%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP667-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:11:39 AM UTC 2026
% Result : Unsatisfiable 78.78s 10.48s
% Output : CNFRefutation 82.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 12
% Syntax : Number of clauses : 767 ( 767 unt; 0 nHn; 8 RR)
% Number of literals : 767 ( 766 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 1494 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
mult(mult(A,B),A) = mult(A,mult(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
cnf(c3,plain,
mult(mult(X,X3),X) = mult(X,mult(X3,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
mult(X,mult(X3,X)) = mult(mult(X,X3),X),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
mult(mult(X,mult(X3,X)),X4) = mult(mult(mult(X,X3),X),X4),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
ifeq(mult(X4,mult(X3,mult(X,X3))),mult(mult(mult(X4,X3),X),X3),mult(X3,mult(X4,mult(X3,X))),mult(mult(X3,mult(X4,X3)),X)) = ifeq(mult(X4,mult(X3,mult(X,X3))),mult(mult(mult(X4,X3),X),X3),mult(X3,mult(X4,mult(X3,X))),mult(mult(mult(X3,X4),X3),X)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
ifeq(mult(X0,mult(X1,mult(X2,X1))),mult(mult(mult(X0,X1),X2),X1),mult(X1,mult(X0,mult(X1,X2))),mult(mult(mult(X1,X0),X1),X2)) = mult(mult(mult(X1,X0),X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
cnf(c8,plain,
ifeq(mult(X4,mult(X3,mult(X,X3))),mult(mult(mult(X4,X3),X),X3),mult(X3,mult(X4,mult(X3,X))),mult(mult(mult(X3,X4),X3),X)) = mult(mult(mult(X3,X4),X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
mult(mult(X,X3),X) = mult(X,mult(X3,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
mult(mult(mult(X3,X4),X3),X) = mult(mult(X3,mult(X4,X3)),X),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq(mult(X4,mult(X3,mult(X,X3))),mult(mult(mult(X4,X3),X),X3),mult(X3,mult(X4,mult(X3,X))),mult(mult(mult(X3,X4),X3),X)) = mult(mult(X3,mult(X4,X3)),X),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
ifeq(mult(X4,mult(X3,mult(X,X3))),mult(mult(mult(X4,X3),X),X3),mult(X3,mult(X4,mult(X3,X))),mult(mult(X3,mult(X4,X3)),X)) = mult(mult(X3,mult(X4,X3)),X),
inference(transitivity,[status(thm)],[c6,c11]) ).
cnf(c13,plain,
ifeq(mult(X3,mult(X4,mult(X,X4))),mult(mult(mult(X3,X4),X),X4),mult(X4,mult(X3,mult(X4,X))),mult(mult(X4,mult(X3,X4)),X)) = mult(mult(X4,mult(X3,X4)),X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
mult(mult(X4,mult(X3,X4)),X) = ifeq(mult(X3,mult(X4,mult(X,X4))),mult(mult(mult(X3,X4),X),X4),mult(X4,mult(X3,mult(X4,X))),mult(mult(X4,mult(X3,X4)),X)),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,axiom,
mult(unit,A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
cnf(c16,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
mult(X,X) = mult(X,mult(unit,X)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
mult(mult(X3,X3),X) = mult(mult(X3,mult(unit,X3)),X),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
ifeq(mult(unit,mult(X3,mult(X,X3))),mult(mult(mult(unit,X3),X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,mult(unit,X3)),X)) = mult(mult(X3,mult(unit,X3)),X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c21,plain,
mult(mult(X3,mult(unit,X3)),X) = ifeq(mult(unit,mult(X3,mult(X,X3))),mult(mult(mult(unit,X3),X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,mult(unit,X3)),X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
mult(unit,mult(X3,mult(X,X3))) = mult(X3,mult(X,X3)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c23,plain,
ifeq(mult(unit,mult(X3,mult(X,X3))),mult(mult(mult(unit,X3),X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,mult(unit,X3)),X)) = ifeq(mult(X3,mult(X,X3)),mult(mult(mult(unit,X3),X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,mult(unit,X3)),X)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c25,plain,
mult(mult(unit,X3),X) = mult(X3,X),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
mult(mult(mult(unit,X3),X),X3) = mult(mult(X3,X),X3),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
ifeq(mult(X3,mult(X,X3)),mult(mult(mult(unit,X3),X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,mult(unit,X3)),X)) = ifeq(mult(X3,mult(X,X3)),mult(mult(X3,X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,mult(unit,X3)),X)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c29,plain,
mult(X,mult(unit,X)) = mult(X,X),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
mult(mult(X3,mult(unit,X3)),X) = mult(mult(X3,X3),X),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
ifeq(mult(X3,mult(X,X3)),mult(mult(X3,X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,mult(unit,X3)),X)) = ifeq(mult(X3,mult(X,X3)),mult(mult(X3,X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,X3),X)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
mult(mult(X3,X),X3) = mult(X3,mult(X,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
ifeq(mult(X3,mult(X,X3)),mult(mult(X3,X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,X3),X)) = ifeq(mult(X3,mult(X,X3)),mult(X3,mult(X,X3)),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,X3),X)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
ifeq(A2,A2,B2,C) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c35,plain,
ifeq(mult(X3,mult(X,X3)),mult(X3,mult(X,X3)),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,X3),X)) = mult(X3,mult(unit,mult(X3,X))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
mult(unit,mult(X3,X)) = mult(X3,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c37,plain,
mult(X3,mult(unit,mult(X3,X))) = mult(X3,mult(X3,X)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
ifeq(mult(X3,mult(X,X3)),mult(X3,mult(X,X3)),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,X3),X)) = mult(X3,mult(X3,X)),
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
ifeq(mult(X3,mult(X,X3)),mult(mult(X3,X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,X3),X)) = mult(X3,mult(X3,X)),
inference(transitivity,[status(thm)],[c33,c38]) ).
cnf(c40,plain,
ifeq(mult(X3,mult(X,X3)),mult(mult(X3,X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,mult(unit,X3)),X)) = mult(X3,mult(X3,X)),
inference(transitivity,[status(thm)],[c31,c39]) ).
cnf(c41,plain,
ifeq(mult(X3,mult(X,X3)),mult(mult(mult(unit,X3),X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,mult(unit,X3)),X)) = mult(X3,mult(X3,X)),
inference(transitivity,[status(thm)],[c27,c40]) ).
cnf(c42,plain,
ifeq(mult(unit,mult(X3,mult(X,X3))),mult(mult(mult(unit,X3),X),X3),mult(X3,mult(unit,mult(X3,X))),mult(mult(X3,mult(unit,X3)),X)) = mult(X3,mult(X3,X)),
inference(transitivity,[status(thm)],[c23,c41]) ).
cnf(c43,plain,
mult(mult(X3,mult(unit,X3)),X) = mult(X3,mult(X3,X)),
inference(transitivity,[status(thm)],[c21,c42]) ).
cnf(c44,plain,
mult(mult(X3,X3),X) = mult(X3,mult(X3,X)),
inference(transitivity,[status(thm)],[c19,c43]) ).
cnf(c45,plain,
mult(mult(f(X3),f(X3)),X) = mult(f(X3),mult(f(X3),X)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
mult(f(X3),mult(f(X3),X)) = mult(mult(f(X3),f(X3)),X),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,axiom,
mult(f(A2),f(A2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
cnf(c48,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
mult(mult(f(X3),f(X3)),X) = mult(X3,X),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
mult(f(X3),mult(f(X3),X)) = mult(X3,X),
inference(transitivity,[status(thm)],[c46,c49]) ).
cnf(c51,plain,
mult(f(X3),mult(f(X3),ld(f(X3),X))) = mult(X3,ld(f(X3),X)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
mult(X3,ld(f(X3),X)) = mult(f(X3),mult(f(X3),ld(f(X3),X))),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(c54,plain,
mult(f(X3),ld(f(X3),X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
mult(f(X3),mult(f(X3),ld(f(X3),X))) = mult(f(X3),X),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
mult(X3,ld(f(X3),X)) = mult(f(X3),X),
inference(transitivity,[status(thm)],[c52,c55]) ).
cnf(c57,plain,
mult(f(X3),X) = mult(X3,ld(f(X3),X)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
ld(X3,mult(f(X3),X)) = ld(X3,mult(X3,ld(f(X3),X))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,axiom,
ld(A2,mult(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(c60,plain,
ld(X3,mult(X3,ld(f(X3),X))) = ld(f(X3),X),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
ld(X3,mult(f(X3),X)) = ld(f(X3),X),
inference(transitivity,[status(thm)],[c58,c60]) ).
cnf(c62,plain,
ld(X,mult(f(X),ld(X,f(X)))) = ld(f(X),ld(X,f(X))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
ld(f(X),ld(X,f(X))) = ld(X,mult(f(X),ld(X,f(X)))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
ld(X3,mult(X3,mult(ld(X3,X),ld(X3,X)))) = mult(ld(X3,X),ld(X3,X)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c65,plain,
mult(ld(X3,X),ld(X3,X)) = ld(X3,mult(X3,mult(ld(X3,X),ld(X3,X)))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
cnf(c67,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
mult(mult(X3,X),X) = mult(mult(X3,X),mult(X,unit)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
mult(unit,mult(X,unit)) = mult(X,unit),
inference(substitution,[status(thm)],[c15]) ).
cnf(c71,plain,
mult(X,unit) = mult(unit,mult(X,unit)),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
mult(mult(X3,X),mult(X,unit)) = mult(mult(X3,X),mult(unit,mult(X,unit))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
mult(mult(X3,X),X3) = mult(X3,mult(X,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c74,plain,
mult(X3,mult(X,X3)) = mult(mult(X3,X),X3),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
mult(X4,mult(X3,mult(X,X3))) = mult(X4,mult(mult(X3,X),X3)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
mult(mult(X4,mult(X3,mult(X,X3))),X) = mult(mult(X4,mult(mult(X3,X),X3)),X),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,axiom,
mult(mult(A2,B2),mult(mult(C2,B2),C2)) = mult(mult(A2,mult(mult(B2,C2),B2)),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
cnf(c78,plain,
mult(mult(X4,X3),mult(mult(X,X3),X)) = mult(mult(X4,mult(mult(X3,X),X3)),X),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
mult(mult(X4,mult(mult(X3,X),X3)),X) = mult(mult(X4,X3),mult(mult(X,X3),X)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
mult(mult(X,X3),X) = mult(X,mult(X3,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c81,plain,
mult(mult(X4,X3),mult(mult(X,X3),X)) = mult(mult(X4,X3),mult(X,mult(X3,X))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
mult(mult(X4,mult(mult(X3,X),X3)),X) = mult(mult(X4,X3),mult(X,mult(X3,X))),
inference(transitivity,[status(thm)],[c79,c81]) ).
cnf(c83,plain,
mult(mult(X4,mult(X3,mult(X,X3))),X) = mult(mult(X4,X3),mult(X,mult(X3,X))),
inference(transitivity,[status(thm)],[c76,c82]) ).
cnf(c84,plain,
mult(mult(X3,mult(X,mult(unit,X))),unit) = mult(mult(X3,X),mult(unit,mult(X,unit))),
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
mult(mult(X3,X),mult(unit,mult(X,unit))) = mult(mult(X3,mult(X,mult(unit,X))),unit),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
mult(mult(X3,mult(X,mult(unit,X))),unit) = mult(X3,mult(X,mult(unit,X))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c87,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c88,plain,
mult(X,mult(unit,X)) = mult(X,X),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
mult(X3,mult(X,mult(unit,X))) = mult(X3,mult(X,X)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
mult(mult(X3,mult(X,mult(unit,X))),unit) = mult(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c86,c89]) ).
cnf(c91,plain,
mult(mult(X3,X),mult(unit,mult(X,unit))) = mult(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c85,c90]) ).
cnf(c92,plain,
mult(mult(X3,X),mult(X,unit)) = mult(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c72,c91]) ).
cnf(c93,plain,
mult(mult(X3,X),X) = mult(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c69,c92]) ).
cnf(c94,plain,
mult(mult(X3,ld(X3,X)),ld(X3,X)) = mult(X3,mult(ld(X3,X),ld(X3,X))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
mult(X3,mult(ld(X3,X),ld(X3,X))) = mult(mult(X3,ld(X3,X)),ld(X3,X)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
mult(X3,ld(X3,X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c97,plain,
mult(mult(X3,ld(X3,X)),ld(X3,X)) = mult(X,ld(X3,X)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
mult(X3,mult(ld(X3,X),ld(X3,X))) = mult(X,ld(X3,X)),
inference(transitivity,[status(thm)],[c95,c97]) ).
cnf(c99,plain,
ld(X3,mult(X3,mult(ld(X3,X),ld(X3,X)))) = ld(X3,mult(X,ld(X3,X))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
mult(ld(X3,X),ld(X3,X)) = ld(X3,mult(X,ld(X3,X))),
inference(transitivity,[status(thm)],[c65,c99]) ).
cnf(c101,plain,
mult(ld(X,f(X)),ld(X,f(X))) = ld(X,mult(f(X),ld(X,f(X)))),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
ld(X,mult(f(X),ld(X,f(X)))) = mult(ld(X,f(X)),ld(X,f(X))),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
mult(X3,ld(X3,X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c104,plain,
X = mult(X3,ld(X3,X)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
mult(X3,X) = mult(X3,mult(X3,ld(X3,X))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
rd(mult(X3,X),ld(X3,X)) = rd(mult(X3,mult(X3,ld(X3,X))),ld(X3,X)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
mult(X3,mult(X3,X)) = mult(mult(X3,X3),X),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c108,plain,
rd(mult(X3,mult(X3,X)),X) = rd(mult(mult(X3,X3),X),X),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
cnf(c110,plain,
rd(mult(mult(X3,X3),X),X) = mult(X3,X3),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
rd(mult(X3,mult(X3,X)),X) = mult(X3,X3),
inference(transitivity,[status(thm)],[c108,c110]) ).
cnf(c112,plain,
rd(mult(X3,mult(X3,ld(X3,X))),ld(X3,X)) = mult(X3,X3),
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
rd(mult(X3,X),ld(X3,X)) = mult(X3,X3),
inference(transitivity,[status(thm)],[c106,c112]) ).
cnf(c114,plain,
rd(mult(ld(X,f(X)),f(X)),ld(ld(X,f(X)),f(X))) = mult(ld(X,f(X)),ld(X,f(X))),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
mult(ld(X,f(X)),ld(X,f(X))) = rd(mult(ld(X,f(X)),f(X)),ld(ld(X,f(X)),f(X))),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c117,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
mult(f(X),X) = mult(f(X),mult(f(X),f(X))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
mult(mult(f(X),f(X)),f(X)) = mult(f(X),mult(f(X),f(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c120,plain,
mult(f(X),mult(f(X),f(X))) = mult(mult(f(X),f(X)),f(X)),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c122,plain,
mult(mult(f(X),f(X)),f(X)) = mult(X,f(X)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
mult(f(X),mult(f(X),f(X))) = mult(X,f(X)),
inference(transitivity,[status(thm)],[c120,c122]) ).
cnf(c124,plain,
mult(f(X),X) = mult(X,f(X)),
inference(transitivity,[status(thm)],[c118,c123]) ).
cnf(c125,plain,
mult(X,f(X)) = mult(f(X),X),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
rd(mult(X,f(X)),X) = rd(mult(f(X),X),X),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
rd(mult(f(X),X),X) = f(X),
inference(substitution,[status(thm)],[c109]) ).
cnf(c128,plain,
rd(mult(X,f(X)),X) = f(X),
inference(transitivity,[status(thm)],[c126,c127]) ).
cnf(c129,plain,
f(X) = rd(mult(X,f(X)),X),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
mult(ld(X,f(X)),f(X)) = mult(ld(X,f(X)),rd(mult(X,f(X)),X)),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
mult(mult(X3,X),X3) = mult(X3,mult(X,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c132,plain,
mult(X3,mult(X,X3)) = mult(mult(X3,X),X3),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
rd(mult(X3,mult(X,X3)),X3) = rd(mult(mult(X3,X),X3),X3),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
rd(mult(mult(X3,X),X3),X3) = mult(X3,X),
inference(substitution,[status(thm)],[c109]) ).
cnf(c135,plain,
rd(mult(X3,mult(X,X3)),X3) = mult(X3,X),
inference(transitivity,[status(thm)],[c133,c134]) ).
cnf(c136,plain,
rd(mult(X3,mult(rd(X,X3),X3)),X3) = mult(X3,rd(X,X3)),
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
mult(X3,rd(X,X3)) = rd(mult(X3,mult(rd(X,X3),X3)),X3),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
cnf(c139,plain,
mult(rd(X,X3),X3) = X,
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
mult(X3,mult(rd(X,X3),X3)) = mult(X3,X),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
rd(mult(X3,mult(rd(X,X3),X3)),X3) = rd(mult(X3,X),X3),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
mult(X3,rd(X,X3)) = rd(mult(X3,X),X3),
inference(transitivity,[status(thm)],[c137,c141]) ).
cnf(c143,plain,
rd(mult(X3,X),X3) = mult(X3,rd(X,X3)),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
ld(X3,rd(mult(X3,X),X3)) = ld(X3,mult(X3,rd(X,X3))),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
ld(X3,mult(X3,rd(X,X3))) = rd(X,X3),
inference(substitution,[status(thm)],[c59]) ).
cnf(c146,plain,
ld(X3,rd(mult(X3,X),X3)) = rd(X,X3),
inference(transitivity,[status(thm)],[c144,c145]) ).
cnf(c147,plain,
ld(X,rd(mult(X,f(X)),X)) = rd(f(X),X),
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
rd(f(X),X) = ld(X,rd(mult(X,f(X)),X)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
ld(X,rd(mult(X,f(X)),X)) = ld(X,f(X)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c150,plain,
rd(f(X),X) = ld(X,f(X)),
inference(transitivity,[status(thm)],[c148,c149]) ).
cnf(c151,plain,
ld(X,f(X)) = rd(f(X),X),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
mult(ld(X,f(X)),rd(mult(X,f(X)),X)) = mult(rd(f(X),X),rd(mult(X,f(X)),X)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
mult(X,rd(X3,X)) = rd(mult(X,X3),X),
inference(substitution,[status(thm)],[c142]) ).
cnf(c154,plain,
rd(mult(X,X3),X) = mult(X,rd(X3,X)),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
mult(rd(X3,X),rd(mult(X,X3),X)) = mult(rd(X3,X),mult(X,rd(X3,X))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
mult(mult(rd(X3,X),X),rd(X3,X)) = mult(rd(X3,X),mult(X,rd(X3,X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c157,plain,
mult(rd(X3,X),mult(X,rd(X3,X))) = mult(mult(rd(X3,X),X),rd(X3,X)),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
mult(rd(X3,X),X) = X3,
inference(substitution,[status(thm)],[c138]) ).
cnf(c159,plain,
mult(mult(rd(X3,X),X),rd(X3,X)) = mult(X3,rd(X3,X)),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
mult(rd(X3,X),mult(X,rd(X3,X))) = mult(X3,rd(X3,X)),
inference(transitivity,[status(thm)],[c157,c159]) ).
cnf(c161,plain,
mult(rd(X3,X),rd(mult(X,X3),X)) = mult(X3,rd(X3,X)),
inference(transitivity,[status(thm)],[c155,c160]) ).
cnf(c162,plain,
mult(rd(f(X),X),rd(mult(X,f(X)),X)) = mult(f(X),rd(f(X),X)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
mult(f(X),rd(f(X),X)) = mult(f(X),ld(X,f(X))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c164,plain,
mult(X3,X) = mult(f(X3),mult(f(X3),X)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c165,plain,
ld(f(X3),mult(X3,X)) = ld(f(X3),mult(f(X3),mult(f(X3),X))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
ld(f(X3),mult(f(X3),mult(f(X3),X))) = mult(f(X3),X),
inference(substitution,[status(thm)],[c59]) ).
cnf(c167,plain,
ld(f(X3),mult(X3,X)) = mult(f(X3),X),
inference(transitivity,[status(thm)],[c165,c166]) ).
cnf(c168,plain,
ld(f(X3),mult(X3,ld(X3,X))) = mult(f(X3),ld(X3,X)),
inference(substitution,[status(thm)],[c167]) ).
cnf(c169,plain,
mult(f(X3),ld(X3,X)) = ld(f(X3),mult(X3,ld(X3,X))),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
mult(X3,ld(X3,X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c171,plain,
ld(f(X3),mult(X3,ld(X3,X))) = ld(f(X3),X),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
mult(f(X3),ld(X3,X)) = ld(f(X3),X),
inference(transitivity,[status(thm)],[c169,c171]) ).
cnf(c173,plain,
mult(f(X),ld(X,f(X))) = ld(f(X),f(X)),
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c66]) ).
cnf(c175,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
ld(X,X) = ld(X,mult(X,unit)),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
ld(X,mult(X,unit)) = unit,
inference(substitution,[status(thm)],[c59]) ).
cnf(c178,plain,
ld(X,X) = unit,
inference(transitivity,[status(thm)],[c176,c177]) ).
cnf(c179,plain,
ld(f(X),f(X)) = unit,
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
mult(f(X),ld(X,f(X))) = unit,
inference(transitivity,[status(thm)],[c173,c179]) ).
cnf(c181,plain,
mult(f(X),rd(f(X),X)) = unit,
inference(transitivity,[status(thm)],[c163,c180]) ).
cnf(c182,plain,
mult(rd(f(X),X),rd(mult(X,f(X)),X)) = unit,
inference(transitivity,[status(thm)],[c162,c181]) ).
cnf(c183,plain,
mult(ld(X,f(X)),rd(mult(X,f(X)),X)) = unit,
inference(transitivity,[status(thm)],[c152,c182]) ).
cnf(c184,plain,
mult(ld(X,f(X)),f(X)) = unit,
inference(transitivity,[status(thm)],[c130,c183]) ).
cnf(c185,plain,
rd(mult(ld(X,f(X)),f(X)),ld(ld(X,f(X)),f(X))) = rd(unit,ld(ld(X,f(X)),f(X))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
ld(X,rd(mult(X,unit),X)) = rd(unit,X),
inference(substitution,[status(thm)],[c146]) ).
cnf(c187,plain,
rd(unit,X) = ld(X,rd(mult(X,unit),X)),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c66]) ).
cnf(c189,plain,
rd(mult(X,unit),X) = rd(X,X),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
ld(X,rd(mult(X,unit),X)) = ld(X,rd(X,X)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c192,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
rd(X,X) = rd(mult(unit,X),X),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
rd(mult(unit,X),X) = unit,
inference(substitution,[status(thm)],[c109]) ).
cnf(c195,plain,
rd(X,X) = unit,
inference(transitivity,[status(thm)],[c193,c194]) ).
cnf(c196,plain,
ld(X,rd(X,X)) = ld(X,unit),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
ld(X,rd(mult(X,unit),X)) = ld(X,unit),
inference(transitivity,[status(thm)],[c190,c196]) ).
cnf(c198,plain,
rd(unit,X) = ld(X,unit),
inference(transitivity,[status(thm)],[c187,c197]) ).
cnf(c199,plain,
rd(unit,ld(ld(X,f(X)),f(X))) = ld(ld(ld(X,f(X)),f(X)),unit),
inference(substitution,[status(thm)],[c198]) ).
cnf(c200,plain,
ld(X,f(X)) = rd(f(X),X),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c201,plain,
ld(ld(X,f(X)),f(X)) = ld(rd(f(X),X),f(X)),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
mult(rd(X3,X),X) = X3,
inference(substitution,[status(thm)],[c138]) ).
cnf(c203,plain,
X3 = mult(rd(X3,X),X),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
ld(rd(X3,X),X3) = ld(rd(X3,X),mult(rd(X3,X),X)),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
ld(rd(X3,X),mult(rd(X3,X),X)) = X,
inference(substitution,[status(thm)],[c59]) ).
cnf(c206,plain,
ld(rd(X3,X),X3) = X,
inference(transitivity,[status(thm)],[c204,c205]) ).
cnf(c207,plain,
ld(rd(f(X),X),f(X)) = X,
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
ld(ld(X,f(X)),f(X)) = X,
inference(transitivity,[status(thm)],[c201,c207]) ).
cnf(c209,plain,
ld(ld(ld(X,f(X)),f(X)),unit) = ld(X,unit),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
rd(unit,ld(ld(X,f(X)),f(X))) = ld(X,unit),
inference(transitivity,[status(thm)],[c199,c209]) ).
cnf(c211,plain,
rd(mult(ld(X,f(X)),f(X)),ld(ld(X,f(X)),f(X))) = ld(X,unit),
inference(transitivity,[status(thm)],[c185,c210]) ).
cnf(c212,plain,
mult(ld(X,f(X)),ld(X,f(X))) = ld(X,unit),
inference(transitivity,[status(thm)],[c115,c211]) ).
cnf(c213,plain,
ld(X,mult(f(X),ld(X,f(X)))) = ld(X,unit),
inference(transitivity,[status(thm)],[c102,c212]) ).
cnf(c214,plain,
ld(f(X),ld(X,f(X))) = ld(X,unit),
inference(transitivity,[status(thm)],[c63,c213]) ).
cnf(c215,plain,
ld(X,unit) = ld(f(X),ld(X,f(X))),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
rd(X3,ld(X,unit)) = rd(X3,ld(f(X),ld(X,f(X)))),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
ld(X,mult(f(X),ld(X,f(X)))) = ld(f(X),ld(X,f(X))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c218,plain,
ld(f(X),ld(X,f(X))) = ld(X,mult(f(X),ld(X,f(X)))),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
rd(X3,ld(f(X),ld(X,f(X)))) = rd(X3,ld(X,mult(f(X),ld(X,f(X))))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
mult(ld(X,f(X)),ld(X,f(X))) = ld(X,mult(f(X),ld(X,f(X)))),
inference(substitution,[status(thm)],[c100]) ).
cnf(c221,plain,
ld(X,mult(f(X),ld(X,f(X)))) = mult(ld(X,f(X)),ld(X,f(X))),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
rd(X3,ld(X,mult(f(X),ld(X,f(X))))) = rd(X3,mult(ld(X,f(X)),ld(X,f(X)))),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
mult(X3,mult(X,X)) = mult(mult(X3,X),X),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c224,plain,
rd(mult(X3,mult(X,X)),X) = rd(mult(mult(X3,X),X),X),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
rd(mult(mult(X3,X),X),X) = mult(X3,X),
inference(substitution,[status(thm)],[c109]) ).
cnf(c226,plain,
rd(mult(X3,mult(X,X)),X) = mult(X3,X),
inference(transitivity,[status(thm)],[c224,c225]) ).
cnf(c227,plain,
rd(mult(rd(X3,mult(X,X)),mult(X,X)),X) = mult(rd(X3,mult(X,X)),X),
inference(substitution,[status(thm)],[c226]) ).
cnf(c228,plain,
mult(rd(X3,mult(X,X)),X) = rd(mult(rd(X3,mult(X,X)),mult(X,X)),X),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
mult(rd(X3,mult(X,X)),mult(X,X)) = X3,
inference(substitution,[status(thm)],[c138]) ).
cnf(c230,plain,
rd(mult(rd(X3,mult(X,X)),mult(X,X)),X) = rd(X3,X),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
mult(rd(X3,mult(X,X)),X) = rd(X3,X),
inference(transitivity,[status(thm)],[c228,c230]) ).
cnf(c232,plain,
rd(X3,X) = mult(rd(X3,mult(X,X)),X),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
rd(rd(X3,X),X) = rd(mult(rd(X3,mult(X,X)),X),X),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
rd(mult(rd(X3,mult(X,X)),X),X) = rd(X3,mult(X,X)),
inference(substitution,[status(thm)],[c109]) ).
cnf(c235,plain,
rd(rd(X3,X),X) = rd(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c233,c234]) ).
cnf(c236,plain,
rd(rd(X3,ld(X,f(X))),ld(X,f(X))) = rd(X3,mult(ld(X,f(X)),ld(X,f(X)))),
inference(substitution,[status(thm)],[c235]) ).
cnf(c237,plain,
rd(X3,mult(ld(X,f(X)),ld(X,f(X)))) = rd(rd(X3,ld(X,f(X))),ld(X,f(X))),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
mult(X,f(X)) = mult(f(X),X),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c239,plain,
mult(X3,mult(X,f(X))) = mult(X3,mult(f(X),X)),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
mult(mult(X3,mult(X,f(X))),ld(X,f(X))) = mult(mult(X3,mult(f(X),X)),ld(X,f(X))),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
mult(mult(X3,ld(X3,X)),X3) = mult(X3,mult(ld(X3,X),X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c242,plain,
mult(X3,mult(ld(X3,X),X3)) = mult(mult(X3,ld(X3,X)),X3),
inference(symmetry,[status(thm)],[c241]) ).
cnf(c243,plain,
mult(X3,ld(X3,X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c244,plain,
mult(mult(X3,ld(X3,X)),X3) = mult(X,X3),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
mult(X3,mult(ld(X3,X),X3)) = mult(X,X3),
inference(transitivity,[status(thm)],[c242,c244]) ).
cnf(c246,plain,
mult(X,mult(ld(X,X3),X)) = mult(X3,X),
inference(substitution,[status(thm)],[c245]) ).
cnf(c247,plain,
mult(X3,X) = mult(X,mult(ld(X,X3),X)),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
mult(X4,mult(X3,X)) = mult(X4,mult(X,mult(ld(X,X3),X))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
mult(mult(X4,mult(X3,X)),ld(X,X3)) = mult(mult(X4,mult(X,mult(ld(X,X3),X))),ld(X,X3)),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
mult(mult(X4,mult(X,mult(ld(X,X3),X))),ld(X,X3)) = mult(mult(X4,X),mult(ld(X,X3),mult(X,ld(X,X3)))),
inference(substitution,[status(thm)],[c83]) ).
cnf(c251,plain,
mult(X,ld(X,X3)) = X3,
inference(substitution,[status(thm)],[c53]) ).
cnf(c252,plain,
mult(ld(X,X3),mult(X,ld(X,X3))) = mult(ld(X,X3),X3),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
mult(mult(X4,X),mult(ld(X,X3),mult(X,ld(X,X3)))) = mult(mult(X4,X),mult(ld(X,X3),X3)),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
rd(mult(mult(ld(X3,X),X),X3),X3) = mult(ld(X3,X),X),
inference(substitution,[status(thm)],[c109]) ).
cnf(c255,plain,
mult(ld(X3,X),X) = rd(mult(mult(ld(X3,X),X),X3),X3),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
mult(X3,ld(X3,X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c257,plain,
X = mult(X3,ld(X3,X)),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
mult(ld(X3,X),X) = mult(ld(X3,X),mult(X3,ld(X3,X))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
mult(mult(ld(X3,X),X),X3) = mult(mult(ld(X3,X),mult(X3,ld(X3,X))),X3),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
mult(unit,mult(X3,mult(X,X3))) = mult(X3,mult(X,X3)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c261,plain,
mult(X3,mult(X,X3)) = mult(unit,mult(X3,mult(X,X3))),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c262,plain,
mult(mult(X3,mult(X,X3)),X) = mult(mult(unit,mult(X3,mult(X,X3))),X),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
mult(mult(unit,mult(X3,mult(X,X3))),X) = mult(mult(unit,X3),mult(X,mult(X3,X))),
inference(substitution,[status(thm)],[c83]) ).
cnf(c264,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c265,plain,
mult(mult(unit,X3),mult(X,mult(X3,X))) = mult(X3,mult(X,mult(X3,X))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
mult(mult(unit,mult(X3,mult(X,X3))),X) = mult(X3,mult(X,mult(X3,X))),
inference(transitivity,[status(thm)],[c263,c265]) ).
cnf(c267,plain,
mult(mult(X3,mult(X,X3)),X) = mult(X3,mult(X,mult(X3,X))),
inference(transitivity,[status(thm)],[c262,c266]) ).
cnf(c268,plain,
mult(mult(ld(X3,X),mult(X3,ld(X3,X))),X3) = mult(ld(X3,X),mult(X3,mult(ld(X3,X),X3))),
inference(substitution,[status(thm)],[c267]) ).
cnf(c269,plain,
mult(ld(X3,X),mult(X3,mult(ld(X3,X),X3))) = mult(ld(X3,X),mult(X,X3)),
inference(congruence,[status(thm)],[c245]) ).
cnf(c270,plain,
mult(mult(ld(X3,X),mult(X3,ld(X3,X))),X3) = mult(ld(X3,X),mult(X,X3)),
inference(transitivity,[status(thm)],[c268,c269]) ).
cnf(c271,plain,
mult(mult(ld(X3,X),X),X3) = mult(ld(X3,X),mult(X,X3)),
inference(transitivity,[status(thm)],[c259,c270]) ).
cnf(c272,plain,
rd(mult(mult(ld(X3,X),X),X3),X3) = rd(mult(ld(X3,X),mult(X,X3)),X3),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
ld(X3,mult(X3,mult(ld(X3,X),mult(X,X3)))) = mult(ld(X3,X),mult(X,X3)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c274,plain,
mult(ld(X3,X),mult(X,X3)) = ld(X3,mult(X3,mult(ld(X3,X),mult(X,X3)))),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
mult(X,X3) = mult(X3,mult(ld(X3,X),X3)),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c276,plain,
mult(ld(X3,X),mult(X,X3)) = mult(ld(X3,X),mult(X3,mult(ld(X3,X),X3))),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
mult(X3,mult(ld(X3,X),mult(X,X3))) = mult(X3,mult(ld(X3,X),mult(X3,mult(ld(X3,X),X3)))),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
mult(mult(X3,mult(X,mult(X3,X))),X3) = mult(mult(X3,X),mult(X3,mult(X,X3))),
inference(substitution,[status(thm)],[c83]) ).
cnf(c279,plain,
mult(mult(X3,X),mult(X3,mult(X,X3))) = mult(mult(X3,mult(X,mult(X3,X))),X3),
inference(symmetry,[status(thm)],[c278]) ).
cnf(c280,plain,
mult(mult(X3,mult(X,mult(X3,X))),X3) = mult(X3,mult(mult(X,mult(X3,X)),X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c281,plain,
mult(mult(X,mult(X3,X)),X3) = mult(X,mult(X3,mult(X,X3))),
inference(substitution,[status(thm)],[c267]) ).
cnf(c282,plain,
mult(X3,mult(mult(X,mult(X3,X)),X3)) = mult(X3,mult(X,mult(X3,mult(X,X3)))),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
mult(mult(X3,mult(X,mult(X3,X))),X3) = mult(X3,mult(X,mult(X3,mult(X,X3)))),
inference(transitivity,[status(thm)],[c280,c282]) ).
cnf(c284,plain,
mult(mult(X3,X),mult(X3,mult(X,X3))) = mult(X3,mult(X,mult(X3,mult(X,X3)))),
inference(transitivity,[status(thm)],[c279,c283]) ).
cnf(c285,plain,
mult(mult(X3,ld(X3,X)),mult(X3,mult(ld(X3,X),X3))) = mult(X3,mult(ld(X3,X),mult(X3,mult(ld(X3,X),X3)))),
inference(substitution,[status(thm)],[c284]) ).
cnf(c286,plain,
mult(X3,mult(ld(X3,X),mult(X3,mult(ld(X3,X),X3)))) = mult(mult(X3,ld(X3,X)),mult(X3,mult(ld(X3,X),X3))),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
mult(X3,ld(X3,X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c288,plain,
mult(mult(X3,ld(X3,X)),mult(X3,mult(ld(X3,X),X3))) = mult(X,mult(X3,mult(ld(X3,X),X3))),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
mult(X,mult(X3,mult(ld(X3,X),X3))) = mult(X,mult(X,X3)),
inference(congruence,[status(thm)],[c245]) ).
cnf(c290,plain,
mult(mult(X3,ld(X3,X)),mult(X3,mult(ld(X3,X),X3))) = mult(X,mult(X,X3)),
inference(transitivity,[status(thm)],[c288,c289]) ).
cnf(c291,plain,
mult(X3,mult(ld(X3,X),mult(X3,mult(ld(X3,X),X3)))) = mult(X,mult(X,X3)),
inference(transitivity,[status(thm)],[c286,c290]) ).
cnf(c292,plain,
mult(X3,mult(ld(X3,X),mult(X,X3))) = mult(X,mult(X,X3)),
inference(transitivity,[status(thm)],[c277,c291]) ).
cnf(c293,plain,
ld(X3,mult(X3,mult(ld(X3,X),mult(X,X3)))) = ld(X3,mult(X,mult(X,X3))),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
mult(ld(X3,X),mult(X,X3)) = ld(X3,mult(X,mult(X,X3))),
inference(transitivity,[status(thm)],[c274,c293]) ).
cnf(c295,plain,
rd(mult(ld(X3,X),mult(X,X3)),X3) = rd(ld(X3,mult(X,mult(X,X3))),X3),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
ld(X3,rd(mult(X3,ld(X3,X)),X3)) = rd(ld(X3,X),X3),
inference(substitution,[status(thm)],[c146]) ).
cnf(c297,plain,
rd(ld(X3,X),X3) = ld(X3,rd(mult(X3,ld(X3,X)),X3)),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
mult(X3,ld(X3,X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c299,plain,
rd(mult(X3,ld(X3,X)),X3) = rd(X,X3),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
ld(X3,rd(mult(X3,ld(X3,X)),X3)) = ld(X3,rd(X,X3)),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
rd(ld(X3,X),X3) = ld(X3,rd(X,X3)),
inference(transitivity,[status(thm)],[c297,c300]) ).
cnf(c302,plain,
rd(ld(X3,mult(X,mult(X,X3))),X3) = ld(X3,rd(mult(X,mult(X,X3)),X3)),
inference(substitution,[status(thm)],[c301]) ).
cnf(c303,plain,
rd(mult(X,mult(X,X3)),X3) = mult(X,X),
inference(substitution,[status(thm)],[c111]) ).
cnf(c304,plain,
ld(X3,rd(mult(X,mult(X,X3)),X3)) = ld(X3,mult(X,X)),
inference(congruence,[status(thm)],[c303]) ).
cnf(c305,plain,
rd(ld(X3,mult(X,mult(X,X3))),X3) = ld(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c302,c304]) ).
cnf(c306,plain,
rd(mult(ld(X3,X),mult(X,X3)),X3) = ld(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c295,c305]) ).
cnf(c307,plain,
rd(mult(mult(ld(X3,X),X),X3),X3) = ld(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c272,c306]) ).
cnf(c308,plain,
mult(ld(X3,X),X) = ld(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c255,c307]) ).
cnf(c309,plain,
mult(ld(X,X3),X3) = ld(X,mult(X3,X3)),
inference(substitution,[status(thm)],[c308]) ).
cnf(c310,plain,
mult(mult(X4,X),mult(ld(X,X3),X3)) = mult(mult(X4,X),ld(X,mult(X3,X3))),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
mult(mult(X4,X),mult(ld(X,X3),mult(X,ld(X,X3)))) = mult(mult(X4,X),ld(X,mult(X3,X3))),
inference(transitivity,[status(thm)],[c253,c310]) ).
cnf(c312,plain,
mult(mult(X4,mult(X,mult(ld(X,X3),X))),ld(X,X3)) = mult(mult(X4,X),ld(X,mult(X3,X3))),
inference(transitivity,[status(thm)],[c250,c311]) ).
cnf(c313,plain,
mult(mult(X4,mult(X3,X)),ld(X,X3)) = mult(mult(X4,X),ld(X,mult(X3,X3))),
inference(transitivity,[status(thm)],[c249,c312]) ).
cnf(c314,plain,
mult(mult(X3,mult(f(X),X)),ld(X,f(X))) = mult(mult(X3,X),ld(X,mult(f(X),f(X)))),
inference(substitution,[status(thm)],[c313]) ).
cnf(c315,plain,
ld(X,mult(f(X),f(X))) = ld(f(X),f(X)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c316,plain,
mult(mult(X3,X),ld(X,mult(f(X),f(X)))) = mult(mult(X3,X),ld(f(X),f(X))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
ld(f(X),f(X)) = unit,
inference(substitution,[status(thm)],[c178]) ).
cnf(c318,plain,
mult(mult(X3,X),ld(f(X),f(X))) = mult(mult(X3,X),unit),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
mult(mult(X3,X),unit) = mult(X3,X),
inference(substitution,[status(thm)],[c66]) ).
cnf(c320,plain,
mult(mult(X3,X),ld(f(X),f(X))) = mult(X3,X),
inference(transitivity,[status(thm)],[c318,c319]) ).
cnf(c321,plain,
mult(mult(X3,X),ld(X,mult(f(X),f(X)))) = mult(X3,X),
inference(transitivity,[status(thm)],[c316,c320]) ).
cnf(c322,plain,
mult(mult(X3,mult(f(X),X)),ld(X,f(X))) = mult(X3,X),
inference(transitivity,[status(thm)],[c314,c321]) ).
cnf(c323,plain,
mult(mult(X3,mult(X,f(X))),ld(X,f(X))) = mult(X3,X),
inference(transitivity,[status(thm)],[c240,c322]) ).
cnf(c324,plain,
mult(X3,X) = mult(mult(X3,mult(X,f(X))),ld(X,f(X))),
inference(symmetry,[status(thm)],[c323]) ).
cnf(c325,plain,
rd(mult(X3,X),ld(X,f(X))) = rd(mult(mult(X3,mult(X,f(X))),ld(X,f(X))),ld(X,f(X))),
inference(congruence,[status(thm)],[c324]) ).
cnf(c326,plain,
rd(mult(mult(X3,mult(X,f(X))),ld(X,f(X))),ld(X,f(X))) = mult(X3,mult(X,f(X))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c327,plain,
rd(mult(X3,X),ld(X,f(X))) = mult(X3,mult(X,f(X))),
inference(transitivity,[status(thm)],[c325,c326]) ).
cnf(c328,plain,
rd(mult(rd(X3,X),X),ld(X,f(X))) = mult(rd(X3,X),mult(X,f(X))),
inference(substitution,[status(thm)],[c327]) ).
cnf(c329,plain,
mult(rd(X3,X),mult(X,f(X))) = rd(mult(rd(X3,X),X),ld(X,f(X))),
inference(symmetry,[status(thm)],[c328]) ).
cnf(c330,plain,
mult(rd(X3,X),X) = X3,
inference(substitution,[status(thm)],[c138]) ).
cnf(c331,plain,
rd(mult(rd(X3,X),X),ld(X,f(X))) = rd(X3,ld(X,f(X))),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
mult(rd(X3,X),mult(X,f(X))) = rd(X3,ld(X,f(X))),
inference(transitivity,[status(thm)],[c329,c331]) ).
cnf(c333,plain,
rd(X3,ld(X,f(X))) = mult(rd(X3,X),mult(X,f(X))),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
mult(f(X),mult(f(X),f(X))) = mult(X,f(X)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c335,plain,
mult(X,f(X)) = mult(f(X),mult(f(X),f(X))),
inference(symmetry,[status(thm)],[c334]) ).
cnf(c336,plain,
mult(rd(X3,X),mult(X,f(X))) = mult(rd(X3,X),mult(f(X),mult(f(X),f(X)))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
ld(X,mult(X,mult(mult(X3,X),mult(X,X)))) = mult(mult(X3,X),mult(X,X)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c338,plain,
mult(mult(X3,X),mult(X,X)) = ld(X,mult(X,mult(mult(X3,X),mult(X,X)))),
inference(symmetry,[status(thm)],[c337]) ).
cnf(c339,plain,
mult(mult(mult(X3,X),X3),X3) = mult(mult(X3,X),mult(X3,X3)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c340,plain,
mult(mult(X3,X),mult(X3,X3)) = mult(mult(mult(X3,X),X3),X3),
inference(symmetry,[status(thm)],[c339]) ).
cnf(c341,plain,
mult(mult(X3,X),X3) = mult(X3,mult(X,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c342,plain,
mult(mult(mult(X3,X),X3),X3) = mult(mult(X3,mult(X,X3)),X3),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
mult(mult(X3,mult(X,X3)),X3) = mult(X3,mult(mult(X,X3),X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c344,plain,
mult(mult(X,X3),X3) = mult(X,mult(X3,X3)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c345,plain,
mult(X3,mult(mult(X,X3),X3)) = mult(X3,mult(X,mult(X3,X3))),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
mult(mult(X3,mult(X,X3)),X3) = mult(X3,mult(X,mult(X3,X3))),
inference(transitivity,[status(thm)],[c343,c345]) ).
cnf(c347,plain,
mult(mult(mult(X3,X),X3),X3) = mult(X3,mult(X,mult(X3,X3))),
inference(transitivity,[status(thm)],[c342,c346]) ).
cnf(c348,plain,
mult(mult(X3,X),mult(X3,X3)) = mult(X3,mult(X,mult(X3,X3))),
inference(transitivity,[status(thm)],[c340,c347]) ).
cnf(c349,plain,
mult(mult(X3,mult(X,X3)),mult(X3,X3)) = mult(X3,mult(mult(X,X3),mult(X3,X3))),
inference(substitution,[status(thm)],[c348]) ).
cnf(c350,plain,
mult(X3,mult(mult(X,X3),mult(X3,X3))) = mult(mult(X3,mult(X,X3)),mult(X3,X3)),
inference(symmetry,[status(thm)],[c349]) ).
cnf(c351,plain,
ifeq(mult(X,mult(X3,mult(mult(X3,X3),X3))),mult(mult(mult(X,X3),mult(X3,X3)),X3),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = mult(mult(X3,mult(X,X3)),mult(X3,X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c352,plain,
mult(mult(X3,mult(X,X3)),mult(X3,X3)) = ifeq(mult(X,mult(X3,mult(mult(X3,X3),X3))),mult(mult(mult(X,X3),mult(X3,X3)),X3),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
mult(X3,mult(X,X)) = mult(mult(X3,X),X),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c354,plain,
mult(mult(X3,mult(X,X)),X) = mult(mult(mult(X3,X),X),X),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
mult(mult(mult(X3,X),X),X) = mult(mult(X3,X),mult(X,X)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c356,plain,
mult(mult(X3,mult(X,X)),X) = mult(mult(X3,X),mult(X,X)),
inference(transitivity,[status(thm)],[c354,c355]) ).
cnf(c357,plain,
mult(mult(mult(X,X3),mult(X3,X3)),X3) = mult(mult(mult(X,X3),X3),mult(X3,X3)),
inference(substitution,[status(thm)],[c356]) ).
cnf(c358,plain,
ifeq(mult(X,mult(X3,mult(mult(X3,X3),X3))),mult(mult(mult(X,X3),mult(X3,X3)),X3),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = ifeq(mult(X,mult(X3,mult(mult(X3,X3),X3))),mult(mult(mult(X,X3),X3),mult(X3,X3)),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
mult(mult(X,X),X) = mult(X,mult(X,X)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c360,plain,
mult(X,mult(mult(X,X),X)) = mult(X,mult(X,mult(X,X))),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
mult(X,mult(X3,mult(mult(X3,X3),X3))) = mult(X,mult(X3,mult(X3,mult(X3,X3)))),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
ifeq(mult(X,mult(X3,mult(mult(X3,X3),X3))),mult(mult(mult(X,X3),X3),mult(X3,X3)),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(mult(mult(X,X3),X3),mult(X3,X3)),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))),
inference(congruence,[status(thm)],[c361]) ).
cnf(c363,plain,
mult(mult(X,X3),X3) = mult(X,mult(X3,X3)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c364,plain,
mult(mult(mult(X,X3),X3),mult(X3,X3)) = mult(mult(X,mult(X3,X3)),mult(X3,X3)),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(mult(mult(X,X3),X3),mult(X3,X3)),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(mult(X,mult(X3,X3)),mult(X3,X3)),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
mult(mult(X,mult(X3,X3)),mult(X3,X3)) = mult(X,mult(mult(X3,X3),mult(X3,X3))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c367,plain,
ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(mult(X,mult(X3,X3)),mult(X3,X3)),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(X,mult(mult(X3,X3),mult(X3,X3))),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
mult(mult(X,X),mult(X,X)) = mult(X,mult(X,mult(X,X))),
inference(substitution,[status(thm)],[c44]) ).
cnf(c369,plain,
mult(X,mult(mult(X3,X3),mult(X3,X3))) = mult(X,mult(X3,mult(X3,mult(X3,X3)))),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(X,mult(mult(X3,X3),mult(X3,X3))),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = mult(X3,mult(X,mult(X3,mult(X3,X3)))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c372,plain,
ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(X,mult(mult(X3,X3),mult(X3,X3))),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = mult(X3,mult(X,mult(X3,mult(X3,X3)))),
inference(transitivity,[status(thm)],[c370,c371]) ).
cnf(c373,plain,
ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(mult(X,mult(X3,X3)),mult(X3,X3)),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = mult(X3,mult(X,mult(X3,mult(X3,X3)))),
inference(transitivity,[status(thm)],[c367,c372]) ).
cnf(c374,plain,
ifeq(mult(X,mult(X3,mult(X3,mult(X3,X3)))),mult(mult(mult(X,X3),X3),mult(X3,X3)),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = mult(X3,mult(X,mult(X3,mult(X3,X3)))),
inference(transitivity,[status(thm)],[c365,c373]) ).
cnf(c375,plain,
ifeq(mult(X,mult(X3,mult(mult(X3,X3),X3))),mult(mult(mult(X,X3),X3),mult(X3,X3)),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = mult(X3,mult(X,mult(X3,mult(X3,X3)))),
inference(transitivity,[status(thm)],[c362,c374]) ).
cnf(c376,plain,
ifeq(mult(X,mult(X3,mult(mult(X3,X3),X3))),mult(mult(mult(X,X3),mult(X3,X3)),X3),mult(X3,mult(X,mult(X3,mult(X3,X3)))),mult(mult(X3,mult(X,X3)),mult(X3,X3))) = mult(X3,mult(X,mult(X3,mult(X3,X3)))),
inference(transitivity,[status(thm)],[c358,c375]) ).
cnf(c377,plain,
mult(mult(X3,mult(X,X3)),mult(X3,X3)) = mult(X3,mult(X,mult(X3,mult(X3,X3)))),
inference(transitivity,[status(thm)],[c352,c376]) ).
cnf(c378,plain,
mult(X3,mult(mult(X,X3),mult(X3,X3))) = mult(X3,mult(X,mult(X3,mult(X3,X3)))),
inference(transitivity,[status(thm)],[c350,c377]) ).
cnf(c379,plain,
mult(X,mult(mult(X3,X),mult(X,X))) = mult(X,mult(X3,mult(X,mult(X,X)))),
inference(substitution,[status(thm)],[c378]) ).
cnf(c380,plain,
ld(X,mult(X,mult(mult(X3,X),mult(X,X)))) = ld(X,mult(X,mult(X3,mult(X,mult(X,X))))),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
ld(X,mult(X,mult(X3,mult(X,mult(X,X))))) = mult(X3,mult(X,mult(X,X))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c382,plain,
ld(X,mult(X,mult(mult(X3,X),mult(X,X)))) = mult(X3,mult(X,mult(X,X))),
inference(transitivity,[status(thm)],[c380,c381]) ).
cnf(c383,plain,
mult(mult(X3,X),mult(X,X)) = mult(X3,mult(X,mult(X,X))),
inference(transitivity,[status(thm)],[c338,c382]) ).
cnf(c384,plain,
mult(mult(rd(X3,X),f(X)),mult(f(X),f(X))) = mult(rd(X3,X),mult(f(X),mult(f(X),f(X)))),
inference(substitution,[status(thm)],[c383]) ).
cnf(c385,plain,
mult(rd(X3,X),mult(f(X),mult(f(X),f(X)))) = mult(mult(rd(X3,X),f(X)),mult(f(X),f(X))),
inference(symmetry,[status(thm)],[c384]) ).
cnf(c386,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c387,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c386]) ).
cnf(c388,plain,
mult(X3,X) = mult(X3,mult(f(X),f(X))),
inference(congruence,[status(thm)],[c387]) ).
cnf(c389,plain,
rd(mult(X3,X),f(X)) = rd(mult(X3,mult(f(X),f(X))),f(X)),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
rd(mult(X3,mult(f(X),f(X))),f(X)) = mult(X3,f(X)),
inference(substitution,[status(thm)],[c226]) ).
cnf(c391,plain,
rd(mult(X3,X),f(X)) = mult(X3,f(X)),
inference(transitivity,[status(thm)],[c389,c390]) ).
cnf(c392,plain,
rd(mult(rd(X3,X),X),f(X)) = mult(rd(X3,X),f(X)),
inference(substitution,[status(thm)],[c391]) ).
cnf(c393,plain,
mult(rd(X3,X),f(X)) = rd(mult(rd(X3,X),X),f(X)),
inference(symmetry,[status(thm)],[c392]) ).
cnf(c394,plain,
mult(rd(X3,X),X) = X3,
inference(substitution,[status(thm)],[c138]) ).
cnf(c395,plain,
rd(mult(rd(X3,X),X),f(X)) = rd(X3,f(X)),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
mult(rd(X3,X),f(X)) = rd(X3,f(X)),
inference(transitivity,[status(thm)],[c393,c395]) ).
cnf(c397,plain,
mult(mult(rd(X3,X),f(X)),mult(f(X),f(X))) = mult(rd(X3,f(X)),mult(f(X),f(X))),
inference(congruence,[status(thm)],[c396]) ).
cnf(c398,plain,
mult(mult(rd(X3,X),X),X) = mult(rd(X3,X),mult(X,X)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c399,plain,
mult(rd(X3,X),mult(X,X)) = mult(mult(rd(X3,X),X),X),
inference(symmetry,[status(thm)],[c398]) ).
cnf(c400,plain,
mult(rd(X3,X),X) = X3,
inference(substitution,[status(thm)],[c138]) ).
cnf(c401,plain,
mult(mult(rd(X3,X),X),X) = mult(X3,X),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
mult(rd(X3,X),mult(X,X)) = mult(X3,X),
inference(transitivity,[status(thm)],[c399,c401]) ).
cnf(c403,plain,
mult(rd(X3,f(X)),mult(f(X),f(X))) = mult(X3,f(X)),
inference(substitution,[status(thm)],[c402]) ).
cnf(c404,plain,
mult(mult(rd(X3,X),f(X)),mult(f(X),f(X))) = mult(X3,f(X)),
inference(transitivity,[status(thm)],[c397,c403]) ).
cnf(c405,plain,
mult(rd(X3,X),mult(f(X),mult(f(X),f(X)))) = mult(X3,f(X)),
inference(transitivity,[status(thm)],[c385,c404]) ).
cnf(c406,plain,
mult(rd(X3,X),mult(X,f(X))) = mult(X3,f(X)),
inference(transitivity,[status(thm)],[c336,c405]) ).
cnf(c407,plain,
rd(X3,ld(X,f(X))) = mult(X3,f(X)),
inference(transitivity,[status(thm)],[c333,c406]) ).
cnf(c408,plain,
rd(rd(X3,ld(X,f(X))),ld(X,f(X))) = mult(rd(X3,ld(X,f(X))),f(X)),
inference(substitution,[status(thm)],[c407]) ).
cnf(c409,plain,
mult(rd(X3,ld(X,f(X))),f(X)) = mult(mult(X3,f(X)),f(X)),
inference(congruence,[status(thm)],[c407]) ).
cnf(c410,plain,
mult(mult(X3,f(X)),f(X)) = mult(X3,mult(f(X),f(X))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c411,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c412,plain,
mult(X3,mult(f(X),f(X))) = mult(X3,X),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
mult(mult(X3,f(X)),f(X)) = mult(X3,X),
inference(transitivity,[status(thm)],[c410,c412]) ).
cnf(c414,plain,
mult(rd(X3,ld(X,f(X))),f(X)) = mult(X3,X),
inference(transitivity,[status(thm)],[c409,c413]) ).
cnf(c415,plain,
rd(rd(X3,ld(X,f(X))),ld(X,f(X))) = mult(X3,X),
inference(transitivity,[status(thm)],[c408,c414]) ).
cnf(c416,plain,
rd(X3,mult(ld(X,f(X)),ld(X,f(X)))) = mult(X3,X),
inference(transitivity,[status(thm)],[c237,c415]) ).
cnf(c417,plain,
rd(X3,ld(X,mult(f(X),ld(X,f(X))))) = mult(X3,X),
inference(transitivity,[status(thm)],[c222,c416]) ).
cnf(c418,plain,
rd(X3,ld(f(X),ld(X,f(X)))) = mult(X3,X),
inference(transitivity,[status(thm)],[c219,c417]) ).
cnf(c419,plain,
rd(X3,ld(X,unit)) = mult(X3,X),
inference(transitivity,[status(thm)],[c216,c418]) ).
cnf(c420,plain,
mult(X3,X) = rd(X3,ld(X,unit)),
inference(symmetry,[status(thm)],[c419]) ).
cnf(c421,plain,
ld(mult(X3,X),X3) = ld(rd(X3,ld(X,unit)),X3),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
ld(rd(X3,ld(X,unit)),X3) = ld(X,unit),
inference(substitution,[status(thm)],[c206]) ).
cnf(c423,plain,
ld(mult(X3,X),X3) = ld(X,unit),
inference(transitivity,[status(thm)],[c421,c422]) ).
cnf(c424,plain,
ld(mult(X,X3),X) = ld(X3,unit),
inference(substitution,[status(thm)],[c423]) ).
cnf(c425,plain,
ld(X3,unit) = ld(mult(X,X3),X),
inference(symmetry,[status(thm)],[c424]) ).
cnf(c426,plain,
ld(ld(X3,unit),X) = ld(ld(mult(X,X3),X),X),
inference(congruence,[status(thm)],[c425]) ).
cnf(c427,plain,
ld(X,mult(X,ld(ld(X3,X),X))) = ld(ld(X3,X),X),
inference(substitution,[status(thm)],[c59]) ).
cnf(c428,plain,
ld(ld(X3,X),X) = ld(X,mult(X,ld(ld(X3,X),X))),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
mult(X,ld(X,X3)) = X3,
inference(substitution,[status(thm)],[c53]) ).
cnf(c430,plain,
X3 = mult(X,ld(X,X3)),
inference(symmetry,[status(thm)],[c429]) ).
cnf(c431,plain,
mult(rd(X3,X),X3) = mult(rd(X3,X),mult(X,ld(X,X3))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
mult(X,ld(X,X3)) = X3,
inference(substitution,[status(thm)],[c53]) ).
cnf(c433,plain,
X3 = mult(X,ld(X,X3)),
inference(symmetry,[status(thm)],[c432]) ).
cnf(c434,plain,
rd(X3,X) = rd(mult(X,ld(X,X3)),X),
inference(congruence,[status(thm)],[c433]) ).
cnf(c435,plain,
mult(rd(X3,X),mult(X,ld(X,X3))) = mult(rd(mult(X,ld(X,X3)),X),mult(X,ld(X,X3))),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
rd(mult(X3,X),X3) = mult(X3,rd(X,X3)),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c437,plain,
mult(rd(mult(X3,X),X3),mult(X3,X)) = mult(mult(X3,rd(X,X3)),mult(X3,X)),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
mult(rd(X,X3),X3) = X,
inference(substitution,[status(thm)],[c138]) ).
cnf(c439,plain,
X = mult(rd(X,X3),X3),
inference(symmetry,[status(thm)],[c438]) ).
cnf(c440,plain,
mult(X3,X) = mult(X3,mult(rd(X,X3),X3)),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
mult(mult(X3,rd(X,X3)),mult(X3,X)) = mult(mult(X3,rd(X,X3)),mult(X3,mult(rd(X,X3),X3))),
inference(congruence,[status(thm)],[c440]) ).
cnf(c442,plain,
mult(mult(X3,rd(X,X3)),mult(X3,mult(rd(X,X3),X3))) = mult(X3,mult(rd(X,X3),mult(X3,mult(rd(X,X3),X3)))),
inference(substitution,[status(thm)],[c284]) ).
cnf(c443,plain,
mult(rd(X,X3),X3) = X,
inference(substitution,[status(thm)],[c138]) ).
cnf(c444,plain,
mult(X3,mult(rd(X,X3),X3)) = mult(X3,X),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
mult(rd(X,X3),mult(X3,mult(rd(X,X3),X3))) = mult(rd(X,X3),mult(X3,X)),
inference(congruence,[status(thm)],[c444]) ).
cnf(c446,plain,
mult(X3,mult(rd(X,X3),mult(X3,mult(rd(X,X3),X3)))) = mult(X3,mult(rd(X,X3),mult(X3,X))),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
mult(ld(rd(X3,X),X3),X3) = ld(rd(X3,X),mult(X3,X3)),
inference(substitution,[status(thm)],[c308]) ).
cnf(c448,plain,
ld(rd(X3,X),mult(X3,X3)) = mult(ld(rd(X3,X),X3),X3),
inference(symmetry,[status(thm)],[c447]) ).
cnf(c449,plain,
mult(ld(rd(X3,X),X3),X3) = mult(X,X3),
inference(congruence,[status(thm)],[c206]) ).
cnf(c450,plain,
ld(rd(X3,X),mult(X3,X3)) = mult(X,X3),
inference(transitivity,[status(thm)],[c448,c449]) ).
cnf(c451,plain,
mult(X,X3) = ld(rd(X3,X),mult(X3,X3)),
inference(symmetry,[status(thm)],[c450]) ).
cnf(c452,plain,
mult(rd(X3,X),mult(X,X3)) = mult(rd(X3,X),ld(rd(X3,X),mult(X3,X3))),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
mult(rd(X3,X),ld(rd(X3,X),mult(X3,X3))) = mult(X3,X3),
inference(substitution,[status(thm)],[c53]) ).
cnf(c454,plain,
mult(rd(X3,X),mult(X,X3)) = mult(X3,X3),
inference(transitivity,[status(thm)],[c452,c453]) ).
cnf(c455,plain,
mult(rd(X,X3),mult(X3,X)) = mult(X,X),
inference(substitution,[status(thm)],[c454]) ).
cnf(c456,plain,
mult(X3,mult(rd(X,X3),mult(X3,X))) = mult(X3,mult(X,X)),
inference(congruence,[status(thm)],[c455]) ).
cnf(c457,plain,
mult(X3,mult(rd(X,X3),mult(X3,mult(rd(X,X3),X3)))) = mult(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c446,c456]) ).
cnf(c458,plain,
mult(mult(X3,rd(X,X3)),mult(X3,mult(rd(X,X3),X3))) = mult(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c442,c457]) ).
cnf(c459,plain,
mult(mult(X3,rd(X,X3)),mult(X3,X)) = mult(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c441,c458]) ).
cnf(c460,plain,
mult(rd(mult(X3,X),X3),mult(X3,X)) = mult(X3,mult(X,X)),
inference(transitivity,[status(thm)],[c437,c459]) ).
cnf(c461,plain,
mult(rd(mult(X,ld(X,X3)),X),mult(X,ld(X,X3))) = mult(X,mult(ld(X,X3),ld(X,X3))),
inference(substitution,[status(thm)],[c460]) ).
cnf(c462,plain,
mult(X,mult(ld(X,X3),ld(X,X3))) = mult(X3,ld(X,X3)),
inference(substitution,[status(thm)],[c98]) ).
cnf(c463,plain,
mult(rd(mult(X,ld(X,X3)),X),mult(X,ld(X,X3))) = mult(X3,ld(X,X3)),
inference(transitivity,[status(thm)],[c461,c462]) ).
cnf(c464,plain,
mult(rd(X3,X),mult(X,ld(X,X3))) = mult(X3,ld(X,X3)),
inference(transitivity,[status(thm)],[c435,c463]) ).
cnf(c465,plain,
mult(rd(X3,X),X3) = mult(X3,ld(X,X3)),
inference(transitivity,[status(thm)],[c431,c464]) ).
cnf(c466,plain,
mult(rd(X3,ld(X,X3)),X3) = mult(X3,ld(ld(X,X3),X3)),
inference(substitution,[status(thm)],[c465]) ).
cnf(c467,plain,
mult(X3,ld(ld(X,X3),X3)) = mult(rd(X3,ld(X,X3)),X3),
inference(symmetry,[status(thm)],[c466]) ).
cnf(c468,plain,
mult(X,ld(X,X3)) = X3,
inference(substitution,[status(thm)],[c53]) ).
cnf(c469,plain,
X3 = mult(X,ld(X,X3)),
inference(symmetry,[status(thm)],[c468]) ).
cnf(c470,plain,
rd(X3,ld(X,X3)) = rd(mult(X,ld(X,X3)),ld(X,X3)),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,plain,
rd(mult(X,ld(X,X3)),ld(X,X3)) = X,
inference(substitution,[status(thm)],[c109]) ).
cnf(c472,plain,
rd(X3,ld(X,X3)) = X,
inference(transitivity,[status(thm)],[c470,c471]) ).
cnf(c473,plain,
mult(rd(X3,ld(X,X3)),X3) = mult(X,X3),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
mult(X3,ld(ld(X,X3),X3)) = mult(X,X3),
inference(transitivity,[status(thm)],[c467,c473]) ).
cnf(c475,plain,
mult(X,ld(ld(X3,X),X)) = mult(X3,X),
inference(substitution,[status(thm)],[c474]) ).
cnf(c476,plain,
ld(X,mult(X,ld(ld(X3,X),X))) = ld(X,mult(X3,X)),
inference(congruence,[status(thm)],[c475]) ).
cnf(c477,plain,
ld(ld(X3,X),X) = ld(X,mult(X3,X)),
inference(transitivity,[status(thm)],[c428,c476]) ).
cnf(c478,plain,
ld(ld(mult(X,X3),X),X) = ld(X,mult(mult(X,X3),X)),
inference(substitution,[status(thm)],[c477]) ).
cnf(c479,plain,
mult(mult(X,X3),X) = mult(X,mult(X3,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c480,plain,
ld(X,mult(mult(X,X3),X)) = ld(X,mult(X,mult(X3,X))),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
ld(X,mult(X,mult(X3,X))) = mult(X3,X),
inference(substitution,[status(thm)],[c59]) ).
cnf(c482,plain,
ld(X,mult(mult(X,X3),X)) = mult(X3,X),
inference(transitivity,[status(thm)],[c480,c481]) ).
cnf(c483,plain,
ld(ld(mult(X,X3),X),X) = mult(X3,X),
inference(transitivity,[status(thm)],[c478,c482]) ).
cnf(c484,plain,
ld(ld(X3,unit),X) = mult(X3,X),
inference(transitivity,[status(thm)],[c426,c483]) ).
cnf(c485,plain,
ld(ld(mult(mult(X4,X3),X),unit),X3) = mult(mult(mult(X4,X3),X),X3),
inference(substitution,[status(thm)],[c484]) ).
cnf(c486,plain,
mult(mult(mult(X4,X3),X),X3) = ld(ld(mult(mult(X4,X3),X),unit),X3),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
ld(mult(mult(X,X),X3),mult(X,X)) = ld(X3,unit),
inference(substitution,[status(thm)],[c423]) ).
cnf(c488,plain,
ld(X3,unit) = ld(mult(mult(X,X),X3),mult(X,X)),
inference(symmetry,[status(thm)],[c487]) ).
cnf(c489,plain,
rd(ld(X3,unit),X) = rd(ld(mult(mult(X,X),X3),mult(X,X)),X),
inference(congruence,[status(thm)],[c488]) ).
cnf(c490,plain,
ld(X3,mult(X,X)) = mult(ld(X3,X),X),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c491,plain,
rd(ld(X3,mult(X,X)),X) = rd(mult(ld(X3,X),X),X),
inference(congruence,[status(thm)],[c490]) ).
cnf(c492,plain,
rd(mult(ld(X3,X),X),X) = ld(X3,X),
inference(substitution,[status(thm)],[c109]) ).
cnf(c493,plain,
rd(ld(X3,mult(X,X)),X) = ld(X3,X),
inference(transitivity,[status(thm)],[c491,c492]) ).
cnf(c494,plain,
rd(ld(mult(mult(X,X),X3),mult(X,X)),X) = ld(mult(mult(X,X),X3),X),
inference(substitution,[status(thm)],[c493]) ).
cnf(c495,plain,
mult(mult(X,X),X3) = mult(X,mult(X,X3)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c496,plain,
ld(mult(mult(X,X),X3),X) = ld(mult(X,mult(X,X3)),X),
inference(congruence,[status(thm)],[c495]) ).
cnf(c497,plain,
ld(mult(X,mult(X,X3)),X) = ld(mult(X,X3),unit),
inference(substitution,[status(thm)],[c423]) ).
cnf(c498,plain,
ld(mult(mult(X,X),X3),X) = ld(mult(X,X3),unit),
inference(transitivity,[status(thm)],[c496,c497]) ).
cnf(c499,plain,
rd(ld(mult(mult(X,X),X3),mult(X,X)),X) = ld(mult(X,X3),unit),
inference(transitivity,[status(thm)],[c494,c498]) ).
cnf(c500,plain,
rd(ld(X3,unit),X) = ld(mult(X,X3),unit),
inference(transitivity,[status(thm)],[c489,c499]) ).
cnf(c501,plain,
rd(ld(X,unit),mult(X4,X3)) = ld(mult(mult(X4,X3),X),unit),
inference(substitution,[status(thm)],[c500]) ).
cnf(c502,plain,
ld(mult(mult(X4,X3),X),unit) = rd(ld(X,unit),mult(X4,X3)),
inference(symmetry,[status(thm)],[c501]) ).
cnf(c503,plain,
ld(ld(mult(mult(X4,X3),X),unit),X3) = ld(rd(ld(X,unit),mult(X4,X3)),X3),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
ld(X,unit) = ld(mult(X3,X),X3),
inference(symmetry,[status(thm)],[c423]) ).
cnf(c505,plain,
rd(ld(X,unit),mult(X4,X3)) = rd(ld(mult(X3,X),X3),mult(X4,X3)),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
ld(rd(ld(X,unit),mult(X4,X3)),X3) = ld(rd(ld(mult(X3,X),X3),mult(X4,X3)),X3),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
ld(mult(f(f(X)),rd(X3,X)),f(f(X))) = ld(rd(X3,X),unit),
inference(substitution,[status(thm)],[c423]) ).
cnf(c508,plain,
ld(rd(X3,X),unit) = ld(mult(f(f(X)),rd(X3,X)),f(f(X))),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c509,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c510,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c509]) ).
cnf(c511,plain,
rd(mult(f(X3),mult(X,X3)),X3) = rd(mult(f(X3),mult(X,X3)),mult(f(X3),f(X3))),
inference(congruence,[status(thm)],[c510]) ).
cnf(c512,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c513,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c512]) ).
cnf(c514,plain,
mult(X,X3) = mult(X,mult(f(X3),f(X3))),
inference(congruence,[status(thm)],[c513]) ).
cnf(c515,plain,
mult(f(X3),mult(X,X3)) = mult(f(X3),mult(X,mult(f(X3),f(X3)))),
inference(congruence,[status(thm)],[c514]) ).
cnf(c516,plain,
rd(mult(f(X3),mult(X,X3)),mult(f(X3),f(X3))) = rd(mult(f(X3),mult(X,mult(f(X3),f(X3)))),mult(f(X3),f(X3))),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
mult(X3,mult(X,mult(X3,X3))) = mult(mult(X3,X),mult(X3,X3)),
inference(symmetry,[status(thm)],[c348]) ).
cnf(c518,plain,
rd(mult(X3,mult(X,mult(X3,X3))),mult(X3,X3)) = rd(mult(mult(X3,X),mult(X3,X3)),mult(X3,X3)),
inference(congruence,[status(thm)],[c517]) ).
cnf(c519,plain,
rd(mult(mult(X3,X),mult(X3,X3)),mult(X3,X3)) = mult(X3,X),
inference(substitution,[status(thm)],[c109]) ).
cnf(c520,plain,
rd(mult(X3,mult(X,mult(X3,X3))),mult(X3,X3)) = mult(X3,X),
inference(transitivity,[status(thm)],[c518,c519]) ).
cnf(c521,plain,
rd(mult(f(X3),mult(X,mult(f(X3),f(X3)))),mult(f(X3),f(X3))) = mult(f(X3),X),
inference(substitution,[status(thm)],[c520]) ).
cnf(c522,plain,
rd(mult(f(X3),mult(X,X3)),mult(f(X3),f(X3))) = mult(f(X3),X),
inference(transitivity,[status(thm)],[c516,c521]) ).
cnf(c523,plain,
rd(mult(f(X3),mult(X,X3)),X3) = mult(f(X3),X),
inference(transitivity,[status(thm)],[c511,c522]) ).
cnf(c524,plain,
rd(mult(f(f(X3)),mult(rd(X,X3),f(X3))),f(X3)) = mult(f(f(X3)),rd(X,X3)),
inference(substitution,[status(thm)],[c523]) ).
cnf(c525,plain,
mult(f(f(X3)),rd(X,X3)) = rd(mult(f(f(X3)),mult(rd(X,X3),f(X3))),f(X3)),
inference(symmetry,[status(thm)],[c524]) ).
cnf(c526,plain,
mult(rd(X,X3),f(X3)) = rd(X,f(X3)),
inference(substitution,[status(thm)],[c396]) ).
cnf(c527,plain,
mult(f(f(X3)),mult(rd(X,X3),f(X3))) = mult(f(f(X3)),rd(X,f(X3))),
inference(congruence,[status(thm)],[c526]) ).
cnf(c528,plain,
rd(mult(f(f(X3)),mult(rd(X,X3),f(X3))),f(X3)) = rd(mult(f(f(X3)),rd(X,f(X3))),f(X3)),
inference(congruence,[status(thm)],[c527]) ).
cnf(c529,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c530,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c531,plain,
rd(X,X3) = rd(X,mult(f(X3),f(X3))),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
mult(f(X3),rd(X,X3)) = mult(f(X3),rd(X,mult(f(X3),f(X3)))),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
rd(mult(X3,mult(rd(X,mult(X3,X3)),X3)),X3) = mult(X3,rd(X,mult(X3,X3))),
inference(substitution,[status(thm)],[c135]) ).
cnf(c534,plain,
mult(X3,rd(X,mult(X3,X3))) = rd(mult(X3,mult(rd(X,mult(X3,X3)),X3)),X3),
inference(symmetry,[status(thm)],[c533]) ).
cnf(c535,plain,
mult(rd(X,mult(X3,X3)),X3) = rd(X,X3),
inference(substitution,[status(thm)],[c231]) ).
cnf(c536,plain,
mult(X3,mult(rd(X,mult(X3,X3)),X3)) = mult(X3,rd(X,X3)),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
rd(mult(X3,mult(rd(X,mult(X3,X3)),X3)),X3) = rd(mult(X3,rd(X,X3)),X3),
inference(congruence,[status(thm)],[c536]) ).
cnf(c538,plain,
rd(mult(X3,rd(X,X3)),X3) = rd(rd(mult(X3,X),X3),X3),
inference(congruence,[status(thm)],[c142]) ).
cnf(c539,plain,
rd(rd(mult(X3,X),X3),X3) = rd(mult(X3,X),mult(X3,X3)),
inference(substitution,[status(thm)],[c235]) ).
cnf(c540,plain,
rd(mult(X3,rd(X,X3)),X3) = rd(mult(X3,X),mult(X3,X3)),
inference(transitivity,[status(thm)],[c538,c539]) ).
cnf(c541,plain,
rd(mult(X3,mult(rd(X,mult(X3,X3)),X3)),X3) = rd(mult(X3,X),mult(X3,X3)),
inference(transitivity,[status(thm)],[c537,c540]) ).
cnf(c542,plain,
mult(X3,rd(X,mult(X3,X3))) = rd(mult(X3,X),mult(X3,X3)),
inference(transitivity,[status(thm)],[c534,c541]) ).
cnf(c543,plain,
mult(f(X3),rd(X,mult(f(X3),f(X3)))) = rd(mult(f(X3),X),mult(f(X3),f(X3))),
inference(substitution,[status(thm)],[c542]) ).
cnf(c544,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c545,plain,
rd(mult(f(X3),X),mult(f(X3),f(X3))) = rd(mult(f(X3),X),X3),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
mult(f(X3),rd(X,mult(f(X3),f(X3)))) = rd(mult(f(X3),X),X3),
inference(transitivity,[status(thm)],[c543,c545]) ).
cnf(c547,plain,
mult(f(X3),rd(X,X3)) = rd(mult(f(X3),X),X3),
inference(transitivity,[status(thm)],[c532,c546]) ).
cnf(c548,plain,
mult(f(f(X3)),rd(X,f(X3))) = rd(mult(f(f(X3)),X),f(X3)),
inference(substitution,[status(thm)],[c547]) ).
cnf(c549,plain,
rd(mult(f(f(X3)),rd(X,f(X3))),f(X3)) = rd(rd(mult(f(f(X3)),X),f(X3)),f(X3)),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
rd(rd(mult(f(f(X3)),X),f(X3)),f(X3)) = rd(mult(f(f(X3)),X),mult(f(X3),f(X3))),
inference(substitution,[status(thm)],[c235]) ).
cnf(c551,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c552,plain,
rd(mult(f(f(X3)),X),mult(f(X3),f(X3))) = rd(mult(f(f(X3)),X),X3),
inference(congruence,[status(thm)],[c551]) ).
cnf(c553,plain,
rd(rd(mult(f(f(X3)),X),f(X3)),f(X3)) = rd(mult(f(f(X3)),X),X3),
inference(transitivity,[status(thm)],[c550,c552]) ).
cnf(c554,plain,
rd(mult(f(f(X3)),rd(X,f(X3))),f(X3)) = rd(mult(f(f(X3)),X),X3),
inference(transitivity,[status(thm)],[c549,c553]) ).
cnf(c555,plain,
rd(mult(f(f(X3)),mult(rd(X,X3),f(X3))),f(X3)) = rd(mult(f(f(X3)),X),X3),
inference(transitivity,[status(thm)],[c528,c554]) ).
cnf(c556,plain,
mult(f(f(X3)),rd(X,X3)) = rd(mult(f(f(X3)),X),X3),
inference(transitivity,[status(thm)],[c525,c555]) ).
cnf(c557,plain,
mult(f(f(X)),rd(X3,X)) = rd(mult(f(f(X)),X3),X),
inference(substitution,[status(thm)],[c556]) ).
cnf(c558,plain,
ld(mult(f(f(X)),rd(X3,X)),f(f(X))) = ld(rd(mult(f(f(X)),X3),X),f(f(X))),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
rd(mult(f(f(X3)),X),X3) = mult(f(f(X3)),rd(X,X3)),
inference(symmetry,[status(thm)],[c556]) ).
cnf(c560,plain,
ld(f(f(X3)),mult(f(X3),rd(X,X3))) = mult(f(f(X3)),rd(X,X3)),
inference(substitution,[status(thm)],[c167]) ).
cnf(c561,plain,
mult(f(f(X3)),rd(X,X3)) = ld(f(f(X3)),mult(f(X3),rd(X,X3))),
inference(symmetry,[status(thm)],[c560]) ).
cnf(c562,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c563,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c562]) ).
cnf(c564,plain,
rd(X,X3) = rd(X,mult(f(X3),f(X3))),
inference(congruence,[status(thm)],[c563]) ).
cnf(c565,plain,
mult(f(X3),rd(X,X3)) = mult(f(X3),rd(X,mult(f(X3),f(X3)))),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
mult(f(X3),rd(X,mult(f(X3),f(X3)))) = rd(mult(f(X3),X),mult(f(X3),f(X3))),
inference(substitution,[status(thm)],[c542]) ).
cnf(c567,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c568,plain,
rd(mult(f(X3),X),mult(f(X3),f(X3))) = rd(mult(f(X3),X),X3),
inference(congruence,[status(thm)],[c567]) ).
cnf(c569,plain,
rd(mult(X3,X),X3) = mult(X3,rd(X,X3)),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c570,plain,
ld(f(X3),rd(mult(X3,X),X3)) = ld(f(X3),mult(X3,rd(X,X3))),
inference(congruence,[status(thm)],[c569]) ).
cnf(c571,plain,
ld(f(X3),mult(X3,rd(X,X3))) = mult(f(X3),rd(X,X3)),
inference(substitution,[status(thm)],[c167]) ).
cnf(c572,plain,
ld(f(X3),mult(X3,rd(X,X3))) = rd(mult(f(X3),X),X3),
inference(transitivity,[status(thm)],[c571,c547]) ).
cnf(c573,plain,
ld(f(X3),rd(mult(X3,X),X3)) = rd(mult(f(X3),X),X3),
inference(transitivity,[status(thm)],[c570,c572]) ).
cnf(c574,plain,
rd(mult(f(X3),X),X3) = ld(f(X3),rd(mult(X3,X),X3)),
inference(symmetry,[status(thm)],[c573]) ).
cnf(c575,plain,
X = ld(rd(X3,X),X3),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c576,plain,
mult(X3,X) = mult(X3,ld(rd(X3,X),X3)),
inference(congruence,[status(thm)],[c575]) ).
cnf(c577,plain,
rd(mult(X3,X),X3) = rd(mult(X3,ld(rd(X3,X),X3)),X3),
inference(congruence,[status(thm)],[c576]) ).
cnf(c578,plain,
mult(X3,ld(X,X3)) = mult(rd(X3,X),X3),
inference(symmetry,[status(thm)],[c465]) ).
cnf(c579,plain,
rd(mult(X3,ld(X,X3)),X3) = rd(mult(rd(X3,X),X3),X3),
inference(congruence,[status(thm)],[c578]) ).
cnf(c580,plain,
rd(mult(rd(X3,X),X3),X3) = rd(X3,X),
inference(substitution,[status(thm)],[c109]) ).
cnf(c581,plain,
rd(mult(X3,ld(X,X3)),X3) = rd(X3,X),
inference(transitivity,[status(thm)],[c579,c580]) ).
cnf(c582,plain,
rd(mult(X3,ld(rd(X3,X),X3)),X3) = rd(X3,rd(X3,X)),
inference(substitution,[status(thm)],[c581]) ).
cnf(c583,plain,
rd(mult(X3,X),X3) = rd(X3,rd(X3,X)),
inference(transitivity,[status(thm)],[c577,c582]) ).
cnf(c584,plain,
ld(f(X3),rd(mult(X3,X),X3)) = ld(f(X3),rd(X3,rd(X3,X))),
inference(congruence,[status(thm)],[c583]) ).
cnf(c585,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c586,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c585]) ).
cnf(c587,plain,
ld(X3,X) = ld(X3,mult(f(X),f(X))),
inference(congruence,[status(thm)],[c586]) ).
cnf(c588,plain,
rd(ld(X3,X),f(X)) = rd(ld(X3,mult(f(X),f(X))),f(X)),
inference(congruence,[status(thm)],[c587]) ).
cnf(c589,plain,
rd(ld(X3,mult(f(X),f(X))),f(X)) = ld(X3,f(X)),
inference(substitution,[status(thm)],[c493]) ).
cnf(c590,plain,
rd(ld(X3,X),f(X)) = ld(X3,f(X)),
inference(transitivity,[status(thm)],[c588,c589]) ).
cnf(c591,plain,
rd(ld(rd(X3,X),X3),f(X3)) = ld(rd(X3,X),f(X3)),
inference(substitution,[status(thm)],[c590]) ).
cnf(c592,plain,
ld(rd(X3,X),f(X3)) = rd(ld(rd(X3,X),X3),f(X3)),
inference(symmetry,[status(thm)],[c591]) ).
cnf(c593,plain,
rd(ld(rd(X3,X),X3),f(X3)) = rd(X,f(X3)),
inference(congruence,[status(thm)],[c206]) ).
cnf(c594,plain,
ld(rd(X3,X),f(X3)) = rd(X,f(X3)),
inference(transitivity,[status(thm)],[c592,c593]) ).
cnf(c595,plain,
rd(X,f(X3)) = ld(rd(X3,X),f(X3)),
inference(symmetry,[status(thm)],[c594]) ).
cnf(c596,plain,
rd(f(X3),rd(X,f(X3))) = rd(f(X3),ld(rd(X3,X),f(X3))),
inference(congruence,[status(thm)],[c595]) ).
cnf(c597,plain,
rd(f(X3),ld(rd(X3,X),f(X3))) = rd(X3,X),
inference(substitution,[status(thm)],[c472]) ).
cnf(c598,plain,
rd(f(X3),rd(X,f(X3))) = rd(X3,X),
inference(transitivity,[status(thm)],[c596,c597]) ).
cnf(c599,plain,
rd(X3,X) = rd(f(X3),rd(X,f(X3))),
inference(symmetry,[status(thm)],[c598]) ).
cnf(c600,plain,
ld(f(X3),rd(X3,X)) = ld(f(X3),rd(f(X3),rd(X,f(X3)))),
inference(congruence,[status(thm)],[c599]) ).
cnf(c601,plain,
rd(X3,ld(rd(mult(X3,X3),X),X3)) = rd(mult(X3,X3),X),
inference(substitution,[status(thm)],[c472]) ).
cnf(c602,plain,
rd(mult(X3,X3),X) = rd(X3,ld(rd(mult(X3,X3),X),X3)),
inference(symmetry,[status(thm)],[c601]) ).
cnf(c603,plain,
rd(ld(rd(mult(X3,X3),X),mult(X3,X3)),X3) = ld(rd(mult(X3,X3),X),X3),
inference(substitution,[status(thm)],[c493]) ).
cnf(c604,plain,
ld(rd(mult(X3,X3),X),X3) = rd(ld(rd(mult(X3,X3),X),mult(X3,X3)),X3),
inference(symmetry,[status(thm)],[c603]) ).
cnf(c605,plain,
ld(rd(mult(X3,X3),X),mult(X3,X3)) = X,
inference(substitution,[status(thm)],[c206]) ).
cnf(c606,plain,
rd(ld(rd(mult(X3,X3),X),mult(X3,X3)),X3) = rd(X,X3),
inference(congruence,[status(thm)],[c605]) ).
cnf(c607,plain,
ld(rd(mult(X3,X3),X),X3) = rd(X,X3),
inference(transitivity,[status(thm)],[c604,c606]) ).
cnf(c608,plain,
rd(X3,ld(rd(mult(X3,X3),X),X3)) = rd(X3,rd(X,X3)),
inference(congruence,[status(thm)],[c607]) ).
cnf(c609,plain,
rd(mult(X3,X3),X) = rd(X3,rd(X,X3)),
inference(transitivity,[status(thm)],[c602,c608]) ).
cnf(c610,plain,
rd(X3,rd(X,X3)) = rd(mult(X3,X3),X),
inference(symmetry,[status(thm)],[c609]) ).
cnf(c611,plain,
ld(X3,rd(X3,rd(X,X3))) = ld(X3,rd(mult(X3,X3),X)),
inference(congruence,[status(thm)],[c610]) ).
cnf(c612,plain,
mult(X,ld(X,mult(X3,X3))) = mult(X3,X3),
inference(substitution,[status(thm)],[c53]) ).
cnf(c613,plain,
mult(X3,X3) = mult(X,ld(X,mult(X3,X3))),
inference(symmetry,[status(thm)],[c612]) ).
cnf(c614,plain,
rd(mult(X3,X3),ld(X,X3)) = rd(mult(X,ld(X,mult(X3,X3))),ld(X,X3)),
inference(congruence,[status(thm)],[c613]) ).
cnf(c615,plain,
mult(ld(X,X3),X3) = ld(X,mult(X3,X3)),
inference(substitution,[status(thm)],[c308]) ).
cnf(c616,plain,
ld(X,mult(X3,X3)) = mult(ld(X,X3),X3),
inference(symmetry,[status(thm)],[c615]) ).
cnf(c617,plain,
mult(X,ld(X,mult(X3,X3))) = mult(X,mult(ld(X,X3),X3)),
inference(congruence,[status(thm)],[c616]) ).
cnf(c618,plain,
rd(mult(X,ld(X,mult(X3,X3))),ld(X,X3)) = rd(mult(X,mult(ld(X,X3),X3)),ld(X,X3)),
inference(congruence,[status(thm)],[c617]) ).
cnf(c619,plain,
mult(X,mult(ld(X,X3),X)) = mult(X3,X),
inference(substitution,[status(thm)],[c245]) ).
cnf(c620,plain,
mult(X3,X) = mult(X,mult(ld(X,X3),X)),
inference(symmetry,[status(thm)],[c619]) ).
cnf(c621,plain,
mult(mult(X3,X),ld(X,X3)) = mult(mult(X,mult(ld(X,X3),X)),ld(X,X3)),
inference(congruence,[status(thm)],[c620]) ).
cnf(c622,plain,
mult(mult(X,mult(ld(X,X3),X)),ld(X,X3)) = mult(X,mult(ld(X,X3),mult(X,ld(X,X3)))),
inference(substitution,[status(thm)],[c267]) ).
cnf(c623,plain,
mult(X,ld(X,X3)) = X3,
inference(substitution,[status(thm)],[c53]) ).
cnf(c624,plain,
mult(ld(X,X3),mult(X,ld(X,X3))) = mult(ld(X,X3),X3),
inference(congruence,[status(thm)],[c623]) ).
cnf(c625,plain,
mult(X,mult(ld(X,X3),mult(X,ld(X,X3)))) = mult(X,mult(ld(X,X3),X3)),
inference(congruence,[status(thm)],[c624]) ).
cnf(c626,plain,
mult(mult(X,mult(ld(X,X3),X)),ld(X,X3)) = mult(X,mult(ld(X,X3),X3)),
inference(transitivity,[status(thm)],[c622,c625]) ).
cnf(c627,plain,
mult(mult(X3,X),ld(X,X3)) = mult(X,mult(ld(X,X3),X3)),
inference(transitivity,[status(thm)],[c621,c626]) ).
cnf(c628,plain,
mult(mult(X,X3),ld(X3,X)) = mult(X3,mult(ld(X3,X),X)),
inference(substitution,[status(thm)],[c627]) ).
cnf(c629,plain,
mult(X3,mult(ld(X3,X),X)) = mult(mult(X,X3),ld(X3,X)),
inference(symmetry,[status(thm)],[c628]) ).
cnf(c630,plain,
rd(mult(X3,mult(ld(X3,X),X)),ld(X3,X)) = rd(mult(mult(X,X3),ld(X3,X)),ld(X3,X)),
inference(congruence,[status(thm)],[c629]) ).
cnf(c631,plain,
rd(mult(mult(X,X3),ld(X3,X)),ld(X3,X)) = mult(X,X3),
inference(substitution,[status(thm)],[c109]) ).
cnf(c632,plain,
rd(mult(X3,mult(ld(X3,X),X)),ld(X3,X)) = mult(X,X3),
inference(transitivity,[status(thm)],[c630,c631]) ).
cnf(c633,plain,
rd(mult(X,mult(ld(X,X3),X3)),ld(X,X3)) = mult(X3,X),
inference(substitution,[status(thm)],[c632]) ).
cnf(c634,plain,
rd(mult(X,ld(X,mult(X3,X3))),ld(X,X3)) = mult(X3,X),
inference(transitivity,[status(thm)],[c618,c633]) ).
cnf(c635,plain,
rd(mult(X3,X3),ld(X,X3)) = mult(X3,X),
inference(transitivity,[status(thm)],[c614,c634]) ).
cnf(c636,plain,
rd(mult(X3,X3),ld(rd(X3,X),X3)) = mult(X3,rd(X3,X)),
inference(substitution,[status(thm)],[c635]) ).
cnf(c637,plain,
mult(X3,rd(X3,X)) = rd(mult(X3,X3),ld(rd(X3,X),X3)),
inference(symmetry,[status(thm)],[c636]) ).
cnf(c638,plain,
rd(mult(X3,X3),ld(rd(X3,X),X3)) = rd(mult(X3,X3),X),
inference(congruence,[status(thm)],[c206]) ).
cnf(c639,plain,
mult(X3,rd(X3,X)) = rd(mult(X3,X3),X),
inference(transitivity,[status(thm)],[c637,c638]) ).
cnf(c640,plain,
rd(mult(X3,X3),X) = mult(X3,rd(X3,X)),
inference(symmetry,[status(thm)],[c639]) ).
cnf(c641,plain,
ld(X3,rd(mult(X3,X3),X)) = ld(X3,mult(X3,rd(X3,X))),
inference(congruence,[status(thm)],[c640]) ).
cnf(c642,plain,
ld(X3,mult(X3,rd(X3,X))) = rd(X3,X),
inference(substitution,[status(thm)],[c59]) ).
cnf(c643,plain,
ld(X3,rd(mult(X3,X3),X)) = rd(X3,X),
inference(transitivity,[status(thm)],[c641,c642]) ).
cnf(c644,plain,
ld(X3,rd(X3,rd(X,X3))) = rd(X3,X),
inference(transitivity,[status(thm)],[c611,c643]) ).
cnf(c645,plain,
ld(f(X3),rd(f(X3),rd(X,f(X3)))) = rd(f(X3),X),
inference(substitution,[status(thm)],[c644]) ).
cnf(c646,plain,
ld(f(X3),rd(X3,X)) = rd(f(X3),X),
inference(transitivity,[status(thm)],[c600,c645]) ).
cnf(c647,plain,
ld(f(X3),rd(X3,rd(X3,X))) = rd(f(X3),rd(X3,X)),
inference(substitution,[status(thm)],[c646]) ).
cnf(c648,plain,
ld(f(X3),rd(mult(X3,X),X3)) = rd(f(X3),rd(X3,X)),
inference(transitivity,[status(thm)],[c584,c647]) ).
cnf(c649,plain,
rd(mult(f(X3),X),X3) = rd(f(X3),rd(X3,X)),
inference(transitivity,[status(thm)],[c574,c648]) ).
cnf(c650,plain,
rd(mult(f(X3),X),mult(f(X3),f(X3))) = rd(f(X3),rd(X3,X)),
inference(transitivity,[status(thm)],[c568,c649]) ).
cnf(c651,plain,
mult(f(X3),rd(X,mult(f(X3),f(X3)))) = rd(f(X3),rd(X3,X)),
inference(transitivity,[status(thm)],[c566,c650]) ).
cnf(c652,plain,
mult(f(X3),rd(X,X3)) = rd(f(X3),rd(X3,X)),
inference(transitivity,[status(thm)],[c565,c651]) ).
cnf(c653,plain,
ld(f(f(X3)),mult(f(X3),rd(X,X3))) = ld(f(f(X3)),rd(f(X3),rd(X3,X))),
inference(congruence,[status(thm)],[c652]) ).
cnf(c654,plain,
ld(f(f(X3)),rd(f(X3),rd(X3,X))) = rd(f(f(X3)),rd(X3,X)),
inference(substitution,[status(thm)],[c646]) ).
cnf(c655,plain,
ld(f(f(X3)),mult(f(X3),rd(X,X3))) = rd(f(f(X3)),rd(X3,X)),
inference(transitivity,[status(thm)],[c653,c654]) ).
cnf(c656,plain,
mult(f(f(X3)),rd(X,X3)) = rd(f(f(X3)),rd(X3,X)),
inference(transitivity,[status(thm)],[c561,c655]) ).
cnf(c657,plain,
rd(mult(f(f(X3)),X),X3) = rd(f(f(X3)),rd(X3,X)),
inference(transitivity,[status(thm)],[c559,c656]) ).
cnf(c658,plain,
rd(mult(f(f(X)),X3),X) = rd(f(f(X)),rd(X,X3)),
inference(substitution,[status(thm)],[c657]) ).
cnf(c659,plain,
ld(rd(mult(f(f(X)),X3),X),f(f(X))) = ld(rd(f(f(X)),rd(X,X3)),f(f(X))),
inference(congruence,[status(thm)],[c658]) ).
cnf(c660,plain,
ld(rd(f(f(X)),rd(X,X3)),f(f(X))) = rd(X,X3),
inference(substitution,[status(thm)],[c206]) ).
cnf(c661,plain,
ld(rd(mult(f(f(X)),X3),X),f(f(X))) = rd(X,X3),
inference(transitivity,[status(thm)],[c659,c660]) ).
cnf(c662,plain,
ld(mult(f(f(X)),rd(X3,X)),f(f(X))) = rd(X,X3),
inference(transitivity,[status(thm)],[c558,c661]) ).
cnf(c663,plain,
ld(rd(X3,X),unit) = rd(X,X3),
inference(transitivity,[status(thm)],[c508,c662]) ).
cnf(c664,plain,
ld(rd(X,X3),unit) = rd(X3,X),
inference(substitution,[status(thm)],[c663]) ).
cnf(c665,plain,
rd(X3,X) = ld(rd(X,X3),unit),
inference(symmetry,[status(thm)],[c664]) ).
cnf(c666,plain,
mult(rd(X4,X3),X) = mult(ld(rd(X3,X4),unit),X),
inference(congruence,[status(thm)],[c665]) ).
cnf(c667,plain,
ld(rd(X,ld(X3,unit)),mult(X,X)) = mult(ld(X3,unit),X),
inference(substitution,[status(thm)],[c450]) ).
cnf(c668,plain,
mult(ld(X3,unit),X) = ld(rd(X,ld(X3,unit)),mult(X,X)),
inference(symmetry,[status(thm)],[c667]) ).
cnf(c669,plain,
rd(X,ld(X3,unit)) = mult(X,X3),
inference(substitution,[status(thm)],[c419]) ).
cnf(c670,plain,
ld(rd(X,ld(X3,unit)),mult(X,X)) = ld(mult(X,X3),mult(X,X)),
inference(congruence,[status(thm)],[c669]) ).
cnf(c671,plain,
mult(X3,X) = rd(mult(X3,X3),ld(X,X3)),
inference(symmetry,[status(thm)],[c635]) ).
cnf(c672,plain,
ld(mult(X3,X),mult(X3,X3)) = ld(rd(mult(X3,X3),ld(X,X3)),mult(X3,X3)),
inference(congruence,[status(thm)],[c671]) ).
cnf(c673,plain,
ld(rd(mult(X3,X3),ld(X,X3)),mult(X3,X3)) = ld(X,X3),
inference(substitution,[status(thm)],[c206]) ).
cnf(c674,plain,
ld(mult(X3,X),mult(X3,X3)) = ld(X,X3),
inference(transitivity,[status(thm)],[c672,c673]) ).
cnf(c675,plain,
ld(mult(X,X3),mult(X,X)) = ld(X3,X),
inference(substitution,[status(thm)],[c674]) ).
cnf(c676,plain,
ld(rd(X,ld(X3,unit)),mult(X,X)) = ld(X3,X),
inference(transitivity,[status(thm)],[c670,c675]) ).
cnf(c677,plain,
mult(ld(X3,unit),X) = ld(X3,X),
inference(transitivity,[status(thm)],[c668,c676]) ).
cnf(c678,plain,
mult(ld(rd(X3,X4),unit),X) = ld(rd(X3,X4),X),
inference(substitution,[status(thm)],[c677]) ).
cnf(c679,plain,
mult(rd(X4,X3),X) = ld(rd(X3,X4),X),
inference(transitivity,[status(thm)],[c666,c678]) ).
cnf(c680,plain,
mult(rd(mult(X,X3),ld(X4,X3)),X3) = ld(rd(ld(X4,X3),mult(X,X3)),X3),
inference(substitution,[status(thm)],[c679]) ).
cnf(c681,plain,
ld(rd(ld(X4,X3),mult(X,X3)),X3) = mult(rd(mult(X,X3),ld(X4,X3)),X3),
inference(symmetry,[status(thm)],[c680]) ).
cnf(c682,plain,
ld(f(X3),mult(f(X3),X)) = X,
inference(substitution,[status(thm)],[c59]) ).
cnf(c683,plain,
X = ld(f(X3),mult(f(X3),X)),
inference(symmetry,[status(thm)],[c682]) ).
cnf(c684,plain,
rd(mult(X4,mult(X3,X)),X) = rd(mult(X4,mult(X3,X)),ld(f(X3),mult(f(X3),X))),
inference(congruence,[status(thm)],[c683]) ).
cnf(c685,plain,
mult(X3,X) = mult(f(X3),mult(f(X3),X)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c686,plain,
mult(X4,mult(X3,X)) = mult(X4,mult(f(X3),mult(f(X3),X))),
inference(congruence,[status(thm)],[c685]) ).
cnf(c687,plain,
rd(mult(X4,mult(X3,X)),ld(f(X3),mult(f(X3),X))) = rd(mult(X4,mult(f(X3),mult(f(X3),X))),ld(f(X3),mult(f(X3),X))),
inference(congruence,[status(thm)],[c686]) ).
cnf(c688,plain,
rd(X4,ld(ld(X3,X),unit)) = mult(X4,ld(X3,X)),
inference(substitution,[status(thm)],[c419]) ).
cnf(c689,plain,
mult(X4,ld(X3,X)) = rd(X4,ld(ld(X3,X),unit)),
inference(symmetry,[status(thm)],[c688]) ).
cnf(c690,plain,
ld(mult(X3,ld(X3,X)),X3) = ld(ld(X3,X),unit),
inference(substitution,[status(thm)],[c423]) ).
cnf(c691,plain,
ld(ld(X3,X),unit) = ld(mult(X3,ld(X3,X)),X3),
inference(symmetry,[status(thm)],[c690]) ).
cnf(c692,plain,
mult(X3,ld(X3,X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c693,plain,
ld(mult(X3,ld(X3,X)),X3) = ld(X,X3),
inference(congruence,[status(thm)],[c692]) ).
cnf(c694,plain,
ld(ld(X3,X),unit) = ld(X,X3),
inference(transitivity,[status(thm)],[c691,c693]) ).
cnf(c695,plain,
rd(X4,ld(ld(X3,X),unit)) = rd(X4,ld(X,X3)),
inference(congruence,[status(thm)],[c694]) ).
cnf(c696,plain,
mult(X4,ld(X3,X)) = rd(X4,ld(X,X3)),
inference(transitivity,[status(thm)],[c689,c695]) ).
cnf(c697,plain,
mult(mult(X4,mult(X3,X)),ld(X,X3)) = rd(mult(X4,mult(X3,X)),ld(X3,X)),
inference(substitution,[status(thm)],[c696]) ).
cnf(c698,plain,
rd(mult(X4,mult(X3,X)),ld(X3,X)) = mult(mult(X4,mult(X3,X)),ld(X,X3)),
inference(symmetry,[status(thm)],[c697]) ).
cnf(c699,plain,
mult(X,mult(ld(X,X3),X)) = mult(X3,X),
inference(substitution,[status(thm)],[c245]) ).
cnf(c700,plain,
mult(X3,X) = mult(X,mult(ld(X,X3),X)),
inference(symmetry,[status(thm)],[c699]) ).
cnf(c701,plain,
mult(X4,mult(X3,X)) = mult(X4,mult(X,mult(ld(X,X3),X))),
inference(congruence,[status(thm)],[c700]) ).
cnf(c702,plain,
mult(mult(X4,mult(X3,X)),ld(X,X3)) = mult(mult(X4,mult(X,mult(ld(X,X3),X))),ld(X,X3)),
inference(congruence,[status(thm)],[c701]) ).
cnf(c703,plain,
mult(mult(X4,mult(X,mult(ld(X,X3),X))),ld(X,X3)) = mult(mult(X4,X),mult(ld(X,X3),mult(X,ld(X,X3)))),
inference(substitution,[status(thm)],[c83]) ).
cnf(c704,plain,
mult(X,ld(X,X3)) = X3,
inference(substitution,[status(thm)],[c53]) ).
cnf(c705,plain,
mult(ld(X,X3),mult(X,ld(X,X3))) = mult(ld(X,X3),X3),
inference(congruence,[status(thm)],[c704]) ).
cnf(c706,plain,
mult(mult(X4,X),mult(ld(X,X3),mult(X,ld(X,X3)))) = mult(mult(X4,X),mult(ld(X,X3),X3)),
inference(congruence,[status(thm)],[c705]) ).
cnf(c707,plain,
mult(ld(X,X3),X3) = ld(X,mult(X3,X3)),
inference(substitution,[status(thm)],[c308]) ).
cnf(c708,plain,
mult(mult(X4,X),mult(ld(X,X3),X3)) = mult(mult(X4,X),ld(X,mult(X3,X3))),
inference(congruence,[status(thm)],[c707]) ).
cnf(c709,plain,
mult(mult(X4,X),ld(X,mult(X3,X3))) = rd(mult(X4,X),ld(mult(X3,X3),X)),
inference(substitution,[status(thm)],[c696]) ).
cnf(c710,plain,
mult(X,ld(X,X3)) = X3,
inference(substitution,[status(thm)],[c53]) ).
cnf(c711,plain,
X3 = mult(X,ld(X,X3)),
inference(symmetry,[status(thm)],[c710]) ).
cnf(c712,plain,
rd(X3,ld(X,ld(X,X3))) = rd(mult(X,ld(X,X3)),ld(X,ld(X,X3))),
inference(congruence,[status(thm)],[c711]) ).
cnf(c713,plain,
rd(mult(X,ld(X,X3)),ld(X,ld(X,X3))) = mult(X,X),
inference(substitution,[status(thm)],[c113]) ).
cnf(c714,plain,
rd(X3,ld(X,ld(X,X3))) = mult(X,X),
inference(transitivity,[status(thm)],[c712,c713]) ).
cnf(c715,plain,
rd(X,ld(X3,ld(X3,X))) = mult(X3,X3),
inference(substitution,[status(thm)],[c714]) ).
cnf(c716,plain,
mult(X3,X3) = rd(X,ld(X3,ld(X3,X))),
inference(symmetry,[status(thm)],[c715]) ).
cnf(c717,plain,
ld(mult(X3,X3),X) = ld(rd(X,ld(X3,ld(X3,X))),X),
inference(congruence,[status(thm)],[c716]) ).
cnf(c718,plain,
ld(rd(X,ld(X3,ld(X3,X))),X) = ld(X3,ld(X3,X)),
inference(substitution,[status(thm)],[c206]) ).
cnf(c719,plain,
ld(mult(X3,X3),X) = ld(X3,ld(X3,X)),
inference(transitivity,[status(thm)],[c717,c718]) ).
cnf(c720,plain,
rd(mult(X4,X),ld(mult(X3,X3),X)) = rd(mult(X4,X),ld(X3,ld(X3,X))),
inference(congruence,[status(thm)],[c719]) ).
cnf(c721,plain,
mult(mult(X4,X),ld(X,mult(X3,X3))) = rd(mult(X4,X),ld(X3,ld(X3,X))),
inference(transitivity,[status(thm)],[c709,c720]) ).
cnf(c722,plain,
mult(mult(X4,X),mult(ld(X,X3),X3)) = rd(mult(X4,X),ld(X3,ld(X3,X))),
inference(transitivity,[status(thm)],[c708,c721]) ).
cnf(c723,plain,
mult(mult(X4,X),mult(ld(X,X3),mult(X,ld(X,X3)))) = rd(mult(X4,X),ld(X3,ld(X3,X))),
inference(transitivity,[status(thm)],[c706,c722]) ).
cnf(c724,plain,
mult(mult(X4,mult(X,mult(ld(X,X3),X))),ld(X,X3)) = rd(mult(X4,X),ld(X3,ld(X3,X))),
inference(transitivity,[status(thm)],[c703,c723]) ).
cnf(c725,plain,
mult(mult(X4,mult(X3,X)),ld(X,X3)) = rd(mult(X4,X),ld(X3,ld(X3,X))),
inference(transitivity,[status(thm)],[c702,c724]) ).
cnf(c726,plain,
rd(mult(X4,mult(X3,X)),ld(X3,X)) = rd(mult(X4,X),ld(X3,ld(X3,X))),
inference(transitivity,[status(thm)],[c698,c725]) ).
cnf(c727,plain,
rd(mult(X4,mult(f(X3),mult(f(X3),X))),ld(f(X3),mult(f(X3),X))) = rd(mult(X4,mult(f(X3),X)),ld(f(X3),ld(f(X3),mult(f(X3),X)))),
inference(substitution,[status(thm)],[c726]) ).
cnf(c728,plain,
ld(f(X3),X) = mult(f(X3),ld(X3,X)),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c729,plain,
ld(f(X3),ld(f(X3),X)) = ld(f(X3),mult(f(X3),ld(X3,X))),
inference(congruence,[status(thm)],[c728]) ).
cnf(c730,plain,
ld(f(X3),mult(f(X3),ld(X3,X))) = ld(X3,X),
inference(substitution,[status(thm)],[c59]) ).
cnf(c731,plain,
ld(f(X3),ld(f(X3),X)) = ld(X3,X),
inference(transitivity,[status(thm)],[c729,c730]) ).
cnf(c732,plain,
ld(f(X3),ld(f(X3),mult(f(X3),X))) = ld(X3,mult(f(X3),X)),
inference(substitution,[status(thm)],[c731]) ).
cnf(c733,plain,
rd(mult(X4,mult(f(X3),X)),ld(f(X3),ld(f(X3),mult(f(X3),X)))) = rd(mult(X4,mult(f(X3),X)),ld(X3,mult(f(X3),X))),
inference(congruence,[status(thm)],[c732]) ).
cnf(c734,plain,
rd(mult(X4,mult(f(X3),X)),ld(X3,mult(f(X3),X))) = rd(mult(X4,mult(f(X3),X)),ld(f(X3),X)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c735,plain,
rd(mult(X4,mult(f(X3),X)),ld(f(X3),X)) = rd(mult(X4,X),ld(f(X3),ld(f(X3),X))),
inference(substitution,[status(thm)],[c726]) ).
cnf(c736,plain,
rd(mult(X4,X),ld(f(X3),ld(f(X3),X))) = rd(mult(X4,X),ld(X3,X)),
inference(congruence,[status(thm)],[c731]) ).
cnf(c737,plain,
rd(mult(X4,mult(f(X3),X)),ld(f(X3),X)) = rd(mult(X4,X),ld(X3,X)),
inference(transitivity,[status(thm)],[c735,c736]) ).
cnf(c738,plain,
rd(mult(X4,mult(f(X3),X)),ld(X3,mult(f(X3),X))) = rd(mult(X4,X),ld(X3,X)),
inference(transitivity,[status(thm)],[c734,c737]) ).
cnf(c739,plain,
rd(mult(X4,mult(f(X3),X)),ld(f(X3),ld(f(X3),mult(f(X3),X)))) = rd(mult(X4,X),ld(X3,X)),
inference(transitivity,[status(thm)],[c733,c738]) ).
cnf(c740,plain,
rd(mult(X4,mult(f(X3),mult(f(X3),X))),ld(f(X3),mult(f(X3),X))) = rd(mult(X4,X),ld(X3,X)),
inference(transitivity,[status(thm)],[c727,c739]) ).
cnf(c741,plain,
rd(mult(X4,mult(X3,X)),ld(f(X3),mult(f(X3),X))) = rd(mult(X4,X),ld(X3,X)),
inference(transitivity,[status(thm)],[c687,c740]) ).
cnf(c742,plain,
rd(mult(X4,mult(X3,X)),X) = rd(mult(X4,X),ld(X3,X)),
inference(transitivity,[status(thm)],[c684,c741]) ).
cnf(c743,plain,
rd(mult(X,mult(X4,X3)),X3) = rd(mult(X,X3),ld(X4,X3)),
inference(substitution,[status(thm)],[c742]) ).
cnf(c744,plain,
rd(mult(X,X3),ld(X4,X3)) = rd(mult(X,mult(X4,X3)),X3),
inference(symmetry,[status(thm)],[c743]) ).
cnf(c745,plain,
mult(rd(mult(X,X3),ld(X4,X3)),X3) = mult(rd(mult(X,mult(X4,X3)),X3),X3),
inference(congruence,[status(thm)],[c744]) ).
cnf(c746,plain,
mult(rd(mult(X,mult(X4,X3)),X3),X3) = mult(X,mult(X4,X3)),
inference(substitution,[status(thm)],[c138]) ).
cnf(c747,plain,
mult(rd(mult(X,X3),ld(X4,X3)),X3) = mult(X,mult(X4,X3)),
inference(transitivity,[status(thm)],[c745,c746]) ).
cnf(c748,plain,
ld(rd(ld(X4,X3),mult(X,X3)),X3) = mult(X,mult(X4,X3)),
inference(transitivity,[status(thm)],[c681,c747]) ).
cnf(c749,plain,
ld(rd(ld(mult(X3,X),X3),mult(X4,X3)),X3) = mult(X4,mult(mult(X3,X),X3)),
inference(substitution,[status(thm)],[c748]) ).
cnf(c750,plain,
mult(mult(X3,X),X3) = mult(X3,mult(X,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c751,plain,
mult(X4,mult(mult(X3,X),X3)) = mult(X4,mult(X3,mult(X,X3))),
inference(congruence,[status(thm)],[c750]) ).
cnf(c752,plain,
ld(rd(ld(mult(X3,X),X3),mult(X4,X3)),X3) = mult(X4,mult(X3,mult(X,X3))),
inference(transitivity,[status(thm)],[c749,c751]) ).
cnf(c753,plain,
ld(rd(ld(X,unit),mult(X4,X3)),X3) = mult(X4,mult(X3,mult(X,X3))),
inference(transitivity,[status(thm)],[c506,c752]) ).
cnf(c754,plain,
ld(ld(mult(mult(X4,X3),X),unit),X3) = mult(X4,mult(X3,mult(X,X3))),
inference(transitivity,[status(thm)],[c503,c753]) ).
cnf(c755,plain,
mult(mult(mult(X4,X3),X),X3) = mult(X4,mult(X3,mult(X,X3))),
inference(transitivity,[status(thm)],[c486,c754]) ).
cnf(c756,plain,
mult(mult(mult(X3,X4),X),X4) = mult(X3,mult(X4,mult(X,X4))),
inference(substitution,[status(thm)],[c755]) ).
cnf(c757,plain,
ifeq(mult(X3,mult(X4,mult(X,X4))),mult(mult(mult(X3,X4),X),X4),mult(X4,mult(X3,mult(X4,X))),mult(mult(X4,mult(X3,X4)),X)) = ifeq(mult(X3,mult(X4,mult(X,X4))),mult(X3,mult(X4,mult(X,X4))),mult(X4,mult(X3,mult(X4,X))),mult(mult(X4,mult(X3,X4)),X)),
inference(congruence,[status(thm)],[c756]) ).
cnf(c758,plain,
ifeq(mult(X3,mult(X4,mult(X,X4))),mult(X3,mult(X4,mult(X,X4))),mult(X4,mult(X3,mult(X4,X))),mult(mult(X4,mult(X3,X4)),X)) = mult(X4,mult(X3,mult(X4,X))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c759,plain,
ifeq(mult(X3,mult(X4,mult(X,X4))),mult(mult(mult(X3,X4),X),X4),mult(X4,mult(X3,mult(X4,X))),mult(mult(X4,mult(X3,X4)),X)) = mult(X4,mult(X3,mult(X4,X))),
inference(transitivity,[status(thm)],[c757,c758]) ).
cnf(c760,plain,
mult(mult(X4,mult(X3,X4)),X) = mult(X4,mult(X3,mult(X4,X))),
inference(transitivity,[status(thm)],[c14,c759]) ).
cnf(c761,plain,
mult(mult(a,mult(b,a)),c) = mult(a,mult(b,mult(a,c))),
inference(substitution,[status(thm)],[c760]) ).
cnf(c762,plain,
mult(a,mult(b,mult(a,c))) = mult(mult(a,mult(b,a)),c),
inference(symmetry,[status(thm)],[c761]) ).
cnf(c763,plain,
mult(mult(a,b),a) = mult(a,mult(b,a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c764,plain,
mult(a,mult(b,a)) = mult(mult(a,b),a),
inference(symmetry,[status(thm)],[c763]) ).
cnf(c765,plain,
mult(mult(a,mult(b,a)),c) = mult(mult(mult(a,b),a),c),
inference(congruence,[status(thm)],[c764]) ).
cnf(c766,plain,
mult(a,mult(b,mult(a,c))) = mult(mult(mult(a,b),a),c),
inference(transitivity,[status(thm)],[c762,c765]) ).
cnf(c767,plain,
$false,
inference(resolution,[status(thm)],[c1,c766]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP667-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:33:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 78.78/10.48 Command-line arguments: --no-flatten-goal
% 78.78/10.48
% 78.78/10.48 % SZS status Unsatisfiable
% 78.78/10.48
% 79.58/10.53 % SZS output start CNFRefutation
% See solution above
% 82.78/10.92
% 82.78/10.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------