X2)))) = ld(X2,mult(i(X),X2)),
inference(transitivity,[status(thm)],[c1014,c1022]) ).
cnf(c1024,plain,
rd(i(X2),ld(X2,X)) = ld(X2,mult(i(X),X2)),
inference(transitivity,[status(thm)],[c1012,c1023]) ).
cnf(c1025,plain,
rd(i(X2),ld(X2,rd(X2,X))) = ld(X2,mult(i(rd(X2,X)),X2)),
inference(substitution,[status(thm)],[c1024]) ).
cnf(c1026,plain,
ld(X2,mult(i(rd(X2,X)),X2)) = rd(i(X2),ld(X2,rd(X2,X))),
inference(symmetry,[status(thm)],[c1025]) ).
cnf(c1027,plain,
rd(X2,ld(X2,mult(i(rd(X2,X)),X2))) = rd(X2,rd(i(X2),ld(X2,rd(X2,X)))),
inference(congruence,[status(thm)],[c1026]) ).
cnf(c1028,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c1029,plain,
ld(X2,rd(X2,X)) = ld(i(i(X2)),rd(X2,X)),
inference(congruence,[status(thm)],[c1028]) ).
cnf(c1030,plain,
rd(i(X2),ld(X2,rd(X2,X))) = rd(i(X2),ld(i(i(X2)),rd(X2,X))),
inference(congruence,[status(thm)],[c1029]) ).
cnf(c1031,plain,
rd(X2,rd(i(X2),ld(X2,rd(X2,X)))) = rd(X2,rd(i(X2),ld(i(i(X2)),rd(X2,X)))),
inference(congruence,[status(thm)],[c1030]) ).
cnf(c1032,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c1033,plain,
rd(X2,X) = rd(i(i(X2)),X),
inference(congruence,[status(thm)],[c1032]) ).
cnf(c1034,plain,
ld(i(i(X2)),rd(X2,X)) = ld(i(i(X2)),rd(i(i(X2)),X)),
inference(congruence,[status(thm)],[c1033]) ).
cnf(c1035,plain,
rd(i(X2),ld(i(i(X2)),rd(X2,X))) = rd(i(X2),ld(i(i(X2)),rd(i(i(X2)),X))),
inference(congruence,[status(thm)],[c1034]) ).
cnf(c1036,plain,
rd(X2,rd(i(X2),ld(i(i(X2)),rd(X2,X)))) = rd(X2,rd(i(X2),ld(i(i(X2)),rd(i(i(X2)),X)))),
inference(congruence,[status(thm)],[c1035]) ).
cnf(c1037,plain,
ld(i(X2),rd(i(X2),rd(mult(X,X2),X2))) = rd(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c676]) ).
cnf(c1038,plain,
rd(X2,mult(X,X2)) = ld(i(X2),rd(i(X2),rd(mult(X,X2),X2))),
inference(symmetry,[status(thm)],[c1037]) ).
cnf(c1039,plain,
rd(mult(X,X2),X2) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c1040,plain,
rd(i(X2),rd(mult(X,X2),X2)) = rd(i(X2),X),
inference(congruence,[status(thm)],[c1039]) ).
cnf(c1041,plain,
ld(i(X2),rd(i(X2),rd(mult(X,X2),X2))) = ld(i(X2),rd(i(X2),X)),
inference(congruence,[status(thm)],[c1040]) ).
cnf(c1042,plain,
rd(X2,mult(X,X2)) = ld(i(X2),rd(i(X2),X)),
inference(transitivity,[status(thm)],[c1038,c1041]) ).
cnf(c1043,plain,
rd(i(X2),mult(X,i(X2))) = ld(i(i(X2)),rd(i(i(X2)),X)),
inference(substitution,[status(thm)],[c1042]) ).
cnf(c1044,plain,
ld(i(i(X2)),rd(i(i(X2)),X)) = rd(i(X2),mult(X,i(X2))),
inference(symmetry,[status(thm)],[c1043]) ).
cnf(c1045,plain,
rd(i(X2),ld(i(i(X2)),rd(i(i(X2)),X))) = rd(i(X2),rd(i(X2),mult(X,i(X2)))),
inference(congruence,[status(thm)],[c1044]) ).
cnf(c1046,plain,
rd(X2,rd(i(X2),ld(i(i(X2)),rd(i(i(X2)),X)))) = rd(X2,rd(i(X2),rd(i(X2),mult(X,i(X2))))),
inference(congruence,[status(thm)],[c1045]) ).
cnf(c1047,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c1048,plain,
rd(X2,rd(i(X2),rd(i(X2),mult(X,i(X2))))) = rd(i(i(X2)),rd(i(X2),rd(i(X2),mult(X,i(X2))))),
inference(congruence,[status(thm)],[c1047]) ).
cnf(c1049,plain,
rd(ld(i(X2),rd(i(X2),mult(X,i(X2)))),i(X2)) = rd(i(i(X2)),rd(i(X2),rd(i(X2),mult(X,i(X2))))),
inference(substitution,[status(thm)],[c679]) ).
cnf(c1050,plain,
rd(i(i(X2)),rd(i(X2),rd(i(X2),mult(X,i(X2))))) = rd(ld(i(X2),rd(i(X2),mult(X,i(X2)))),i(X2)),
inference(symmetry,[status(thm)],[c1049]) ).
cnf(c1051,plain,
rd(i(X2),ld(i(X2),mult(ld(X2,X),i(X2)))) = mult(i(ld(X2,X)),i(X2)),
inference(substitution,[status(thm)],[c466]) ).
cnf(c1052,plain,
mult(i(ld(X2,X)),i(X2)) = rd(i(X2),ld(i(X2),mult(ld(X2,X),i(X2)))),
inference(symmetry,[status(thm)],[c1051]) ).
cnf(c1053,plain,
ld(i(X2),mult(ld(X2,X),i(X2))) = ld(i(X2),ld(X2,rd(X,X2))),
inference(congruence,[status(thm)],[c524]) ).
cnf(c1054,plain,
rd(i(X2),ld(i(X2),mult(ld(X2,X),i(X2)))) = rd(i(X2),ld(i(X2),ld(X2,rd(X,X2)))),
inference(congruence,[status(thm)],[c1053]) ).
cnf(c1055,plain,
rd(i(X2),ld(i(X2),ld(X2,rd(X,X2)))) = rd(i(X2),mult(X,i(X2))),
inference(congruence,[status(thm)],[c571]) ).
cnf(c1056,plain,
rd(i(X2),ld(i(X2),mult(ld(X2,X),i(X2)))) = rd(i(X2),mult(X,i(X2))),
inference(transitivity,[status(thm)],[c1054,c1055]) ).
cnf(c1057,plain,
mult(i(ld(X2,X)),i(X2)) = rd(i(X2),mult(X,i(X2))),
inference(transitivity,[status(thm)],[c1052,c1056]) ).
cnf(c1058,plain,
rd(i(X2),mult(X,i(X2))) = mult(i(ld(X2,X)),i(X2)),
inference(symmetry,[status(thm)],[c1057]) ).
cnf(c1059,plain,
ld(i(X2),rd(i(X2),mult(X,i(X2)))) = ld(i(X2),mult(i(ld(X2,X)),i(X2))),
inference(congruence,[status(thm)],[c1058]) ).
cnf(c1060,plain,
rd(ld(i(X2),rd(i(X2),mult(X,i(X2)))),i(X2)) = rd(ld(i(X2),mult(i(ld(X2,X)),i(X2))),i(X2)),
inference(congruence,[status(thm)],[c1059]) ).
cnf(c1061,plain,
rd(ld(i(X2),mult(i(ld(X2,X)),i(X2))),i(X2)) = mult(i(i(X2)),i(ld(X2,X))),
inference(substitution,[status(thm)],[c179]) ).
cnf(c1062,plain,
mult(i(i(X2)),i(ld(X2,X))) = mult(X2,i(ld(X2,X))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1063,plain,
rd(ld(i(X2),mult(i(ld(X2,X)),i(X2))),i(X2)) = mult(X2,i(ld(X2,X))),
inference(transitivity,[status(thm)],[c1061,c1062]) ).
cnf(c1064,plain,
rd(ld(i(X2),rd(i(X2),mult(X,i(X2)))),i(X2)) = mult(X2,i(ld(X2,X))),
inference(transitivity,[status(thm)],[c1060,c1063]) ).
cnf(c1065,plain,
rd(i(i(X2)),rd(i(X2),rd(i(X2),mult(X,i(X2))))) = mult(X2,i(ld(X2,X))),
inference(transitivity,[status(thm)],[c1050,c1064]) ).
cnf(c1066,plain,
rd(X2,rd(i(X2),rd(i(X2),mult(X,i(X2))))) = mult(X2,i(ld(X2,X))),
inference(transitivity,[status(thm)],[c1048,c1065]) ).
cnf(c1067,plain,
rd(X2,rd(i(X2),ld(i(i(X2)),rd(i(i(X2)),X)))) = mult(X2,i(ld(X2,X))),
inference(transitivity,[status(thm)],[c1046,c1066]) ).
cnf(c1068,plain,
rd(X2,rd(i(X2),ld(i(i(X2)),rd(X2,X)))) = mult(X2,i(ld(X2,X))),
inference(transitivity,[status(thm)],[c1036,c1067]) ).
cnf(c1069,plain,
rd(X2,rd(i(X2),ld(X2,rd(X2,X)))) = mult(X2,i(ld(X2,X))),
inference(transitivity,[status(thm)],[c1031,c1068]) ).
cnf(c1070,plain,
rd(X2,ld(X2,mult(i(rd(X2,X)),X2))) = mult(X2,i(ld(X2,X))),
inference(transitivity,[status(thm)],[c1027,c1069]) ).
cnf(c1071,plain,
mult(rd(X2,X),X2) = mult(X2,i(ld(X2,X))),
inference(transitivity,[status(thm)],[c1010,c1070]) ).
cnf(c1072,plain,
mult(rd(i(X2),rd(X2,X)),i(X2)) = mult(i(X2),i(ld(i(X2),rd(X2,X)))),
inference(substitution,[status(thm)],[c1071]) ).
cnf(c1073,plain,
mult(i(X2),i(ld(i(X2),rd(X2,X)))) = mult(rd(i(X2),rd(X2,X)),i(X2)),
inference(symmetry,[status(thm)],[c1072]) ).
cnf(c1074,plain,
ld(i(X2),mult(i(X2),i(ld(i(X2),rd(X2,X))))) = ld(i(X2),mult(rd(i(X2),rd(X2,X)),i(X2))),
inference(congruence,[status(thm)],[c1073]) ).
cnf(c1075,plain,
rd(i(X2),rd(X2,X)) = rd(ld(X2,X),X2),
inference(symmetry,[status(thm)],[c679]) ).
cnf(c1076,plain,
rd(rd(i(X2),rd(X2,X)),rd(X,X2)) = rd(rd(ld(X2,X),X2),rd(X,X2)),
inference(congruence,[status(thm)],[c1075]) ).
cnf(c1077,plain,
rd(ld(X2,X),X2) = mult(i(X2),rd(X,X2)),
inference(symmetry,[status(thm)],[c316]) ).
cnf(c1078,plain,
rd(rd(ld(X2,X),X2),rd(X,X2)) = rd(mult(i(X2),rd(X,X2)),rd(X,X2)),
inference(congruence,[status(thm)],[c1077]) ).
cnf(c1079,plain,
rd(mult(i(X2),rd(X,X2)),rd(X,X2)) = i(X2),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1080,plain,
rd(rd(ld(X2,X),X2),rd(X,X2)) = i(X2),
inference(transitivity,[status(thm)],[c1078,c1079]) ).
cnf(c1081,plain,
rd(rd(i(X2),rd(X2,X)),rd(X,X2)) = i(X2),
inference(transitivity,[status(thm)],[c1076,c1080]) ).
cnf(c1082,plain,
i(X2) = rd(rd(i(X2),rd(X2,X)),rd(X,X2)),
inference(symmetry,[status(thm)],[c1081]) ).
cnf(c1083,plain,
mult(rd(i(X2),rd(X2,X)),i(X2)) = mult(rd(i(X2),rd(X2,X)),rd(rd(i(X2),rd(X2,X)),rd(X,X2))),
inference(congruence,[status(thm)],[c1082]) ).
cnf(c1084,plain,
ld(i(X2),mult(rd(i(X2),rd(X2,X)),i(X2))) = ld(i(X2),mult(rd(i(X2),rd(X2,X)),rd(rd(i(X2),rd(X2,X)),rd(X,X2)))),
inference(congruence,[status(thm)],[c1083]) ).
cnf(c1085,plain,
i(X2) = rd(rd(i(X2),rd(X2,X)),rd(X,X2)),
inference(symmetry,[status(thm)],[c1081]) ).
cnf(c1086,plain,
ld(i(X2),mult(rd(i(X2),rd(X2,X)),rd(rd(i(X2),rd(X2,X)),rd(X,X2)))) = ld(rd(rd(i(X2),rd(X2,X)),rd(X,X2)),mult(rd(i(X2),rd(X2,X)),rd(rd(i(X2),rd(X2,X)),rd(X,X2)))),
inference(congruence,[status(thm)],[c1085]) ).
cnf(c1087,plain,
rd(ld(rd(X2,X),X2),i(rd(X2,X))) = ld(rd(X2,X),mult(X2,rd(X2,X))),
inference(substitution,[status(thm)],[c716]) ).
cnf(c1088,plain,
ld(rd(X2,X),mult(X2,rd(X2,X))) = rd(ld(rd(X2,X),X2),i(rd(X2,X))),
inference(symmetry,[status(thm)],[c1087]) ).
cnf(c1089,plain,
rd(ld(rd(X2,X),X2),i(rd(X2,X))) = rd(X,i(rd(X2,X))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c1090,plain,
ld(rd(X2,X),mult(X2,rd(X2,X))) = rd(X,i(rd(X2,X))),
inference(transitivity,[status(thm)],[c1088,c1089]) ).
cnf(c1091,plain,
ld(rd(rd(i(X2),rd(X2,X)),rd(X,X2)),mult(rd(i(X2),rd(X2,X)),rd(rd(i(X2),rd(X2,X)),rd(X,X2)))) = rd(rd(X,X2),i(rd(rd(i(X2),rd(X2,X)),rd(X,X2)))),
inference(substitution,[status(thm)],[c1090]) ).
cnf(c1092,plain,
i(rd(rd(i(X2),rd(X2,X)),rd(X,X2))) = i(i(X2)),
inference(congruence,[status(thm)],[c1081]) ).
cnf(c1093,plain,
rd(rd(X,X2),i(rd(rd(i(X2),rd(X2,X)),rd(X,X2)))) = rd(rd(X,X2),i(i(X2))),
inference(congruence,[status(thm)],[c1092]) ).
cnf(c1094,plain,
rd(rd(X,X2),i(i(X2))) = rd(rd(X,X2),X2),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1095,plain,
rd(rd(X,X2),i(rd(rd(i(X2),rd(X2,X)),rd(X,X2)))) = rd(rd(X,X2),X2),
inference(transitivity,[status(thm)],[c1093,c1094]) ).
cnf(c1096,plain,
ld(rd(rd(i(X2),rd(X2,X)),rd(X,X2)),mult(rd(i(X2),rd(X2,X)),rd(rd(i(X2),rd(X2,X)),rd(X,X2)))) = rd(rd(X,X2),X2),
inference(transitivity,[status(thm)],[c1091,c1095]) ).
cnf(c1097,plain,
ld(i(X2),mult(rd(i(X2),rd(X2,X)),rd(rd(i(X2),rd(X2,X)),rd(X,X2)))) = rd(rd(X,X2),X2),
inference(transitivity,[status(thm)],[c1086,c1096]) ).
cnf(c1098,plain,
ld(i(X2),mult(rd(i(X2),rd(X2,X)),i(X2))) = rd(rd(X,X2),X2),
inference(transitivity,[status(thm)],[c1084,c1097]) ).
cnf(c1099,plain,
ld(i(X2),mult(i(X2),i(ld(i(X2),rd(X2,X))))) = rd(rd(X,X2),X2),
inference(transitivity,[status(thm)],[c1074,c1098]) ).
cnf(c1100,plain,
i(ld(i(X2),rd(X2,X))) = rd(rd(X,X2),X2),
inference(transitivity,[status(thm)],[c1008,c1099]) ).
cnf(c1101,plain,
i(ld(i(X),rd(X,ld(X2,X)))) = rd(rd(ld(X2,X),X),X),
inference(substitution,[status(thm)],[c1100]) ).
cnf(c1102,plain,
rd(rd(ld(X2,X),X),X) = i(ld(i(X),rd(X,ld(X2,X)))),
inference(symmetry,[status(thm)],[c1101]) ).
cnf(c1103,plain,
rd(X,ld(X2,X)) = X2,
inference(substitution,[status(thm)],[c462]) ).
cnf(c1104,plain,
ld(i(X),rd(X,ld(X2,X))) = ld(i(X),X2),
inference(congruence,[status(thm)],[c1103]) ).
cnf(c1105,plain,
i(ld(i(X),rd(X,ld(X2,X)))) = i(ld(i(X),X2)),
inference(congruence,[status(thm)],[c1104]) ).
cnf(c1106,plain,
rd(rd(ld(X2,X),X),X) = i(ld(i(X),X2)),
inference(transitivity,[status(thm)],[c1102,c1105]) ).
cnf(c1107,plain,
mult(rd(rd(ld(X2,X),X),X),X) = mult(i(ld(i(X),X2)),X),
inference(congruence,[status(thm)],[c1106]) ).
cnf(c1108,plain,
mult(i(ld(i(X),X2)),X) = rd(X,mult(X2,X)),
inference(substitution,[status(thm)],[c642]) ).
cnf(c1109,plain,
rd(X,mult(X2,X)) = ld(i(X),rd(i(X),X2)),
inference(substitution,[status(thm)],[c1042]) ).
cnf(c1110,plain,
mult(i(ld(i(X),X2)),X) = ld(i(X),rd(i(X),X2)),
inference(transitivity,[status(thm)],[c1108,c1109]) ).
cnf(c1111,plain,
mult(rd(rd(ld(X2,X),X),X),X) = ld(i(X),rd(i(X),X2)),
inference(transitivity,[status(thm)],[c1107,c1110]) ).
cnf(c1112,plain,
rd(ld(X2,X),X) = ld(i(X),rd(i(X),X2)),
inference(transitivity,[status(thm)],[c1006,c1111]) ).
cnf(c1113,plain,
rd(ld(X,X2),X2) = ld(i(X2),rd(i(X2),X)),
inference(substitution,[status(thm)],[c1112]) ).
cnf(c1114,plain,
rd(ld(X2,mult(i(rd(X,X2)),X2)),X2) = ld(i(X2),rd(i(X2),X)),
inference(transitivity,[status(thm)],[c1004,c1113]) ).
cnf(c1115,plain,
mult(i(X2),i(rd(X,X2))) = ld(i(X2),rd(i(X2),X)),
inference(transitivity,[status(thm)],[c1003,c1114]) ).
cnf(c1116,plain,
mult(i(X2),i(rd(rd(mult(X,mult(X2,X2)),X2),X2))) = ld(i(X2),rd(i(X2),rd(mult(X,mult(X2,X2)),X2))),
inference(substitution,[status(thm)],[c1115]) ).
cnf(c1117,plain,
ld(i(X2),rd(i(X2),rd(mult(X,mult(X2,X2)),X2))) = mult(i(X2),i(rd(rd(mult(X,mult(X2,X2)),X2),X2))),
inference(symmetry,[status(thm)],[c1116]) ).
cnf(c1118,plain,
rd(mult(X2,mult(X,X)),X) = mult(rd(X2,X),mult(X,X)),
inference(symmetry,[status(thm)],[c963]) ).
cnf(c1119,plain,
rd(rd(mult(X2,mult(X,X)),X),X) = rd(mult(rd(X2,X),mult(X,X)),X),
inference(congruence,[status(thm)],[c1118]) ).
cnf(c1120,plain,
mult(rd(X2,X),mult(X,X)) = ld(X,ld(i(X),mult(X2,X))),
inference(substitution,[status(thm)],[c948]) ).
cnf(c1121,plain,
rd(mult(rd(X2,X),mult(X,X)),X) = rd(ld(X,ld(i(X),mult(X2,X))),X),
inference(congruence,[status(thm)],[c1120]) ).
cnf(c1122,plain,
rd(ld(X,ld(i(X),mult(X2,X))),X) = mult(mult(X2,X),i(X)),
inference(substitution,[status(thm)],[c557]) ).
cnf(c1123,plain,
rd(ld(X,ld(i(X),mult(X2,X))),X) = ld(X,ld(i(X),X2)),
inference(transitivity,[status(thm)],[c1122,c541]) ).
cnf(c1124,plain,
rd(mult(rd(X2,X),mult(X,X)),X) = ld(X,ld(i(X),X2)),
inference(transitivity,[status(thm)],[c1121,c1123]) ).
cnf(c1125,plain,
rd(rd(mult(X2,mult(X,X)),X),X) = ld(X,ld(i(X),X2)),
inference(transitivity,[status(thm)],[c1119,c1124]) ).
cnf(c1126,plain,
rd(rd(mult(X,mult(X2,X2)),X2),X2) = ld(X2,ld(i(X2),X)),
inference(substitution,[status(thm)],[c1125]) ).
cnf(c1127,plain,
i(rd(rd(mult(X,mult(X2,X2)),X2),X2)) = i(ld(X2,ld(i(X2),X))),
inference(congruence,[status(thm)],[c1126]) ).
cnf(c1128,plain,
mult(i(X2),i(rd(rd(mult(X,mult(X2,X2)),X2),X2))) = mult(i(X2),i(ld(X2,ld(i(X2),X)))),
inference(congruence,[status(thm)],[c1127]) ).
cnf(c1129,plain,
ld(X2,ld(i(X2),X)) = ld(i(X2),ld(X2,X)),
inference(symmetry,[status(thm)],[c575]) ).
cnf(c1130,plain,
i(ld(X2,ld(i(X2),X))) = i(ld(i(X2),ld(X2,X))),
inference(congruence,[status(thm)],[c1129]) ).
cnf(c1131,plain,
mult(mult(X,i(X2)),X2) = ld(i(X2),ld(X2,X)),
inference(substitution,[status(thm)],[c783]) ).
cnf(c1132,plain,
ld(i(X2),ld(X2,X)) = mult(mult(X,i(X2)),X2),
inference(symmetry,[status(thm)],[c1131]) ).
cnf(c1133,plain,
i(ld(i(X2),ld(X2,X))) = i(mult(mult(X,i(X2)),X2)),
inference(congruence,[status(thm)],[c1132]) ).
cnf(c1134,plain,
ld(X2,mult(ld(mult(X,i(X2)),i(X2)),X2)) = i(mult(mult(X,i(X2)),X2)),
inference(substitution,[status(thm)],[c389]) ).
cnf(c1135,plain,
i(mult(mult(X,i(X2)),X2)) = ld(X2,mult(ld(mult(X,i(X2)),i(X2)),X2)),
inference(symmetry,[status(thm)],[c1134]) ).
cnf(c1136,plain,
ld(mult(X,i(X2)),i(X2)) = ld(i(X2),mult(i(X),i(X2))),
inference(substitution,[status(thm)],[c440]) ).
cnf(c1137,plain,
mult(ld(mult(X,i(X2)),i(X2)),X2) = mult(ld(i(X2),mult(i(X),i(X2))),X2),
inference(congruence,[status(thm)],[c1136]) ).
cnf(c1138,plain,
ld(X2,mult(ld(mult(X,i(X2)),i(X2)),X2)) = ld(X2,mult(ld(i(X2),mult(i(X),i(X2))),X2)),
inference(congruence,[status(thm)],[c1137]) ).
cnf(c1139,plain,
ld(X2,mult(ld(i(X2),mult(i(X),i(X2))),X2)) = mult(mult(i(X),i(X2)),X2),
inference(substitution,[status(thm)],[c533]) ).
cnf(c1140,plain,
mult(mult(i(X),i(X2)),X2) = ld(i(X2),ld(X2,i(X))),
inference(substitution,[status(thm)],[c783]) ).
cnf(c1141,plain,
ld(i(X2),ld(X2,i(X))) = ld(X2,ld(i(X2),i(X))),
inference(substitution,[status(thm)],[c575]) ).
cnf(c1142,plain,
mult(mult(i(X),i(X2)),X2) = ld(X2,ld(i(X2),i(X))),
inference(transitivity,[status(thm)],[c1140,c1141]) ).
cnf(c1143,plain,
ld(X2,mult(ld(i(X2),mult(i(X),i(X2))),X2)) = ld(X2,ld(i(X2),i(X))),
inference(transitivity,[status(thm)],[c1139,c1142]) ).
cnf(c1144,plain,
ld(X2,mult(ld(mult(X,i(X2)),i(X2)),X2)) = ld(X2,ld(i(X2),i(X))),
inference(transitivity,[status(thm)],[c1138,c1143]) ).
cnf(c1145,plain,
i(mult(mult(X,i(X2)),X2)) = ld(X2,ld(i(X2),i(X))),
inference(transitivity,[status(thm)],[c1135,c1144]) ).
cnf(c1146,plain,
i(ld(i(X2),ld(X2,X))) = ld(X2,ld(i(X2),i(X))),
inference(transitivity,[status(thm)],[c1133,c1145]) ).
cnf(c1147,plain,
i(ld(X2,ld(i(X2),X))) = ld(X2,ld(i(X2),i(X))),
inference(transitivity,[status(thm)],[c1130,c1146]) ).
cnf(c1148,plain,
mult(i(X2),i(ld(X2,ld(i(X2),X)))) = mult(i(X2),ld(X2,ld(i(X2),i(X)))),
inference(congruence,[status(thm)],[c1147]) ).
cnf(c1149,plain,
ld(X2,rd(rd(ld(X2,X),X2),i(X2))) = mult(i(X2),ld(X2,X)),
inference(substitution,[status(thm)],[c619]) ).
cnf(c1150,plain,
mult(i(X2),ld(X2,X)) = ld(X2,rd(rd(ld(X2,X),X2),i(X2))),
inference(symmetry,[status(thm)],[c1149]) ).
cnf(c1151,plain,
rd(rd(ld(X2,X),i(X2)),X2) = rd(rd(ld(X2,X),X2),i(X2)),
inference(substitution,[status(thm)],[c898]) ).
cnf(c1152,plain,
rd(rd(ld(X2,X),X2),i(X2)) = rd(rd(ld(X2,X),i(X2)),X2),
inference(symmetry,[status(thm)],[c1151]) ).
cnf(c1153,plain,
mult(X2,mult(i(X2),ld(X2,X))) = rd(rd(ld(X2,X),i(X2)),X2),
inference(substitution,[status(thm)],[c322]) ).
cnf(c1154,plain,
rd(rd(ld(X2,X),i(X2)),X2) = mult(X2,mult(i(X2),ld(X2,X))),
inference(symmetry,[status(thm)],[c1153]) ).
cnf(c1155,plain,
mult(i(X2),mult(X2,ld(X2,X))) = mult(X2,mult(i(X2),ld(X2,X))),
inference(substitution,[status(thm)],[c302]) ).
cnf(c1156,plain,
mult(X2,mult(i(X2),ld(X2,X))) = mult(i(X2),mult(X2,ld(X2,X))),
inference(symmetry,[status(thm)],[c1155]) ).
cnf(c1157,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c1158,plain,
mult(i(X2),mult(X2,ld(X2,X))) = mult(i(X2),X),
inference(congruence,[status(thm)],[c1157]) ).
cnf(c1159,plain,
mult(X2,mult(i(X2),ld(X2,X))) = mult(i(X2),X),
inference(transitivity,[status(thm)],[c1156,c1158]) ).
cnf(c1160,plain,
rd(rd(ld(X2,X),i(X2)),X2) = mult(i(X2),X),
inference(transitivity,[status(thm)],[c1154,c1159]) ).
cnf(c1161,plain,
rd(rd(ld(X2,X),X2),i(X2)) = mult(i(X2),X),
inference(transitivity,[status(thm)],[c1152,c1160]) ).
cnf(c1162,plain,
ld(X2,rd(rd(ld(X2,X),X2),i(X2))) = ld(X2,mult(i(X2),X)),
inference(congruence,[status(thm)],[c1161]) ).
cnf(c1163,plain,
mult(i(X2),ld(X2,X)) = ld(X2,mult(i(X2),X)),
inference(transitivity,[status(thm)],[c1150,c1162]) ).
cnf(c1164,plain,
mult(i(X2),ld(X2,ld(i(X2),i(X)))) = ld(X2,mult(i(X2),ld(i(X2),i(X)))),
inference(substitution,[status(thm)],[c1163]) ).
cnf(c1165,plain,
mult(i(X2),ld(i(X2),i(X))) = i(X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c1166,plain,
ld(X2,mult(i(X2),ld(i(X2),i(X)))) = ld(X2,i(X)),
inference(congruence,[status(thm)],[c1165]) ).
cnf(c1167,plain,
mult(i(X2),ld(X2,ld(i(X2),i(X)))) = ld(X2,i(X)),
inference(transitivity,[status(thm)],[c1164,c1166]) ).
cnf(c1168,plain,
mult(i(X2),i(ld(X2,ld(i(X2),X)))) = ld(X2,i(X)),
inference(transitivity,[status(thm)],[c1148,c1167]) ).
cnf(c1169,plain,
mult(i(X2),i(rd(rd(mult(X,mult(X2,X2)),X2),X2))) = ld(X2,i(X)),
inference(transitivity,[status(thm)],[c1128,c1168]) ).
cnf(c1170,plain,
ld(i(X2),rd(i(X2),rd(mult(X,mult(X2,X2)),X2))) = ld(X2,i(X)),
inference(transitivity,[status(thm)],[c1117,c1169]) ).
cnf(c1171,plain,
rd(X2,mult(X,mult(X2,X2))) = ld(X2,i(X)),
inference(transitivity,[status(thm)],[c1001,c1170]) ).
cnf(c1172,plain,
ld(rd(X2,mult(X,mult(X2,X2))),X2) = ld(ld(X2,i(X)),X2),
inference(congruence,[status(thm)],[c1171]) ).
cnf(c1173,plain,
mult(X,mult(X2,X2)) = ld(ld(X2,i(X)),X2),
inference(transitivity,[status(thm)],[c999,c1172]) ).
cnf(c1174,plain,
mult(i(X),mult(X2,X2)) = ld(ld(X2,i(i(X))),X2),
inference(substitution,[status(thm)],[c1173]) ).
cnf(c1175,plain,
ld(X2,i(i(X))) = ld(X2,X),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1176,plain,
ld(ld(X2,i(i(X))),X2) = ld(ld(X2,X),X2),
inference(congruence,[status(thm)],[c1175]) ).
cnf(c1177,plain,
mult(i(X),mult(X2,X2)) = ld(ld(X2,X),X2),
inference(transitivity,[status(thm)],[c1174,c1176]) ).
cnf(c1178,plain,
mult(i(mult(mult(X2,X2),X)),mult(X2,X2)) = ld(ld(X2,mult(mult(X2,X2),X)),X2),
inference(substitution,[status(thm)],[c1177]) ).
cnf(c1179,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c1180,plain,
rd(X2,rd(i(X2),rd(X,X2))) = rd(i(i(X2)),rd(i(X2),rd(X,X2))),
inference(congruence,[status(thm)],[c1179]) ).
cnf(c1181,plain,
rd(ld(i(X2),rd(X,X2)),i(X2)) = rd(i(i(X2)),rd(i(X2),rd(X,X2))),
inference(substitution,[status(thm)],[c679]) ).
cnf(c1182,plain,
rd(i(i(X2)),rd(i(X2),rd(X,X2))) = rd(ld(i(X2),rd(X,X2)),i(X2)),
inference(symmetry,[status(thm)],[c1181]) ).
cnf(c1183,plain,
ld(X2,mult(mult(X2,X2),mult(rd(X,X2),X2))) = rd(ld(i(X2),rd(X,X2)),i(X2)),
inference(substitution,[status(thm)],[c417]) ).
cnf(c1184,plain,
rd(ld(i(X2),rd(X,X2)),i(X2)) = ld(X2,mult(mult(X2,X2),mult(rd(X,X2),X2))),
inference(symmetry,[status(thm)],[c1183]) ).
cnf(c1185,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c151]) ).
cnf(c1186,plain,
mult(mult(X2,X2),mult(rd(X,X2),X2)) = mult(mult(X2,X2),X),
inference(congruence,[status(thm)],[c1185]) ).
cnf(c1187,plain,
ld(X2,mult(mult(X2,X2),mult(rd(X,X2),X2))) = ld(X2,mult(mult(X2,X2),X)),
inference(congruence,[status(thm)],[c1186]) ).
cnf(c1188,plain,
rd(ld(i(X2),rd(X,X2)),i(X2)) = ld(X2,mult(mult(X2,X2),X)),
inference(transitivity,[status(thm)],[c1184,c1187]) ).
cnf(c1189,plain,
rd(i(i(X2)),rd(i(X2),rd(X,X2))) = ld(X2,mult(mult(X2,X2),X)),
inference(transitivity,[status(thm)],[c1182,c1188]) ).
cnf(c1190,plain,
rd(X2,rd(i(X2),rd(X,X2))) = ld(X2,mult(mult(X2,X2),X)),
inference(transitivity,[status(thm)],[c1180,c1189]) ).
cnf(c1191,plain,
ld(X2,mult(mult(X2,X2),X)) = rd(X2,rd(i(X2),rd(X,X2))),
inference(symmetry,[status(thm)],[c1190]) ).
cnf(c1192,plain,
ld(ld(X2,mult(mult(X2,X2),X)),X2) = ld(rd(X2,rd(i(X2),rd(X,X2))),X2),
inference(congruence,[status(thm)],[c1191]) ).
cnf(c1193,plain,
ld(rd(X2,rd(i(X2),rd(X,X2))),X2) = rd(i(X2),rd(X,X2)),
inference(substitution,[status(thm)],[c205]) ).
cnf(c1194,plain,
ld(ld(X2,mult(mult(X2,X2),X)),X2) = rd(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c1192,c1193]) ).
cnf(c1195,plain,
mult(i(mult(mult(X2,X2),X)),mult(X2,X2)) = rd(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c1178,c1194]) ).
cnf(c1196,plain,
rd(mult(X2,X2),rd(X,i(mult(X2,X2)))) = rd(i(X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c997,c1195]) ).
cnf(c1197,plain,
rd(mult(X2,X2),rd(ld(mult(X2,X2),mult(X2,X)),i(mult(X2,X2)))) = rd(i(X2),rd(ld(mult(X2,X2),mult(X2,X)),X2)),
inference(substitution,[status(thm)],[c1196]) ).
cnf(c1198,plain,
rd(ld(mult(X2,X2),mult(X2,X)),X2) = rd(ld(X2,ld(X2,ld(i(X2),X))),X2),
inference(congruence,[status(thm)],[c790]) ).
cnf(c1199,plain,
mult(i(X2),rd(ld(X2,X),X2)) = rd(ld(X2,ld(X2,X)),X2),
inference(substitution,[status(thm)],[c316]) ).
cnf(c1200,plain,
rd(ld(X2,ld(X2,X)),X2) = mult(i(X2),rd(ld(X2,X),X2)),
inference(symmetry,[status(thm)],[c1199]) ).
cnf(c1201,plain,
rd(rd(X,i(X2)),X2) = rd(rd(X,X2),i(X2)),
inference(substitution,[status(thm)],[c898]) ).
cnf(c1202,plain,
rd(rd(X,X2),i(X2)) = rd(rd(X,i(X2)),X2),
inference(symmetry,[status(thm)],[c1201]) ).
cnf(c1203,plain,
ld(i(X2),rd(rd(X,X2),i(X2))) = ld(i(X2),rd(rd(X,i(X2)),X2)),
inference(congruence,[status(thm)],[c1202]) ).
cnf(c1204,plain,
rd(rd(X,i(X2)),X2) = mult(X2,mult(i(X2),X)),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c1205,plain,
ld(i(X2),rd(rd(X,i(X2)),X2)) = ld(i(X2),mult(X2,mult(i(X2),X))),
inference(congruence,[status(thm)],[c1204]) ).
cnf(c1206,plain,
mult(X2,mult(i(X2),X)) = mult(i(X2),mult(X2,X)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c1207,plain,
ld(i(X2),mult(X2,mult(i(X2),X))) = ld(i(X2),mult(i(X2),mult(X2,X))),
inference(congruence,[status(thm)],[c1206]) ).
cnf(c1208,plain,
ld(i(X2),mult(i(X2),mult(X2,X))) = mult(X2,X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c1209,plain,
ld(i(X2),mult(X2,mult(i(X2),X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c1207,c1208]) ).
cnf(c1210,plain,
ld(i(X2),rd(rd(X,i(X2)),X2)) = mult(X2,X),
inference(transitivity,[status(thm)],[c1205,c1209]) ).
cnf(c1211,plain,
ld(i(X2),rd(rd(X,X2),i(X2))) = mult(X2,X),
inference(transitivity,[status(thm)],[c1203,c1210]) ).
cnf(c1212,plain,
ld(i(i(X2)),rd(rd(rd(ld(X2,X),X2),i(X2)),i(i(X2)))) = mult(i(X2),rd(ld(X2,X),X2)),
inference(substitution,[status(thm)],[c1211]) ).
cnf(c1213,plain,
mult(i(X2),rd(ld(X2,X),X2)) = ld(i(i(X2)),rd(rd(rd(ld(X2,X),X2),i(X2)),i(i(X2)))),
inference(symmetry,[status(thm)],[c1212]) ).
cnf(c1214,plain,
rd(rd(rd(ld(X2,X),X2),i(X2)),i(i(X2))) = rd(mult(i(X2),X),i(i(X2))),
inference(congruence,[status(thm)],[c1161]) ).
cnf(c1215,plain,
ld(i(i(X2)),rd(rd(rd(ld(X2,X),X2),i(X2)),i(i(X2)))) = ld(i(i(X2)),rd(mult(i(X2),X),i(i(X2)))),
inference(congruence,[status(thm)],[c1214]) ).
cnf(c1216,plain,
ld(i(i(X2)),rd(mult(i(X2),X),i(i(X2)))) = ld(X2,rd(mult(i(X2),X),i(i(X2)))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1217,plain,
rd(mult(i(X2),X),i(i(X2))) = rd(mult(i(X2),X),X2),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1218,plain,
ld(X2,rd(mult(i(X2),X),i(i(X2)))) = ld(X2,rd(mult(i(X2),X),X2)),
inference(congruence,[status(thm)],[c1217]) ).
cnf(c1219,plain,
ld(i(i(X2)),rd(mult(i(X2),X),i(i(X2)))) = ld(X2,rd(mult(i(X2),X),X2)),
inference(transitivity,[status(thm)],[c1216,c1218]) ).
cnf(c1220,plain,
ld(i(i(X2)),rd(rd(rd(ld(X2,X),X2),i(X2)),i(i(X2)))) = ld(X2,rd(mult(i(X2),X),X2)),
inference(transitivity,[status(thm)],[c1215,c1219]) ).
cnf(c1221,plain,
mult(i(X2),rd(ld(X2,X),X2)) = ld(X2,rd(mult(i(X2),X),X2)),
inference(transitivity,[status(thm)],[c1213,c1220]) ).
cnf(c1222,plain,
rd(ld(X2,ld(X2,X)),X2) = ld(X2,rd(mult(i(X2),X),X2)),
inference(transitivity,[status(thm)],[c1200,c1221]) ).
cnf(c1223,plain,
rd(ld(X2,ld(X2,ld(i(X2),X))),X2) = ld(X2,rd(mult(i(X2),ld(i(X2),X)),X2)),
inference(substitution,[status(thm)],[c1222]) ).
cnf(c1224,plain,
mult(i(X2),ld(i(X2),X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c1225,plain,
rd(mult(i(X2),ld(i(X2),X)),X2) = rd(X,X2),
inference(congruence,[status(thm)],[c1224]) ).
cnf(c1226,plain,
ld(X2,rd(mult(i(X2),ld(i(X2),X)),X2)) = ld(X2,rd(X,X2)),
inference(congruence,[status(thm)],[c1225]) ).
cnf(c1227,plain,
rd(ld(X2,ld(X2,ld(i(X2),X))),X2) = ld(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c1223,c1226]) ).
cnf(c1228,plain,
rd(ld(mult(X2,X2),mult(X2,X)),X2) = ld(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c1198,c1227]) ).
cnf(c1229,plain,
rd(i(X2),rd(ld(mult(X2,X2),mult(X2,X)),X2)) = rd(i(X2),ld(X2,rd(X,X2))),
inference(congruence,[status(thm)],[c1228]) ).
cnf(c1230,plain,
rd(i(X2),ld(X2,rd(X,X2))) = ld(X2,mult(i(rd(X,X2)),X2)),
inference(substitution,[status(thm)],[c1024]) ).
cnf(c1231,plain,
rd(i(X2),ld(X2,rd(X,X2))) = ld(X,X2),
inference(transitivity,[status(thm)],[c1230,c445]) ).
cnf(c1232,plain,
rd(i(X2),rd(ld(mult(X2,X2),mult(X2,X)),X2)) = ld(X,X2),
inference(transitivity,[status(thm)],[c1229,c1231]) ).
cnf(c1233,plain,
rd(mult(X2,X2),rd(ld(mult(X2,X2),mult(X2,X)),i(mult(X2,X2)))) = ld(X,X2),
inference(transitivity,[status(thm)],[c1197,c1232]) ).
cnf(c1234,plain,
rd(mult(X2,X2),ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2)))) = ld(X,X2),
inference(transitivity,[status(thm)],[c995,c1233]) ).
cnf(c1235,plain,
mult(i(mult(X2,X)),mult(X2,X2)) = ld(X,X2),
inference(transitivity,[status(thm)],[c992,c1234]) ).
cnf(c1236,plain,
ld(mult(i(mult(X2,X)),mult(X2,X2)),mult(X2,X2)) = ld(ld(X,X2),mult(X2,X2)),
inference(congruence,[status(thm)],[c1235]) ).
cnf(c1237,plain,
ld(mult(X2,X2),mult(i(i(mult(X2,X))),mult(X2,X2))) = ld(ld(X,X2),mult(X2,X2)),
inference(transitivity,[status(thm)],[c990,c1236]) ).
cnf(c1238,plain,
ld(mult(X2,X2),mult(mult(X2,X),mult(X2,X2))) = ld(ld(X,X2),mult(X2,X2)),
inference(transitivity,[status(thm)],[c988,c1237]) ).
cnf(c1239,plain,
mult(i(X2),mult(X,mult(X2,X2))) = ld(ld(X,X2),mult(X2,X2)),
inference(transitivity,[status(thm)],[c984,c1238]) ).
cnf(c1240,plain,
mult(i(X2),mult(ld(i(X2),X),mult(X2,X2))) = ld(ld(ld(i(X2),X),X2),mult(X2,X2)),
inference(substitution,[status(thm)],[c1239]) ).
cnf(c1241,plain,
ld(ld(ld(i(X2),X),X2),mult(X2,X2)) = mult(i(X2),mult(ld(i(X2),X),mult(X2,X2))),
inference(symmetry,[status(thm)],[c1240]) ).
cnf(c1242,plain,
mult(rd(X,i(X2)),mult(i(X2),mult(X2,X2))) = mult(i(X2),mult(ld(i(X2),X),mult(X2,X2))),
inference(substitution,[status(thm)],[c43]) ).
cnf(c1243,plain,
mult(i(X2),mult(ld(i(X2),X),mult(X2,X2))) = mult(rd(X,i(X2)),mult(i(X2),mult(X2,X2))),
inference(symmetry,[status(thm)],[c1242]) ).
cnf(c1244,plain,
mult(rd(X,i(X2)),mult(i(X2),mult(X2,X2))) = mult(rd(X,i(X2)),X2),
inference(congruence,[status(thm)],[c141]) ).
cnf(c1245,plain,
mult(rd(X,i(X2)),X2) = rd(mult(X,X2),i(X2)),
inference(substitution,[status(thm)],[c818]) ).
cnf(c1246,plain,
mult(rd(X,i(X2)),mult(i(X2),mult(X2,X2))) = rd(mult(X,X2),i(X2)),
inference(transitivity,[status(thm)],[c1244,c1245]) ).
cnf(c1247,plain,
mult(i(X2),mult(ld(i(X2),X),mult(X2,X2))) = rd(mult(X,X2),i(X2)),
inference(transitivity,[status(thm)],[c1243,c1246]) ).
cnf(c1248,plain,
ld(ld(ld(i(X2),X),X2),mult(X2,X2)) = rd(mult(X,X2),i(X2)),
inference(transitivity,[status(thm)],[c1241,c1247]) ).
cnf(c1249,plain,
ld(ld(ld(i(X2),rd(i(X2),rd(X,X2))),X2),mult(X2,X2)) = rd(mult(rd(i(X2),rd(X,X2)),X2),i(X2)),
inference(substitution,[status(thm)],[c1248]) ).
cnf(c1250,plain,
rd(mult(rd(i(X2),rd(X,X2)),X2),i(X2)) = ld(ld(ld(i(X2),rd(i(X2),rd(X,X2))),X2),mult(X2,X2)),
inference(symmetry,[status(thm)],[c1249]) ).
cnf(c1251,plain,
ld(ld(i(X2),rd(i(X2),rd(X,X2))),X2) = ld(rd(X2,X),X2),
inference(congruence,[status(thm)],[c676]) ).
cnf(c1252,plain,
ld(ld(ld(i(X2),rd(i(X2),rd(X,X2))),X2),mult(X2,X2)) = ld(ld(rd(X2,X),X2),mult(X2,X2)),
inference(congruence,[status(thm)],[c1251]) ).
cnf(c1253,plain,
ld(ld(rd(X2,X),X2),mult(X2,X2)) = ld(X,mult(X2,X2)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c1254,plain,
ld(ld(ld(i(X2),rd(i(X2),rd(X,X2))),X2),mult(X2,X2)) = ld(X,mult(X2,X2)),
inference(transitivity,[status(thm)],[c1252,c1253]) ).
cnf(c1255,plain,
rd(mult(rd(i(X2),rd(X,X2)),X2),i(X2)) = ld(X,mult(X2,X2)),
inference(transitivity,[status(thm)],[c1250,c1254]) ).
cnf(c1256,plain,
rd(ld(X2,ld(rd(X,X2),X2)),i(X2)) = ld(X,mult(X2,X2)),
inference(transitivity,[status(thm)],[c847,c1255]) ).
cnf(c1257,plain,
ld(X2,mult(ld(rd(X,X2),X2),X2)) = ld(X,mult(X2,X2)),
inference(transitivity,[status(thm)],[c718,c1256]) ).
cnf(c1258,plain,
ld(X2,i(ld(mult(X2,X2),rd(X,X2)))) = ld(X,mult(X2,X2)),
inference(transitivity,[status(thm)],[c703,c1257]) ).
cnf(c1259,plain,
ld(op_c,i(ld(mult(op_c,op_c),rd(mult(op_d,i(mult(X,op_d))),op_c)))) = ld(mult(op_d,i(mult(X,op_d))),mult(op_c,op_c)),
inference(substitution,[status(thm)],[c1258]) ).
cnf(c1260,plain,
ld(mult(op_d,i(mult(X,op_d))),mult(op_c,op_c)) = ld(op_c,i(ld(mult(op_c,op_c),rd(mult(op_d,i(mult(X,op_d))),op_c)))),
inference(symmetry,[status(thm)],[c1259]) ).
cnf(c1261,plain,
mult(op_c,ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c))) = rd(mult(op_d,i(mult(X,op_d))),op_c),
inference(substitution,[status(thm)],[c35]) ).
cnf(c1262,plain,
rd(mult(op_d,i(mult(X,op_d))),op_c) = mult(op_c,ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c))),
inference(symmetry,[status(thm)],[c1261]) ).
cnf(c1263,plain,
ld(mult(op_c,op_c),rd(mult(op_d,i(mult(X,op_d))),op_c)) = ld(mult(op_c,op_c),mult(op_c,ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)))),
inference(congruence,[status(thm)],[c1262]) ).
cnf(c1264,plain,
ld(mult(X2,X2),mult(mult(X2,X2),mult(X2,ld(mult(X2,X2),X)))) = mult(X2,ld(mult(X2,X2),X)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c1265,plain,
mult(X2,ld(mult(X2,X2),X)) = ld(mult(X2,X2),mult(mult(X2,X2),mult(X2,ld(mult(X2,X2),X)))),
inference(symmetry,[status(thm)],[c1264]) ).
cnf(c1266,plain,
mult(mult(X2,X2),mult(X2,ld(mult(X2,X2),X))) = mult(X2,mult(mult(X2,X2),ld(mult(X2,X2),X))),
inference(substitution,[status(thm)],[c369]) ).
cnf(c1267,plain,
mult(mult(X2,X2),ld(mult(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c1268,plain,
mult(X2,mult(mult(X2,X2),ld(mult(X2,X2),X))) = mult(X2,X),
inference(congruence,[status(thm)],[c1267]) ).
cnf(c1269,plain,
mult(mult(X2,X2),mult(X2,ld(mult(X2,X2),X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c1266,c1268]) ).
cnf(c1270,plain,
ld(mult(X2,X2),mult(mult(X2,X2),mult(X2,ld(mult(X2,X2),X)))) = ld(mult(X2,X2),mult(X2,X)),
inference(congruence,[status(thm)],[c1269]) ).
cnf(c1271,plain,
mult(X2,ld(mult(X2,X2),X)) = ld(mult(X2,X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c1265,c1270]) ).
cnf(c1272,plain,
mult(op_c,ld(mult(op_c,op_c),ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)))) = ld(mult(op_c,op_c),mult(op_c,ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)))),
inference(substitution,[status(thm)],[c1271]) ).
cnf(c1273,plain,
ld(mult(op_c,op_c),mult(op_c,ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)))) = mult(op_c,ld(mult(op_c,op_c),ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)))),
inference(symmetry,[status(thm)],[c1272]) ).
cnf(c1274,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c1275,plain,
ld(X2,X) = ld(i(i(X2)),X),
inference(congruence,[status(thm)],[c1274]) ).
cnf(c1276,plain,
mult(ld(X3,X2),mult(X,i(X3))) = mult(ld(i(i(X3)),X2),mult(X,i(X3))),
inference(congruence,[status(thm)],[c1275]) ).
cnf(c1277,plain,
mult(X3,ld(X3,mult(ld(i(X3),X2),mult(X,X3)))) = mult(ld(i(X3),X2),mult(X,X3)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c1278,plain,
mult(ld(i(X3),X2),mult(X,X3)) = mult(X3,ld(X3,mult(ld(i(X3),X2),mult(X,X3)))),
inference(symmetry,[status(thm)],[c1277]) ).
cnf(c1279,plain,
ld(X2,mult(X2,mult(mult(X3,X2),ld(X2,X)))) = mult(mult(X3,X2),ld(X2,X)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c1280,plain,
mult(mult(X3,X2),ld(X2,X)) = ld(X2,mult(X2,mult(mult(X3,X2),ld(X2,X)))),
inference(symmetry,[status(thm)],[c1279]) ).
cnf(c1281,plain,
mult(ld(i(X3),rd(mult(X2,X3),X3)),X) = mult(X3,mult(mult(X2,X3),ld(X3,X))),
inference(substitution,[status(thm)],[c345]) ).
cnf(c1282,plain,
mult(X3,mult(mult(X2,X3),ld(X3,X))) = mult(ld(i(X3),rd(mult(X2,X3),X3)),X),
inference(symmetry,[status(thm)],[c1281]) ).
cnf(c1283,plain,
rd(mult(X,X2),X2) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c1284,plain,
ld(i(X2),rd(mult(X,X2),X2)) = ld(i(X2),X),
inference(congruence,[status(thm)],[c1283]) ).
cnf(c1285,plain,
mult(ld(i(X3),rd(mult(X2,X3),X3)),X) = mult(ld(i(X3),X2),X),
inference(congruence,[status(thm)],[c1284]) ).
cnf(c1286,plain,
mult(X3,mult(mult(X2,X3),ld(X3,X))) = mult(ld(i(X3),X2),X),
inference(transitivity,[status(thm)],[c1282,c1285]) ).
cnf(c1287,plain,
mult(X2,mult(mult(X3,X2),ld(X2,X))) = mult(ld(i(X2),X3),X),
inference(substitution,[status(thm)],[c1286]) ).
cnf(c1288,plain,
ld(X2,mult(X2,mult(mult(X3,X2),ld(X2,X)))) = ld(X2,mult(ld(i(X2),X3),X)),
inference(congruence,[status(thm)],[c1287]) ).
cnf(c1289,plain,
mult(mult(X3,X2),ld(X2,X)) = ld(X2,mult(ld(i(X2),X3),X)),
inference(transitivity,[status(thm)],[c1280,c1288]) ).
cnf(c1290,plain,
mult(mult(X2,X3),ld(X3,mult(X,X3))) = ld(X3,mult(ld(i(X3),X2),mult(X,X3))),
inference(substitution,[status(thm)],[c1289]) ).
cnf(c1291,plain,
ld(X3,mult(ld(i(X3),X2),mult(X,X3))) = mult(mult(X2,X3),ld(X3,mult(X,X3))),
inference(symmetry,[status(thm)],[c1290]) ).
cnf(c1292,plain,
mult(mult(X2,X),X3) = mult(mult(X2,X3),ld(X3,mult(X,X3))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c1293,plain,
mult(mult(X2,X3),ld(X3,mult(X,X3))) = mult(mult(X2,X),X3),
inference(symmetry,[status(thm)],[c1292]) ).
cnf(c1294,plain,
ld(X3,mult(ld(i(X3),X2),mult(X,X3))) = mult(mult(X2,X),X3),
inference(transitivity,[status(thm)],[c1291,c1293]) ).
cnf(c1295,plain,
mult(X3,ld(X3,mult(ld(i(X3),X2),mult(X,X3)))) = mult(X3,mult(mult(X2,X),X3)),
inference(congruence,[status(thm)],[c1294]) ).
cnf(c1296,plain,
mult(X3,mult(mult(X2,X),X3)) = ld(i(X3),rd(mult(X2,X),i(X3))),
inference(substitution,[status(thm)],[c942]) ).
cnf(c1297,plain,
mult(X3,ld(X3,mult(ld(i(X3),X2),mult(X,X3)))) = ld(i(X3),rd(mult(X2,X),i(X3))),
inference(transitivity,[status(thm)],[c1295,c1296]) ).
cnf(c1298,plain,
mult(ld(i(X3),X2),mult(X,X3)) = ld(i(X3),rd(mult(X2,X),i(X3))),
inference(transitivity,[status(thm)],[c1278,c1297]) ).
cnf(c1299,plain,
mult(ld(i(i(X3)),X2),mult(X,i(X3))) = ld(i(i(X3)),rd(mult(X2,X),i(i(X3)))),
inference(substitution,[status(thm)],[c1298]) ).
cnf(c1300,plain,
ld(i(i(X3)),rd(mult(X2,X),i(i(X3)))) = ld(X3,rd(mult(X2,X),i(i(X3)))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1301,plain,
rd(mult(X2,X),i(i(X3))) = rd(mult(X2,X),X3),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1302,plain,
ld(X3,rd(mult(X2,X),i(i(X3)))) = ld(X3,rd(mult(X2,X),X3)),
inference(congruence,[status(thm)],[c1301]) ).
cnf(c1303,plain,
ld(i(i(X3)),rd(mult(X2,X),i(i(X3)))) = ld(X3,rd(mult(X2,X),X3)),
inference(transitivity,[status(thm)],[c1300,c1302]) ).
cnf(c1304,plain,
mult(ld(i(i(X3)),X2),mult(X,i(X3))) = ld(X3,rd(mult(X2,X),X3)),
inference(transitivity,[status(thm)],[c1299,c1303]) ).
cnf(c1305,plain,
mult(ld(X3,X2),mult(X,i(X3))) = ld(X3,rd(mult(X2,X),X3)),
inference(transitivity,[status(thm)],[c1276,c1304]) ).
cnf(c1306,plain,
mult(ld(X3,mult(X3,X2)),mult(X,i(X3))) = ld(X3,rd(mult(mult(X3,X2),X),X3)),
inference(substitution,[status(thm)],[c1305]) ).
cnf(c1307,plain,
ld(X3,rd(mult(mult(X3,X2),X),X3)) = mult(ld(X3,mult(X3,X2)),mult(X,i(X3))),
inference(symmetry,[status(thm)],[c1306]) ).
cnf(c1308,plain,
ld(X2,mult(X2,X)) = X,
inference(substitution,[status(thm)],[c18]) ).
cnf(c1309,plain,
mult(ld(X3,mult(X3,X2)),mult(X,i(X3))) = mult(X2,mult(X,i(X3))),
inference(congruence,[status(thm)],[c1308]) ).
cnf(c1310,plain,
ld(X3,rd(mult(mult(X3,X2),X),X3)) = mult(X2,mult(X,i(X3))),
inference(transitivity,[status(thm)],[c1307,c1309]) ).
cnf(c1311,plain,
ld(op_c,rd(mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))),op_c)) = mult(mult(op_c,op_c),mult(i(mult(X,op_d)),i(op_c))),
inference(substitution,[status(thm)],[c1310]) ).
cnf(c1312,plain,
mult(mult(op_c,op_c),mult(i(mult(X,op_d)),i(op_c))) = ld(op_c,rd(mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))),op_c)),
inference(symmetry,[status(thm)],[c1311]) ).
cnf(c1313,plain,
rd(mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))),op_c) = rd(mult(op_d,i(mult(X,op_d))),op_c),
inference(congruence,[status(thm)],[c12]) ).
cnf(c1314,plain,
ld(op_c,rd(mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))),op_c)) = ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)),
inference(congruence,[status(thm)],[c1313]) ).
cnf(c1315,plain,
mult(mult(op_c,op_c),mult(i(mult(X,op_d)),i(op_c))) = ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)),
inference(transitivity,[status(thm)],[c1312,c1314]) ).
cnf(c1316,plain,
ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)) = mult(mult(op_c,op_c),mult(i(mult(X,op_d)),i(op_c))),
inference(symmetry,[status(thm)],[c1315]) ).
cnf(c1317,plain,
ld(mult(op_c,op_c),ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c))) = ld(mult(op_c,op_c),mult(mult(op_c,op_c),mult(i(mult(X,op_d)),i(op_c)))),
inference(congruence,[status(thm)],[c1316]) ).
cnf(c1318,plain,
ld(mult(op_c,op_c),mult(mult(op_c,op_c),mult(i(mult(X,op_d)),i(op_c)))) = mult(i(mult(X,op_d)),i(op_c)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c1319,plain,
ld(mult(op_c,op_c),ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c))) = mult(i(mult(X,op_d)),i(op_c)),
inference(transitivity,[status(thm)],[c1317,c1318]) ).
cnf(c1320,plain,
mult(op_c,ld(mult(op_c,op_c),ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)))) = mult(op_c,mult(i(mult(X,op_d)),i(op_c))),
inference(congruence,[status(thm)],[c1319]) ).
cnf(c1321,plain,
mult(op_c,mult(i(mult(X,op_d)),i(op_c))) = rd(mult(op_c,i(mult(X,op_d))),op_c),
inference(substitution,[status(thm)],[c89]) ).
cnf(c1322,plain,
rd(mult(op_c,i(mult(X,op_d))),op_c) = ld(i(op_c),rd(i(mult(X,op_d)),op_c)),
inference(substitution,[status(thm)],[c336]) ).
cnf(c1323,plain,
mult(op_c,mult(i(mult(X,op_d)),i(op_c))) = ld(i(op_c),rd(i(mult(X,op_d)),op_c)),
inference(transitivity,[status(thm)],[c1321,c1322]) ).
cnf(c1324,plain,
mult(op_c,ld(mult(op_c,op_c),ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)))) = ld(i(op_c),rd(i(mult(X,op_d)),op_c)),
inference(transitivity,[status(thm)],[c1320,c1323]) ).
cnf(c1325,plain,
ld(mult(op_c,op_c),mult(op_c,ld(op_c,rd(mult(op_d,i(mult(X,op_d))),op_c)))) = ld(i(op_c),rd(i(mult(X,op_d)),op_c)),
inference(transitivity,[status(thm)],[c1273,c1324]) ).
cnf(c1326,plain,
ld(mult(op_c,op_c),rd(mult(op_d,i(mult(X,op_d))),op_c)) = ld(i(op_c),rd(i(mult(X,op_d)),op_c)),
inference(transitivity,[status(thm)],[c1263,c1325]) ).
cnf(c1327,plain,
i(ld(mult(op_c,op_c),rd(mult(op_d,i(mult(X,op_d))),op_c))) = i(ld(i(op_c),rd(i(mult(X,op_d)),op_c))),
inference(congruence,[status(thm)],[c1326]) ).
cnf(c1328,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c1329,plain,
rd(X,X2) = rd(X,i(i(X2))),
inference(congruence,[status(thm)],[c1328]) ).
cnf(c1330,plain,
ld(i(X2),rd(X,X2)) = ld(i(X2),rd(X,i(i(X2)))),
inference(congruence,[status(thm)],[c1329]) ).
cnf(c1331,plain,
i(ld(i(X2),rd(X,X2))) = i(ld(i(X2),rd(X,i(i(X2))))),
inference(congruence,[status(thm)],[c1330]) ).
cnf(c1332,plain,
ld(i(X2),mult(i(X2),i(ld(i(X2),rd(X,i(i(X2))))))) = i(ld(i(X2),rd(X,i(i(X2))))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c1333,plain,
i(ld(i(X2),rd(X,i(i(X2))))) = ld(i(X2),mult(i(X2),i(ld(i(X2),rd(X,i(i(X2))))))),
inference(symmetry,[status(thm)],[c1332]) ).
cnf(c1334,plain,
mult(rd(i(X2),rd(X,i(i(X2)))),i(X2)) = mult(i(X2),i(ld(i(X2),rd(X,i(i(X2)))))),
inference(substitution,[status(thm)],[c1071]) ).
cnf(c1335,plain,
mult(i(X2),i(ld(i(X2),rd(X,i(i(X2)))))) = mult(rd(i(X2),rd(X,i(i(X2)))),i(X2)),
inference(symmetry,[status(thm)],[c1334]) ).
cnf(c1336,plain,
ld(i(X2),mult(i(X2),i(ld(i(X2),rd(X,i(i(X2))))))) = ld(i(X2),mult(rd(i(X2),rd(X,i(i(X2)))),i(X2))),
inference(congruence,[status(thm)],[c1335]) ).
cnf(c1337,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c1338,plain,
rd(ld(i(X2),X),X2) = rd(ld(i(X2),X),i(i(X2))),
inference(congruence,[status(thm)],[c1337]) ).
cnf(c1339,plain,
rd(ld(i(X2),X),i(i(X2))) = ld(i(X2),mult(X,i(X2))),
inference(substitution,[status(thm)],[c716]) ).
cnf(c1340,plain,
rd(ld(i(X2),X),X2) = ld(i(X2),mult(X,i(X2))),
inference(transitivity,[status(thm)],[c1338,c1339]) ).
cnf(c1341,plain,
rd(ld(i(X2),rd(i(X2),rd(X,i(i(X2))))),X2) = ld(i(X2),mult(rd(i(X2),rd(X,i(i(X2)))),i(X2))),
inference(substitution,[status(thm)],[c1340]) ).
cnf(c1342,plain,
ld(i(X2),mult(rd(i(X2),rd(X,i(i(X2)))),i(X2))) = rd(ld(i(X2),rd(i(X2),rd(X,i(i(X2))))),X2),
inference(symmetry,[status(thm)],[c1341]) ).
cnf(c1343,plain,
ld(i(X2),rd(i(X2),rd(X,i(i(X2))))) = rd(i(i(X2)),X),
inference(substitution,[status(thm)],[c755]) ).
cnf(c1344,plain,
rd(ld(i(X2),rd(i(X2),rd(X,i(i(X2))))),X2) = rd(rd(i(i(X2)),X),X2),
inference(congruence,[status(thm)],[c1343]) ).
cnf(c1345,plain,
rd(i(i(X2)),X) = rd(X2,X),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1346,plain,
rd(rd(i(i(X2)),X),X2) = rd(rd(X2,X),X2),
inference(congruence,[status(thm)],[c1345]) ).
cnf(c1347,plain,
rd(ld(i(X2),rd(i(X2),rd(X,i(i(X2))))),X2) = rd(rd(X2,X),X2),
inference(transitivity,[status(thm)],[c1344,c1346]) ).
cnf(c1348,plain,
ld(i(X2),mult(rd(i(X2),rd(X,i(i(X2)))),i(X2))) = rd(rd(X2,X),X2),
inference(transitivity,[status(thm)],[c1342,c1347]) ).
cnf(c1349,plain,
ld(i(X2),mult(i(X2),i(ld(i(X2),rd(X,i(i(X2))))))) = rd(rd(X2,X),X2),
inference(transitivity,[status(thm)],[c1336,c1348]) ).
cnf(c1350,plain,
i(ld(i(X2),rd(X,i(i(X2))))) = rd(rd(X2,X),X2),
inference(transitivity,[status(thm)],[c1333,c1349]) ).
cnf(c1351,plain,
i(ld(i(X2),rd(X,X2))) = rd(rd(X2,X),X2),
inference(transitivity,[status(thm)],[c1331,c1350]) ).
cnf(c1352,plain,
i(ld(i(op_c),rd(i(mult(X,op_d)),op_c))) = rd(rd(op_c,i(mult(X,op_d))),op_c),
inference(substitution,[status(thm)],[c1351]) ).
cnf(c1353,plain,
i(ld(mult(op_c,op_c),rd(mult(op_d,i(mult(X,op_d))),op_c))) = rd(rd(op_c,i(mult(X,op_d))),op_c),
inference(transitivity,[status(thm)],[c1327,c1352]) ).
cnf(c1354,plain,
ld(op_c,i(ld(mult(op_c,op_c),rd(mult(op_d,i(mult(X,op_d))),op_c)))) = ld(op_c,rd(rd(op_c,i(mult(X,op_d))),op_c)),
inference(congruence,[status(thm)],[c1353]) ).
cnf(c1355,plain,
mult(ld(X2,rd(X2,X)),i(X2)) = ld(X2,rd(rd(X2,X),X2)),
inference(substitution,[status(thm)],[c524]) ).
cnf(c1356,plain,
ld(X2,rd(rd(X2,X),X2)) = mult(ld(X2,rd(X2,X)),i(X2)),
inference(symmetry,[status(thm)],[c1355]) ).
cnf(c1357,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c1358,plain,
mult(X2,i(rd(X,i(X2)))) = mult(i(i(X2)),i(rd(X,i(X2)))),
inference(congruence,[status(thm)],[c1357]) ).
cnf(c1359,plain,
rd(ld(X2,mult(i(rd(X,X2)),X2)),X2) = mult(i(X2),i(rd(X,X2))),
inference(substitution,[status(thm)],[c179]) ).
cnf(c1360,plain,
mult(i(X2),i(rd(X,X2))) = rd(ld(X2,mult(i(rd(X,X2)),X2)),X2),
inference(symmetry,[status(thm)],[c1359]) ).
cnf(c1361,plain,
rd(ld(X2,mult(i(rd(X,X2)),X2)),X2) = rd(ld(X,X2),X2),
inference(congruence,[status(thm)],[c445]) ).
cnf(c1362,plain,
mult(i(X2),i(rd(X,X2))) = rd(ld(X,X2),X2),
inference(transitivity,[status(thm)],[c1360,c1361]) ).
cnf(c1363,plain,
mult(i(i(X2)),i(rd(X,i(X2)))) = rd(ld(X,i(X2)),i(X2)),
inference(substitution,[status(thm)],[c1362]) ).
cnf(c1364,plain,
rd(ld(X,i(X2)),i(X2)) = ld(i(i(X2)),rd(i(i(X2)),X)),
inference(substitution,[status(thm)],[c1112]) ).
cnf(c1365,plain,
ld(i(i(X2)),rd(i(i(X2)),X)) = ld(X2,rd(i(i(X2)),X)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1366,plain,
rd(i(i(X2)),X) = rd(X2,X),
inference(congruence,[status(thm)],[c117]) ).
cnf(c1367,plain,
ld(X2,rd(i(i(X2)),X)) = ld(X2,rd(X2,X)),
inference(congruence,[status(thm)],[c1366]) ).
cnf(c1368,plain,
ld(i(i(X2)),rd(i(i(X2)),X)) = ld(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c1365,c1367]) ).
cnf(c1369,plain,
rd(ld(X,i(X2)),i(X2)) = ld(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c1364,c1368]) ).
cnf(c1370,plain,
mult(i(i(X2)),i(rd(X,i(X2)))) = ld(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c1363,c1369]) ).
cnf(c1371,plain,
mult(X2,i(rd(X,i(X2)))) = ld(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c1358,c1370]) ).
cnf(c1372,plain,
ld(X2,rd(X2,X)) = mult(X2,i(rd(X,i(X2)))),
inference(symmetry,[status(thm)],[c1371]) ).
cnf(c1373,plain,
mult(ld(X2,rd(X2,X)),i(X2)) = mult(mult(X2,i(rd(X,i(X2)))),i(X2)),
inference(congruence,[status(thm)],[c1372]) ).
cnf(c1374,plain,
mult(mult(X2,i(rd(X,i(X2)))),i(X2)) = ld(i(X2),mult(i(rd(X,i(X2))),i(X2))),
inference(substitution,[status(thm)],[c104]) ).
cnf(c1375,plain,
ld(i(X2),mult(i(rd(X,i(X2))),i(X2))) = ld(X,i(X2)),
inference(substitution,[status(thm)],[c445]) ).
cnf(c1376,plain,
mult(mult(X2,i(rd(X,i(X2)))),i(X2)) = ld(X,i(X2)),
inference(transitivity,[status(thm)],[c1374,c1375]) ).
cnf(c1377,plain,
mult(ld(X2,rd(X2,X)),i(X2)) = ld(X,i(X2)),
inference(transitivity,[status(thm)],[c1373,c1376]) ).
cnf(c1378,plain,
ld(X2,rd(rd(X2,X),X2)) = ld(X,i(X2)),
inference(transitivity,[status(thm)],[c1356,c1377]) ).
cnf(c1379,plain,
ld(op_c,rd(rd(op_c,i(mult(X,op_d))),op_c)) = ld(i(mult(X,op_d)),i(op_c)),
inference(substitution,[status(thm)],[c1378]) ).
cnf(c1380,plain,
ld(op_c,i(ld(mult(op_c,op_c),rd(mult(op_d,i(mult(X,op_d))),op_c)))) = ld(i(mult(X,op_d)),i(op_c)),
inference(transitivity,[status(thm)],[c1354,c1379]) ).
cnf(c1381,plain,
ld(mult(op_d,i(mult(X,op_d))),mult(op_c,op_c)) = ld(i(mult(X,op_d)),i(op_c)),
inference(transitivity,[status(thm)],[c1260,c1380]) ).
cnf(c1382,plain,
ld(i(mult(X,op_d)),i(op_c)) = ld(mult(op_d,i(mult(X,op_d))),mult(op_c,op_c)),
inference(symmetry,[status(thm)],[c1381]) ).
cnf(c1383,plain,
mult(mult(op_d,i(mult(X,op_d))),ld(i(mult(X,op_d)),i(op_c))) = mult(mult(op_d,i(mult(X,op_d))),ld(mult(op_d,i(mult(X,op_d))),mult(op_c,op_c))),
inference(congruence,[status(thm)],[c1382]) ).
cnf(c1384,plain,
mult(i(mult(X,op_d)),mult(mult(op_d,i(mult(X,op_d))),ld(i(mult(X,op_d)),i(op_c)))) = mult(i(mult(X,op_d)),mult(mult(op_d,i(mult(X,op_d))),ld(mult(op_d,i(mult(X,op_d))),mult(op_c,op_c)))),
inference(congruence,[status(thm)],[c1383]) ).
cnf(c1385,plain,
mult(mult(op_d,i(mult(X,op_d))),ld(mult(op_d,i(mult(X,op_d))),mult(op_c,op_c))) = mult(op_c,op_c),
inference(substitution,[status(thm)],[c35]) ).
cnf(c1386,plain,
mult(i(mult(X,op_d)),mult(mult(op_d,i(mult(X,op_d))),ld(mult(op_d,i(mult(X,op_d))),mult(op_c,op_c)))) = mult(i(mult(X,op_d)),mult(op_c,op_c)),
inference(congruence,[status(thm)],[c1385]) ).
cnf(c1387,plain,
mult(i(mult(X,op_d)),mult(mult(op_d,i(mult(X,op_d))),ld(i(mult(X,op_d)),i(op_c)))) = mult(i(mult(X,op_d)),mult(op_c,op_c)),
inference(transitivity,[status(thm)],[c1384,c1386]) ).
cnf(c1388,plain,
mult(ld(mult(X,op_d),mult(op_c,mult(op_c,op_c))),i(op_c)) = mult(i(mult(X,op_d)),mult(op_c,op_c)),
inference(transitivity,[status(thm)],[c360,c1387]) ).
cnf(c1389,plain,
ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(op_c,op_c))) = mult(i(mult(X,op_d)),mult(op_c,op_c)),
inference(transitivity,[status(thm)],[c291,c1388]) ).
cnf(c1390,plain,
mult(i(mult(X,op_d)),mult(op_c,op_c)) = ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(op_c,op_c))),
inference(symmetry,[status(thm)],[c1389]) ).
cnf(c1391,plain,
mult(mult(i(mult(X,op_d)),mult(op_c,op_c)),ld(mult(i(X),mult(op_c,op_c)),mult(op_c,op_c))) = mult(ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(op_c,op_c))),ld(mult(i(X),mult(op_c,op_c)),mult(op_c,op_c))),
inference(congruence,[status(thm)],[c1390]) ).
cnf(c1392,plain,
ld(X,mult(X2,X2)) = ld(X2,i(ld(mult(X2,X2),rd(X,X2)))),
inference(symmetry,[status(thm)],[c1258]) ).
cnf(c1393,plain,
rd(i(X2),ld(X,mult(X2,X2))) = rd(i(X2),ld(X2,i(ld(mult(X2,X2),rd(X,X2))))),
inference(congruence,[status(thm)],[c1392]) ).
cnf(c1394,plain,
rd(i(X2),ld(X2,i(ld(mult(X2,X2),rd(X,X2))))) = ld(X2,mult(i(i(ld(mult(X2,X2),rd(X,X2)))),X2)),
inference(substitution,[status(thm)],[c1024]) ).
cnf(c1395,plain,
i(i(ld(mult(X2,X2),rd(X,X2)))) = ld(mult(X2,X2),rd(X,X2)),
inference(substitution,[status(thm)],[c117]) ).
cnf(c1396,plain,
mult(i(i(ld(mult(X2,X2),rd(X,X2)))),X2) = mult(ld(mult(X2,X2),rd(X,X2)),X2),
inference(congruence,[status(thm)],[c1395]) ).
cnf(c1397,plain,
ld(X2,mult(i(i(ld(mult(X2,X2),rd(X,X2)))),X2)) = ld(X2,mult(ld(mult(X2,X2),rd(X,X2)),X2)),
inference(congruence,[status(thm)],[c1396]) ).
cnf(c1398,plain,
mult(X,mult(X,X)) = mult(mult(X,X),X),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c1399,plain,
ld(mult(X2,mult(X2,X2)),mult(X,X2)) = ld(mult(mult(X2,X2),X2),mult(X,X2)),
inference(congruence,[status(thm)],[c1398]) ).
cnf(c1400,plain,
ld(mult(mult(X2,X2),X2),mult(X,X2)) = ld(X2,mult(ld(mult(X2,X2),X),X2)),
inference(substitution,[status(thm)],[c382]) ).
cnf(c1401,plain,
ld(mult(X2,mult(X2,X2)),mult(X,X2)) = ld(X2,mult(ld(mult(X2,X2),X),X2)),
inference(transitivity,[status(thm)],[c1399,c1400]) ).
cnf(c1402,plain,
ld(mult(X2,mult(X2,X2)),mult(rd(X,X2),X2)) = ld(X2,mult(ld(mult(X2,X2),rd(X,X2)),X2)),
inference(substitution,[status(thm)],[c1401]) ).
cnf(c1403,plain,
ld(X2,mult(ld(mult(X2,X2),rd(X,X2)),X2)) = ld(mult(X2,mult(X2,X2)),mult(rd(X,X2),X2)),
inference(symmetry,[status(thm)],[c1402]) ).
cnf(c1404,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c151]) ).
cnf(c1405,plain,
ld(mult(X2,mult(X2,X2)),mult(rd(X,X2),X2)) = ld(mult(X2,mult(X2,X2)),X),
inference(congruence,[status(thm)],[c1404]) ).
cnf(c1406,plain,
ld(X2,mult(ld(mult(X2,X2),rd(X,X2)),X2)) = ld(mult(X2,mult(X2,X2)),X),
inference(transitivity,[status(thm)],[c1403,c1405]) ).
cnf(c1407,plain,
ld(X2,mult(i(i(ld(mult(X2,X2),rd(X,X2)))),X2)) = ld(mult(X2,mult(X2,X2)),X),
inference(transitivity,[status(thm)],[c1397,c1406]) ).
cnf(c1408,plain,
rd(i(X2),ld(X2,i(ld(mult(X2,X2),rd(X,X2))))) = ld(mult(X2,mult(X2,X2)),X),
inference(transitivity,[status(thm)],[c1394,c1407]) ).
cnf(c1409,plain,
rd(i(X2),ld(X,mult(X2,X2))) = ld(mult(X2,mult(X2,X2)),X),
inference(transitivity,[status(thm)],[c1393,c1408]) ).
cnf(c1410,plain,
ld(mult(X2,mult(X2,X2)),X) = rd(i(X2),ld(X,mult(X2,X2))),
inference(symmetry,[status(thm)],[c1409]) ).
cnf(c1411,plain,
mult(ld(mult(X2,mult(X2,X2)),X),ld(X,mult(X2,X2))) = mult(rd(i(X2),ld(X,mult(X2,X2))),ld(X,mult(X2,X2))),
inference(congruence,[status(thm)],[c1410]) ).
cnf(c1412,plain,
mult(rd(i(X2),ld(X,mult(X2,X2))),ld(X,mult(X2,X2))) = i(X2),
inference(substitution,[status(thm)],[c151]) ).
cnf(c1413,plain,
mult(ld(mult(X2,mult(X2,X2)),X),ld(X,mult(X2,X2))) = i(X2),
inference(transitivity,[status(thm)],[c1411,c1412]) ).
cnf(c1414,plain,
mult(ld(mult(op_c,mult(op_c,op_c)),mult(i(X),mult(op_c,op_c))),ld(mult(i(X),mult(op_c,op_c)),mult(op_c,op_c))) = i(op_c),
inference(substitution,[status(thm)],[c1413]) ).
cnf(c1415,plain,
mult(mult(i(mult(X,op_d)),mult(op_c,op_c)),ld(mult(i(X),mult(op_c,op_c)),mult(op_c,op_c))) = i(op_c),
inference(transitivity,[status(thm)],[c1391,c1414]) ).
cnf(c1416,plain,
mult(mult(i(mult(X,op_d)),mult(op_c,op_c)),ld(mult(op_c,op_c),mult(X,mult(op_c,op_c)))) = i(op_c),
inference(transitivity,[status(thm)],[c272,c1415]) ).
cnf(c1417,plain,
mult(mult(i(mult(X,op_d)),X),mult(op_c,op_c)) = i(op_c),
inference(transitivity,[status(thm)],[c255,c1416]) ).
cnf(c1418,plain,
i(op_c) = mult(mult(i(mult(X,op_d)),X),mult(op_c,op_c)),
inference(symmetry,[status(thm)],[c1417]) ).
cnf(c1419,plain,
rd(i(op_c),mult(op_c,op_c)) = rd(mult(mult(i(mult(X,op_d)),X),mult(op_c,op_c)),mult(op_c,op_c)),
inference(congruence,[status(thm)],[c1418]) ).
cnf(c1420,plain,
rd(mult(mult(i(mult(X,op_d)),X),mult(op_c,op_c)),mult(op_c,op_c)) = mult(i(mult(X,op_d)),X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1421,plain,
rd(i(op_c),mult(op_c,op_c)) = mult(i(mult(X,op_d)),X),
inference(transitivity,[status(thm)],[c1419,c1420]) ).
cnf(c1422,plain,
ld(op_c,i(mult(op_c,op_c))) = mult(i(mult(X,op_d)),X),
inference(transitivity,[status(thm)],[c254,c1421]) ).
cnf(c1423,plain,
i(mult(op_c,mult(op_c,op_c))) = mult(i(mult(X,op_d)),X),
inference(transitivity,[status(thm)],[c231,c1422]) ).
cnf(c1424,plain,
mult(i(mult(X,op_d)),X) = i(mult(op_c,mult(op_c,op_c))),
inference(symmetry,[status(thm)],[c1423]) ).
cnf(c1425,plain,
mult(mult(i(mult(X,op_d)),X),mult(op_c,mult(op_c,op_c))) = mult(i(mult(op_c,mult(op_c,op_c))),mult(op_c,mult(op_c,op_c))),
inference(congruence,[status(thm)],[c1424]) ).
cnf(c1426,plain,
ld(mult(X,op_d),mult(mult(i(mult(X,op_d)),X),mult(op_c,mult(op_c,op_c)))) = ld(mult(X,op_d),mult(i(mult(op_c,mult(op_c,op_c))),mult(op_c,mult(op_c,op_c)))),
inference(congruence,[status(thm)],[c1425]) ).
cnf(c1427,plain,
mult(i(mult(op_c,mult(op_c,op_c))),mult(op_c,mult(op_c,op_c))) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c1428,plain,
ld(mult(X,op_d),mult(i(mult(op_c,mult(op_c,op_c))),mult(op_c,mult(op_c,op_c)))) = ld(mult(X,op_d),unit),
inference(congruence,[status(thm)],[c1427]) ).
cnf(c1429,plain,
ld(mult(X,op_d),unit) = i(mult(X,op_d)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c1430,plain,
ld(mult(X,op_d),mult(i(mult(op_c,mult(op_c,op_c))),mult(op_c,mult(op_c,op_c)))) = i(mult(X,op_d)),
inference(transitivity,[status(thm)],[c1428,c1429]) ).
cnf(c1431,plain,
ld(mult(X,op_d),mult(mult(i(mult(X,op_d)),X),mult(op_c,mult(op_c,op_c)))) = i(mult(X,op_d)),
inference(transitivity,[status(thm)],[c1426,c1430]) ).
cnf(c1432,plain,
ld(mult(op_c,mult(op_c,op_c)),ld(X,mult(i(mult(X,op_d)),mult(X,op_d)))) = i(mult(X,op_d)),
inference(transitivity,[status(thm)],[c80,c1431]) ).
cnf(c1433,plain,
ld(mult(op_c,mult(op_c,op_c)),ld(X,unit)) = i(mult(X,op_d)),
inference(transitivity,[status(thm)],[c27,c1432]) ).
cnf(c1434,plain,
ld(mult(op_c,mult(op_c,op_c)),i(X)) = i(mult(X,op_d)),
inference(transitivity,[status(thm)],[c22,c1433]) ).
cnf(c1435,plain,
i(mult(X,op_d)) = ld(mult(op_c,mult(op_c,op_c)),i(X)),
inference(symmetry,[status(thm)],[c1434]) ).
cnf(c1436,plain,
mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))) = mult(mult(op_c,mult(op_c,op_c)),ld(mult(op_c,mult(op_c,op_c)),i(X))),
inference(congruence,[status(thm)],[c1435]) ).
cnf(c1437,plain,
mult(mult(op_c,mult(op_c,op_c)),ld(mult(op_c,mult(op_c,op_c)),i(X))) = i(X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c1438,plain,
mult(mult(op_c,mult(op_c,op_c)),i(mult(X,op_d))) = i(X),
inference(transitivity,[status(thm)],[c1436,c1437]) ).
cnf(c1439,plain,
mult(op_d,i(mult(X,op_d))) = i(X),
inference(transitivity,[status(thm)],[c13,c1438]) ).
cnf(c1440,plain,
mult(op_d,i(mult(a,op_d))) = i(a),
inference(substitution,[status(thm)],[c1439]) ).
cnf(c1441,plain,
$false,
inference(resolution,[status(thm)],[c1,c1440]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP691-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:36:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 198.25/25.49 Command-line arguments: --flatten --complete-subsets
% 198.25/25.49
% 198.25/25.49 % SZS status Unsatisfiable
% 198.25/25.49
% 199.85/25.63 % SZS output start CNFRefutation
% See solution above
% 207.74/26.64
% 207.74/26.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------