%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP721-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 10:11:51 AM UTC 2026
% Result : Unsatisfiable 213.12s 31.21s
% Output : CNFRefutation 218.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 100
% Number of leaves : 9
% Syntax : Number of clauses : 830 ( 830 unt; 0 nHn; 12 RR)
% Number of literals : 830 ( 829 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 1683 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(mult(a,a),mult(b,b)) != mult(f(a,b),f(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c3,plain,
ld(X,mult(X,ld(mult(X,X),X))) = ld(mult(X,X),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
ld(mult(X,X),X) = ld(X,mult(X,ld(mult(X,X),X))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c6,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
ld(mult(X,X),X) = ld(mult(X,X),mult(X,unit)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
mult(X,ld(mult(X,X),X)) = mult(X,ld(mult(X,X),mult(X,unit))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c11,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
mult(X2,X) = mult(X2,mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
ld(mult(X2,X2),mult(X2,X)) = ld(mult(X2,X2),mult(X2,mult(X2,ld(X2,X)))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
mult(X2,ld(mult(X2,X2),mult(X2,X))) = mult(X2,ld(mult(X2,X2),mult(X2,mult(X2,ld(X2,X))))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
mult(A2,B2) = mult(B2,A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c17,plain,
mult(X2,X) = mult(X,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
mult(X,X2) = mult(X2,X),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
ld(X2,mult(X,X2)) = ld(X2,mult(X2,X)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
ld(X2,mult(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
ld(X2,mult(X,X2)) = X,
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
ld(mult(X,X),mult(X,mult(X,X))) = X,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
X = ld(mult(X,X),mult(X,mult(X,X))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
mult(X2,ld(mult(X2,X2),mult(X2,mult(X2,X)))) = mult(ld(mult(X2,X2),mult(X2,mult(X2,X2))),ld(mult(X2,X2),mult(X2,mult(X2,X)))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,axiom,
ld(mult(A2,B2),mult(A2,mult(B2,mult(C,D)))) = mult(ld(mult(A2,B2),mult(A2,mult(B2,C))),ld(mult(A2,B2),mult(A2,mult(B2,D)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c26,plain,
ld(mult(X2,X2),mult(X2,mult(X2,mult(X2,X)))) = mult(ld(mult(X2,X2),mult(X2,mult(X2,X2))),ld(mult(X2,X2),mult(X2,mult(X2,X)))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
mult(ld(mult(X2,X2),mult(X2,mult(X2,X2))),ld(mult(X2,X2),mult(X2,mult(X2,X)))) = ld(mult(X2,X2),mult(X2,mult(X2,mult(X2,X)))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
mult(X2,ld(mult(X2,X2),mult(X2,mult(X2,X)))) = ld(mult(X2,X2),mult(X2,mult(X2,mult(X2,X)))),
inference(transitivity,[status(thm)],[c24,c27]) ).
cnf(c29,plain,
mult(X2,ld(mult(X2,X2),mult(X2,mult(X2,ld(X2,X))))) = ld(mult(X2,X2),mult(X2,mult(X2,mult(X2,ld(X2,X))))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c31,plain,
mult(X2,mult(X2,ld(X2,X))) = mult(X2,X),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
mult(X2,mult(X2,mult(X2,ld(X2,X)))) = mult(X2,mult(X2,X)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
ld(mult(X2,X2),mult(X2,mult(X2,mult(X2,ld(X2,X))))) = ld(mult(X2,X2),mult(X2,mult(X2,X))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
mult(X2,ld(mult(X2,X2),mult(X2,mult(X2,ld(X2,X))))) = ld(mult(X2,X2),mult(X2,mult(X2,X))),
inference(transitivity,[status(thm)],[c29,c33]) ).
cnf(c35,plain,
mult(X2,ld(mult(X2,X2),mult(X2,X))) = ld(mult(X2,X2),mult(X2,mult(X2,X))),
inference(transitivity,[status(thm)],[c15,c34]) ).
cnf(c36,plain,
mult(X,ld(mult(X,X),mult(X,unit))) = ld(mult(X,X),mult(X,mult(X,unit))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c38,plain,
mult(X,mult(X,unit)) = mult(X,X),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
ld(mult(X,X),mult(X,mult(X,unit))) = ld(mult(X,X),mult(X,X)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c41,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
ld(X,X) = ld(X,mult(X,unit)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
ld(X,mult(X,unit)) = unit,
inference(substitution,[status(thm)],[c2]) ).
cnf(c44,plain,
ld(X,X) = unit,
inference(transitivity,[status(thm)],[c42,c43]) ).
cnf(c45,plain,
ld(mult(X,X),mult(X,X)) = unit,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
ld(mult(X,X),mult(X,mult(X,unit))) = unit,
inference(transitivity,[status(thm)],[c39,c45]) ).
cnf(c47,plain,
mult(X,ld(mult(X,X),mult(X,unit))) = unit,
inference(transitivity,[status(thm)],[c36,c46]) ).
cnf(c48,plain,
mult(X,ld(mult(X,X),X)) = unit,
inference(transitivity,[status(thm)],[c9,c47]) ).
cnf(c49,plain,
ld(X,mult(X,ld(mult(X,X),X))) = ld(X,unit),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
ld(mult(X,X),X) = ld(X,unit),
inference(transitivity,[status(thm)],[c4,c49]) ).
cnf(c51,plain,
ld(X,unit) = ld(mult(X,X),X),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
ld(ld(X,unit),X) = ld(ld(mult(X,X),X),X),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c54,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
ld(ld(X2,X),X) = ld(ld(X2,X),mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
ld(ld(X2,X),mult(X2,ld(X2,X))) = X2,
inference(substitution,[status(thm)],[c21]) ).
cnf(c57,plain,
ld(ld(X2,X),X) = X2,
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
ld(ld(mult(X,X),X),X) = mult(X,X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
ld(ld(X,unit),X) = mult(X,X),
inference(transitivity,[status(thm)],[c52,c58]) ).
cnf(c60,plain,
mult(X,X) = ld(ld(X,unit),X),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
ld(ld(X,unit),unit) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c62,plain,
X = ld(ld(X,unit),unit),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
ld(ld(X,unit),X) = ld(ld(X,unit),ld(ld(X,unit),unit)),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
ld(X,unit) = ld(mult(X,X),X),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c65,plain,
ld(ld(X,unit),unit) = ld(ld(mult(X,X),X),unit),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
ld(ld(X,unit),ld(ld(X,unit),unit)) = ld(ld(X,unit),ld(ld(mult(X,X),X),unit)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
ld(X,unit) = ld(mult(X,X),X),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c68,plain,
ld(ld(X,unit),ld(ld(mult(X,X),X),unit)) = ld(ld(mult(X,X),X),ld(ld(mult(X,X),X),unit)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
ld(ld(mult(X,X),X),mult(ld(mult(X,X),X),mult(f(X,X),ld(mult(X,X),X)))) = mult(f(X,X),ld(mult(X,X),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c70,plain,
mult(f(X,X),ld(mult(X,X),X)) = ld(ld(mult(X,X),X),mult(ld(mult(X,X),X),mult(f(X,X),ld(mult(X,X),X)))),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
mult(ld(mult(X,X),X),f(X,X)) = mult(f(X,X),ld(mult(X,X),X)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c72,plain,
mult(f(X,X),ld(mult(X,X),X)) = mult(ld(mult(X,X),X),f(X,X)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
mult(ld(mult(X,X),X),mult(f(X,X),ld(mult(X,X),X))) = mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),f(X,X))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,axiom,
f(A2,B2) = ld(mult(ld(mult(A2,B2),A2),ld(mult(A2,B2),B2)),unit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
cnf(c75,plain,
f(X,X) = ld(mult(ld(mult(X,X),X),ld(mult(X,X),X)),unit),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
mult(ld(mult(X,X),X),f(X,X)) = mult(ld(mult(X,X),X),ld(mult(ld(mult(X,X),X),ld(mult(X,X),X)),unit)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),f(X,X))) = mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),ld(mult(ld(mult(X,X),X),ld(mult(X,X),X)),unit))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
mult(X,mult(X2,X2)) = mult(mult(X2,X2),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c79,plain,
mult(mult(X2,X2),X) = mult(X,mult(X2,X2)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
mult(X2,mult(mult(X2,X2),X)) = mult(X2,mult(X,mult(X2,X2))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
mult(X2,mult(X2,mult(mult(X2,X2),X))) = mult(X2,mult(X2,mult(X,mult(X2,X2)))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
ld(mult(X2,X2),mult(X2,mult(X2,mult(mult(X2,X2),X)))) = ld(mult(X2,X2),mult(X2,mult(X2,mult(X,mult(X2,X2))))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
mult(mult(X2,X2),X) = mult(X,mult(X2,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c84,plain,
mult(X,mult(X2,X2)) = mult(mult(X2,X2),X),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
mult(X2,mult(X,mult(X2,X2))) = mult(X2,mult(mult(X2,X2),X)),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
mult(X2,mult(X2,mult(X,mult(X2,X2)))) = mult(X2,mult(X2,mult(mult(X2,X2),X))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
ld(mult(X2,X2),mult(X2,mult(X2,mult(X,mult(X2,X2))))) = ld(mult(X2,X2),mult(X2,mult(X2,mult(mult(X2,X2),X)))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
ld(mult(X2,X2),mult(X2,mult(X2,mult(mult(X2,X2),X)))) = mult(ld(mult(X2,X2),mult(X2,mult(X2,mult(X2,X2)))),ld(mult(X2,X2),mult(X2,mult(X2,X)))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c89,plain,
ld(mult(X,X),mult(X,mult(X,mult(X,X)))) = mult(ld(mult(X,X),mult(X,mult(X,X))),ld(mult(X,X),mult(X,mult(X,X)))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c90,axiom,
ld(A2,mult(mult(B2,C2),A2)) = mult(ld(A2,mult(B2,A2)),ld(A2,mult(C2,A2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c91,plain,
ld(mult(X,X),mult(mult(X,X),mult(X,X))) = mult(ld(mult(X,X),mult(X,mult(X,X))),ld(mult(X,X),mult(X,mult(X,X)))),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
mult(ld(mult(X,X),mult(X,mult(X,X))),ld(mult(X,X),mult(X,mult(X,X)))) = ld(mult(X,X),mult(mult(X,X),mult(X,X))),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
ld(mult(X,X),mult(mult(X,X),mult(X,X))) = mult(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c94,plain,
mult(ld(mult(X,X),mult(X,mult(X,X))),ld(mult(X,X),mult(X,mult(X,X)))) = mult(X,X),
inference(transitivity,[status(thm)],[c92,c93]) ).
cnf(c95,plain,
ld(mult(X,X),mult(X,mult(X,mult(X,X)))) = mult(X,X),
inference(transitivity,[status(thm)],[c89,c94]) ).
cnf(c96,plain,
mult(ld(mult(X2,X2),mult(X2,mult(X2,mult(X2,X2)))),ld(mult(X2,X2),mult(X2,mult(X2,X)))) = mult(mult(X2,X2),ld(mult(X2,X2),mult(X2,mult(X2,X)))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
mult(mult(X2,X2),ld(mult(X2,X2),mult(X2,mult(X2,X)))) = mult(X2,mult(X2,X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c98,plain,
mult(ld(mult(X2,X2),mult(X2,mult(X2,mult(X2,X2)))),ld(mult(X2,X2),mult(X2,mult(X2,X)))) = mult(X2,mult(X2,X)),
inference(transitivity,[status(thm)],[c96,c97]) ).
cnf(c99,plain,
ld(mult(X2,X2),mult(X2,mult(X2,mult(mult(X2,X2),X)))) = mult(X2,mult(X2,X)),
inference(transitivity,[status(thm)],[c88,c98]) ).
cnf(c100,plain,
ld(mult(X2,X2),mult(X2,mult(X2,mult(X,mult(X2,X2))))) = mult(X2,mult(X2,X)),
inference(transitivity,[status(thm)],[c87,c99]) ).
cnf(c101,plain,
ld(mult(X2,X2),mult(X2,mult(X2,mult(mult(X2,X2),X)))) = mult(X2,mult(X2,X)),
inference(transitivity,[status(thm)],[c82,c100]) ).
cnf(c102,plain,
ld(mult(X2,X2),mult(X2,mult(X2,mult(mult(X2,X2),ld(mult(X2,X2),X))))) = mult(X2,mult(X2,ld(mult(X2,X2),X))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
mult(X2,mult(X2,ld(mult(X2,X2),X))) = ld(mult(X2,X2),mult(X2,mult(X2,mult(mult(X2,X2),ld(mult(X2,X2),X))))),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
mult(mult(X2,X2),ld(mult(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c105,plain,
mult(X2,mult(mult(X2,X2),ld(mult(X2,X2),X))) = mult(X2,X),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
mult(X2,mult(X2,mult(mult(X2,X2),ld(mult(X2,X2),X)))) = mult(X2,mult(X2,X)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
ld(mult(X2,X2),mult(X2,mult(X2,mult(mult(X2,X2),ld(mult(X2,X2),X))))) = ld(mult(X2,X2),mult(X2,mult(X2,X))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
mult(X2,mult(X2,ld(mult(X2,X2),X))) = ld(mult(X2,X2),mult(X2,mult(X2,X))),
inference(transitivity,[status(thm)],[c103,c107]) ).
cnf(c109,plain,
mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),ld(mult(ld(mult(X,X),X),ld(mult(X,X),X)),unit))) = ld(mult(ld(mult(X,X),X),ld(mult(X,X),X)),mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),unit))),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
ld(ld(mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)),unit),unit) = mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c111,plain,
mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)) = ld(ld(mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)),unit),unit),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
f(X2,X) = ld(mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)),unit),
inference(substitution,[status(thm)],[c74]) ).
cnf(c113,plain,
ld(mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)),unit) = f(X2,X),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
ld(ld(mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)),unit),unit) = ld(f(X2,X),unit),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)) = ld(f(X2,X),unit),
inference(transitivity,[status(thm)],[c111,c114]) ).
cnf(c116,plain,
mult(ld(mult(X,X),X),ld(mult(X,X),X)) = ld(f(X,X),unit),
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
ld(mult(ld(mult(X,X),X),ld(mult(X,X),X)),mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),unit))) = ld(ld(f(X,X),unit),mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),unit))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
mult(ld(mult(X,X),X),unit) = ld(mult(X,X),X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c119,plain,
mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),unit)) = mult(ld(mult(X,X),X),ld(mult(X,X),X)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
ld(ld(f(X,X),unit),mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),unit))) = ld(ld(f(X,X),unit),mult(ld(mult(X,X),X),ld(mult(X,X),X))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
mult(ld(mult(X,X),X),ld(mult(X,X),X)) = ld(f(X,X),unit),
inference(substitution,[status(thm)],[c115]) ).
cnf(c122,plain,
ld(ld(f(X,X),unit),mult(ld(mult(X,X),X),ld(mult(X,X),X))) = ld(ld(f(X,X),unit),ld(f(X,X),unit)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
ld(ld(f(X,X),unit),ld(f(X,X),unit)) = unit,
inference(substitution,[status(thm)],[c44]) ).
cnf(c124,plain,
ld(ld(f(X,X),unit),mult(ld(mult(X,X),X),ld(mult(X,X),X))) = unit,
inference(transitivity,[status(thm)],[c122,c123]) ).
cnf(c125,plain,
ld(ld(f(X,X),unit),mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),unit))) = unit,
inference(transitivity,[status(thm)],[c120,c124]) ).
cnf(c126,plain,
ld(mult(ld(mult(X,X),X),ld(mult(X,X),X)),mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),unit))) = unit,
inference(transitivity,[status(thm)],[c117,c125]) ).
cnf(c127,plain,
mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),ld(mult(ld(mult(X,X),X),ld(mult(X,X),X)),unit))) = unit,
inference(transitivity,[status(thm)],[c109,c126]) ).
cnf(c128,plain,
mult(ld(mult(X,X),X),mult(ld(mult(X,X),X),f(X,X))) = unit,
inference(transitivity,[status(thm)],[c77,c127]) ).
cnf(c129,plain,
mult(ld(mult(X,X),X),mult(f(X,X),ld(mult(X,X),X))) = unit,
inference(transitivity,[status(thm)],[c73,c128]) ).
cnf(c130,plain,
ld(ld(mult(X,X),X),mult(ld(mult(X,X),X),mult(f(X,X),ld(mult(X,X),X)))) = ld(ld(mult(X,X),X),unit),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
mult(f(X,X),ld(mult(X,X),X)) = ld(ld(mult(X,X),X),unit),
inference(transitivity,[status(thm)],[c70,c130]) ).
cnf(c132,plain,
ld(ld(mult(X,X),X),unit) = mult(f(X,X),ld(mult(X,X),X)),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
ld(ld(mult(X,X),X),ld(ld(mult(X,X),X),unit)) = ld(ld(mult(X,X),X),mult(f(X,X),ld(mult(X,X),X))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
ld(ld(mult(X,X),X),mult(f(X,X),ld(mult(X,X),X))) = f(X,X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c135,plain,
ld(ld(mult(X,X),X),ld(ld(mult(X,X),X),unit)) = f(X,X),
inference(transitivity,[status(thm)],[c133,c134]) ).
cnf(c136,plain,
ld(ld(X,unit),ld(ld(mult(X,X),X),unit)) = f(X,X),
inference(transitivity,[status(thm)],[c68,c135]) ).
cnf(c137,plain,
ld(ld(X,unit),ld(ld(X,unit),unit)) = f(X,X),
inference(transitivity,[status(thm)],[c66,c136]) ).
cnf(c138,plain,
ld(ld(X,unit),X) = f(X,X),
inference(transitivity,[status(thm)],[c63,c137]) ).
cnf(c139,plain,
mult(X,X) = f(X,X),
inference(transitivity,[status(thm)],[c60,c138]) ).
cnf(c140,plain,
mult(a,a) = f(a,a),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
mult(mult(a,a),mult(b,b)) = mult(f(a,a),mult(b,b)),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
mult(b,b) = f(b,b),
inference(substitution,[status(thm)],[c139]) ).
cnf(c143,plain,
mult(f(a,a),mult(b,b)) = mult(f(a,a),f(b,b)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
mult(f(X,X),f(X2,X2)) = mult(f(X2,X2),f(X,X)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c145,plain,
mult(f(X2,X2),f(X,X)) = mult(f(X,X),f(X2,X2)),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)) = mult(ld(mult(X2,X),X),ld(mult(X2,X),X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c147,plain,
mult(ld(mult(X2,X),X),ld(mult(X2,X),X2)) = mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
ld(mult(ld(mult(X2,X),X),ld(mult(X2,X),X2)),unit) = ld(mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)),unit),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
f(X2,X) = ld(mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)),unit),
inference(substitution,[status(thm)],[c74]) ).
cnf(c150,plain,
ld(mult(ld(mult(X2,X),X2),ld(mult(X2,X),X)),unit) = f(X2,X),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
ld(mult(ld(mult(X2,X),X),ld(mult(X2,X),X2)),unit) = f(X2,X),
inference(transitivity,[status(thm)],[c148,c150]) ).
cnf(c152,plain,
ld(mult(ld(mult(X,X2),X2),ld(mult(X,X2),X)),unit) = f(X,X2),
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
f(X,X2) = ld(mult(ld(mult(X,X2),X2),ld(mult(X,X2),X)),unit),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
X = ld(X2,mult(X,X2)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c155,plain,
ld(mult(X,X2),X) = ld(mult(X,X2),ld(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
mult(ld(mult(X,X2),X2),ld(mult(X,X2),X)) = mult(ld(mult(X,X2),X2),ld(mult(X,X2),ld(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
ld(mult(ld(mult(X,X2),X2),ld(mult(X,X2),X)),unit) = ld(mult(ld(mult(X,X2),X2),ld(mult(X,X2),ld(X2,mult(X,X2)))),unit),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c159,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
ld(X2,ld(X,X2)) = ld(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
mult(ld(X2,X),ld(X2,ld(X,X2))) = mult(ld(X2,X),ld(mult(X,ld(X,X2)),ld(X,X2))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
ld(mult(ld(X2,X),ld(X2,ld(X,X2))),unit) = ld(mult(ld(X2,X),ld(mult(X,ld(X,X2)),ld(X,X2))),unit),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c164,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
ld(X2,X) = ld(mult(X,ld(X,X2)),X),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
mult(ld(X2,X),ld(mult(X,ld(X,X2)),ld(X,X2))) = mult(ld(mult(X,ld(X,X2)),X),ld(mult(X,ld(X,X2)),ld(X,X2))),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
ld(mult(ld(X2,X),ld(mult(X,ld(X,X2)),ld(X,X2))),unit) = ld(mult(ld(mult(X,ld(X,X2)),X),ld(mult(X,ld(X,X2)),ld(X,X2))),unit),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
f(X,ld(X,X2)) = ld(mult(ld(mult(X,ld(X,X2)),X),ld(mult(X,ld(X,X2)),ld(X,X2))),unit),
inference(substitution,[status(thm)],[c74]) ).
cnf(c169,plain,
ld(mult(ld(mult(X,ld(X,X2)),X),ld(mult(X,ld(X,X2)),ld(X,X2))),unit) = f(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
ld(mult(ld(X2,X),ld(mult(X,ld(X,X2)),ld(X,X2))),unit) = f(X,ld(X,X2)),
inference(transitivity,[status(thm)],[c167,c169]) ).
cnf(c171,plain,
ld(mult(ld(X2,X),ld(X2,ld(X,X2))),unit) = f(X,ld(X,X2)),
inference(transitivity,[status(thm)],[c162,c170]) ).
cnf(c172,plain,
ld(mult(ld(mult(X,X2),X2),ld(mult(X,X2),ld(X2,mult(X,X2)))),unit) = f(X2,ld(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
f(X2,ld(X2,mult(X,X2))) = f(X2,X),
inference(congruence,[status(thm)],[c21]) ).
cnf(c174,plain,
ld(mult(ld(mult(X,X2),X2),ld(mult(X,X2),ld(X2,mult(X,X2)))),unit) = f(X2,X),
inference(transitivity,[status(thm)],[c172,c173]) ).
cnf(c175,plain,
ld(mult(ld(mult(X,X2),X2),ld(mult(X,X2),X)),unit) = f(X2,X),
inference(transitivity,[status(thm)],[c157,c174]) ).
cnf(c176,plain,
f(X,X2) = f(X2,X),
inference(transitivity,[status(thm)],[c153,c175]) ).
cnf(c177,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c178,plain,
f(f(X2,X),f(X2,X)) = f(f(X,X2),f(X2,X)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
ld(f(X2,X2),f(f(X2,X),f(X2,X))) = ld(f(X2,X2),f(f(X,X2),f(X2,X))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c181,plain,
f(f(X,X2),f(X2,X)) = f(f(X,X2),f(X,X2)),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
ld(f(X2,X2),f(f(X,X2),f(X2,X))) = ld(f(X2,X2),f(f(X,X2),f(X,X2))),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
f(X,X) = mult(X,X),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c184,plain,
ld(X2,f(X,X)) = ld(X2,mult(X,X)),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
mult(ld(X2,f(X,X)),ld(ld(X2,X),unit)) = mult(ld(X2,mult(X,X)),ld(ld(X2,X),unit)),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
ld(X,mult(X,ld(ld(X2,X),unit))) = ld(ld(X2,X),unit),
inference(substitution,[status(thm)],[c2]) ).
cnf(c187,plain,
ld(ld(X2,X),unit) = ld(X,mult(X,ld(ld(X2,X),unit))),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
mult(ld(X2,mult(X,X3)),ld(ld(X2,X),unit)) = mult(ld(X2,mult(X,X3)),ld(X,mult(X,ld(ld(X2,X),unit)))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
mult(X2,X) = mult(X,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c190,plain,
mult(X,X2) = mult(X2,X),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
mult(ld(X2,unit),mult(X,X2)) = mult(ld(X2,unit),mult(X2,X)),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
ld(X2,mult(X2,mult(ld(X2,unit),mult(X2,X)))) = mult(ld(X2,unit),mult(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c193,plain,
mult(ld(X2,unit),mult(X2,X)) = ld(X2,mult(X2,mult(ld(X2,unit),mult(X2,X)))),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,axiom,
mult(unit,A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c195,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c194]) ).
cnf(c196,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
ld(unit,X) = ld(unit,mult(unit,X)),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
ld(unit,mult(unit,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c199,plain,
ld(unit,X) = X,
inference(transitivity,[status(thm)],[c197,c198]) ).
cnf(c200,plain,
ld(unit,mult(X2,mult(ld(X2,unit),mult(X2,X)))) = mult(X2,mult(ld(X2,unit),mult(X2,X))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
mult(X2,mult(ld(X2,unit),mult(X2,X))) = ld(unit,mult(X2,mult(ld(X2,unit),mult(X2,X)))),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
mult(ld(X3,X2),X) = mult(X,ld(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c203,plain,
mult(X,ld(X3,X2)) = mult(ld(X3,X2),X),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
mult(X3,mult(X,ld(X3,X2))) = mult(X3,mult(ld(X3,X2),X)),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
ld(X2,mult(X3,mult(X,ld(X3,X2)))) = ld(X2,mult(X3,mult(ld(X3,X2),X))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
mult(X3,ld(X2,mult(X3,mult(X,ld(X3,X2))))) = mult(X3,ld(X2,mult(X3,mult(ld(X3,X2),X)))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c208,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
ld(X2,mult(X3,mult(ld(X3,X2),X))) = ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),X))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
mult(X3,ld(X2,mult(X3,mult(ld(X3,X2),X)))) = mult(X3,ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),X)))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
ld(mult(X2,X),mult(X2,mult(X2,X))) = X2,
inference(substitution,[status(thm)],[c21]) ).
cnf(c212,plain,
X2 = ld(mult(X2,X),mult(X2,mult(X2,X))),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
mult(X3,ld(mult(X3,X2),mult(X3,mult(X2,X)))) = mult(ld(mult(X3,X2),mult(X3,mult(X3,X2))),ld(mult(X3,X2),mult(X3,mult(X2,X)))),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c215,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
mult(X3,X) = mult(X3,mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
ld(mult(X3,X2),mult(X3,X)) = ld(mult(X3,X2),mult(X3,mult(X2,ld(X2,X)))),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
mult(ld(mult(X3,X2),mult(X3,X)),ld(mult(X3,X2),mult(X3,mult(X2,X4)))) = mult(ld(mult(X3,X2),mult(X3,mult(X2,ld(X2,X)))),ld(mult(X3,X2),mult(X3,mult(X2,X4)))),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
ld(mult(X4,X3),mult(X4,mult(X3,mult(ld(X3,X2),X)))) = mult(ld(mult(X4,X3),mult(X4,mult(X3,ld(X3,X2)))),ld(mult(X4,X3),mult(X4,mult(X3,X)))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c220,plain,
mult(ld(mult(X4,X3),mult(X4,mult(X3,ld(X3,X2)))),ld(mult(X4,X3),mult(X4,mult(X3,X)))) = ld(mult(X4,X3),mult(X4,mult(X3,mult(ld(X3,X2),X)))),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
mult(ld(X3,X2),X) = mult(X,ld(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c222,plain,
mult(X3,mult(ld(X3,X2),X)) = mult(X3,mult(X,ld(X3,X2))),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
mult(X4,mult(X3,mult(ld(X3,X2),X))) = mult(X4,mult(X3,mult(X,ld(X3,X2)))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
ld(mult(X4,X3),mult(X4,mult(X3,mult(ld(X3,X2),X)))) = ld(mult(X4,X3),mult(X4,mult(X3,mult(X,ld(X3,X2))))),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
mult(ld(mult(X4,X3),mult(X4,mult(X3,ld(X3,X2)))),ld(mult(X4,X3),mult(X4,mult(X3,X)))) = ld(mult(X4,X3),mult(X4,mult(X3,mult(X,ld(X3,X2))))),
inference(transitivity,[status(thm)],[c220,c224]) ).
cnf(c226,plain,
mult(ld(mult(X4,X3),mult(X4,X2)),ld(mult(X4,X3),mult(X4,mult(X3,X)))) = ld(mult(X4,X3),mult(X4,mult(X3,mult(X,ld(X3,X2))))),
inference(transitivity,[status(thm)],[c218,c225]) ).
cnf(c227,plain,
mult(ld(mult(X3,X2),mult(X3,mult(X3,X2))),ld(mult(X3,X2),mult(X3,mult(X2,X)))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(X,ld(X2,mult(X3,X2)))))),
inference(substitution,[status(thm)],[c226]) ).
cnf(c228,plain,
ld(X,mult(X2,X)) = X2,
inference(substitution,[status(thm)],[c21]) ).
cnf(c229,plain,
mult(X,ld(X2,mult(X3,X2))) = mult(X,X3),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
mult(X2,mult(X,ld(X2,mult(X3,X2)))) = mult(X2,mult(X,X3)),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
mult(X3,mult(X2,mult(X,ld(X2,mult(X3,X2))))) = mult(X3,mult(X2,mult(X,X3))),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
ld(mult(X3,X2),mult(X3,mult(X2,mult(X,ld(X2,mult(X3,X2)))))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(X,X3)))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
mult(X,X2) = mult(X2,X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c234,plain,
mult(X2,mult(X,X3)) = mult(X2,mult(X3,X)),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
mult(X3,mult(X2,mult(X,X3))) = mult(X3,mult(X2,mult(X3,X))),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
ld(mult(X3,X2),mult(X3,mult(X2,mult(X,X3)))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,X)))),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
ld(mult(X3,X2),mult(X3,mult(X2,mult(X,ld(X2,mult(X3,X2)))))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,X)))),
inference(transitivity,[status(thm)],[c232,c236]) ).
cnf(c238,plain,
mult(ld(mult(X3,X2),mult(X3,mult(X3,X2))),ld(mult(X3,X2),mult(X3,mult(X2,X)))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,X)))),
inference(transitivity,[status(thm)],[c227,c237]) ).
cnf(c239,plain,
mult(X3,ld(mult(X3,X2),mult(X3,mult(X2,X)))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,X)))),
inference(transitivity,[status(thm)],[c213,c238]) ).
cnf(c240,plain,
mult(X3,ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),X)))) = ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),mult(X3,X)))),
inference(substitution,[status(thm)],[c239]) ).
cnf(c241,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c242,plain,
ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),mult(X3,X)))) = ld(X2,mult(X3,mult(ld(X3,X2),mult(X3,X)))),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
mult(X3,ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),X)))) = ld(X2,mult(X3,mult(ld(X3,X2),mult(X3,X)))),
inference(transitivity,[status(thm)],[c240,c242]) ).
cnf(c244,plain,
mult(X3,ld(X2,mult(X3,mult(ld(X3,X2),X)))) = ld(X2,mult(X3,mult(ld(X3,X2),mult(X3,X)))),
inference(transitivity,[status(thm)],[c210,c243]) ).
cnf(c245,plain,
mult(X3,ld(X2,mult(X3,mult(X,ld(X3,X2))))) = ld(X2,mult(X3,mult(ld(X3,X2),mult(X3,X)))),
inference(transitivity,[status(thm)],[c206,c244]) ).
cnf(c246,plain,
mult(X2,ld(unit,mult(X2,mult(X,ld(X2,unit))))) = ld(unit,mult(X2,mult(ld(X2,unit),mult(X2,X)))),
inference(substitution,[status(thm)],[c245]) ).
cnf(c247,plain,
ld(unit,mult(X2,mult(ld(X2,unit),mult(X2,X)))) = mult(X2,ld(unit,mult(X2,mult(X,ld(X2,unit))))),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
ld(unit,mult(X2,mult(X,ld(X2,unit)))) = mult(X2,mult(X,ld(X2,unit))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c249,plain,
mult(X2,ld(unit,mult(X2,mult(X,ld(X2,unit))))) = mult(X2,mult(X2,mult(X,ld(X2,unit)))),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
ld(unit,mult(X2,mult(ld(X2,unit),mult(X2,X)))) = mult(X2,mult(X2,mult(X,ld(X2,unit)))),
inference(transitivity,[status(thm)],[c247,c249]) ).
cnf(c251,plain,
mult(X2,mult(ld(X2,unit),mult(X2,X))) = mult(X2,mult(X2,mult(X,ld(X2,unit)))),
inference(transitivity,[status(thm)],[c201,c250]) ).
cnf(c252,plain,
ld(X2,mult(X2,mult(ld(X2,unit),mult(X2,X)))) = ld(X2,mult(X2,mult(X2,mult(X,ld(X2,unit))))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
ld(X2,mult(X2,mult(X2,mult(X,ld(X2,unit))))) = mult(X2,mult(X,ld(X2,unit))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c254,plain,
ld(X2,mult(X2,mult(ld(X2,unit),mult(X2,X)))) = mult(X2,mult(X,ld(X2,unit))),
inference(transitivity,[status(thm)],[c252,c253]) ).
cnf(c255,plain,
mult(ld(X2,unit),mult(X2,X)) = mult(X2,mult(X,ld(X2,unit))),
inference(transitivity,[status(thm)],[c193,c254]) ).
cnf(c256,plain,
mult(ld(X2,unit),mult(X,X2)) = mult(X2,mult(X,ld(X2,unit))),
inference(transitivity,[status(thm)],[c191,c255]) ).
cnf(c257,plain,
mult(ld(ld(X2,X),unit),mult(X2,ld(X2,X))) = mult(ld(X2,X),mult(X2,ld(ld(X2,X),unit))),
inference(substitution,[status(thm)],[c256]) ).
cnf(c258,plain,
mult(ld(X2,X),mult(X2,ld(ld(X2,X),unit))) = mult(ld(ld(X2,X),unit),mult(X2,ld(X2,X))),
inference(symmetry,[status(thm)],[c257]) ).
cnf(c259,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c260,plain,
mult(ld(ld(X2,X),unit),mult(X2,ld(X2,X))) = mult(ld(ld(X2,X),unit),X),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
mult(ld(ld(X2,X),unit),X) = mult(X,ld(ld(X2,X),unit)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c262,plain,
mult(ld(ld(X2,X),unit),mult(X2,ld(X2,X))) = mult(X,ld(ld(X2,X),unit)),
inference(transitivity,[status(thm)],[c260,c261]) ).
cnf(c263,plain,
mult(ld(X2,X),mult(X2,ld(ld(X2,X),unit))) = mult(X,ld(ld(X2,X),unit)),
inference(transitivity,[status(thm)],[c258,c262]) ).
cnf(c264,plain,
mult(X,ld(ld(X2,X),unit)) = mult(ld(X2,X),mult(X2,ld(ld(X2,X),unit))),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
mult(X2,mult(X,ld(ld(X2,X),unit))) = mult(X2,mult(ld(X2,X),mult(X2,ld(ld(X2,X),unit)))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c267,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
ld(mult(X2,X),X2) = ld(mult(X2,X),mult(X2,unit)),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
mult(X2,ld(mult(X2,X),X2)) = mult(X2,ld(mult(X2,X),mult(X2,unit))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
mult(mult(X2,X),mult(X2,ld(mult(X2,X),X2))) = mult(mult(X2,X),mult(X2,ld(mult(X2,X),mult(X2,unit)))),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
mult(X3,ld(mult(X3,X2),mult(X3,mult(X2,ld(X2,X))))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,ld(X2,X))))),
inference(substitution,[status(thm)],[c239]) ).
cnf(c272,plain,
ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,ld(X2,X))))) = mult(X3,ld(mult(X3,X2),mult(X3,mult(X2,ld(X2,X))))),
inference(symmetry,[status(thm)],[c271]) ).
cnf(c273,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c274,plain,
mult(X3,mult(X2,ld(X2,X))) = mult(X3,X),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
ld(mult(X3,X2),mult(X3,mult(X2,ld(X2,X)))) = ld(mult(X3,X2),mult(X3,X)),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
mult(X3,ld(mult(X3,X2),mult(X3,mult(X2,ld(X2,X))))) = mult(X3,ld(mult(X3,X2),mult(X3,X))),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,ld(X2,X))))) = mult(X3,ld(mult(X3,X2),mult(X3,X))),
inference(transitivity,[status(thm)],[c272,c276]) ).
cnf(c278,plain,
mult(X3,ld(mult(X3,X2),mult(X3,X))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,ld(X2,X))))),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
mult(mult(X3,X2),mult(X3,ld(mult(X3,X2),mult(X3,X)))) = mult(mult(X3,X2),ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,ld(X2,X)))))),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
mult(mult(X3,X2),ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,ld(X2,X)))))) = mult(X3,mult(X2,mult(X3,ld(X2,X)))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c281,plain,
mult(mult(X3,X2),mult(X3,ld(mult(X3,X2),mult(X3,X)))) = mult(X3,mult(X2,mult(X3,ld(X2,X)))),
inference(transitivity,[status(thm)],[c279,c280]) ).
cnf(c282,plain,
mult(mult(X2,X),mult(X2,ld(mult(X2,X),mult(X2,unit)))) = mult(X2,mult(X,mult(X2,ld(X,unit)))),
inference(substitution,[status(thm)],[c281]) ).
cnf(c283,plain,
mult(mult(X2,X),mult(X2,ld(mult(X2,X),X2))) = mult(X2,mult(X,mult(X2,ld(X,unit)))),
inference(transitivity,[status(thm)],[c270,c282]) ).
cnf(c284,plain,
mult(mult(X2,ld(X2,X)),mult(X2,ld(mult(X2,ld(X2,X)),X2))) = mult(X2,mult(ld(X2,X),mult(X2,ld(ld(X2,X),unit)))),
inference(substitution,[status(thm)],[c283]) ).
cnf(c285,plain,
mult(X2,mult(ld(X2,X),mult(X2,ld(ld(X2,X),unit)))) = mult(mult(X2,ld(X2,X)),mult(X2,ld(mult(X2,ld(X2,X)),X2))),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c287,plain,
mult(mult(X2,ld(X2,X)),mult(X2,ld(mult(X2,ld(X2,X)),X2))) = mult(X,mult(X2,ld(mult(X2,ld(X2,X)),X2))),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c289,plain,
ld(mult(X2,ld(X2,X)),X2) = ld(X,X2),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
mult(X2,ld(mult(X2,ld(X2,X)),X2)) = mult(X2,ld(X,X2)),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
mult(X,mult(X2,ld(mult(X2,ld(X2,X)),X2))) = mult(X,mult(X2,ld(X,X2))),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
mult(mult(X2,ld(X2,X)),mult(X2,ld(mult(X2,ld(X2,X)),X2))) = mult(X,mult(X2,ld(X,X2))),
inference(transitivity,[status(thm)],[c287,c291]) ).
cnf(c293,plain,
mult(X2,mult(ld(X2,X),mult(X2,ld(ld(X2,X),unit)))) = mult(X,mult(X2,ld(X,X2))),
inference(transitivity,[status(thm)],[c285,c292]) ).
cnf(c294,plain,
mult(X2,mult(X,ld(ld(X2,X),unit))) = mult(X,mult(X2,ld(X,X2))),
inference(transitivity,[status(thm)],[c265,c293]) ).
cnf(c295,plain,
mult(X,mult(X2,ld(X,X2))) = mult(X2,mult(X,ld(ld(X2,X),unit))),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c296,plain,
ld(X2,mult(X,mult(X2,ld(X,X2)))) = ld(X2,mult(X2,mult(X,ld(ld(X2,X),unit)))),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
ld(X2,mult(X2,mult(X,ld(ld(X2,X),unit)))) = mult(X,ld(ld(X2,X),unit)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c298,plain,
ld(X2,mult(X,mult(X2,ld(X,X2)))) = mult(X,ld(ld(X2,X),unit)),
inference(transitivity,[status(thm)],[c296,c297]) ).
cnf(c299,plain,
mult(X,ld(ld(X2,X),unit)) = ld(X2,mult(X,mult(X2,ld(X,X2)))),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
ld(X,mult(X,ld(ld(X2,X),unit))) = ld(X,ld(X2,mult(X,mult(X2,ld(X,X2))))),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
mult(ld(X3,mult(X2,X)),ld(X2,mult(X2,ld(ld(X3,X2),unit)))) = mult(ld(X3,mult(X2,X)),ld(X2,ld(X3,mult(X2,mult(X3,ld(X2,X3)))))),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c303,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
ld(X3,mult(X2,X)) = ld(mult(X2,ld(X2,X3)),mult(X2,X)),
inference(congruence,[status(thm)],[c303]) ).
cnf(c305,plain,
mult(ld(X3,mult(X2,X)),ld(X2,ld(X3,mult(X2,mult(X3,ld(X2,X3)))))) = mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(X2,ld(X3,mult(X2,mult(X3,ld(X2,X3)))))),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c307,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c306]) ).
cnf(c308,plain,
ld(X2,mult(X,mult(X2,ld(X,X2)))) = ld(mult(X,ld(X,X2)),mult(X,mult(X2,ld(X,X2)))),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
ld(X,ld(X2,mult(X,mult(X2,ld(X,X2))))) = ld(X,ld(mult(X,ld(X,X2)),mult(X,mult(X2,ld(X,X2))))),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(X2,ld(X3,mult(X2,mult(X3,ld(X2,X3)))))) = mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(X2,ld(mult(X2,ld(X2,X3)),mult(X2,mult(X3,ld(X2,X3)))))),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c312,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c311]) ).
cnf(c313,plain,
ld(X,X2) = ld(X,mult(X,ld(X,X2))),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
mult(X2,ld(X,X2)) = mult(X2,ld(X,mult(X,ld(X,X2)))),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
mult(X,mult(X2,ld(X,X2))) = mult(X,mult(X2,ld(X,mult(X,ld(X,X2))))),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
ld(mult(X,ld(X,X2)),mult(X,mult(X2,ld(X,X2)))) = ld(mult(X,ld(X,X2)),mult(X,mult(X2,ld(X,mult(X,ld(X,X2)))))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
ld(X,ld(mult(X,ld(X,X2)),mult(X,mult(X2,ld(X,X2))))) = ld(X,ld(mult(X,ld(X,X2)),mult(X,mult(X2,ld(X,mult(X,ld(X,X2))))))),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(X2,ld(mult(X2,ld(X2,X3)),mult(X2,mult(X3,ld(X2,X3)))))) = mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(X2,ld(mult(X2,ld(X2,X3)),mult(X2,mult(X3,ld(X2,mult(X2,ld(X2,X3)))))))),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
mult(ld(X3,X2),ld(X3,X)) = mult(ld(X3,X),ld(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c320,plain,
mult(ld(X3,X),ld(X3,X2)) = mult(ld(X3,X2),ld(X3,X)),
inference(symmetry,[status(thm)],[c319]) ).
cnf(c321,plain,
mult(X3,mult(ld(X3,X),ld(X3,X2))) = mult(X3,mult(ld(X3,X2),ld(X3,X))),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
ld(X2,mult(X3,mult(ld(X3,X),ld(X3,X2)))) = ld(X2,mult(X3,mult(ld(X3,X2),ld(X3,X)))),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c324,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c323]) ).
cnf(c325,plain,
ld(X2,mult(X3,mult(ld(X3,X2),ld(X3,X)))) = ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),ld(X3,X)))),
inference(congruence,[status(thm)],[c324]) ).
cnf(c326,plain,
ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,X)))) = mult(X3,ld(mult(X3,X2),mult(X3,mult(X2,X)))),
inference(symmetry,[status(thm)],[c239]) ).
cnf(c327,plain,
ld(X3,ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,X))))) = ld(X3,mult(X3,ld(mult(X3,X2),mult(X3,mult(X2,X))))),
inference(congruence,[status(thm)],[c326]) ).
cnf(c328,plain,
ld(X3,mult(X3,ld(mult(X3,X2),mult(X3,mult(X2,X))))) = ld(mult(X3,X2),mult(X3,mult(X2,X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c329,plain,
ld(X3,ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,X))))) = ld(mult(X3,X2),mult(X3,mult(X2,X))),
inference(transitivity,[status(thm)],[c327,c328]) ).
cnf(c330,plain,
ld(X3,ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,ld(X3,X)))))) = ld(mult(X3,X2),mult(X3,mult(X2,ld(X3,X)))),
inference(substitution,[status(thm)],[c329]) ).
cnf(c331,plain,
ld(mult(X3,X2),mult(X3,mult(X2,ld(X3,X)))) = ld(X3,ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,ld(X3,X)))))),
inference(symmetry,[status(thm)],[c330]) ).
cnf(c332,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c333,plain,
mult(X2,mult(X3,ld(X3,X))) = mult(X2,X),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
mult(X3,mult(X2,mult(X3,ld(X3,X)))) = mult(X3,mult(X2,X)),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,ld(X3,X))))) = ld(mult(X3,X2),mult(X3,mult(X2,X))),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
ld(X3,ld(mult(X3,X2),mult(X3,mult(X2,mult(X3,ld(X3,X)))))) = ld(X3,ld(mult(X3,X2),mult(X3,mult(X2,X)))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
ld(mult(X3,X2),mult(X3,mult(X2,ld(X3,X)))) = ld(X3,ld(mult(X3,X2),mult(X3,mult(X2,X)))),
inference(transitivity,[status(thm)],[c331,c336]) ).
cnf(c338,plain,
ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),ld(X3,X)))) = ld(X3,ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),X)))),
inference(substitution,[status(thm)],[c337]) ).
cnf(c339,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c340,plain,
ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),X))) = ld(X2,mult(X3,mult(ld(X3,X2),X))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
ld(X3,ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),X)))) = ld(X3,ld(X2,mult(X3,mult(ld(X3,X2),X)))),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
mult(ld(X3,X2),X) = mult(X,ld(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c343,plain,
mult(X3,mult(ld(X3,X2),X)) = mult(X3,mult(X,ld(X3,X2))),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,plain,
ld(X2,mult(X3,mult(ld(X3,X2),X))) = ld(X2,mult(X3,mult(X,ld(X3,X2)))),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
ld(X3,ld(X2,mult(X3,mult(ld(X3,X2),X)))) = ld(X3,ld(X2,mult(X3,mult(X,ld(X3,X2))))),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
ld(X3,ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),X)))) = ld(X3,ld(X2,mult(X3,mult(X,ld(X3,X2))))),
inference(transitivity,[status(thm)],[c341,c345]) ).
cnf(c347,plain,
ld(mult(X3,ld(X3,X2)),mult(X3,mult(ld(X3,X2),ld(X3,X)))) = ld(X3,ld(X2,mult(X3,mult(X,ld(X3,X2))))),
inference(transitivity,[status(thm)],[c338,c346]) ).
cnf(c348,plain,
ld(X2,mult(X3,mult(ld(X3,X2),ld(X3,X)))) = ld(X3,ld(X2,mult(X3,mult(X,ld(X3,X2))))),
inference(transitivity,[status(thm)],[c325,c347]) ).
cnf(c349,plain,
ld(X2,mult(X3,mult(ld(X3,X),ld(X3,X2)))) = ld(X3,ld(X2,mult(X3,mult(X,ld(X3,X2))))),
inference(transitivity,[status(thm)],[c322,c348]) ).
cnf(c350,plain,
ld(mult(X,ld(X,X2)),mult(X,mult(ld(X,X2),ld(X,mult(X,ld(X,X2)))))) = ld(X,ld(mult(X,ld(X,X2)),mult(X,mult(X2,ld(X,mult(X,ld(X,X2))))))),
inference(substitution,[status(thm)],[c349]) ).
cnf(c351,plain,
ld(X,ld(mult(X,ld(X,X2)),mult(X,mult(X2,ld(X,mult(X,ld(X,X2))))))) = ld(mult(X,ld(X,X2)),mult(X,mult(ld(X,X2),ld(X,mult(X,ld(X,X2)))))),
inference(symmetry,[status(thm)],[c350]) ).
cnf(c352,plain,
mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(X2,ld(mult(X2,ld(X2,X3)),mult(X2,mult(X3,ld(X2,mult(X2,ld(X2,X3)))))))) = mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(mult(X2,ld(X2,X3)),mult(X2,mult(ld(X2,X3),ld(X2,mult(X2,ld(X2,X3))))))),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(mult(X2,ld(X2,X3)),mult(X2,mult(ld(X2,X3),ld(X2,mult(X2,ld(X2,X3))))))) = ld(mult(X2,ld(X2,X3)),mult(X2,mult(ld(X2,X3),mult(ld(X2,mult(X2,ld(X2,X3))),ld(ld(X2,X3),X))))),
inference(substitution,[status(thm)],[c226]) ).
cnf(c354,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c355,plain,
ld(mult(X2,ld(X2,X3)),mult(X2,mult(ld(X2,X3),mult(ld(X2,mult(X2,ld(X2,X3))),ld(ld(X2,X3),X))))) = ld(X3,mult(X2,mult(ld(X2,X3),mult(ld(X2,mult(X2,ld(X2,X3))),ld(ld(X2,X3),X))))),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c357,plain,
ld(X,mult(X,ld(X,X2))) = ld(X,X2),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
mult(ld(X2,mult(X2,ld(X2,X3))),ld(ld(X2,X3),X)) = mult(ld(X2,X3),ld(ld(X2,X3),X)),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
mult(ld(X2,X3),mult(ld(X2,mult(X2,ld(X2,X3))),ld(ld(X2,X3),X))) = mult(ld(X2,X3),mult(ld(X2,X3),ld(ld(X2,X3),X))),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
mult(X2,mult(ld(X2,X3),mult(ld(X2,mult(X2,ld(X2,X3))),ld(ld(X2,X3),X)))) = mult(X2,mult(ld(X2,X3),mult(ld(X2,X3),ld(ld(X2,X3),X)))),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
ld(X3,mult(X2,mult(ld(X2,X3),mult(ld(X2,mult(X2,ld(X2,X3))),ld(ld(X2,X3),X))))) = ld(X3,mult(X2,mult(ld(X2,X3),mult(ld(X2,X3),ld(ld(X2,X3),X))))),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
mult(ld(X2,X3),ld(ld(X2,X3),X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c363,plain,
mult(ld(X2,X3),mult(ld(X2,X3),ld(ld(X2,X3),X))) = mult(ld(X2,X3),X),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
mult(X2,mult(ld(X2,X3),mult(ld(X2,X3),ld(ld(X2,X3),X)))) = mult(X2,mult(ld(X2,X3),X)),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
ld(X3,mult(X2,mult(ld(X2,X3),mult(ld(X2,X3),ld(ld(X2,X3),X))))) = ld(X3,mult(X2,mult(ld(X2,X3),X))),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
mult(ld(X2,X3),X) = mult(X,ld(X2,X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c367,plain,
mult(X2,mult(ld(X2,X3),X)) = mult(X2,mult(X,ld(X2,X3))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
ld(X3,mult(X2,mult(ld(X2,X3),X))) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
ld(X3,mult(X2,mult(ld(X2,X3),mult(ld(X2,X3),ld(ld(X2,X3),X))))) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(transitivity,[status(thm)],[c365,c368]) ).
cnf(c370,plain,
ld(X3,mult(X2,mult(ld(X2,X3),mult(ld(X2,mult(X2,ld(X2,X3))),ld(ld(X2,X3),X))))) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(transitivity,[status(thm)],[c361,c369]) ).
cnf(c371,plain,
ld(mult(X2,ld(X2,X3)),mult(X2,mult(ld(X2,X3),mult(ld(X2,mult(X2,ld(X2,X3))),ld(ld(X2,X3),X))))) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(transitivity,[status(thm)],[c355,c370]) ).
cnf(c372,plain,
mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(mult(X2,ld(X2,X3)),mult(X2,mult(ld(X2,X3),ld(X2,mult(X2,ld(X2,X3))))))) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(transitivity,[status(thm)],[c353,c371]) ).
cnf(c373,plain,
mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(X2,ld(mult(X2,ld(X2,X3)),mult(X2,mult(X3,ld(X2,mult(X2,ld(X2,X3)))))))) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(transitivity,[status(thm)],[c352,c372]) ).
cnf(c374,plain,
mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(X2,ld(mult(X2,ld(X2,X3)),mult(X2,mult(X3,ld(X2,X3)))))) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(transitivity,[status(thm)],[c318,c373]) ).
cnf(c375,plain,
mult(ld(mult(X2,ld(X2,X3)),mult(X2,X)),ld(X2,ld(X3,mult(X2,mult(X3,ld(X2,X3)))))) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(transitivity,[status(thm)],[c310,c374]) ).
cnf(c376,plain,
mult(ld(X3,mult(X2,X)),ld(X2,ld(X3,mult(X2,mult(X3,ld(X2,X3)))))) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(transitivity,[status(thm)],[c305,c375]) ).
cnf(c377,plain,
mult(ld(X3,mult(X2,X)),ld(X2,mult(X2,ld(ld(X3,X2),unit)))) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(transitivity,[status(thm)],[c301,c376]) ).
cnf(c378,plain,
mult(ld(X3,mult(X2,X)),ld(ld(X3,X2),unit)) = ld(X3,mult(X2,mult(X,ld(X2,X3)))),
inference(transitivity,[status(thm)],[c188,c377]) ).
cnf(c379,plain,
mult(ld(X2,mult(X,X)),ld(ld(X2,X),unit)) = ld(X2,mult(X,mult(X,ld(X,X2)))),
inference(substitution,[status(thm)],[c378]) ).
cnf(c380,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c381,plain,
mult(X,mult(X,ld(X,X2))) = mult(X,X2),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
ld(X2,mult(X,mult(X,ld(X,X2)))) = ld(X2,mult(X,X2)),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
ld(X2,mult(X,mult(X,ld(X,X2)))) = X,
inference(transitivity,[status(thm)],[c382,c21]) ).
cnf(c384,plain,
mult(ld(X2,mult(X,X)),ld(ld(X2,X),unit)) = X,
inference(transitivity,[status(thm)],[c379,c383]) ).
cnf(c385,plain,
mult(ld(X2,f(X,X)),ld(ld(X2,X),unit)) = X,
inference(transitivity,[status(thm)],[c185,c384]) ).
cnf(c386,plain,
X = mult(ld(X2,f(X,X)),ld(ld(X2,X),unit)),
inference(symmetry,[status(thm)],[c385]) ).
cnf(c387,plain,
ld(ld(ld(X2,X),unit),X) = ld(ld(ld(X2,X),unit),mult(ld(X2,f(X,X)),ld(ld(X2,X),unit))),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
ld(ld(ld(X2,X),unit),mult(ld(X2,f(X,X)),ld(ld(X2,X),unit))) = ld(X2,f(X,X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c389,plain,
ld(ld(ld(X2,X),unit),X) = ld(X2,f(X,X)),
inference(transitivity,[status(thm)],[c387,c388]) ).
cnf(c390,plain,
ld(ld(ld(f(X2,X2),f(X,X2)),unit),f(X,X2)) = ld(f(X2,X2),f(f(X,X2),f(X,X2))),
inference(substitution,[status(thm)],[c389]) ).
cnf(c391,plain,
ld(f(X2,X2),f(f(X,X2),f(X,X2))) = ld(ld(ld(f(X2,X2),f(X,X2)),unit),f(X,X2)),
inference(symmetry,[status(thm)],[c390]) ).
cnf(c392,plain,
mult(ld(ld(X2,unit),X),X2) = mult(X2,ld(ld(X2,unit),X)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c393,plain,
mult(X2,ld(ld(X2,unit),X)) = mult(ld(ld(X2,unit),X),X2),
inference(symmetry,[status(thm)],[c392]) ).
cnf(c394,plain,
ld(ld(X,unit),unit) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c395,plain,
X = ld(ld(X,unit),unit),
inference(symmetry,[status(thm)],[c394]) ).
cnf(c396,plain,
mult(ld(ld(X2,unit),X),X2) = mult(ld(ld(X2,unit),X),ld(ld(X2,unit),unit)),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
ld(X2,mult(X2,mult(ld(X2,X),ld(X2,unit)))) = mult(ld(X2,X),ld(X2,unit)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c398,plain,
mult(ld(X2,X),ld(X2,unit)) = ld(X2,mult(X2,mult(ld(X2,X),ld(X2,unit)))),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
mult(ld(X2,unit),mult(X2,ld(X2,X))) = mult(X2,mult(ld(X2,X),ld(X2,unit))),
inference(substitution,[status(thm)],[c255]) ).
cnf(c400,plain,
mult(X2,mult(ld(X2,X),ld(X2,unit))) = mult(ld(X2,unit),mult(X2,ld(X2,X))),
inference(symmetry,[status(thm)],[c399]) ).
cnf(c401,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c402,plain,
mult(ld(X2,unit),mult(X2,ld(X2,X))) = mult(ld(X2,unit),X),
inference(congruence,[status(thm)],[c401]) ).
cnf(c403,plain,
mult(ld(X2,unit),X) = mult(X,ld(X2,unit)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c404,plain,
mult(ld(X2,unit),mult(X2,ld(X2,X))) = mult(X,ld(X2,unit)),
inference(transitivity,[status(thm)],[c402,c403]) ).
cnf(c405,plain,
mult(X2,mult(ld(X2,X),ld(X2,unit))) = mult(X,ld(X2,unit)),
inference(transitivity,[status(thm)],[c400,c404]) ).
cnf(c406,plain,
ld(X2,mult(X2,mult(ld(X2,X),ld(X2,unit)))) = ld(X2,mult(X,ld(X2,unit))),
inference(congruence,[status(thm)],[c405]) ).
cnf(c407,plain,
mult(ld(X2,X),ld(X2,unit)) = ld(X2,mult(X,ld(X2,unit))),
inference(transitivity,[status(thm)],[c398,c406]) ).
cnf(c408,plain,
mult(ld(ld(X2,unit),X),ld(ld(X2,unit),unit)) = ld(ld(X2,unit),mult(X,ld(ld(X2,unit),unit))),
inference(substitution,[status(thm)],[c407]) ).
cnf(c409,plain,
ld(ld(X,unit),unit) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c410,plain,
mult(X,ld(ld(X2,unit),unit)) = mult(X,X2),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
ld(ld(X2,unit),mult(X,ld(ld(X2,unit),unit))) = ld(ld(X2,unit),mult(X,X2)),
inference(congruence,[status(thm)],[c410]) ).
cnf(c412,plain,
mult(X,X2) = mult(X2,X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c413,plain,
ld(ld(X2,unit),mult(X,X2)) = ld(ld(X2,unit),mult(X2,X)),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
ld(ld(X2,unit),mult(X,ld(ld(X2,unit),unit))) = ld(ld(X2,unit),mult(X2,X)),
inference(transitivity,[status(thm)],[c411,c413]) ).
cnf(c415,plain,
mult(ld(ld(X2,unit),X),ld(ld(X2,unit),unit)) = ld(ld(X2,unit),mult(X2,X)),
inference(transitivity,[status(thm)],[c408,c414]) ).
cnf(c416,plain,
mult(ld(ld(X2,unit),X),X2) = ld(ld(X2,unit),mult(X2,X)),
inference(transitivity,[status(thm)],[c396,c415]) ).
cnf(c417,plain,
mult(X2,ld(ld(X2,unit),X)) = ld(ld(X2,unit),mult(X2,X)),
inference(transitivity,[status(thm)],[c393,c416]) ).
cnf(c418,plain,
ld(ld(X2,unit),mult(X2,X)) = mult(X2,ld(ld(X2,unit),X)),
inference(symmetry,[status(thm)],[c417]) ).
cnf(c419,plain,
ld(X2,ld(ld(X2,unit),mult(X2,X))) = ld(X2,mult(X2,ld(ld(X2,unit),X))),
inference(congruence,[status(thm)],[c418]) ).
cnf(c420,plain,
ld(X2,mult(X2,ld(ld(X2,unit),X))) = ld(ld(X2,unit),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c421,plain,
ld(X2,ld(ld(X2,unit),mult(X2,X))) = ld(ld(X2,unit),X),
inference(transitivity,[status(thm)],[c419,c420]) ).
cnf(c422,plain,
ld(X,ld(ld(X,unit),mult(X,ld(mult(X,X2),X)))) = ld(ld(X,unit),ld(mult(X,X2),X)),
inference(substitution,[status(thm)],[c421]) ).
cnf(c423,plain,
ld(ld(X,unit),ld(mult(X,X2),X)) = ld(X,ld(ld(X,unit),mult(X,ld(mult(X,X2),X)))),
inference(symmetry,[status(thm)],[c422]) ).
cnf(c424,plain,
mult(X,X2) = mult(X2,X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c425,plain,
mult(X2,X) = mult(X,X2),
inference(symmetry,[status(thm)],[c424]) ).
cnf(c426,plain,
ld(mult(X2,X),X2) = ld(mult(X,X2),X2),
inference(congruence,[status(thm)],[c425]) ).
cnf(c427,plain,
mult(X2,ld(mult(X2,X),X2)) = mult(X2,ld(mult(X,X2),X2)),
inference(congruence,[status(thm)],[c426]) ).
cnf(c428,plain,
ld(ld(X2,unit),mult(X2,ld(mult(X2,X),X2))) = ld(ld(X2,unit),mult(X2,ld(mult(X,X2),X2))),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
ld(X,mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c430,plain,
X2 = ld(X,mult(X,X2)),
inference(symmetry,[status(thm)],[c429]) ).
cnf(c431,plain,
ld(mult(X,X2),X2) = ld(mult(X,X2),ld(X,mult(X,X2))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
mult(X2,ld(mult(X,X2),X2)) = mult(X2,ld(mult(X,X2),ld(X,mult(X,X2)))),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
ld(ld(X2,unit),mult(X2,ld(mult(X,X2),X2))) = ld(ld(X2,unit),mult(X2,ld(mult(X,X2),ld(X,mult(X,X2))))),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
ld(X,mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c435,plain,
X2 = ld(X,mult(X,X2)),
inference(symmetry,[status(thm)],[c434]) ).
cnf(c436,plain,
mult(X2,ld(mult(X,X2),ld(X,mult(X,X2)))) = mult(ld(X,mult(X,X2)),ld(mult(X,X2),ld(X,mult(X,X2)))),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
ld(ld(X2,unit),mult(X2,ld(mult(X,X2),ld(X,mult(X,X2))))) = ld(ld(X2,unit),mult(ld(X,mult(X,X2)),ld(mult(X,X2),ld(X,mult(X,X2))))),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
ld(X,mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c439,plain,
X2 = ld(X,mult(X,X2)),
inference(symmetry,[status(thm)],[c438]) ).
cnf(c440,plain,
ld(X2,unit) = ld(ld(X,mult(X,X2)),unit),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
ld(ld(X2,unit),mult(ld(X,mult(X,X2)),ld(mult(X,X2),ld(X,mult(X,X2))))) = ld(ld(ld(X,mult(X,X2)),unit),mult(ld(X,mult(X,X2)),ld(mult(X,X2),ld(X,mult(X,X2))))),
inference(congruence,[status(thm)],[c440]) ).
cnf(c442,plain,
mult(ld(X2,ld(ld(X,X2),unit)),ld(ld(X2,X),unit)) = mult(ld(ld(X2,X),unit),ld(X2,ld(ld(X,X2),unit))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c443,plain,
mult(ld(ld(X2,X),unit),ld(X2,ld(ld(X,X2),unit))) = mult(ld(X2,ld(ld(X,X2),unit)),ld(ld(X2,X),unit)),
inference(symmetry,[status(thm)],[c442]) ).
cnf(c444,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c445,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c444]) ).
cnf(c446,plain,
ld(X3,mult(X2,mult(X,ld(ld(X2,X3),unit)))) = ld(mult(X2,ld(X2,X3)),mult(X2,mult(X,ld(ld(X2,X3),unit)))),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c448,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c447]) ).
cnf(c449,plain,
mult(X3,X) = mult(X3,mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c448]) ).
cnf(c450,plain,
ld(mult(X3,X2),mult(X3,X)) = ld(mult(X3,X2),mult(X3,mult(X2,ld(X2,X)))),
inference(congruence,[status(thm)],[c449]) ).
cnf(c451,plain,
mult(ld(mult(X3,X2),X3),ld(mult(X3,X2),mult(X3,X))) = mult(ld(mult(X3,X2),X3),ld(mult(X3,X2),mult(X3,mult(X2,ld(X2,X))))),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c453,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c452]) ).
cnf(c454,plain,
ld(mult(X2,X),X2) = ld(mult(X2,X),mult(X2,unit)),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
mult(ld(mult(X3,X2),X3),ld(mult(X3,X2),mult(X3,mult(X2,X)))) = mult(ld(mult(X3,X2),mult(X3,unit)),ld(mult(X3,X2),mult(X3,mult(X2,X)))),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
mult(ld(mult(X3,X2),mult(X3,unit)),ld(mult(X3,X2),mult(X3,mult(X2,X)))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(X,ld(X2,unit))))),
inference(substitution,[status(thm)],[c226]) ).
cnf(c457,plain,
mult(ld(mult(X3,X2),X3),ld(mult(X3,X2),mult(X3,mult(X2,X)))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(X,ld(X2,unit))))),
inference(transitivity,[status(thm)],[c455,c456]) ).
cnf(c458,plain,
mult(ld(mult(X3,X2),X3),ld(mult(X3,X2),mult(X3,mult(X2,ld(X2,X))))) = ld(mult(X3,X2),mult(X3,mult(X2,mult(ld(X2,X),ld(X2,unit))))),
inference(substitution,[status(thm)],[c457]) ).
cnf(c459,plain,
mult(X3,mult(X2,mult(ld(X2,X),ld(X2,unit)))) = mult(X3,mult(X,ld(X2,unit))),
inference(congruence,[status(thm)],[c405]) ).
cnf(c460,plain,
ld(mult(X3,X2),mult(X3,mult(X2,mult(ld(X2,X),ld(X2,unit))))) = ld(mult(X3,X2),mult(X3,mult(X,ld(X2,unit)))),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
mult(ld(mult(X3,X2),X3),ld(mult(X3,X2),mult(X3,mult(X2,ld(X2,X))))) = ld(mult(X3,X2),mult(X3,mult(X,ld(X2,unit)))),
inference(transitivity,[status(thm)],[c458,c460]) ).
cnf(c462,plain,
mult(ld(mult(X3,X2),X3),ld(mult(X3,X2),mult(X3,X))) = ld(mult(X3,X2),mult(X3,mult(X,ld(X2,unit)))),
inference(transitivity,[status(thm)],[c451,c461]) ).
cnf(c463,plain,
mult(ld(mult(X2,ld(X2,X3)),X2),ld(mult(X2,ld(X2,X3)),mult(X2,X))) = ld(mult(X2,ld(X2,X3)),mult(X2,mult(X,ld(ld(X2,X3),unit)))),
inference(substitution,[status(thm)],[c462]) ).
cnf(c464,plain,
ld(mult(X2,ld(X2,X3)),mult(X2,mult(X,ld(ld(X2,X3),unit)))) = mult(ld(mult(X2,ld(X2,X3)),X2),ld(mult(X2,ld(X2,X3)),mult(X2,X))),
inference(symmetry,[status(thm)],[c463]) ).
cnf(c465,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c466,plain,
ld(mult(X,ld(X,X2)),X) = ld(X2,X),
inference(congruence,[status(thm)],[c465]) ).
cnf(c467,plain,
mult(ld(mult(X2,ld(X2,X3)),X2),ld(mult(X2,ld(X2,X3)),mult(X2,X))) = mult(ld(X3,X2),ld(mult(X2,ld(X2,X3)),mult(X2,X))),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c469,plain,
ld(mult(X2,ld(X2,X3)),mult(X2,X)) = ld(X3,mult(X2,X)),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
mult(ld(X3,X2),ld(mult(X2,ld(X2,X3)),mult(X2,X))) = mult(ld(X3,X2),ld(X3,mult(X2,X))),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,plain,
mult(ld(mult(X2,ld(X2,X3)),X2),ld(mult(X2,ld(X2,X3)),mult(X2,X))) = mult(ld(X3,X2),ld(X3,mult(X2,X))),
inference(transitivity,[status(thm)],[c467,c470]) ).
cnf(c472,plain,
ld(mult(X2,ld(X2,X3)),mult(X2,mult(X,ld(ld(X2,X3),unit)))) = mult(ld(X3,X2),ld(X3,mult(X2,X))),
inference(transitivity,[status(thm)],[c464,c471]) ).
cnf(c473,plain,
ld(X3,mult(X2,mult(X,ld(ld(X2,X3),unit)))) = mult(ld(X3,X2),ld(X3,mult(X2,X))),
inference(transitivity,[status(thm)],[c446,c472]) ).
cnf(c474,plain,
mult(ld(X3,X2),ld(X3,mult(X2,X))) = ld(X3,mult(X2,mult(X,ld(ld(X2,X3),unit)))),
inference(symmetry,[status(thm)],[c473]) ).
cnf(c475,plain,
mult(X3,mult(ld(X3,X2),ld(X3,mult(X2,X)))) = mult(X3,ld(X3,mult(X2,mult(X,ld(ld(X2,X3),unit))))),
inference(congruence,[status(thm)],[c474]) ).
cnf(c476,plain,
mult(X3,ld(X3,mult(X2,mult(X,ld(ld(X2,X3),unit))))) = mult(X2,mult(X,ld(ld(X2,X3),unit))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c477,plain,
mult(X3,mult(ld(X3,X2),ld(X3,mult(X2,X)))) = mult(X2,mult(X,ld(ld(X2,X3),unit))),
inference(transitivity,[status(thm)],[c475,c476]) ).
cnf(c478,plain,
mult(X,mult(ld(X,X3),ld(X,mult(X3,ld(X3,X2))))) = mult(X3,mult(ld(X3,X2),ld(ld(X3,X),unit))),
inference(substitution,[status(thm)],[c477]) ).
cnf(c479,plain,
mult(X3,mult(ld(X3,X2),ld(ld(X3,X),unit))) = mult(X,mult(ld(X,X3),ld(X,mult(X3,ld(X3,X2))))),
inference(symmetry,[status(thm)],[c478]) ).
cnf(c480,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c481,plain,
ld(X,mult(X3,ld(X3,X2))) = ld(X,X2),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
mult(ld(X,X3),ld(X,mult(X3,ld(X3,X2)))) = mult(ld(X,X3),ld(X,X2)),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
mult(X,mult(ld(X,X3),ld(X,mult(X3,ld(X3,X2))))) = mult(X,mult(ld(X,X3),ld(X,X2))),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
mult(X3,mult(ld(X3,X2),ld(ld(X3,X),unit))) = mult(X,mult(ld(X,X3),ld(X,X2))),
inference(transitivity,[status(thm)],[c479,c483]) ).
cnf(c485,plain,
mult(X3,mult(ld(X3,X),ld(ld(X3,X2),unit))) = mult(X2,mult(ld(X2,X3),ld(X2,X))),
inference(substitution,[status(thm)],[c484]) ).
cnf(c486,plain,
mult(X2,mult(ld(X2,X3),ld(X2,X))) = mult(X3,mult(ld(X3,X),ld(ld(X3,X2),unit))),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
ld(X3,mult(X2,mult(ld(X2,X3),ld(X2,X)))) = ld(X3,mult(X3,mult(ld(X3,X),ld(ld(X3,X2),unit)))),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,plain,
ld(X3,mult(X3,mult(ld(X3,X),ld(ld(X3,X2),unit)))) = mult(ld(X3,X),ld(ld(X3,X2),unit)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c489,plain,
ld(X3,mult(X2,mult(ld(X2,X3),ld(X2,X)))) = mult(ld(X3,X),ld(ld(X3,X2),unit)),
inference(transitivity,[status(thm)],[c487,c488]) ).
cnf(c490,plain,
ld(X2,mult(X,mult(ld(X,X2),ld(X,ld(ld(X,X2),unit))))) = mult(ld(X2,ld(ld(X,X2),unit)),ld(ld(X2,X),unit)),
inference(substitution,[status(thm)],[c489]) ).
cnf(c491,plain,
mult(ld(X2,ld(ld(X,X2),unit)),ld(ld(X2,X),unit)) = ld(X2,mult(X,mult(ld(X,X2),ld(X,ld(ld(X,X2),unit))))),
inference(symmetry,[status(thm)],[c490]) ).
cnf(c492,plain,
ld(X3,mult(X2,mult(ld(X2,X3),ld(X2,X)))) = ld(X2,ld(X3,mult(X2,mult(X,ld(X2,X3))))),
inference(substitution,[status(thm)],[c348]) ).
cnf(c493,plain,
mult(X,ld(X2,X3)) = mult(ld(X2,X3),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c494,plain,
mult(X2,mult(X,ld(X2,X3))) = mult(X2,mult(ld(X2,X3),X)),
inference(congruence,[status(thm)],[c493]) ).
cnf(c495,plain,
ld(X3,mult(X2,mult(X,ld(X2,X3)))) = ld(X3,mult(X2,mult(ld(X2,X3),X))),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
ld(X2,ld(X3,mult(X2,mult(X,ld(X2,X3))))) = ld(X2,ld(X3,mult(X2,mult(ld(X2,X3),X)))),
inference(congruence,[status(thm)],[c495]) ).
cnf(c497,plain,
ld(X3,mult(X2,mult(ld(X2,X3),ld(X2,X)))) = ld(X2,ld(X3,mult(X2,mult(ld(X2,X3),X)))),
inference(transitivity,[status(thm)],[c492,c496]) ).
cnf(c498,plain,
ld(X2,mult(X,mult(ld(X,X2),ld(X,ld(ld(X,X2),unit))))) = ld(X,ld(X2,mult(X,mult(ld(X,X2),ld(ld(X,X2),unit))))),
inference(substitution,[status(thm)],[c497]) ).
cnf(c499,plain,
ld(X2,mult(X,mult(ld(X,X2),ld(ld(X,X2),unit)))) = mult(ld(X2,X),ld(X2,mult(X,ld(X,X2)))),
inference(substitution,[status(thm)],[c473]) ).
cnf(c500,plain,
ld(X,ld(X2,mult(X,mult(ld(X,X2),ld(ld(X,X2),unit))))) = ld(X,mult(ld(X2,X),ld(X2,mult(X,ld(X,X2))))),
inference(congruence,[status(thm)],[c499]) ).
cnf(c501,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c502,plain,
ld(X2,mult(X,ld(X,X2))) = ld(X2,X2),
inference(congruence,[status(thm)],[c501]) ).
cnf(c503,plain,
mult(ld(X2,X),ld(X2,mult(X,ld(X,X2)))) = mult(ld(X2,X),ld(X2,X2)),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
ld(X,mult(ld(X2,X),ld(X2,mult(X,ld(X,X2))))) = ld(X,mult(ld(X2,X),ld(X2,X2))),
inference(congruence,[status(thm)],[c503]) ).
cnf(c505,plain,
mult(ld(X2,X),ld(X2,X2)) = mult(ld(X2,X),unit),
inference(congruence,[status(thm)],[c44]) ).
cnf(c506,plain,
ld(X,mult(ld(X2,X),ld(X2,X2))) = ld(X,mult(ld(X2,X),unit)),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
mult(ld(X2,X),unit) = ld(X2,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c508,plain,
ld(X,mult(ld(X2,X),unit)) = ld(X,ld(X2,X)),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
ld(X,mult(ld(X2,X),ld(X2,X2))) = ld(X,ld(X2,X)),
inference(transitivity,[status(thm)],[c506,c508]) ).
cnf(c510,plain,
ld(X,mult(ld(X2,X),ld(X2,mult(X,ld(X,X2))))) = ld(X,ld(X2,X)),
inference(transitivity,[status(thm)],[c504,c509]) ).
cnf(c511,plain,
ld(X,ld(X2,mult(X,mult(ld(X,X2),ld(ld(X,X2),unit))))) = ld(X,ld(X2,X)),
inference(transitivity,[status(thm)],[c500,c510]) ).
cnf(c512,plain,
ld(X2,mult(X,mult(ld(X,X2),ld(X,ld(ld(X,X2),unit))))) = ld(X,ld(X2,X)),
inference(transitivity,[status(thm)],[c498,c511]) ).
cnf(c513,plain,
mult(ld(X2,ld(ld(X,X2),unit)),ld(ld(X2,X),unit)) = ld(X,ld(X2,X)),
inference(transitivity,[status(thm)],[c491,c512]) ).
cnf(c514,plain,
mult(ld(ld(X2,X),unit),ld(X2,ld(ld(X,X2),unit))) = ld(X,ld(X2,X)),
inference(transitivity,[status(thm)],[c443,c513]) ).
cnf(c515,plain,
ld(X,ld(X2,X)) = mult(ld(ld(X2,X),unit),ld(X2,ld(ld(X,X2),unit))),
inference(symmetry,[status(thm)],[c514]) ).
cnf(c516,plain,
mult(ld(X2,X),ld(X,ld(X2,X))) = mult(ld(X2,X),mult(ld(ld(X2,X),unit),ld(X2,ld(ld(X,X2),unit)))),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
ld(ld(ld(X2,X),unit),mult(ld(X2,X),ld(X,ld(X2,X)))) = ld(ld(ld(X2,X),unit),mult(ld(X2,X),mult(ld(ld(X2,X),unit),ld(X2,ld(ld(X,X2),unit))))),
inference(congruence,[status(thm)],[c516]) ).
cnf(c518,plain,
mult(X,ld(X2,unit)) = mult(ld(X2,unit),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c519,plain,
mult(ld(X2,unit),X) = mult(X,ld(X2,unit)),
inference(symmetry,[status(thm)],[c518]) ).
cnf(c520,plain,
mult(X2,mult(ld(X2,unit),X)) = mult(X2,mult(X,ld(X2,unit))),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
ld(ld(X2,unit),mult(X2,mult(ld(X2,unit),X))) = ld(ld(X2,unit),mult(X2,mult(X,ld(X2,unit)))),
inference(congruence,[status(thm)],[c520]) ).
cnf(c522,plain,
mult(X2,mult(X,ld(X2,unit))) = mult(ld(X2,unit),mult(X2,X)),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c523,plain,
ld(ld(X2,unit),mult(X2,mult(X,ld(X2,unit)))) = ld(ld(X2,unit),mult(ld(X2,unit),mult(X2,X))),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
ld(ld(X2,unit),mult(ld(X2,unit),mult(X2,X))) = mult(X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c525,plain,
ld(ld(X2,unit),mult(X2,mult(X,ld(X2,unit)))) = mult(X2,X),
inference(transitivity,[status(thm)],[c523,c524]) ).
cnf(c526,plain,
ld(ld(X2,unit),mult(X2,mult(ld(X2,unit),X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c521,c525]) ).
cnf(c527,plain,
ld(ld(ld(X2,X),unit),mult(ld(X2,X),mult(ld(ld(X2,X),unit),ld(X2,ld(ld(X,X2),unit))))) = mult(ld(X2,X),ld(X2,ld(ld(X,X2),unit))),
inference(substitution,[status(thm)],[c526]) ).
cnf(c528,plain,
ld(ld(ld(X2,X),unit),mult(ld(X2,X),ld(X,ld(X2,X)))) = mult(ld(X2,X),ld(X2,ld(ld(X,X2),unit))),
inference(transitivity,[status(thm)],[c517,c527]) ).
cnf(c529,plain,
ld(ld(ld(X,mult(X,X2)),unit),mult(ld(X,mult(X,X2)),ld(mult(X,X2),ld(X,mult(X,X2))))) = mult(ld(X,mult(X,X2)),ld(X,ld(ld(mult(X,X2),X),unit))),
inference(substitution,[status(thm)],[c528]) ).
cnf(c530,plain,
ld(X,mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c531,plain,
mult(ld(X,mult(X,X2)),ld(X,ld(ld(mult(X,X2),X),unit))) = mult(X2,ld(X,ld(ld(mult(X,X2),X),unit))),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
ld(ld(X,X2),X2) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c533,plain,
X = ld(ld(X,X2),X2),
inference(symmetry,[status(thm)],[c532]) ).
cnf(c534,plain,
ld(X2,X) = ld(X2,ld(ld(X,X2),X2)),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
f(X2,ld(X2,X)) = f(X2,ld(X2,ld(ld(X,X2),X2))),
inference(congruence,[status(thm)],[c534]) ).
cnf(c536,plain,
ld(f(X2,X2),f(X2,ld(X2,X))) = ld(f(X2,X2),f(X2,ld(X2,ld(ld(X,X2),X2)))),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
mult(X,ld(X,mult(X2,f(ld(X2,X),ld(X2,X))))) = mult(X2,f(ld(X2,X),ld(X2,X))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c538,plain,
mult(X2,f(ld(X2,X),ld(X2,X))) = mult(X,ld(X,mult(X2,f(ld(X2,X),ld(X2,X))))),
inference(symmetry,[status(thm)],[c537]) ).
cnf(c539,plain,
mult(ld(X,X2),ld(X,X2)) = f(ld(X,X2),ld(X,X2)),
inference(substitution,[status(thm)],[c139]) ).
cnf(c540,plain,
f(ld(X,X2),ld(X,X2)) = mult(ld(X,X2),ld(X,X2)),
inference(symmetry,[status(thm)],[c539]) ).
cnf(c541,plain,
mult(X,f(ld(X,X2),ld(X,X2))) = mult(X,mult(ld(X,X2),ld(X,X2))),
inference(congruence,[status(thm)],[c540]) ).
cnf(c542,plain,
ld(X2,mult(X,f(ld(X,X2),ld(X,X2)))) = ld(X2,mult(X,mult(ld(X,X2),ld(X,X2)))),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
ld(X2,mult(X,mult(ld(X,X2),ld(X,X2)))) = ld(X,ld(X2,mult(X,mult(X2,ld(X,X2))))),
inference(substitution,[status(thm)],[c348]) ).
cnf(c544,plain,
ld(X,ld(X2,mult(X,mult(X2,ld(X,X2))))) = ld(X,mult(X,ld(ld(X2,X),unit))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c545,plain,
ld(X,mult(X,ld(ld(X2,X),unit))) = ld(ld(X2,X),unit),
inference(substitution,[status(thm)],[c2]) ).
cnf(c546,plain,
ld(X,ld(X2,mult(X,mult(X2,ld(X,X2))))) = ld(ld(X2,X),unit),
inference(transitivity,[status(thm)],[c544,c545]) ).
cnf(c547,plain,
ld(X2,mult(X,mult(ld(X,X2),ld(X,X2)))) = ld(ld(X2,X),unit),
inference(transitivity,[status(thm)],[c543,c546]) ).
cnf(c548,plain,
ld(X2,mult(X,f(ld(X,X2),ld(X,X2)))) = ld(ld(X2,X),unit),
inference(transitivity,[status(thm)],[c542,c547]) ).
cnf(c549,plain,
ld(X,mult(X2,f(ld(X2,X),ld(X2,X)))) = ld(ld(X,X2),unit),
inference(substitution,[status(thm)],[c548]) ).
cnf(c550,plain,
mult(X,ld(X,mult(X2,f(ld(X2,X),ld(X2,X))))) = mult(X,ld(ld(X,X2),unit)),
inference(congruence,[status(thm)],[c549]) ).
cnf(c551,plain,
mult(X2,f(ld(X2,X),ld(X2,X))) = mult(X,ld(ld(X,X2),unit)),
inference(transitivity,[status(thm)],[c538,c550]) ).
cnf(c552,plain,
mult(ld(X,X2),f(ld(ld(X,X2),X2),ld(ld(X,X2),X2))) = mult(X2,ld(ld(X2,ld(X,X2)),unit)),
inference(substitution,[status(thm)],[c551]) ).
cnf(c553,plain,
mult(X2,ld(ld(X2,ld(X,X2)),unit)) = mult(ld(X,X2),f(ld(ld(X,X2),X2),ld(ld(X,X2),X2))),
inference(symmetry,[status(thm)],[c552]) ).
cnf(c554,plain,
ld(ld(X,X2),X2) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c555,plain,
f(ld(ld(X,X2),X2),ld(ld(X,X2),X2)) = f(X,ld(ld(X,X2),X2)),
inference(congruence,[status(thm)],[c554]) ).
cnf(c556,plain,
mult(ld(X,X2),f(ld(ld(X,X2),X2),ld(ld(X,X2),X2))) = mult(ld(X,X2),f(X,ld(ld(X,X2),X2))),
inference(congruence,[status(thm)],[c555]) ).
cnf(c557,plain,
ld(ld(X,X2),X2) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c558,plain,
f(X,ld(ld(X,X2),X2)) = f(X,X),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
mult(ld(X,X2),f(X,ld(ld(X,X2),X2))) = mult(ld(X,X2),f(X,X)),
inference(congruence,[status(thm)],[c558]) ).
cnf(c560,plain,
mult(f(X2,X2),ld(X2,X)) = mult(ld(X2,X),f(X2,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c561,plain,
mult(ld(X2,X),f(X2,X2)) = mult(f(X2,X2),ld(X2,X)),
inference(symmetry,[status(thm)],[c560]) ).
cnf(c562,plain,
ld(f(X2,X2),mult(f(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c563,plain,
X = ld(f(X2,X2),mult(f(X2,X2),X)),
inference(symmetry,[status(thm)],[c562]) ).
cnf(c564,plain,
ld(X2,X) = ld(X2,ld(f(X2,X2),mult(f(X2,X2),X))),
inference(congruence,[status(thm)],[c563]) ).
cnf(c565,plain,
mult(f(X2,X2),ld(X2,X)) = mult(f(X2,X2),ld(X2,ld(f(X2,X2),mult(f(X2,X2),X)))),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
f(X,X) = mult(X,X),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c567,plain,
ld(f(X2,X2),X) = ld(mult(X2,X2),X),
inference(congruence,[status(thm)],[c566]) ).
cnf(c568,plain,
mult(X2,ld(f(X2,X2),X)) = mult(X2,ld(mult(X2,X2),X)),
inference(congruence,[status(thm)],[c567]) ).
cnf(c569,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c570,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c569]) ).
cnf(c571,plain,
ld(mult(X2,X2),X) = ld(mult(X2,X2),mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c570]) ).
cnf(c572,plain,
mult(X2,ld(mult(X2,X2),X)) = mult(X2,ld(mult(X2,X2),mult(X2,ld(X2,X)))),
inference(congruence,[status(thm)],[c571]) ).
cnf(c573,plain,
mult(X2,ld(mult(X2,X2),mult(X2,ld(X2,X)))) = ld(mult(X2,X2),mult(X2,mult(X2,ld(X2,X)))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c574,plain,
ld(mult(X2,X2),mult(X2,mult(X2,ld(X2,X)))) = ld(f(X2,X2),mult(X2,mult(X2,ld(X2,X)))),
inference(congruence,[status(thm)],[c139]) ).
cnf(c575,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c576,plain,
mult(X2,mult(X2,ld(X2,X))) = mult(X2,X),
inference(congruence,[status(thm)],[c575]) ).
cnf(c577,plain,
ld(f(X2,X2),mult(X2,mult(X2,ld(X2,X)))) = ld(f(X2,X2),mult(X2,X)),
inference(congruence,[status(thm)],[c576]) ).
cnf(c578,plain,
ld(mult(X2,X2),mult(X2,mult(X2,ld(X2,X)))) = ld(f(X2,X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c574,c577]) ).
cnf(c579,plain,
mult(X2,ld(mult(X2,X2),mult(X2,ld(X2,X)))) = ld(f(X2,X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c573,c578]) ).
cnf(c580,plain,
mult(X2,ld(mult(X2,X2),X)) = ld(f(X2,X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c572,c579]) ).
cnf(c581,plain,
mult(X2,ld(f(X2,X2),X)) = ld(f(X2,X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c568,c580]) ).
cnf(c582,plain,
ld(f(X2,X2),mult(X2,X)) = mult(X2,ld(f(X2,X2),X)),
inference(symmetry,[status(thm)],[c581]) ).
cnf(c583,plain,
ld(X2,ld(f(X2,X2),mult(X2,X))) = ld(X2,mult(X2,ld(f(X2,X2),X))),
inference(congruence,[status(thm)],[c582]) ).
cnf(c584,plain,
ld(X2,mult(X2,ld(f(X2,X2),X))) = ld(f(X2,X2),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c585,plain,
ld(X2,ld(f(X2,X2),mult(X2,X))) = ld(f(X2,X2),X),
inference(transitivity,[status(thm)],[c583,c584]) ).
cnf(c586,plain,
ld(X2,ld(f(X2,X2),mult(X2,ld(X2,X)))) = ld(f(X2,X2),ld(X2,X)),
inference(substitution,[status(thm)],[c585]) ).
cnf(c587,plain,
ld(f(X2,X2),ld(X2,X)) = ld(X2,ld(f(X2,X2),mult(X2,ld(X2,X)))),
inference(symmetry,[status(thm)],[c586]) ).
cnf(c588,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c589,plain,
ld(f(X2,X2),mult(X2,ld(X2,X))) = ld(f(X2,X2),X),
inference(congruence,[status(thm)],[c588]) ).
cnf(c590,plain,
ld(X2,ld(f(X2,X2),mult(X2,ld(X2,X)))) = ld(X2,ld(f(X2,X2),X)),
inference(congruence,[status(thm)],[c589]) ).
cnf(c591,plain,
ld(f(X2,X2),ld(X2,X)) = ld(X2,ld(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c587,c590]) ).
cnf(c592,plain,
ld(X2,ld(f(X2,X2),X)) = ld(f(X2,X2),ld(X2,X)),
inference(symmetry,[status(thm)],[c591]) ).
cnf(c593,plain,
mult(f(X2,X2),ld(X2,ld(f(X2,X2),X))) = mult(f(X2,X2),ld(f(X2,X2),ld(X2,X))),
inference(congruence,[status(thm)],[c592]) ).
cnf(c594,plain,
mult(f(X2,X2),ld(f(X2,X2),ld(X2,X))) = ld(X2,X),
inference(substitution,[status(thm)],[c10]) ).
cnf(c595,plain,
mult(f(X2,X2),ld(X2,ld(f(X2,X2),X))) = ld(X2,X),
inference(transitivity,[status(thm)],[c593,c594]) ).
cnf(c596,plain,
mult(f(X2,X2),ld(X2,ld(f(X2,X2),mult(f(X2,X2),X)))) = ld(X2,mult(f(X2,X2),X)),
inference(substitution,[status(thm)],[c595]) ).
cnf(c597,plain,
mult(f(X2,X2),X) = mult(X,f(X2,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c598,plain,
ld(X2,mult(f(X2,X2),X)) = ld(X2,mult(X,f(X2,X2))),
inference(congruence,[status(thm)],[c597]) ).
cnf(c599,plain,
mult(f(X2,X2),ld(X2,ld(f(X2,X2),mult(f(X2,X2),X)))) = ld(X2,mult(X,f(X2,X2))),
inference(transitivity,[status(thm)],[c596,c598]) ).
cnf(c600,plain,
mult(f(X2,X2),ld(X2,X)) = ld(X2,mult(X,f(X2,X2))),
inference(transitivity,[status(thm)],[c565,c599]) ).
cnf(c601,plain,
mult(ld(X2,X),f(X2,X2)) = ld(X2,mult(X,f(X2,X2))),
inference(transitivity,[status(thm)],[c561,c600]) ).
cnf(c602,plain,
mult(ld(X,X2),f(X,X)) = ld(X,mult(X2,f(X,X))),
inference(substitution,[status(thm)],[c601]) ).
cnf(c603,plain,
mult(ld(X,X2),f(X,ld(ld(X,X2),X2))) = ld(X,mult(X2,f(X,X))),
inference(transitivity,[status(thm)],[c559,c602]) ).
cnf(c604,plain,
mult(ld(X,X2),f(ld(ld(X,X2),X2),ld(ld(X,X2),X2))) = ld(X,mult(X2,f(X,X))),
inference(transitivity,[status(thm)],[c556,c603]) ).
cnf(c605,plain,
mult(X2,ld(ld(X2,ld(X,X2)),unit)) = ld(X,mult(X2,f(X,X))),
inference(transitivity,[status(thm)],[c553,c604]) ).
cnf(c606,plain,
mult(ld(X,unit),ld(ld(ld(X,unit),ld(X2,ld(X,unit))),unit)) = ld(X2,mult(ld(X,unit),f(X2,X2))),
inference(substitution,[status(thm)],[c605]) ).
cnf(c607,plain,
ld(X2,mult(ld(X,unit),f(X2,X2))) = mult(ld(X,unit),ld(ld(ld(X,unit),ld(X2,ld(X,unit))),unit)),
inference(symmetry,[status(thm)],[c606]) ).
cnf(c608,plain,
X2 = ld(ld(X2,X),X),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c609,plain,
ld(X2,unit) = ld(ld(ld(X2,X),X),unit),
inference(congruence,[status(thm)],[c608]) ).
cnf(c610,plain,
ld(X,ld(X2,unit)) = ld(X,ld(ld(ld(X2,X),X),unit)),
inference(congruence,[status(thm)],[c609]) ).
cnf(c611,plain,
ld(ld(X2,unit),ld(X,ld(X2,unit))) = ld(ld(X2,unit),ld(X,ld(ld(ld(X2,X),X),unit))),
inference(congruence,[status(thm)],[c610]) ).
cnf(c612,plain,
X2 = ld(ld(X2,X),X),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c613,plain,
ld(X2,unit) = ld(ld(ld(X2,X),X),unit),
inference(congruence,[status(thm)],[c612]) ).
cnf(c614,plain,
ld(ld(X2,unit),ld(X,ld(ld(ld(X2,X),X),unit))) = ld(ld(ld(ld(X2,X),X),unit),ld(X,ld(ld(ld(X2,X),X),unit))),
inference(congruence,[status(thm)],[c613]) ).
cnf(c615,plain,
ld(X2,mult(X3,mult(ld(X3,X2),ld(X3,X)))) = ld(X3,ld(X2,mult(X3,mult(ld(X3,X2),X)))),
inference(substitution,[status(thm)],[c497]) ).
cnf(c616,plain,
ld(X3,ld(X2,mult(X3,mult(ld(X3,X2),X)))) = ld(X2,mult(X3,mult(ld(X3,X2),ld(X3,X)))),
inference(symmetry,[status(thm)],[c615]) ).
cnf(c617,plain,
mult(X2,mult(ld(X2,X),ld(ld(X2,X3),unit))) = mult(X3,mult(ld(X3,X2),ld(X3,X))),
inference(substitution,[status(thm)],[c484]) ).
cnf(c618,plain,
mult(X3,mult(ld(X3,X2),ld(X3,X))) = mult(X2,mult(ld(X2,X),ld(ld(X2,X3),unit))),
inference(symmetry,[status(thm)],[c617]) ).
cnf(c619,plain,
ld(X2,mult(X3,mult(ld(X3,X2),ld(X3,X)))) = ld(X2,mult(X2,mult(ld(X2,X),ld(ld(X2,X3),unit)))),
inference(congruence,[status(thm)],[c618]) ).
cnf(c620,plain,
ld(X2,mult(X2,mult(ld(X2,X),ld(ld(X2,X3),unit)))) = mult(ld(X2,X),ld(ld(X2,X3),unit)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c621,plain,
ld(X2,mult(X3,mult(ld(X3,X2),ld(X3,X)))) = mult(ld(X2,X),ld(ld(X2,X3),unit)),
inference(transitivity,[status(thm)],[c619,c620]) ).
cnf(c622,plain,
ld(X3,ld(X2,mult(X3,mult(ld(X3,X2),X)))) = mult(ld(X2,X),ld(ld(X2,X3),unit)),
inference(transitivity,[status(thm)],[c616,c621]) ).
cnf(c623,plain,
ld(X,ld(X2,mult(X,mult(ld(X,X2),ld(X,X2))))) = mult(ld(X2,ld(X,X2)),ld(ld(X2,X),unit)),
inference(substitution,[status(thm)],[c622]) ).
cnf(c624,plain,
mult(ld(X2,ld(X,X2)),ld(ld(X2,X),unit)) = ld(X,ld(X2,mult(X,mult(ld(X,X2),ld(X,X2))))),
inference(symmetry,[status(thm)],[c623]) ).
cnf(c625,plain,
ld(X2,mult(X,mult(ld(X,X2),ld(X,X2)))) = ld(X,ld(X2,mult(X,mult(X2,ld(X,X2))))),
inference(substitution,[status(thm)],[c349]) ).
cnf(c626,plain,
ld(X,ld(X2,mult(X,mult(ld(X,X2),ld(X,X2))))) = ld(X,ld(X,ld(X2,mult(X,mult(X2,ld(X,X2)))))),
inference(congruence,[status(thm)],[c625]) ).
cnf(c627,plain,
ld(X,ld(X2,mult(X,mult(X2,ld(X,X2))))) = ld(X,mult(X,ld(ld(X2,X),unit))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c628,plain,
ld(X,ld(X,ld(X2,mult(X,mult(X2,ld(X,X2)))))) = ld(X,ld(X,mult(X,ld(ld(X2,X),unit)))),
inference(congruence,[status(thm)],[c627]) ).
cnf(c629,plain,
ld(X,mult(X,ld(ld(X2,X),unit))) = ld(ld(X2,X),unit),
inference(substitution,[status(thm)],[c2]) ).
cnf(c630,plain,
ld(X,ld(X,mult(X,ld(ld(X2,X),unit)))) = ld(X,ld(ld(X2,X),unit)),
inference(congruence,[status(thm)],[c629]) ).
cnf(c631,plain,
ld(X,ld(X,ld(X2,mult(X,mult(X2,ld(X,X2)))))) = ld(X,ld(ld(X2,X),unit)),
inference(transitivity,[status(thm)],[c628,c630]) ).
cnf(c632,plain,
ld(X,ld(X2,mult(X,mult(ld(X,X2),ld(X,X2))))) = ld(X,ld(ld(X2,X),unit)),
inference(transitivity,[status(thm)],[c626,c631]) ).
cnf(c633,plain,
mult(ld(X2,ld(X,X2)),ld(ld(X2,X),unit)) = ld(X,ld(ld(X2,X),unit)),
inference(transitivity,[status(thm)],[c624,c632]) ).
cnf(c634,plain,
ld(X,ld(ld(X2,X),unit)) = mult(ld(X2,ld(X,X2)),ld(ld(X2,X),unit)),
inference(symmetry,[status(thm)],[c633]) ).
cnf(c635,plain,
ld(ld(ld(X2,X),unit),ld(X,ld(ld(X2,X),unit))) = ld(ld(ld(X2,X),unit),mult(ld(X2,ld(X,X2)),ld(ld(X2,X),unit))),
inference(congruence,[status(thm)],[c634]) ).
cnf(c636,plain,
ld(ld(ld(X2,X),unit),mult(ld(X2,ld(X,X2)),ld(ld(X2,X),unit))) = ld(X2,ld(X,X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c637,plain,
ld(ld(ld(X2,X),unit),ld(X,ld(ld(X2,X),unit))) = ld(X2,ld(X,X2)),
inference(transitivity,[status(thm)],[c635,c636]) ).
cnf(c638,plain,
ld(ld(ld(ld(X2,X),X),unit),ld(X,ld(ld(ld(X2,X),X),unit))) = ld(ld(X2,X),ld(X,ld(X2,X))),
inference(substitution,[status(thm)],[c637]) ).
cnf(c639,plain,
ld(ld(X2,unit),ld(X,ld(ld(ld(X2,X),X),unit))) = ld(ld(X2,X),ld(X,ld(X2,X))),
inference(transitivity,[status(thm)],[c614,c638]) ).
cnf(c640,plain,
ld(ld(X2,unit),ld(X,ld(X2,unit))) = ld(ld(X2,X),ld(X,ld(X2,X))),
inference(transitivity,[status(thm)],[c611,c639]) ).
cnf(c641,plain,
ld(ld(X,unit),ld(X2,ld(X,unit))) = ld(ld(X,X2),ld(X2,ld(X,X2))),
inference(substitution,[status(thm)],[c640]) ).
cnf(c642,plain,
ld(ld(ld(X,unit),ld(X2,ld(X,unit))),unit) = ld(ld(ld(X,X2),ld(X2,ld(X,X2))),unit),
inference(congruence,[status(thm)],[c641]) ).
cnf(c643,plain,
mult(ld(X,unit),ld(ld(ld(X,unit),ld(X2,ld(X,unit))),unit)) = mult(ld(X,unit),ld(ld(ld(X,X2),ld(X2,ld(X,X2))),unit)),
inference(congruence,[status(thm)],[c642]) ).
cnf(c644,plain,
mult(ld(X,unit),ld(X2,unit)) = mult(ld(X2,unit),ld(X,unit)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c645,plain,
mult(ld(X2,unit),ld(X,unit)) = mult(ld(X,unit),ld(X2,unit)),
inference(symmetry,[status(thm)],[c644]) ).
cnf(c646,plain,
ld(X,mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c647,plain,
X2 = ld(X,mult(X,X2)),
inference(symmetry,[status(thm)],[c646]) ).
cnf(c648,plain,
ld(X2,unit) = ld(ld(X,mult(X,X2)),unit),
inference(congruence,[status(thm)],[c647]) ).
cnf(c649,plain,
mult(ld(X,unit),ld(X2,unit)) = mult(ld(X,unit),ld(ld(X,mult(X,X2)),unit)),
inference(congruence,[status(thm)],[c648]) ).
cnf(c650,plain,
ld(X2,ld(ld(X2,unit),mult(X2,ld(X,unit)))) = ld(ld(X2,unit),ld(X,unit)),
inference(substitution,[status(thm)],[c421]) ).
cnf(c651,plain,
ld(ld(X2,unit),ld(X,unit)) = ld(X2,ld(ld(X2,unit),mult(X2,ld(X,unit)))),
inference(symmetry,[status(thm)],[c650]) ).
cnf(c652,plain,
mult(ld(X2,unit),ld(ld(X2,unit),X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c653,plain,
X = mult(ld(X2,unit),ld(ld(X2,unit),X)),
inference(symmetry,[status(thm)],[c652]) ).
cnf(c654,plain,
ld(X2,X) = ld(X2,mult(ld(X2,unit),ld(ld(X2,unit),X))),
inference(congruence,[status(thm)],[c653]) ).
cnf(c655,plain,
ld(ld(X2,unit),ld(X2,X)) = ld(ld(X2,unit),ld(X2,mult(ld(X2,unit),ld(ld(X2,unit),X)))),
inference(congruence,[status(thm)],[c654]) ).
cnf(c656,plain,
mult(X,ld(X2,unit)) = mult(ld(X2,unit),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c657,plain,
mult(ld(X2,unit),X) = mult(X,ld(X2,unit)),
inference(symmetry,[status(thm)],[c656]) ).
cnf(c658,plain,
ld(X2,mult(ld(X2,unit),X)) = ld(X2,mult(X,ld(X2,unit))),
inference(congruence,[status(thm)],[c657]) ).
cnf(c659,plain,
ld(ld(X2,unit),ld(X2,mult(ld(X2,unit),X))) = ld(ld(X2,unit),ld(X2,mult(X,ld(X2,unit)))),
inference(congruence,[status(thm)],[c658]) ).
cnf(c660,plain,
ld(X2,mult(X,ld(X2,unit))) = mult(ld(X2,X),ld(X2,unit)),
inference(symmetry,[status(thm)],[c407]) ).
cnf(c661,plain,
ld(ld(X2,unit),ld(X2,mult(X,ld(X2,unit)))) = ld(ld(X2,unit),mult(ld(X2,X),ld(X2,unit))),
inference(congruence,[status(thm)],[c660]) ).
cnf(c662,plain,
ld(ld(X2,unit),mult(ld(X2,X),ld(X2,unit))) = ld(X2,X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c663,plain,
ld(ld(X2,unit),ld(X2,mult(X,ld(X2,unit)))) = ld(X2,X),
inference(transitivity,[status(thm)],[c661,c662]) ).
cnf(c664,plain,
ld(ld(X2,unit),ld(X2,mult(ld(X2,unit),X))) = ld(X2,X),
inference(transitivity,[status(thm)],[c659,c663]) ).
cnf(c665,plain,
ld(ld(X2,unit),ld(X2,mult(ld(X2,unit),ld(ld(X2,unit),X)))) = ld(X2,ld(ld(X2,unit),X)),
inference(substitution,[status(thm)],[c664]) ).
cnf(c666,plain,
ld(ld(X2,unit),ld(X2,X)) = ld(X2,ld(ld(X2,unit),X)),
inference(transitivity,[status(thm)],[c655,c665]) ).
cnf(c667,plain,
ld(ld(X2,unit),ld(X2,mult(X2,ld(X,unit)))) = ld(X2,ld(ld(X2,unit),mult(X2,ld(X,unit)))),
inference(substitution,[status(thm)],[c666]) ).
cnf(c668,plain,
ld(X2,ld(ld(X2,unit),mult(X2,ld(X,unit)))) = ld(ld(X2,unit),ld(X2,mult(X2,ld(X,unit)))),
inference(symmetry,[status(thm)],[c667]) ).
cnf(c669,plain,
ld(ld(X,unit),unit) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c670,plain,
X = ld(ld(X,unit),unit),
inference(symmetry,[status(thm)],[c669]) ).
cnf(c671,plain,
ld(X2,mult(X2,ld(X,unit))) = ld(ld(ld(X2,unit),unit),mult(X2,ld(X,unit))),
inference(congruence,[status(thm)],[c670]) ).
cnf(c672,plain,
ld(ld(X2,unit),ld(X2,mult(X2,ld(X,unit)))) = ld(ld(X2,unit),ld(ld(ld(X2,unit),unit),mult(X2,ld(X,unit)))),
inference(congruence,[status(thm)],[c671]) ).
cnf(c673,plain,
ld(ld(ld(X2,unit),unit),ld(ld(X2,unit),mult(X2,ld(X,unit)))) = ld(ld(X2,unit),ld(ld(ld(X2,unit),unit),mult(X2,ld(X,unit)))),
inference(substitution,[status(thm)],[c666]) ).
cnf(c674,plain,
ld(ld(X2,unit),ld(ld(ld(X2,unit),unit),mult(X2,ld(X,unit)))) = ld(ld(ld(X2,unit),unit),ld(ld(X2,unit),mult(X2,ld(X,unit)))),
inference(symmetry,[status(thm)],[c673]) ).
cnf(c675,plain,
mult(X,mult(ld(X,X2),ld(X,unit))) = mult(X2,ld(X,unit)),
inference(substitution,[status(thm)],[c405]) ).
cnf(c676,plain,
mult(X2,ld(X,unit)) = mult(X,mult(ld(X,X2),ld(X,unit))),
inference(symmetry,[status(thm)],[c675]) ).
cnf(c677,plain,
ld(ld(X2,unit),mult(X2,ld(X,unit))) = ld(ld(X2,unit),mult(X,mult(ld(X,X2),ld(X,unit)))),
inference(congruence,[status(thm)],[c676]) ).
cnf(c678,plain,
mult(X2,mult(ld(X2,unit),ld(ld(X2,X),unit))) = mult(X,mult(ld(X,X2),ld(X,unit))),
inference(substitution,[status(thm)],[c484]) ).
cnf(c679,plain,
mult(X,mult(ld(X,X2),ld(X,unit))) = mult(X2,mult(ld(X2,unit),ld(ld(X2,X),unit))),
inference(symmetry,[status(thm)],[c678]) ).
cnf(c680,plain,
ld(ld(X2,unit),mult(X,mult(ld(X,X2),ld(X,unit)))) = ld(ld(X2,unit),mult(X2,mult(ld(X2,unit),ld(ld(X2,X),unit)))),
inference(congruence,[status(thm)],[c679]) ).
cnf(c681,plain,
ld(ld(X2,unit),mult(X2,mult(ld(X2,unit),ld(ld(X2,X),unit)))) = mult(X2,ld(ld(X2,X),unit)),
inference(substitution,[status(thm)],[c526]) ).
cnf(c682,plain,
ld(ld(X2,unit),mult(X,mult(ld(X,X2),ld(X,unit)))) = mult(X2,ld(ld(X2,X),unit)),
inference(transitivity,[status(thm)],[c680,c681]) ).
cnf(c683,plain,
ld(ld(X2,unit),mult(X2,ld(X,unit))) = mult(X2,ld(ld(X2,X),unit)),
inference(transitivity,[status(thm)],[c677,c682]) ).
cnf(c684,plain,
ld(ld(ld(X2,unit),unit),ld(ld(X2,unit),mult(X2,ld(X,unit)))) = ld(ld(ld(X2,unit),unit),mult(X2,ld(ld(X2,X),unit))),
inference(congruence,[status(thm)],[c683]) ).
cnf(c685,plain,
ld(ld(X,unit),unit) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c686,plain,
ld(ld(ld(X2,unit),unit),mult(X2,ld(ld(X2,X),unit))) = ld(X2,mult(X2,ld(ld(X2,X),unit))),
inference(congruence,[status(thm)],[c685]) ).
cnf(c687,plain,
ld(X2,mult(X2,ld(ld(X2,X),unit))) = ld(ld(X2,X),unit),
inference(substitution,[status(thm)],[c2]) ).
cnf(c688,plain,
ld(ld(ld(X2,unit),unit),mult(X2,ld(ld(X2,X),unit))) = ld(ld(X2,X),unit),
inference(transitivity,[status(thm)],[c686,c687]) ).
cnf(c689,plain,
ld(ld(ld(X2,unit),unit),ld(ld(X2,unit),mult(X2,ld(X,unit)))) = ld(ld(X2,X),unit),
inference(transitivity,[status(thm)],[c684,c688]) ).
cnf(c690,plain,
ld(ld(X2,unit),ld(ld(ld(X2,unit),unit),mult(X2,ld(X,unit)))) = ld(ld(X2,X),unit),
inference(transitivity,[status(thm)],[c674,c689]) ).
cnf(c691,plain,
ld(ld(X2,unit),ld(X2,mult(X2,ld(X,unit)))) = ld(ld(X2,X),unit),
inference(transitivity,[status(thm)],[c672,c690]) ).
cnf(c692,plain,
ld(X2,ld(ld(X2,unit),mult(X2,ld(X,unit)))) = ld(ld(X2,X),unit),
inference(transitivity,[status(thm)],[c668,c691]) ).
cnf(c693,plain,
ld(ld(X2,unit),ld(X,unit)) = ld(ld(X2,X),unit),
inference(transitivity,[status(thm)],[c651,c692]) ).
cnf(c694,plain,
ld(ld(X2,X),unit) = ld(ld(X2,unit),ld(X,unit)),
inference(symmetry,[status(thm)],[c693]) ).
cnf(c695,plain,
mult(ld(X2,unit),ld(ld(X2,X),unit)) = mult(ld(X2,unit),ld(ld(X2,unit),ld(X,unit))),
inference(congruence,[status(thm)],[c694]) ).
cnf(c696,plain,
mult(ld(X2,unit),ld(ld(X2,unit),ld(X,unit))) = ld(X,unit),
inference(substitution,[status(thm)],[c10]) ).
cnf(c697,plain,
mult(ld(X2,unit),ld(ld(X2,X),unit)) = ld(X,unit),
inference(transitivity,[status(thm)],[c695,c696]) ).
cnf(c698,plain,
mult(ld(X,unit),ld(ld(X,mult(X,X2)),unit)) = ld(mult(X,X2),unit),
inference(substitution,[status(thm)],[c697]) ).
cnf(c699,plain,
mult(X,X2) = mult(X2,X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c700,plain,
ld(mult(X,X2),unit) = ld(mult(X2,X),unit),
inference(congruence,[status(thm)],[c699]) ).
cnf(c701,plain,
mult(ld(X,unit),ld(ld(X,mult(X,X2)),unit)) = ld(mult(X2,X),unit),
inference(transitivity,[status(thm)],[c698,c700]) ).
cnf(c702,plain,
mult(ld(X,unit),ld(X2,unit)) = ld(mult(X2,X),unit),
inference(transitivity,[status(thm)],[c649,c701]) ).
cnf(c703,plain,
mult(ld(X2,unit),ld(X,unit)) = ld(mult(X2,X),unit),
inference(transitivity,[status(thm)],[c645,c702]) ).
cnf(c704,plain,
mult(ld(X,unit),ld(ld(ld(X,X2),ld(X2,ld(X,X2))),unit)) = ld(mult(X,ld(ld(X,X2),ld(X2,ld(X,X2)))),unit),
inference(substitution,[status(thm)],[c703]) ).
cnf(c705,plain,
X2 = ld(ld(X2,X),X),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c706,plain,
mult(X2,ld(ld(X2,X),ld(X,ld(X2,X)))) = mult(ld(ld(X2,X),X),ld(ld(X2,X),ld(X,ld(X2,X)))),
inference(congruence,[status(thm)],[c705]) ).
cnf(c707,plain,
ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))) = mult(ld(X2,X),ld(X2,ld(X,X2))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c708,plain,
mult(ld(X2,X),ld(X2,ld(X,X2))) = ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))),
inference(symmetry,[status(thm)],[c707]) ).
cnf(c709,plain,
f(unit,X) = ld(mult(ld(mult(unit,X),unit),ld(mult(unit,X),X)),unit),
inference(substitution,[status(thm)],[c74]) ).
cnf(c710,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c194]) ).
cnf(c711,plain,
ld(mult(unit,X),unit) = ld(X,unit),
inference(congruence,[status(thm)],[c710]) ).
cnf(c712,plain,
mult(ld(mult(unit,X),unit),ld(mult(unit,X),X)) = mult(ld(X,unit),ld(mult(unit,X),X)),
inference(congruence,[status(thm)],[c711]) ).
cnf(c713,plain,
ld(mult(ld(mult(unit,X),unit),ld(mult(unit,X),X)),unit) = ld(mult(ld(X,unit),ld(mult(unit,X),X)),unit),
inference(congruence,[status(thm)],[c712]) ).
cnf(c714,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c194]) ).
cnf(c715,plain,
ld(mult(unit,X),X) = ld(X,X),
inference(congruence,[status(thm)],[c714]) ).
cnf(c716,plain,
mult(ld(X,unit),ld(mult(unit,X),X)) = mult(ld(X,unit),ld(X,X)),
inference(congruence,[status(thm)],[c715]) ).
cnf(c717,plain,
ld(mult(ld(X,unit),ld(mult(unit,X),X)),unit) = ld(mult(ld(X,unit),ld(X,X)),unit),
inference(congruence,[status(thm)],[c716]) ).
cnf(c718,plain,
mult(ld(X,unit),ld(X,X)) = mult(ld(X,unit),unit),
inference(congruence,[status(thm)],[c44]) ).
cnf(c719,plain,
ld(mult(ld(X,unit),ld(X,X)),unit) = ld(mult(ld(X,unit),unit),unit),
inference(congruence,[status(thm)],[c718]) ).
cnf(c720,plain,
mult(ld(X,unit),unit) = ld(X,unit),
inference(substitution,[status(thm)],[c5]) ).
cnf(c721,plain,
ld(mult(ld(X,unit),unit),unit) = ld(ld(X,unit),unit),
inference(congruence,[status(thm)],[c720]) ).
cnf(c722,plain,
ld(ld(X,unit),unit) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c723,plain,
ld(mult(ld(X,unit),unit),unit) = X,
inference(transitivity,[status(thm)],[c721,c722]) ).
cnf(c724,plain,
ld(mult(ld(X,unit),ld(X,X)),unit) = X,
inference(transitivity,[status(thm)],[c719,c723]) ).
cnf(c725,plain,
ld(mult(ld(X,unit),ld(mult(unit,X),X)),unit) = X,
inference(transitivity,[status(thm)],[c717,c724]) ).
cnf(c726,plain,
ld(mult(ld(mult(unit,X),unit),ld(mult(unit,X),X)),unit) = X,
inference(transitivity,[status(thm)],[c713,c725]) ).
cnf(c727,plain,
f(unit,X) = X,
inference(transitivity,[status(thm)],[c709,c726]) ).
cnf(c728,plain,
f(unit,ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2))))) = ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))),
inference(substitution,[status(thm)],[c727]) ).
cnf(c729,plain,
ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))) = f(unit,ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2))))),
inference(symmetry,[status(thm)],[c728]) ).
cnf(c730,plain,
ld(mult(ld(mult(ld(X2,X),ld(X2,ld(X,X2))),unit),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))))),unit) = f(unit,ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2))))),
inference(substitution,[status(thm)],[c171]) ).
cnf(c731,plain,
f(unit,ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2))))) = ld(mult(ld(mult(ld(X2,X),ld(X2,ld(X,X2))),unit),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))))),unit),
inference(symmetry,[status(thm)],[c730]) ).
cnf(c732,plain,
mult(ld(mult(ld(X2,X),ld(X2,ld(X,X2))),unit),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))))) = mult(f(X,ld(X,X2)),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c733,plain,
ld(mult(ld(mult(ld(X2,X),ld(X2,ld(X,X2))),unit),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))))),unit) = ld(mult(f(X,ld(X,X2)),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))))),unit),
inference(congruence,[status(thm)],[c732]) ).
cnf(c734,plain,
ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))) = mult(ld(X2,X),ld(X2,ld(X,X2))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c735,plain,
ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2))))) = ld(mult(ld(X2,X),ld(X2,ld(X,X2))),mult(ld(X2,X),ld(X2,ld(X,X2)))),
inference(congruence,[status(thm)],[c734]) ).
cnf(c736,plain,
mult(f(X,ld(X,X2)),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))))) = mult(f(X,ld(X,X2)),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),mult(ld(X2,X),ld(X2,ld(X,X2))))),
inference(congruence,[status(thm)],[c735]) ).
cnf(c737,plain,
ld(mult(f(X,ld(X,X2)),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))))),unit) = ld(mult(f(X,ld(X,X2)),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),mult(ld(X2,X),ld(X2,ld(X,X2))))),unit),
inference(congruence,[status(thm)],[c736]) ).
cnf(c738,plain,
ld(mult(ld(X2,X),ld(X2,ld(X,X2))),mult(ld(X2,X),ld(X2,ld(X,X2)))) = unit,
inference(substitution,[status(thm)],[c44]) ).
cnf(c739,plain,
mult(f(X,ld(X,X2)),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),mult(ld(X2,X),ld(X2,ld(X,X2))))) = mult(f(X,ld(X,X2)),unit),
inference(congruence,[status(thm)],[c738]) ).
cnf(c740,plain,
ld(mult(f(X,ld(X,X2)),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),mult(ld(X2,X),ld(X2,ld(X,X2))))),unit) = ld(mult(f(X,ld(X,X2)),unit),unit),
inference(congruence,[status(thm)],[c739]) ).
cnf(c741,plain,
mult(f(X,ld(X,X2)),unit) = f(X,ld(X,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c742,plain,
ld(mult(f(X,ld(X,X2)),unit),unit) = ld(f(X,ld(X,X2)),unit),
inference(congruence,[status(thm)],[c741]) ).
cnf(c743,plain,
ld(mult(f(X,ld(X,X2)),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),mult(ld(X2,X),ld(X2,ld(X,X2))))),unit) = ld(f(X,ld(X,X2)),unit),
inference(transitivity,[status(thm)],[c740,c742]) ).
cnf(c744,plain,
ld(mult(f(X,ld(X,X2)),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))))),unit) = ld(f(X,ld(X,X2)),unit),
inference(transitivity,[status(thm)],[c737,c743]) ).
cnf(c745,plain,
ld(mult(ld(mult(ld(X2,X),ld(X2,ld(X,X2))),unit),ld(mult(ld(X2,X),ld(X2,ld(X,X2))),ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))))),unit) = ld(f(X,ld(X,X2)),unit),
inference(transitivity,[status(thm)],[c733,c744]) ).
cnf(c746,plain,
f(unit,ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2))))) = ld(f(X,ld(X,X2)),unit),
inference(transitivity,[status(thm)],[c731,c745]) ).
cnf(c747,plain,
ld(unit,mult(ld(X2,X),ld(X2,ld(X,X2)))) = ld(f(X,ld(X,X2)),unit),
inference(transitivity,[status(thm)],[c729,c746]) ).
cnf(c748,plain,
mult(ld(X2,X),ld(X2,ld(X,X2))) = ld(f(X,ld(X,X2)),unit),
inference(transitivity,[status(thm)],[c708,c747]) ).
cnf(c749,plain,
mult(ld(ld(X2,X),X),ld(ld(X2,X),ld(X,ld(X2,X)))) = ld(f(X,ld(X,ld(X2,X))),unit),
inference(substitution,[status(thm)],[c748]) ).
cnf(c750,plain,
mult(X2,ld(ld(X2,X),ld(X,ld(X2,X)))) = ld(f(X,ld(X,ld(X2,X))),unit),
inference(transitivity,[status(thm)],[c706,c749]) ).
cnf(c751,plain,
mult(X,ld(ld(X,X2),ld(X2,ld(X,X2)))) = ld(f(X2,ld(X2,ld(X,X2))),unit),
inference(substitution,[status(thm)],[c750]) ).
cnf(c752,plain,
ld(mult(X,ld(ld(X,X2),ld(X2,ld(X,X2)))),unit) = ld(ld(f(X2,ld(X2,ld(X,X2))),unit),unit),
inference(congruence,[status(thm)],[c751]) ).
cnf(c753,plain,
ld(ld(f(X2,ld(X2,ld(X,X2))),unit),unit) = f(X2,ld(X2,ld(X,X2))),
inference(substitution,[status(thm)],[c57]) ).
cnf(c754,plain,
ld(mult(X,ld(ld(X,X2),ld(X2,ld(X,X2)))),unit) = f(X2,ld(X2,ld(X,X2))),
inference(transitivity,[status(thm)],[c752,c753]) ).
cnf(c755,plain,
mult(ld(X,unit),ld(ld(ld(X,X2),ld(X2,ld(X,X2))),unit)) = f(X2,ld(X2,ld(X,X2))),
inference(transitivity,[status(thm)],[c704,c754]) ).
cnf(c756,plain,
mult(ld(X,unit),ld(ld(ld(X,unit),ld(X2,ld(X,unit))),unit)) = f(X2,ld(X2,ld(X,X2))),
inference(transitivity,[status(thm)],[c643,c755]) ).
cnf(c757,plain,
ld(X2,mult(ld(X,unit),f(X2,X2))) = f(X2,ld(X2,ld(X,X2))),
inference(transitivity,[status(thm)],[c607,c756]) ).
cnf(c758,plain,
f(X2,ld(X2,ld(X,X2))) = ld(X2,mult(ld(X,unit),f(X2,X2))),
inference(symmetry,[status(thm)],[c757]) ).
cnf(c759,plain,
ld(f(X2,X2),f(X2,ld(X2,ld(X,X2)))) = ld(f(X2,X2),ld(X2,mult(ld(X,unit),f(X2,X2)))),
inference(congruence,[status(thm)],[c758]) ).
cnf(c760,plain,
ld(f(X2,X2),ld(X2,mult(ld(X,unit),f(X2,X2)))) = ld(X2,ld(f(X2,X2),mult(ld(X,unit),f(X2,X2)))),
inference(substitution,[status(thm)],[c591]) ).
cnf(c761,plain,
ld(f(X2,X2),mult(ld(X,unit),f(X2,X2))) = ld(X,unit),
inference(substitution,[status(thm)],[c21]) ).
cnf(c762,plain,
ld(X2,ld(f(X2,X2),mult(ld(X,unit),f(X2,X2)))) = ld(X2,ld(X,unit)),
inference(congruence,[status(thm)],[c761]) ).
cnf(c763,plain,
ld(f(X2,X2),ld(X2,mult(ld(X,unit),f(X2,X2)))) = ld(X2,ld(X,unit)),
inference(transitivity,[status(thm)],[c760,c762]) ).
cnf(c764,plain,
ld(f(X2,X2),f(X2,ld(X2,ld(X,X2)))) = ld(X2,ld(X,unit)),
inference(transitivity,[status(thm)],[c759,c763]) ).
cnf(c765,plain,
ld(f(X2,X2),f(X2,ld(X2,ld(ld(X,X2),X2)))) = ld(X2,ld(ld(X,X2),unit)),
inference(substitution,[status(thm)],[c764]) ).
cnf(c766,plain,
ld(f(X2,X2),f(X2,ld(X2,X))) = ld(X2,ld(ld(X,X2),unit)),
inference(transitivity,[status(thm)],[c536,c765]) ).
cnf(c767,plain,
ld(f(X2,X2),f(X2,ld(X2,mult(X2,X)))) = ld(X2,ld(ld(mult(X2,X),X2),unit)),
inference(substitution,[status(thm)],[c766]) ).
cnf(c768,plain,
ld(X2,ld(ld(mult(X2,X),X2),unit)) = ld(f(X2,X2),f(X2,ld(X2,mult(X2,X)))),
inference(symmetry,[status(thm)],[c767]) ).
cnf(c769,plain,
ld(X2,mult(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c770,plain,
f(X2,ld(X2,mult(X2,X))) = f(X2,X),
inference(congruence,[status(thm)],[c769]) ).
cnf(c771,plain,
ld(f(X2,X2),f(X2,ld(X2,mult(X2,X)))) = ld(f(X2,X2),f(X2,X)),
inference(congruence,[status(thm)],[c770]) ).
cnf(c772,plain,
ld(X2,ld(ld(mult(X2,X),X2),unit)) = ld(f(X2,X2),f(X2,X)),
inference(transitivity,[status(thm)],[c768,c771]) ).
cnf(c773,plain,
ld(X,ld(ld(mult(X,X2),X),unit)) = ld(f(X,X),f(X,X2)),
inference(substitution,[status(thm)],[c772]) ).
cnf(c774,plain,
mult(X2,ld(X,ld(ld(mult(X,X2),X),unit))) = mult(X2,ld(f(X,X),f(X,X2))),
inference(congruence,[status(thm)],[c773]) ).
cnf(c775,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c776,plain,
f(X,X2) = f(X2,X),
inference(symmetry,[status(thm)],[c775]) ).
cnf(c777,plain,
ld(f(X,X),f(X,X2)) = ld(f(X,X),f(X2,X)),
inference(congruence,[status(thm)],[c776]) ).
cnf(c778,plain,
mult(X2,ld(f(X,X),f(X,X2))) = mult(X2,ld(f(X,X),f(X2,X))),
inference(congruence,[status(thm)],[c777]) ).
cnf(c779,plain,
mult(X2,ld(X,ld(ld(mult(X,X2),X),unit))) = mult(X2,ld(f(X,X),f(X2,X))),
inference(transitivity,[status(thm)],[c774,c778]) ).
cnf(c780,plain,
mult(ld(X,mult(X,X2)),ld(X,ld(ld(mult(X,X2),X),unit))) = mult(X2,ld(f(X,X),f(X2,X))),
inference(transitivity,[status(thm)],[c531,c779]) ).
cnf(c781,plain,
ld(ld(ld(X,mult(X,X2)),unit),mult(ld(X,mult(X,X2)),ld(mult(X,X2),ld(X,mult(X,X2))))) = mult(X2,ld(f(X,X),f(X2,X))),
inference(transitivity,[status(thm)],[c529,c780]) ).
cnf(c782,plain,
ld(ld(X2,unit),mult(ld(X,mult(X,X2)),ld(mult(X,X2),ld(X,mult(X,X2))))) = mult(X2,ld(f(X,X),f(X2,X))),
inference(transitivity,[status(thm)],[c441,c781]) ).
cnf(c783,plain,
ld(ld(X2,unit),mult(X2,ld(mult(X,X2),ld(X,mult(X,X2))))) = mult(X2,ld(f(X,X),f(X2,X))),
inference(transitivity,[status(thm)],[c437,c782]) ).
cnf(c784,plain,
ld(ld(X2,unit),mult(X2,ld(mult(X,X2),X2))) = mult(X2,ld(f(X,X),f(X2,X))),
inference(transitivity,[status(thm)],[c433,c783]) ).
cnf(c785,plain,
ld(ld(X2,unit),mult(X2,ld(mult(X2,X),X2))) = mult(X2,ld(f(X,X),f(X2,X))),
inference(transitivity,[status(thm)],[c428,c784]) ).
cnf(c786,plain,
ld(ld(X,unit),mult(X,ld(mult(X,X2),X))) = mult(X,ld(f(X2,X2),f(X,X2))),
inference(substitution,[status(thm)],[c785]) ).
cnf(c787,plain,
ld(X,ld(ld(X,unit),mult(X,ld(mult(X,X2),X)))) = ld(X,mult(X,ld(f(X2,X2),f(X,X2)))),
inference(congruence,[status(thm)],[c786]) ).
cnf(c788,plain,
ld(X,mult(X,ld(f(X2,X2),f(X,X2)))) = ld(f(X2,X2),f(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c789,plain,
ld(X,ld(ld(X,unit),mult(X,ld(mult(X,X2),X)))) = ld(f(X2,X2),f(X,X2)),
inference(transitivity,[status(thm)],[c787,c788]) ).
cnf(c790,plain,
ld(ld(X,unit),ld(mult(X,X2),X)) = ld(f(X2,X2),f(X,X2)),
inference(transitivity,[status(thm)],[c423,c789]) ).
cnf(c791,plain,
ld(f(X2,X2),f(X,X2)) = ld(ld(X,unit),ld(mult(X,X2),X)),
inference(symmetry,[status(thm)],[c790]) ).
cnf(c792,plain,
ld(ld(f(X2,X2),f(X,X2)),unit) = ld(ld(ld(X,unit),ld(mult(X,X2),X)),unit),
inference(congruence,[status(thm)],[c791]) ).
cnf(c793,plain,
ld(ld(ld(f(X2,X2),f(X,X2)),unit),f(X,X2)) = ld(ld(ld(ld(X,unit),ld(mult(X,X2),X)),unit),f(X,X2)),
inference(congruence,[status(thm)],[c792]) ).
cnf(c794,plain,
ld(ld(ld(X2,unit),unit),ld(X,unit)) = ld(ld(ld(X2,unit),X),unit),
inference(substitution,[status(thm)],[c693]) ).
cnf(c795,plain,
ld(ld(ld(X2,unit),X),unit) = ld(ld(ld(X2,unit),unit),ld(X,unit)),
inference(symmetry,[status(thm)],[c794]) ).
cnf(c796,plain,
ld(ld(X,unit),unit) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c797,plain,
ld(ld(ld(X2,unit),unit),ld(X,unit)) = ld(X2,ld(X,unit)),
inference(congruence,[status(thm)],[c796]) ).
cnf(c798,plain,
ld(ld(ld(X2,unit),X),unit) = ld(X2,ld(X,unit)),
inference(transitivity,[status(thm)],[c795,c797]) ).
cnf(c799,plain,
ld(ld(ld(X,unit),ld(mult(X,X2),X)),unit) = ld(X,ld(ld(mult(X,X2),X),unit)),
inference(substitution,[status(thm)],[c798]) ).
cnf(c800,plain,
ld(ld(ld(ld(X,unit),ld(mult(X,X2),X)),unit),f(X,X2)) = ld(ld(X,ld(ld(mult(X,X2),X),unit)),f(X,X2)),
inference(congruence,[status(thm)],[c799]) ).
cnf(c801,plain,
ld(X,ld(ld(mult(X,X2),X),unit)) = ld(f(X,X),f(X,X2)),
inference(substitution,[status(thm)],[c772]) ).
cnf(c802,plain,
ld(ld(X,ld(ld(mult(X,X2),X),unit)),f(X,X2)) = ld(ld(f(X,X),f(X,X2)),f(X,X2)),
inference(congruence,[status(thm)],[c801]) ).
cnf(c803,plain,
ld(ld(f(X,X),f(X,X2)),f(X,X2)) = f(X,X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c804,plain,
ld(ld(X,ld(ld(mult(X,X2),X),unit)),f(X,X2)) = f(X,X),
inference(transitivity,[status(thm)],[c802,c803]) ).
cnf(c805,plain,
ld(ld(ld(ld(X,unit),ld(mult(X,X2),X)),unit),f(X,X2)) = f(X,X),
inference(transitivity,[status(thm)],[c800,c804]) ).
cnf(c806,plain,
ld(ld(ld(f(X2,X2),f(X,X2)),unit),f(X,X2)) = f(X,X),
inference(transitivity,[status(thm)],[c793,c805]) ).
cnf(c807,plain,
ld(f(X2,X2),f(f(X,X2),f(X,X2))) = f(X,X),
inference(transitivity,[status(thm)],[c391,c806]) ).
cnf(c808,plain,
ld(f(X2,X2),f(f(X,X2),f(X2,X))) = f(X,X),
inference(transitivity,[status(thm)],[c182,c807]) ).
cnf(c809,plain,
ld(f(X2,X2),f(f(X2,X),f(X2,X))) = f(X,X),
inference(transitivity,[status(thm)],[c179,c808]) ).
cnf(c810,plain,
ld(f(X,X),f(f(X,X2),f(X,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c809]) ).
cnf(c811,plain,
f(X2,X2) = ld(f(X,X),f(f(X,X2),f(X,X2))),
inference(symmetry,[status(thm)],[c810]) ).
cnf(c812,plain,
mult(f(X,X),f(X2,X2)) = mult(f(X,X),ld(f(X,X),f(f(X,X2),f(X,X2)))),
inference(congruence,[status(thm)],[c811]) ).
cnf(c813,plain,
mult(f(X,X),ld(f(X,X),f(f(X,X2),f(X,X2)))) = f(f(X,X2),f(X,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c814,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c815,plain,
f(X,X2) = f(X2,X),
inference(symmetry,[status(thm)],[c814]) ).
cnf(c816,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X,X2)),
inference(congruence,[status(thm)],[c815]) ).
cnf(c817,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c818,plain,
f(X,X2) = f(X2,X),
inference(symmetry,[status(thm)],[c817]) ).
cnf(c819,plain,
f(f(X2,X),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(congruence,[status(thm)],[c818]) ).
cnf(c820,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c816,c819]) ).
cnf(c821,plain,
mult(f(X,X),ld(f(X,X),f(f(X,X2),f(X,X2)))) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c813,c820]) ).
cnf(c822,plain,
mult(f(X,X),f(X2,X2)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c812,c821]) ).
cnf(c823,plain,
mult(f(X2,X2),f(X,X)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c145,c822]) ).
cnf(c824,plain,
mult(f(a,a),f(b,b)) = f(f(a,b),f(a,b)),
inference(substitution,[status(thm)],[c823]) ).
cnf(c825,plain,
mult(f(a,b),f(a,b)) = f(f(a,b),f(a,b)),
inference(substitution,[status(thm)],[c139]) ).
cnf(c826,plain,
f(f(a,b),f(a,b)) = mult(f(a,b),f(a,b)),
inference(symmetry,[status(thm)],[c825]) ).
cnf(c827,plain,
mult(f(a,a),f(b,b)) = mult(f(a,b),f(a,b)),
inference(transitivity,[status(thm)],[c824,c826]) ).
cnf(c828,plain,
mult(f(a,a),mult(b,b)) = mult(f(a,b),f(a,b)),
inference(transitivity,[status(thm)],[c143,c827]) ).
cnf(c829,plain,
mult(mult(a,a),mult(b,b)) = mult(f(a,b),f(a,b)),
inference(transitivity,[status(thm)],[c141,c828]) ).
cnf(c830,plain,
$false,
inference(resolution,[status(thm)],[c1,c829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP721-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 % Computer : n020.cluster.edu
% 0.19/0.47 % Model : x86_64 x86_64
% 0.19/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47 % Memory : 8046.5625MB
% 0.19/0.47 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Sun Sep 27 10:38:19 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.48 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 213.12/31.21 Command-line arguments: --no-flatten-goal
% 213.12/31.21
% 213.12/31.21 % SZS status Unsatisfiable
% 213.12/31.21
% 213.12/31.28 % SZS output start CNFRefutation
% See solution above
% 218.75/32.03
% 218.75/32.03 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------