%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP655-13 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:11:34 AM UTC 2026
% Result : Unsatisfiable 3.90s 0.99s
% Output : CNFRefutation 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 94
% Number of leaves : 6
% Syntax : Number of clauses : 569 ( 569 unt; 0 nHn; 3 RR)
% Number of literals : 569 ( 568 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 1340 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(x0,ld(x1,x1)) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
cnf(c3,plain,
rd(mult(mult(mult(X3,ld(X2,X)),ld(X,X2)),ld(X2,X)),ld(X2,X)) = mult(mult(X3,ld(X2,X)),ld(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
mult(mult(X3,ld(X2,X)),ld(X,X2)) = rd(mult(mult(mult(X3,ld(X2,X)),ld(X,X2)),ld(X2,X)),ld(X2,X)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
mult(A2,mult(B2,mult(C,B2))) = mult(mult(mult(A2,B2),C),B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
cnf(c6,plain,
mult(X3,mult(ld(X2,X),mult(ld(X,X2),ld(X2,X)))) = mult(mult(mult(X3,ld(X2,X)),ld(X,X2)),ld(X2,X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
mult(mult(mult(X3,ld(X2,X)),ld(X,X2)),ld(X2,X)) = mult(X3,mult(ld(X2,X),mult(ld(X,X2),ld(X2,X)))),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
mult(X3,mult(ld(X3,X2),mult(X,ld(X3,X2)))) = mult(mult(mult(X3,ld(X3,X2)),X),ld(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c9,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(c10,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
mult(mult(X3,ld(X3,X2)),X) = mult(X2,X),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
mult(mult(mult(X3,ld(X3,X2)),X),ld(X3,X2)) = mult(mult(X2,X),ld(X3,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
mult(X3,mult(ld(X3,X2),mult(X,ld(X3,X2)))) = mult(mult(X2,X),ld(X3,X2)),
inference(transitivity,[status(thm)],[c8,c12]) ).
cnf(c14,plain,
mult(mult(X2,X),ld(X3,X2)) = mult(X3,mult(ld(X3,X2),mult(X,ld(X3,X2)))),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
ld(X3,mult(mult(X2,X),ld(X3,X2))) = ld(X3,mult(X3,mult(ld(X3,X2),mult(X,ld(X3,X2))))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
ld(A2,mult(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(c17,plain,
ld(X3,mult(X3,mult(ld(X3,X2),mult(X,ld(X3,X2))))) = mult(ld(X3,X2),mult(X,ld(X3,X2))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
ld(X3,mult(mult(X2,X),ld(X3,X2))) = mult(ld(X3,X2),mult(X,ld(X3,X2))),
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
ld(X2,mult(mult(X,ld(X,X2)),ld(X2,X))) = mult(ld(X2,X),mult(ld(X,X2),ld(X2,X))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
mult(ld(X2,X),mult(ld(X,X2),ld(X2,X))) = ld(X2,mult(mult(X,ld(X,X2)),ld(X2,X))),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c22,plain,
mult(mult(X,ld(X,X2)),ld(X2,X)) = mult(X2,ld(X2,X)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
ld(X2,mult(mult(X,ld(X,X2)),ld(X2,X))) = ld(X2,mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
ld(X2,mult(X2,ld(X2,X))) = ld(X2,X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c25,plain,
ld(X2,mult(mult(X,ld(X,X2)),ld(X2,X))) = ld(X2,X),
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
mult(ld(X2,X),mult(ld(X,X2),ld(X2,X))) = ld(X2,X),
inference(transitivity,[status(thm)],[c20,c25]) ).
cnf(c27,plain,
mult(X3,mult(ld(X2,X),mult(ld(X,X2),ld(X2,X)))) = mult(X3,ld(X2,X)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
mult(mult(mult(X3,ld(X2,X)),ld(X,X2)),ld(X2,X)) = mult(X3,ld(X2,X)),
inference(transitivity,[status(thm)],[c7,c27]) ).
cnf(c29,plain,
rd(mult(mult(mult(X3,ld(X2,X)),ld(X,X2)),ld(X2,X)),ld(X2,X)) = rd(mult(X3,ld(X2,X)),ld(X2,X)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
rd(mult(X3,ld(X2,X)),ld(X2,X)) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
rd(mult(mult(mult(X3,ld(X2,X)),ld(X,X2)),ld(X2,X)),ld(X2,X)) = X3,
inference(transitivity,[status(thm)],[c29,c30]) ).
cnf(c32,plain,
mult(mult(X3,ld(X2,X)),ld(X,X2)) = X3,
inference(transitivity,[status(thm)],[c4,c31]) ).
cnf(c33,plain,
mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))) = ld(X,X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
ld(X,X) = mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
rd(mult(ld(X,rd(X,X2)),X2),X2) = ld(X,rd(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
ld(X,rd(X,X2)) = rd(mult(ld(X,rd(X,X2)),X2),X2),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
ld(X,mult(X,mult(ld(X2,rd(X2,X)),X))) = mult(ld(X2,rd(X2,X)),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c38,plain,
mult(ld(X2,rd(X2,X)),X) = ld(X,mult(X,mult(ld(X2,rd(X2,X)),X))),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c40,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
mult(X,X2) = mult(mult(X3,ld(X3,X)),X2),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
ld(rd(X3,X2),mult(X,X2)) = ld(rd(X3,X2),mult(mult(X3,ld(X3,X)),X2)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
mult(rd(X3,X2),mult(X2,mult(X,X2))) = mult(mult(mult(rd(X3,X2),X2),X),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c44,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
cnf(c45,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
mult(mult(rd(X3,X2),X2),X) = mult(X3,X),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
mult(mult(mult(rd(X3,X2),X2),X),X2) = mult(mult(X3,X),X2),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
mult(rd(X3,X2),mult(X2,mult(X,X2))) = mult(mult(X3,X),X2),
inference(transitivity,[status(thm)],[c43,c47]) ).
cnf(c49,plain,
mult(mult(X3,X),X2) = mult(rd(X3,X2),mult(X2,mult(X,X2))),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
ld(rd(X3,X2),mult(mult(X3,X),X2)) = ld(rd(X3,X2),mult(rd(X3,X2),mult(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
ld(rd(X3,X2),mult(rd(X3,X2),mult(X2,mult(X,X2)))) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c52,plain,
ld(rd(X3,X2),mult(mult(X3,X),X2)) = mult(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c50,c51]) ).
cnf(c53,plain,
ld(rd(X3,X2),mult(mult(X3,ld(X3,X)),X2)) = mult(X2,mult(ld(X3,X),X2)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
ld(rd(X3,X2),mult(X,X2)) = mult(X2,mult(ld(X3,X),X2)),
inference(transitivity,[status(thm)],[c42,c53]) ).
cnf(c55,plain,
ld(rd(X,X2),mult(rd(X,X2),X2)) = mult(X2,mult(ld(X,rd(X,X2)),X2)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
mult(X2,mult(ld(X,rd(X,X2)),X2)) = ld(rd(X,X2),mult(rd(X,X2),X2)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
ld(rd(X,X2),mult(rd(X,X2),X2)) = X2,
inference(substitution,[status(thm)],[c16]) ).
cnf(c58,plain,
mult(X2,mult(ld(X,rd(X,X2)),X2)) = X2,
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
mult(X,mult(ld(X2,rd(X2,X)),X)) = X,
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
ld(X,mult(X,mult(ld(X2,rd(X2,X)),X))) = ld(X,X),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
mult(ld(X2,rd(X2,X)),X) = ld(X,X),
inference(transitivity,[status(thm)],[c38,c60]) ).
cnf(c62,plain,
mult(ld(X,rd(X,X2)),X2) = ld(X2,X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
rd(mult(ld(X,rd(X,X2)),X2),X2) = rd(ld(X2,X2),X2),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
ld(X,X) = mult(ld(X2,rd(X2,X)),X),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c65,plain,
rd(ld(X,X),X) = rd(mult(ld(X2,rd(X2,X)),X),X),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
rd(mult(ld(X2,rd(X2,X)),X),X) = ld(X2,rd(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c67,plain,
rd(ld(X,X),X) = ld(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
rd(mult(ld(X,rd(X,X2)),X2),X2) = ld(X3,rd(X3,X2)),
inference(transitivity,[status(thm)],[c63,c67]) ).
cnf(c69,plain,
ld(X,rd(X,X2)) = ld(X3,rd(X3,X2)),
inference(transitivity,[status(thm)],[c36,c68]) ).
cnf(c70,plain,
ld(X2,rd(X2,X)) = ld(X3,rd(X3,X)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
mult(X3,ld(X2,rd(X2,X))) = mult(X3,ld(X3,rd(X3,X))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
mult(X2,ld(X2,rd(X2,X))) = rd(X2,X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c73,plain,
mult(X3,ld(X2,rd(X2,X))) = rd(X3,X),
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
mult(X3,ld(X4,rd(X4,ld(X2,X)))) = rd(X3,ld(X2,X)),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
rd(X4,ld(X3,X2)) = mult(X4,ld(X,rd(X,ld(X3,X2)))),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
ld(X3,rd(X3,ld(X2,X))) = ld(X,rd(X,ld(X2,X))),
inference(substitution,[status(thm)],[c69]) ).
cnf(c77,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c78,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
rd(X2,ld(X,X2)) = rd(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
rd(mult(X,ld(X,X2)),ld(X,X2)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c81,plain,
rd(X2,ld(X,X2)) = X,
inference(transitivity,[status(thm)],[c79,c80]) ).
cnf(c82,plain,
rd(X,ld(X2,X)) = X2,
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,plain,
ld(X,rd(X,ld(X2,X))) = ld(X,X2),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
ld(X3,rd(X3,ld(X2,X))) = ld(X,X2),
inference(transitivity,[status(thm)],[c76,c83]) ).
cnf(c85,plain,
ld(X,rd(X,ld(X3,X2))) = ld(X2,X3),
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
mult(X4,ld(X,rd(X,ld(X3,X2)))) = mult(X4,ld(X2,X3)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
rd(X3,ld(X2,X)) = mult(X3,ld(X,X2)),
inference(transitivity,[status(thm)],[c75,c86]) ).
cnf(c88,plain,
rd(ld(X3,X3),ld(mult(X,ld(X3,X3)),mult(X2,ld(X3,X3)))) = mult(ld(X3,X3),ld(mult(X2,ld(X3,X3)),mult(X,ld(X3,X3)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
mult(ld(X3,X3),ld(mult(X2,ld(X3,X3)),mult(X,ld(X3,X3)))) = rd(ld(X3,X3),ld(mult(X,ld(X3,X3)),mult(X2,ld(X3,X3)))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
rd(X,ld(X3,X2)) = mult(X,ld(X2,X3)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c91,plain,
mult(X,ld(X2,X3)) = rd(X,ld(X3,X2)),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
ld(mult(X2,ld(X3,X4)),mult(X,ld(X4,X3))) = ld(rd(X2,ld(X4,X3)),mult(X,ld(X4,X3))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
ld(rd(X2,ld(X4,X3)),mult(X,ld(X4,X3))) = mult(ld(X4,X3),mult(ld(X2,X),ld(X4,X3))),
inference(substitution,[status(thm)],[c54]) ).
cnf(c94,plain,
ld(mult(X2,ld(X3,X4)),mult(X,ld(X4,X3))) = mult(ld(X4,X3),mult(ld(X2,X),ld(X4,X3))),
inference(transitivity,[status(thm)],[c92,c93]) ).
cnf(c95,plain,
ld(mult(X,ld(X3,X3)),mult(X2,ld(X3,X3))) = mult(ld(X3,X3),mult(ld(X,X2),ld(X3,X3))),
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
rd(ld(X3,X3),ld(mult(X,ld(X3,X3)),mult(X2,ld(X3,X3)))) = rd(ld(X3,X3),mult(ld(X3,X3),mult(ld(X,X2),ld(X3,X3)))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
mult(rd(mult(ld(X,X),ld(X,X)),X),X) = mult(ld(X,X),ld(X,X)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c98,plain,
mult(ld(X,X),ld(X,X)) = mult(rd(mult(ld(X,X),ld(X,X)),X),X),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c100,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
mult(X2,rd(ld(X,X),X)) = mult(mult(rd(X2,X),X),rd(ld(X,X),X)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c103,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
mult(X2,X) = mult(X2,mult(rd(X,X2),X2)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
mult(X3,mult(X2,X)) = mult(X3,mult(X2,mult(rd(X,X2),X2))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
rd(mult(X3,mult(X2,X)),X2) = rd(mult(X3,mult(X2,mult(rd(X,X2),X2))),X2),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
mult(X3,mult(X2,mult(X,X2))) = mult(mult(mult(X3,X2),X),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c108,plain,
rd(mult(X3,mult(X2,mult(X,X2))),X2) = rd(mult(mult(mult(X3,X2),X),X2),X2),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
rd(mult(mult(mult(X3,X2),X),X2),X2) = mult(mult(X3,X2),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c110,plain,
rd(mult(X3,mult(X2,mult(X,X2))),X2) = mult(mult(X3,X2),X),
inference(transitivity,[status(thm)],[c108,c109]) ).
cnf(c111,plain,
rd(mult(X3,mult(X2,mult(rd(X,X2),X2))),X2) = mult(mult(X3,X2),rd(X,X2)),
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
rd(mult(X3,mult(X2,X)),X2) = mult(mult(X3,X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c106,c111]) ).
cnf(c113,plain,
rd(mult(X2,mult(X,ld(X,X))),X) = mult(mult(X2,X),rd(ld(X,X),X)),
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
mult(mult(X2,X),rd(ld(X,X),X)) = rd(mult(X2,mult(X,ld(X,X))),X),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
mult(X,ld(X,X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c116,plain,
mult(X2,mult(X,ld(X,X))) = mult(X2,X),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
rd(mult(X2,mult(X,ld(X,X))),X) = rd(mult(X2,X),X),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
rd(mult(X2,X),X) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c119,plain,
rd(mult(X2,mult(X,ld(X,X))),X) = X2,
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
mult(mult(X2,X),rd(ld(X,X),X)) = X2,
inference(transitivity,[status(thm)],[c114,c119]) ).
cnf(c121,plain,
mult(mult(rd(X2,X),X),rd(ld(X,X),X)) = rd(X2,X),
inference(substitution,[status(thm)],[c120]) ).
cnf(c122,plain,
mult(X2,rd(ld(X,X),X)) = rd(X2,X),
inference(transitivity,[status(thm)],[c101,c121]) ).
cnf(c123,plain,
mult(mult(ld(X,X),ld(X,X)),rd(ld(X,X),X)) = rd(mult(ld(X,X),ld(X,X)),X),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
rd(mult(ld(X,X),ld(X,X)),X) = mult(mult(ld(X,X),ld(X,X)),rd(ld(X,X),X)),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
mult(ld(X,X),rd(ld(X,X),X)) = rd(ld(X,X),X),
inference(substitution,[status(thm)],[c122]) ).
cnf(c126,plain,
rd(ld(X,X),X) = mult(ld(X,X),rd(ld(X,X),X)),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
mult(mult(ld(X,X),ld(X,X)),rd(ld(X,X),X)) = mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),rd(ld(X,X),X))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
rd(ld(X2,X),ld(X,X2)) = mult(ld(X2,X),ld(X2,X)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c129,plain,
mult(ld(X2,X),ld(X2,X)) = rd(ld(X2,X),ld(X,X2)),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
mult(mult(ld(X3,X2),ld(X3,X2)),mult(ld(X2,X3),X)) = mult(rd(ld(X3,X2),ld(X2,X3)),mult(ld(X2,X3),X)),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
mult(rd(X3,X),mult(X,mult(rd(X2,X),X))) = mult(mult(X3,rd(X2,X)),X),
inference(substitution,[status(thm)],[c48]) ).
cnf(c132,plain,
mult(mult(X3,rd(X2,X)),X) = mult(rd(X3,X),mult(X,mult(rd(X2,X),X))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c134,plain,
mult(X,mult(rd(X2,X),X)) = mult(X,X2),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
mult(rd(X3,X),mult(X,mult(rd(X2,X),X))) = mult(rd(X3,X),mult(X,X2)),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
mult(mult(X3,rd(X2,X)),X) = mult(rd(X3,X),mult(X,X2)),
inference(transitivity,[status(thm)],[c132,c135]) ).
cnf(c137,plain,
mult(mult(ld(X3,X2),rd(X,ld(X2,X3))),ld(X2,X3)) = mult(rd(ld(X3,X2),ld(X2,X3)),mult(ld(X2,X3),X)),
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
mult(rd(ld(X3,X2),ld(X2,X3)),mult(ld(X2,X3),X)) = mult(mult(ld(X3,X2),rd(X,ld(X2,X3))),ld(X2,X3)),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
ld(X3,mult(X3,mult(X,ld(X3,X2)))) = mult(X,ld(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c140,plain,
mult(X,ld(X3,X2)) = ld(X3,mult(X3,mult(X,ld(X3,X2)))),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
ld(ld(X3,X2),mult(X,ld(X3,X2))) = ld(ld(X3,X2),ld(X3,mult(X3,mult(X,ld(X3,X2))))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
mult(X,mult(ld(X,X3),mult(rd(X2,ld(X,X3)),ld(X,X3)))) = mult(mult(X3,rd(X2,ld(X,X3))),ld(X,X3)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c143,plain,
mult(mult(X3,rd(X2,ld(X,X3))),ld(X,X3)) = mult(X,mult(ld(X,X3),mult(rd(X2,ld(X,X3)),ld(X,X3)))),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
mult(rd(X2,ld(X,X3)),ld(X,X3)) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c145,plain,
mult(ld(X,X3),mult(rd(X2,ld(X,X3)),ld(X,X3))) = mult(ld(X,X3),X2),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
mult(X,mult(ld(X,X3),mult(rd(X2,ld(X,X3)),ld(X,X3)))) = mult(X,mult(ld(X,X3),X2)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
mult(mult(X3,rd(X2,ld(X,X3))),ld(X,X3)) = mult(X,mult(ld(X,X3),X2)),
inference(transitivity,[status(thm)],[c143,c146]) ).
cnf(c148,plain,
mult(mult(X2,rd(X,ld(X3,X2))),ld(X3,X2)) = mult(X3,mult(ld(X3,X2),X)),
inference(substitution,[status(thm)],[c147]) ).
cnf(c149,plain,
mult(X3,mult(ld(X3,X2),X)) = mult(mult(X2,rd(X,ld(X3,X2))),ld(X3,X2)),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
mult(mult(X3,mult(ld(X3,X2),X)),ld(X2,X3)) = mult(mult(mult(X2,rd(X,ld(X3,X2))),ld(X3,X2)),ld(X2,X3)),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
mult(mult(mult(X2,rd(X,ld(X3,X2))),ld(X3,X2)),ld(X2,X3)) = mult(X2,rd(X,ld(X3,X2))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c152,plain,
rd(X,ld(X3,X2)) = mult(X,ld(X2,X3)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c153,plain,
mult(X2,rd(X,ld(X3,X2))) = mult(X2,mult(X,ld(X2,X3))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
mult(mult(mult(X2,rd(X,ld(X3,X2))),ld(X3,X2)),ld(X2,X3)) = mult(X2,mult(X,ld(X2,X3))),
inference(transitivity,[status(thm)],[c151,c153]) ).
cnf(c155,plain,
mult(mult(X3,mult(ld(X3,X2),X)),ld(X2,X3)) = mult(X2,mult(X,ld(X2,X3))),
inference(transitivity,[status(thm)],[c150,c154]) ).
cnf(c156,plain,
mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2)) = mult(X3,mult(X,ld(X3,X2))),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
mult(X3,mult(X,ld(X3,X2))) = mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2)),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
ld(X3,mult(X3,mult(X,ld(X3,X2)))) = ld(X3,mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
ld(ld(X3,X2),ld(X3,mult(X3,mult(X,ld(X3,X2))))) = ld(ld(X3,X2),ld(X3,mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2)))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
ld(X3,mult(mult(X2,ld(X2,X)),ld(X3,X2))) = mult(ld(X3,X2),mult(ld(X2,X),ld(X3,X2))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c161,plain,
mult(ld(X3,X2),mult(ld(X2,X),ld(X3,X2))) = ld(X3,mult(mult(X2,ld(X2,X)),ld(X3,X2))),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c163,plain,
mult(mult(X2,ld(X2,X)),ld(X3,X2)) = mult(X,ld(X3,X2)),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
ld(X3,mult(mult(X2,ld(X2,X)),ld(X3,X2))) = ld(X3,mult(X,ld(X3,X2))),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
mult(ld(X3,X2),mult(ld(X2,X),ld(X3,X2))) = ld(X3,mult(X,ld(X3,X2))),
inference(transitivity,[status(thm)],[c161,c164]) ).
cnf(c166,plain,
ld(X3,mult(X,ld(X3,X2))) = mult(ld(X3,X2),mult(ld(X2,X),ld(X3,X2))),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
ld(ld(X3,X2),ld(X3,mult(X,ld(X3,X2)))) = ld(ld(X3,X2),mult(ld(X3,X2),mult(ld(X2,X),ld(X3,X2)))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
ld(ld(X3,X2),mult(ld(X3,X2),mult(ld(X2,X),ld(X3,X2)))) = mult(ld(X2,X),ld(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c169,plain,
ld(ld(X3,X2),ld(X3,mult(X,ld(X3,X2)))) = mult(ld(X2,X),ld(X3,X2)),
inference(transitivity,[status(thm)],[c167,c168]) ).
cnf(c170,plain,
ld(ld(X3,X2),ld(X3,mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2)))) = mult(ld(X2,mult(X2,mult(ld(X2,X3),X))),ld(X3,X2)),
inference(substitution,[status(thm)],[c169]) ).
cnf(c171,plain,
ld(X2,mult(X2,mult(ld(X2,X3),X))) = mult(ld(X2,X3),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c172,plain,
mult(ld(X2,mult(X2,mult(ld(X2,X3),X))),ld(X3,X2)) = mult(mult(ld(X2,X3),X),ld(X3,X2)),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
ld(ld(X3,X2),ld(X3,mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2)))) = mult(mult(ld(X2,X3),X),ld(X3,X2)),
inference(transitivity,[status(thm)],[c170,c172]) ).
cnf(c174,plain,
ld(ld(X3,X2),ld(X3,mult(X3,mult(X,ld(X3,X2))))) = mult(mult(ld(X2,X3),X),ld(X3,X2)),
inference(transitivity,[status(thm)],[c159,c173]) ).
cnf(c175,plain,
ld(ld(X3,X2),mult(X,ld(X3,X2))) = mult(mult(ld(X2,X3),X),ld(X3,X2)),
inference(transitivity,[status(thm)],[c141,c174]) ).
cnf(c176,plain,
ld(ld(X2,X3),mult(rd(X,ld(X2,X3)),ld(X2,X3))) = mult(mult(ld(X3,X2),rd(X,ld(X2,X3))),ld(X2,X3)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
mult(mult(ld(X3,X2),rd(X,ld(X2,X3))),ld(X2,X3)) = ld(ld(X2,X3),mult(rd(X,ld(X2,X3)),ld(X2,X3))),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
mult(rd(X,ld(X2,X3)),ld(X2,X3)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c179,plain,
ld(ld(X2,X3),mult(rd(X,ld(X2,X3)),ld(X2,X3))) = ld(ld(X2,X3),X),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
mult(mult(ld(X3,X2),rd(X,ld(X2,X3))),ld(X2,X3)) = ld(ld(X2,X3),X),
inference(transitivity,[status(thm)],[c177,c179]) ).
cnf(c181,plain,
mult(rd(ld(X3,X2),ld(X2,X3)),mult(ld(X2,X3),X)) = ld(ld(X2,X3),X),
inference(transitivity,[status(thm)],[c138,c180]) ).
cnf(c182,plain,
mult(mult(ld(X3,X2),ld(X3,X2)),mult(ld(X2,X3),X)) = ld(ld(X2,X3),X),
inference(transitivity,[status(thm)],[c130,c181]) ).
cnf(c183,plain,
mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),rd(ld(X,X),X))) = ld(ld(X,X),rd(ld(X,X),X)),
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
ld(mult(X2,X),mult(mult(X2,X),rd(ld(X,X),X))) = rd(ld(X,X),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c185,plain,
rd(ld(X,X),X) = ld(mult(X2,X),mult(mult(X2,X),rd(ld(X,X),X))),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
ld(mult(X2,X),mult(mult(X2,X),rd(ld(X,X),X))) = ld(mult(X2,X),X2),
inference(congruence,[status(thm)],[c120]) ).
cnf(c187,plain,
rd(ld(X,X),X) = ld(mult(X2,X),X2),
inference(transitivity,[status(thm)],[c185,c186]) ).
cnf(c188,plain,
rd(ld(X,X),X) = ld(mult(rd(X2,X),X),rd(X2,X)),
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c190,plain,
ld(mult(rd(X2,X),X),rd(X2,X)) = ld(X2,rd(X2,X)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
rd(ld(X,X),X) = ld(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c188,c190]) ).
cnf(c192,plain,
rd(ld(X,X),X) = ld(ld(X,X),rd(ld(X,X),X)),
inference(substitution,[status(thm)],[c191]) ).
cnf(c193,plain,
ld(ld(X,X),rd(ld(X,X),X)) = rd(ld(X,X),X),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),rd(ld(X,X),X))) = rd(ld(X,X),X),
inference(transitivity,[status(thm)],[c183,c193]) ).
cnf(c195,plain,
mult(mult(ld(X,X),ld(X,X)),rd(ld(X,X),X)) = rd(ld(X,X),X),
inference(transitivity,[status(thm)],[c127,c194]) ).
cnf(c196,plain,
rd(mult(ld(X,X),ld(X,X)),X) = rd(ld(X,X),X),
inference(transitivity,[status(thm)],[c124,c195]) ).
cnf(c197,plain,
mult(rd(mult(ld(X,X),ld(X,X)),X),X) = mult(rd(ld(X,X),X),X),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
mult(rd(ld(X,X),X),X) = ld(X,X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c199,plain,
mult(rd(mult(ld(X,X),ld(X,X)),X),X) = ld(X,X),
inference(transitivity,[status(thm)],[c197,c198]) ).
cnf(c200,plain,
mult(ld(X,X),ld(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c98,c199]) ).
cnf(c201,plain,
ld(X,X) = mult(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
mult(ld(X2,X2),mult(ld(X,ld(X2,X2)),ld(X2,X2))) = mult(mult(ld(X2,X2),ld(X2,X2)),mult(ld(X,ld(X2,X2)),ld(X2,X2))),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
ld(X,X) = mult(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c204,plain,
mult(ld(X,ld(X2,X2)),ld(X2,X2)) = mult(ld(X,ld(X2,X2)),mult(ld(X2,X2),ld(X2,X2))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
mult(mult(ld(X2,X2),ld(X2,X2)),mult(ld(X,ld(X2,X2)),ld(X2,X2))) = mult(mult(ld(X2,X2),ld(X2,X2)),mult(ld(X,ld(X2,X2)),mult(ld(X2,X2),ld(X2,X2)))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
ld(rd(X,mult(ld(X2,X2),ld(X2,X2))),mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2)))) = mult(mult(ld(X2,X2),ld(X2,X2)),mult(ld(X,ld(X2,X2)),mult(ld(X2,X2),ld(X2,X2)))),
inference(substitution,[status(thm)],[c54]) ).
cnf(c207,plain,
mult(mult(ld(X2,X2),ld(X2,X2)),mult(ld(X,ld(X2,X2)),mult(ld(X2,X2),ld(X2,X2)))) = ld(rd(X,mult(ld(X2,X2),ld(X2,X2))),mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2)))),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
mult(ld(X,X),mult(ld(X,X),ld(X,X))) = ld(X,X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c209,plain,
ld(rd(X,mult(ld(X2,X2),ld(X2,X2))),mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2)))) = ld(rd(X,mult(ld(X2,X2),ld(X2,X2))),ld(X2,X2)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(mult(ld(X,X),ld(X,X)),mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X))))) = mult(mult(X2,mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c211,plain,
mult(mult(X2,mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))) = mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(mult(ld(X,X),ld(X,X)),mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X))))),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
mult(rd(X4,ld(X,X2)),mult(ld(X,X2),mult(mult(X3,ld(X2,X)),ld(X,X2)))) = mult(mult(X4,mult(X3,ld(X2,X))),ld(X,X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c213,plain,
mult(mult(X4,mult(X3,ld(X2,X))),ld(X,X2)) = mult(rd(X4,ld(X,X2)),mult(ld(X,X2),mult(mult(X3,ld(X2,X)),ld(X,X2)))),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
mult(ld(X,X2),mult(mult(X3,ld(X2,X)),ld(X,X2))) = mult(ld(X,X2),X3),
inference(congruence,[status(thm)],[c32]) ).
cnf(c215,plain,
mult(rd(X4,ld(X,X2)),mult(ld(X,X2),mult(mult(X3,ld(X2,X)),ld(X,X2)))) = mult(rd(X4,ld(X,X2)),mult(ld(X,X2),X3)),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
rd(X3,ld(X,X2)) = mult(X3,ld(X2,X)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c217,plain,
mult(rd(X4,ld(X,X2)),mult(ld(X,X2),X3)) = mult(mult(X4,ld(X2,X)),mult(ld(X,X2),X3)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
mult(rd(X4,ld(X,X2)),mult(ld(X,X2),mult(mult(X3,ld(X2,X)),ld(X,X2)))) = mult(mult(X4,ld(X2,X)),mult(ld(X,X2),X3)),
inference(transitivity,[status(thm)],[c215,c217]) ).
cnf(c219,plain,
mult(mult(X4,mult(X3,ld(X2,X))),ld(X,X2)) = mult(mult(X4,ld(X2,X)),mult(ld(X,X2),X3)),
inference(transitivity,[status(thm)],[c213,c218]) ).
cnf(c220,plain,
mult(mult(ld(X2,X),mult(ld(X,X2),ld(X2,X))),ld(X,X2)) = mult(mult(ld(X2,X),ld(X2,X)),mult(ld(X,X2),ld(X,X2))),
inference(substitution,[status(thm)],[c219]) ).
cnf(c221,plain,
mult(mult(ld(X2,X),ld(X2,X)),mult(ld(X,X2),ld(X,X2))) = mult(mult(ld(X2,X),mult(ld(X,X2),ld(X2,X))),ld(X,X2)),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
mult(mult(ld(X2,X),mult(ld(X,X2),ld(X2,X))),ld(X,X2)) = mult(ld(X2,X),ld(X,X2)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c223,plain,
mult(mult(ld(X2,X),ld(X2,X)),mult(ld(X,X2),ld(X,X2))) = mult(ld(X2,X),ld(X,X2)),
inference(transitivity,[status(thm)],[c221,c222]) ).
cnf(c224,plain,
mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X))) = mult(ld(X,X),ld(X,X)),
inference(substitution,[status(thm)],[c223]) ).
cnf(c225,plain,
mult(mult(ld(X,X),ld(X,X)),mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X)))) = mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(mult(ld(X,X),ld(X,X)),mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X))))) = mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X)))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X))) = mult(ld(X,X),ld(X,X)),
inference(substitution,[status(thm)],[c223]) ).
cnf(c228,plain,
mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X)))) = mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c230,plain,
mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X)))) = X2,
inference(transitivity,[status(thm)],[c228,c229]) ).
cnf(c231,plain,
mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(mult(ld(X,X),ld(X,X)),mult(mult(ld(X,X),ld(X,X)),mult(ld(X,X),ld(X,X))))) = X2,
inference(transitivity,[status(thm)],[c226,c230]) ).
cnf(c232,plain,
mult(mult(X2,mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))) = X2,
inference(transitivity,[status(thm)],[c211,c231]) ).
cnf(c233,plain,
mult(mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))) = rd(X2,mult(ld(X,X),ld(X,X))),
inference(substitution,[status(thm)],[c232]) ).
cnf(c234,plain,
rd(X2,mult(ld(X,X),ld(X,X))) = mult(mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c236,plain,
mult(mult(rd(X2,mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))),mult(ld(X,X),ld(X,X))) = mult(X2,mult(ld(X,X),ld(X,X))),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
rd(X2,mult(ld(X,X),ld(X,X))) = mult(X2,mult(ld(X,X),ld(X,X))),
inference(transitivity,[status(thm)],[c234,c236]) ).
cnf(c238,plain,
rd(X,mult(ld(X2,X2),ld(X2,X2))) = mult(X,mult(ld(X2,X2),ld(X2,X2))),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
ld(rd(X,mult(ld(X2,X2),ld(X2,X2))),ld(X2,X2)) = ld(mult(X,mult(ld(X2,X2),ld(X2,X2))),ld(X2,X2)),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
mult(X,mult(ld(X2,X2),ld(X2,X2))) = mult(X,ld(X2,X2)),
inference(congruence,[status(thm)],[c200]) ).
cnf(c241,plain,
ld(mult(X,mult(ld(X2,X2),ld(X2,X2))),ld(X2,X2)) = ld(mult(X,ld(X2,X2)),ld(X2,X2)),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
ld(rd(X,mult(ld(X2,X2),ld(X2,X2))),ld(X2,X2)) = ld(mult(X,ld(X2,X2)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c239,c241]) ).
cnf(c243,plain,
ld(rd(X,mult(ld(X2,X2),ld(X2,X2))),mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2)))) = ld(mult(X,ld(X2,X2)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c209,c242]) ).
cnf(c244,plain,
mult(mult(ld(X2,X2),ld(X2,X2)),mult(ld(X,ld(X2,X2)),mult(ld(X2,X2),ld(X2,X2)))) = ld(mult(X,ld(X2,X2)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c207,c243]) ).
cnf(c245,plain,
mult(mult(ld(X2,X2),ld(X2,X2)),mult(ld(X,ld(X2,X2)),ld(X2,X2))) = ld(mult(X,ld(X2,X2)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c205,c244]) ).
cnf(c246,plain,
mult(ld(X2,X2),mult(ld(X,ld(X2,X2)),ld(X2,X2))) = ld(mult(X,ld(X2,X2)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c202,c245]) ).
cnf(c247,plain,
mult(ld(X2,X2),mult(ld(rd(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2))) = ld(mult(rd(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)),
inference(substitution,[status(thm)],[c246]) ).
cnf(c248,plain,
ld(mult(rd(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)) = mult(ld(X2,X2),mult(ld(rd(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2))),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c250,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
ld(rd(X2,X),X2) = ld(rd(X2,X),mult(rd(X2,X),X)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
ld(rd(X2,X),mult(rd(X2,X),X)) = X,
inference(substitution,[status(thm)],[c16]) ).
cnf(c253,plain,
ld(rd(X2,X),X2) = X,
inference(transitivity,[status(thm)],[c251,c252]) ).
cnf(c254,plain,
ld(rd(ld(X2,X2),X),ld(X2,X2)) = X,
inference(substitution,[status(thm)],[c253]) ).
cnf(c255,plain,
mult(ld(rd(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)) = mult(X,ld(X2,X2)),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
mult(ld(X2,X2),mult(ld(rd(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2))) = mult(ld(X2,X2),mult(X,ld(X2,X2))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
ld(mult(rd(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)) = mult(ld(X2,X2),mult(X,ld(X2,X2))),
inference(transitivity,[status(thm)],[c248,c256]) ).
cnf(c258,plain,
mult(ld(X2,X2),mult(X,ld(X2,X2))) = ld(mult(rd(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)),
inference(symmetry,[status(thm)],[c257]) ).
cnf(c259,plain,
rd(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))) = rd(ld(X2,X2),ld(mult(rd(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2))),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
rd(ld(X2,X2),ld(mult(rd(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2))) = mult(rd(ld(X2,X2),X),ld(X2,X2)),
inference(substitution,[status(thm)],[c81]) ).
cnf(c261,plain,
rd(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))) = mult(rd(ld(X2,X2),X),ld(X2,X2)),
inference(transitivity,[status(thm)],[c259,c260]) ).
cnf(c262,plain,
rd(ld(X3,X3),mult(ld(X3,X3),mult(ld(X,X2),ld(X3,X3)))) = mult(rd(ld(X3,X3),ld(X,X2)),ld(X3,X3)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c263,plain,
rd(ld(X3,X3),ld(X,X2)) = mult(ld(X3,X3),ld(X2,X)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c264,plain,
mult(rd(ld(X3,X3),ld(X,X2)),ld(X3,X3)) = mult(mult(ld(X3,X3),ld(X2,X)),ld(X3,X3)),
inference(congruence,[status(thm)],[c263]) ).
cnf(c265,plain,
rd(ld(X3,X3),mult(ld(X3,X3),mult(ld(X,X2),ld(X3,X3)))) = mult(mult(ld(X3,X3),ld(X2,X)),ld(X3,X3)),
inference(transitivity,[status(thm)],[c262,c264]) ).
cnf(c266,plain,
rd(ld(X3,X3),ld(mult(X,ld(X3,X3)),mult(X2,ld(X3,X3)))) = mult(mult(ld(X3,X3),ld(X2,X)),ld(X3,X3)),
inference(transitivity,[status(thm)],[c96,c265]) ).
cnf(c267,plain,
mult(ld(X3,X3),ld(mult(X2,ld(X3,X3)),mult(X,ld(X3,X3)))) = mult(mult(ld(X3,X3),ld(X2,X)),ld(X3,X3)),
inference(transitivity,[status(thm)],[c89,c266]) ).
cnf(c268,plain,
mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))) = mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2)),
inference(substitution,[status(thm)],[c267]) ).
cnf(c269,plain,
mult(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2))))) = mult(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
ld(X,X) = mult(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c271,plain,
mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))) = mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
mult(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2))) = mult(mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
rd(mult(ld(mult(X3,ld(X4,X)),mult(X2,ld(X,X4))),ld(X4,X)),ld(X4,X)) = ld(mult(X3,ld(X4,X)),mult(X2,ld(X,X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c274,plain,
ld(mult(X4,ld(X,X2)),mult(X3,ld(X2,X))) = rd(mult(ld(mult(X4,ld(X,X2)),mult(X3,ld(X2,X))),ld(X,X2)),ld(X,X2)),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
mult(mult(X5,ld(X,X2)),ld(mult(X4,ld(X,X2)),mult(X3,ld(X2,X)))) = mult(mult(X5,ld(X,X2)),rd(mult(ld(mult(X4,ld(X,X2)),mult(X3,ld(X2,X))),ld(X,X2)),ld(X,X2))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
mult(X3,mult(X2,mult(X,X2))) = mult(mult(mult(X3,X2),X),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c277,plain,
mult(mult(mult(X3,X2),X),X2) = mult(X3,mult(X2,mult(X,X2))),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
ld(X3,mult(mult(mult(X3,X2),X),X2)) = ld(X3,mult(X3,mult(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
ld(X3,mult(X3,mult(X2,mult(X,X2)))) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c280,plain,
ld(X3,mult(mult(mult(X3,X2),X),X2)) = mult(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c278,c279]) ).
cnf(c281,plain,
ld(X2,mult(mult(mult(X2,X3),ld(mult(X2,X3),X)),X3)) = mult(X3,mult(ld(mult(X2,X3),X),X3)),
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
mult(X3,mult(ld(mult(X2,X3),X),X3)) = ld(X2,mult(mult(mult(X2,X3),ld(mult(X2,X3),X)),X3)),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
mult(mult(X2,X3),ld(mult(X2,X3),X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c284,plain,
mult(mult(mult(X2,X3),ld(mult(X2,X3),X)),X3) = mult(X,X3),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
ld(X2,mult(mult(mult(X2,X3),ld(mult(X2,X3),X)),X3)) = ld(X2,mult(X,X3)),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
mult(X3,mult(ld(mult(X2,X3),X),X3)) = ld(X2,mult(X,X3)),
inference(transitivity,[status(thm)],[c282,c285]) ).
cnf(c287,plain,
ld(X2,mult(X,X3)) = mult(X3,mult(ld(mult(X2,X3),X),X3)),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
ld(X3,ld(X2,mult(X,X3))) = ld(X3,mult(X3,mult(ld(mult(X2,X3),X),X3))),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
ld(X3,mult(X3,mult(ld(mult(X2,X3),X),X3))) = mult(ld(mult(X2,X3),X),X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c290,plain,
ld(X3,ld(X2,mult(X,X3))) = mult(ld(mult(X2,X3),X),X3),
inference(transitivity,[status(thm)],[c288,c289]) ).
cnf(c291,plain,
ld(ld(X4,X3),ld(X2,mult(mult(X,ld(X3,X4)),ld(X4,X3)))) = mult(ld(mult(X2,ld(X4,X3)),mult(X,ld(X3,X4))),ld(X4,X3)),
inference(substitution,[status(thm)],[c290]) ).
cnf(c292,plain,
mult(ld(mult(X2,ld(X4,X3)),mult(X,ld(X3,X4))),ld(X4,X3)) = ld(ld(X4,X3),ld(X2,mult(mult(X,ld(X3,X4)),ld(X4,X3)))),
inference(symmetry,[status(thm)],[c291]) ).
cnf(c293,plain,
mult(mult(X,ld(X2,X3)),ld(X3,X2)) = X,
inference(substitution,[status(thm)],[c32]) ).
cnf(c294,plain,
ld(X2,mult(mult(X,ld(X3,X4)),ld(X4,X3))) = ld(X2,X),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
ld(ld(X4,X3),ld(X2,mult(mult(X,ld(X3,X4)),ld(X4,X3)))) = ld(ld(X4,X3),ld(X2,X)),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
mult(ld(mult(X2,ld(X4,X3)),mult(X,ld(X3,X4))),ld(X4,X3)) = ld(ld(X4,X3),ld(X2,X)),
inference(transitivity,[status(thm)],[c292,c295]) ).
cnf(c297,plain,
mult(ld(mult(X4,ld(X,X2)),mult(X3,ld(X2,X))),ld(X,X2)) = ld(ld(X,X2),ld(X4,X3)),
inference(substitution,[status(thm)],[c296]) ).
cnf(c298,plain,
rd(mult(ld(mult(X4,ld(X,X2)),mult(X3,ld(X2,X))),ld(X,X2)),ld(X,X2)) = rd(ld(ld(X,X2),ld(X4,X3)),ld(X,X2)),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
mult(mult(X5,ld(X,X2)),rd(mult(ld(mult(X4,ld(X,X2)),mult(X3,ld(X2,X))),ld(X,X2)),ld(X,X2))) = mult(mult(X5,ld(X,X2)),rd(ld(ld(X,X2),ld(X4,X3)),ld(X,X2))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
rd(mult(X3,mult(X2,ld(X2,X))),X2) = mult(mult(X3,X2),rd(ld(X2,X),X2)),
inference(substitution,[status(thm)],[c112]) ).
cnf(c301,plain,
mult(mult(X3,X2),rd(ld(X2,X),X2)) = rd(mult(X3,mult(X2,ld(X2,X))),X2),
inference(symmetry,[status(thm)],[c300]) ).
cnf(c302,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c303,plain,
mult(X3,mult(X2,ld(X2,X))) = mult(X3,X),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
rd(mult(X3,mult(X2,ld(X2,X))),X2) = rd(mult(X3,X),X2),
inference(congruence,[status(thm)],[c303]) ).
cnf(c305,plain,
mult(mult(X3,X2),rd(ld(X2,X),X2)) = rd(mult(X3,X),X2),
inference(transitivity,[status(thm)],[c301,c304]) ).
cnf(c306,plain,
mult(mult(X5,ld(X,X2)),rd(ld(ld(X,X2),ld(X4,X3)),ld(X,X2))) = rd(mult(X5,ld(X4,X3)),ld(X,X2)),
inference(substitution,[status(thm)],[c305]) ).
cnf(c307,plain,
rd(mult(X5,ld(X4,X3)),ld(X,X2)) = mult(mult(X5,ld(X4,X3)),ld(X2,X)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c308,plain,
mult(mult(X5,ld(X,X2)),rd(ld(ld(X,X2),ld(X4,X3)),ld(X,X2))) = mult(mult(X5,ld(X4,X3)),ld(X2,X)),
inference(transitivity,[status(thm)],[c306,c307]) ).
cnf(c309,plain,
mult(mult(X5,ld(X,X2)),rd(mult(ld(mult(X4,ld(X,X2)),mult(X3,ld(X2,X))),ld(X,X2)),ld(X,X2))) = mult(mult(X5,ld(X4,X3)),ld(X2,X)),
inference(transitivity,[status(thm)],[c299,c308]) ).
cnf(c310,plain,
mult(mult(X5,ld(X,X2)),ld(mult(X4,ld(X,X2)),mult(X3,ld(X2,X)))) = mult(mult(X5,ld(X4,X3)),ld(X2,X)),
inference(transitivity,[status(thm)],[c275,c309]) ).
cnf(c311,plain,
mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))) = mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2)),
inference(substitution,[status(thm)],[c310]) ).
cnf(c312,plain,
mult(mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2))) = mult(mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2)),mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2))),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
ld(ld(X2,X2),mult(X,ld(X2,X2))) = mult(mult(ld(X2,X2),X),ld(X2,X2)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c314,plain,
mult(mult(ld(X2,X2),X),ld(X2,X2)) = ld(ld(X2,X2),mult(X,ld(X2,X2))),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c315,plain,
mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),mult(mult(ld(X2,X2),X),ld(X2,X2))) = mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),ld(ld(X2,X2),mult(X,ld(X2,X2)))),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
ld(X,X) = mult(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c317,plain,
mult(ld(X2,X2),mult(ld(X2,X2),X)) = mult(mult(ld(X2,X2),ld(X2,X2)),mult(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
mult(mult(ld(X2,X2),ld(X2,X2)),mult(ld(X2,X2),X)) = ld(ld(X2,X2),X),
inference(substitution,[status(thm)],[c182]) ).
cnf(c319,plain,
mult(ld(X2,X2),mult(ld(X2,X2),X)) = ld(ld(X2,X2),X),
inference(transitivity,[status(thm)],[c317,c318]) ).
cnf(c320,plain,
mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))) = ld(ld(X2,X2),mult(X,ld(X2,X2))),
inference(substitution,[status(thm)],[c319]) ).
cnf(c321,plain,
ld(ld(X2,X2),mult(X,ld(X2,X2))) = mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))),
inference(symmetry,[status(thm)],[c320]) ).
cnf(c322,plain,
mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),ld(ld(X2,X2),mult(X,ld(X2,X2)))) = mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2))))),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
rd(ld(ld(X3,X2),X),ld(X3,X2)) = mult(ld(ld(X3,X2),X),ld(X2,X3)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c324,plain,
mult(ld(ld(X3,X2),X),ld(X2,X3)) = rd(ld(ld(X3,X2),X),ld(X3,X2)),
inference(symmetry,[status(thm)],[c323]) ).
cnf(c325,plain,
ld(X3,mult(X3,rd(ld(ld(X2,X3),X),ld(X2,X3)))) = rd(ld(ld(X2,X3),X),ld(X2,X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c326,plain,
rd(ld(ld(X2,X3),X),ld(X2,X3)) = ld(X3,mult(X3,rd(ld(ld(X2,X3),X),ld(X2,X3)))),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
mult(mult(X2,rd(X,ld(X3,X2))),ld(X3,X2)) = mult(X3,mult(ld(X3,X2),X)),
inference(substitution,[status(thm)],[c147]) ).
cnf(c328,plain,
mult(X3,mult(ld(X3,X2),X)) = mult(mult(X2,rd(X,ld(X3,X2))),ld(X3,X2)),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c329,plain,
rd(mult(X3,mult(ld(X3,X2),X)),ld(X3,X2)) = rd(mult(mult(X2,rd(X,ld(X3,X2))),ld(X3,X2)),ld(X3,X2)),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
rd(mult(mult(X2,rd(X,ld(X3,X2))),ld(X3,X2)),ld(X3,X2)) = mult(X2,rd(X,ld(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c331,plain,
rd(mult(X3,mult(ld(X3,X2),X)),ld(X3,X2)) = mult(X2,rd(X,ld(X3,X2))),
inference(transitivity,[status(thm)],[c329,c330]) ).
cnf(c332,plain,
rd(mult(X2,mult(ld(X2,X3),ld(ld(X2,X3),X))),ld(X2,X3)) = mult(X3,rd(ld(ld(X2,X3),X),ld(X2,X3))),
inference(substitution,[status(thm)],[c331]) ).
cnf(c333,plain,
mult(X3,rd(ld(ld(X2,X3),X),ld(X2,X3))) = rd(mult(X2,mult(ld(X2,X3),ld(ld(X2,X3),X))),ld(X2,X3)),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
mult(ld(X2,X3),ld(ld(X2,X3),X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c335,plain,
mult(X2,mult(ld(X2,X3),ld(ld(X2,X3),X))) = mult(X2,X),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
rd(mult(X2,mult(ld(X2,X3),ld(ld(X2,X3),X))),ld(X2,X3)) = rd(mult(X2,X),ld(X2,X3)),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
mult(X3,rd(ld(ld(X2,X3),X),ld(X2,X3))) = rd(mult(X2,X),ld(X2,X3)),
inference(transitivity,[status(thm)],[c333,c336]) ).
cnf(c338,plain,
ld(X3,mult(X3,rd(ld(ld(X2,X3),X),ld(X2,X3)))) = ld(X3,rd(mult(X2,X),ld(X2,X3))),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
rd(ld(ld(X2,X3),X),ld(X2,X3)) = ld(X3,rd(mult(X2,X),ld(X2,X3))),
inference(transitivity,[status(thm)],[c326,c338]) ).
cnf(c340,plain,
rd(ld(ld(X3,X2),X),ld(X3,X2)) = ld(X2,rd(mult(X3,X),ld(X3,X2))),
inference(substitution,[status(thm)],[c339]) ).
cnf(c341,plain,
rd(mult(X3,X),ld(X3,X2)) = mult(mult(X3,X),ld(X2,X3)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c342,plain,
ld(X2,rd(mult(X3,X),ld(X3,X2))) = ld(X2,mult(mult(X3,X),ld(X2,X3))),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
ld(X2,mult(mult(X3,X),ld(X2,X3))) = mult(ld(X2,X3),mult(X,ld(X2,X3))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c344,plain,
ld(X2,rd(mult(X3,X),ld(X3,X2))) = mult(ld(X2,X3),mult(X,ld(X2,X3))),
inference(transitivity,[status(thm)],[c342,c343]) ).
cnf(c345,plain,
rd(ld(ld(X3,X2),X),ld(X3,X2)) = mult(ld(X2,X3),mult(X,ld(X2,X3))),
inference(transitivity,[status(thm)],[c340,c344]) ).
cnf(c346,plain,
mult(ld(ld(X3,X2),X),ld(X2,X3)) = mult(ld(X2,X3),mult(X,ld(X2,X3))),
inference(transitivity,[status(thm)],[c324,c345]) ).
cnf(c347,plain,
mult(ld(ld(X2,X2),X),ld(X2,X2)) = mult(ld(X2,X2),mult(X,ld(X2,X2))),
inference(substitution,[status(thm)],[c346]) ).
cnf(c348,plain,
mult(ld(X2,X2),mult(X,ld(X2,X2))) = mult(ld(ld(X2,X2),X),ld(X2,X2)),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c349,plain,
mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))) = mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2))),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2))))) = mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
ld(ld(X2,X2),mult(X,ld(X2,X2))) = mult(mult(ld(X2,X2),X),ld(X2,X2)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c352,plain,
mult(mult(ld(X2,X2),X),ld(X2,X2)) = ld(ld(X2,X2),mult(X,ld(X2,X2))),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = mult(ld(ld(X2,X2),mult(X,ld(X2,X2))),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))) = ld(ld(X2,X2),mult(X,ld(X2,X2))),
inference(substitution,[status(thm)],[c319]) ).
cnf(c355,plain,
ld(ld(X2,X2),mult(X,ld(X2,X2))) = mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))),
inference(symmetry,[status(thm)],[c354]) ).
cnf(c356,plain,
mult(ld(ld(X2,X2),mult(X,ld(X2,X2))),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = mult(mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
mult(ld(ld(X2,X2),X),ld(X2,X2)) = mult(ld(X2,X2),mult(X,ld(X2,X2))),
inference(substitution,[status(thm)],[c346]) ).
cnf(c358,plain,
mult(ld(X2,X2),mult(X,ld(X2,X2))) = mult(ld(ld(X2,X2),X),ld(X2,X2)),
inference(symmetry,[status(thm)],[c357]) ).
cnf(c359,plain,
mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))) = mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2))),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
mult(mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = mult(mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2))),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
mult(ld(X2,X2),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),X))) = ld(ld(X2,X2),mult(ld(ld(X2,X2),X),X)),
inference(substitution,[status(thm)],[c319]) ).
cnf(c362,plain,
ld(ld(X2,X2),mult(ld(ld(X2,X2),X),X)) = mult(ld(X2,X2),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),X))),
inference(symmetry,[status(thm)],[c361]) ).
cnf(c363,plain,
mult(X,mult(ld(X,X2),mult(X,ld(X,X2)))) = mult(mult(X2,X),ld(X,X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c364,plain,
mult(mult(X2,X),ld(X,X2)) = mult(X,mult(ld(X,X2),mult(X,ld(X,X2)))),
inference(symmetry,[status(thm)],[c363]) ).
cnf(c365,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c366,plain,
mult(ld(X,X2),mult(X,ld(X,X2))) = mult(ld(X,X2),X2),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
mult(X,mult(ld(X,X2),mult(X,ld(X,X2)))) = mult(X,mult(ld(X,X2),X2)),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
mult(mult(X2,X),ld(X,X2)) = mult(X,mult(ld(X,X2),X2)),
inference(transitivity,[status(thm)],[c364,c367]) ).
cnf(c369,plain,
mult(mult(X,ld(X2,X2)),ld(ld(X2,X2),X)) = mult(ld(X2,X2),mult(ld(ld(X2,X2),X),X)),
inference(substitution,[status(thm)],[c368]) ).
cnf(c370,plain,
mult(ld(X2,X2),mult(ld(ld(X2,X2),X),X)) = mult(mult(X,ld(X2,X2)),ld(ld(X2,X2),X)),
inference(symmetry,[status(thm)],[c369]) ).
cnf(c371,plain,
mult(ld(X2,X2),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),X))) = mult(ld(X2,X2),mult(mult(X,ld(X2,X2)),ld(ld(X2,X2),X))),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
ld(ld(X2,X2),X) = mult(ld(X2,X2),mult(ld(X2,X2),X)),
inference(symmetry,[status(thm)],[c319]) ).
cnf(c373,plain,
mult(mult(X,ld(X2,X2)),ld(ld(X2,X2),X)) = mult(mult(X,ld(X2,X2)),mult(ld(X2,X2),mult(ld(X2,X2),X))),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
mult(ld(X2,X2),mult(mult(X,ld(X2,X2)),ld(ld(X2,X2),X))) = mult(ld(X2,X2),mult(mult(X,ld(X2,X2)),mult(ld(X2,X2),mult(ld(X2,X2),X)))),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
mult(mult(X,mult(mult(ld(X2,X2),X),ld(X2,X2))),ld(X2,X2)) = mult(mult(X,ld(X2,X2)),mult(ld(X2,X2),mult(ld(X2,X2),X))),
inference(substitution,[status(thm)],[c219]) ).
cnf(c376,plain,
mult(mult(X,ld(X2,X2)),mult(ld(X2,X2),mult(ld(X2,X2),X))) = mult(mult(X,mult(mult(ld(X2,X2),X),ld(X2,X2))),ld(X2,X2)),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
mult(ld(X2,X2),mult(mult(X,ld(X2,X2)),mult(ld(X2,X2),mult(ld(X2,X2),X)))) = mult(ld(X2,X2),mult(mult(X,mult(mult(ld(X2,X2),X),ld(X2,X2))),ld(X2,X2))),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
ld(ld(X2,X2),mult(X,ld(X2,X2))) = mult(mult(ld(X2,X2),X),ld(X2,X2)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c379,plain,
mult(mult(ld(X2,X2),X),ld(X2,X2)) = ld(ld(X2,X2),mult(X,ld(X2,X2))),
inference(symmetry,[status(thm)],[c378]) ).
cnf(c380,plain,
mult(X,mult(mult(ld(X2,X2),X),ld(X2,X2))) = mult(X,ld(ld(X2,X2),mult(X,ld(X2,X2)))),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
mult(mult(X,mult(mult(ld(X2,X2),X),ld(X2,X2))),ld(X2,X2)) = mult(mult(X,ld(ld(X2,X2),mult(X,ld(X2,X2)))),ld(X2,X2)),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
mult(ld(X2,X2),mult(mult(X,mult(mult(ld(X2,X2),X),ld(X2,X2))),ld(X2,X2))) = mult(ld(X2,X2),mult(mult(X,ld(ld(X2,X2),mult(X,ld(X2,X2)))),ld(X2,X2))),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
rd(X,ld(X2,X2)) = mult(X,ld(X2,X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c384,plain,
mult(X,ld(X2,X2)) = rd(X,ld(X2,X2)),
inference(symmetry,[status(thm)],[c383]) ).
cnf(c385,plain,
ld(ld(X2,X2),mult(X,ld(X2,X2))) = ld(ld(X2,X2),rd(X,ld(X2,X2))),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
mult(X,ld(ld(X2,X2),mult(X,ld(X2,X2)))) = mult(X,ld(ld(X2,X2),rd(X,ld(X2,X2)))),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
mult(mult(X,ld(ld(X2,X2),mult(X,ld(X2,X2)))),ld(X2,X2)) = mult(mult(X,ld(ld(X2,X2),rd(X,ld(X2,X2)))),ld(X2,X2)),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
mult(ld(X2,X2),mult(mult(X,ld(ld(X2,X2),mult(X,ld(X2,X2)))),ld(X2,X2))) = mult(ld(X2,X2),mult(mult(X,ld(ld(X2,X2),rd(X,ld(X2,X2)))),ld(X2,X2))),
inference(congruence,[status(thm)],[c387]) ).
cnf(c389,plain,
mult(mult(rd(X,X2),X2),ld(X2,rd(X,X2))) = mult(X2,mult(ld(X2,rd(X,X2)),rd(X,X2))),
inference(substitution,[status(thm)],[c368]) ).
cnf(c390,plain,
mult(X2,mult(ld(X2,rd(X,X2)),rd(X,X2))) = mult(mult(rd(X,X2),X2),ld(X2,rd(X,X2))),
inference(symmetry,[status(thm)],[c389]) ).
cnf(c391,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c392,plain,
mult(mult(rd(X,X2),X2),ld(X2,rd(X,X2))) = mult(X,ld(X2,rd(X,X2))),
inference(congruence,[status(thm)],[c391]) ).
cnf(c393,plain,
mult(X2,mult(ld(X2,rd(X,X2)),rd(X,X2))) = mult(X,ld(X2,rd(X,X2))),
inference(transitivity,[status(thm)],[c390,c392]) ).
cnf(c394,plain,
mult(ld(X2,X2),mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),rd(X,ld(X2,X2)))) = mult(X,ld(ld(X2,X2),rd(X,ld(X2,X2)))),
inference(substitution,[status(thm)],[c393]) ).
cnf(c395,plain,
mult(X,ld(ld(X2,X2),rd(X,ld(X2,X2)))) = mult(ld(X2,X2),mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),rd(X,ld(X2,X2)))),
inference(symmetry,[status(thm)],[c394]) ).
cnf(c396,plain,
mult(mult(X,ld(ld(X2,X2),rd(X,ld(X2,X2)))),ld(X2,X2)) = mult(mult(ld(X2,X2),mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),rd(X,ld(X2,X2)))),ld(X2,X2)),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
mult(ld(X2,X2),mult(mult(X,ld(ld(X2,X2),rd(X,ld(X2,X2)))),ld(X2,X2))) = mult(ld(X2,X2),mult(mult(ld(X2,X2),mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),rd(X,ld(X2,X2)))),ld(X2,X2))),
inference(congruence,[status(thm)],[c396]) ).
cnf(c398,plain,
ld(X3,mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2))) = mult(ld(X3,X2),mult(mult(ld(X2,X3),X),ld(X3,X2))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c399,plain,
mult(ld(X3,X2),mult(mult(ld(X2,X3),X),ld(X3,X2))) = ld(X3,mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2))),
inference(symmetry,[status(thm)],[c398]) ).
cnf(c400,plain,
mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2)) = mult(X3,mult(X,ld(X3,X2))),
inference(substitution,[status(thm)],[c155]) ).
cnf(c401,plain,
ld(X3,mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2))) = ld(X3,mult(X3,mult(X,ld(X3,X2)))),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
ld(X3,mult(X3,mult(X,ld(X3,X2)))) = mult(X,ld(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c403,plain,
ld(X3,mult(mult(X2,mult(ld(X2,X3),X)),ld(X3,X2))) = mult(X,ld(X3,X2)),
inference(transitivity,[status(thm)],[c401,c402]) ).
cnf(c404,plain,
mult(ld(X3,X2),mult(mult(ld(X2,X3),X),ld(X3,X2))) = mult(X,ld(X3,X2)),
inference(transitivity,[status(thm)],[c399,c403]) ).
cnf(c405,plain,
mult(ld(X2,X2),mult(mult(ld(X2,X2),mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),rd(X,ld(X2,X2)))),ld(X2,X2))) = mult(mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),rd(X,ld(X2,X2))),ld(X2,X2)),
inference(substitution,[status(thm)],[c404]) ).
cnf(c406,plain,
mult(mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),rd(X,ld(X2,X2))),ld(X2,X2)) = mult(rd(ld(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)),mult(ld(X2,X2),X)),
inference(substitution,[status(thm)],[c136]) ).
cnf(c407,plain,
rd(ld(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)) = mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c408,plain,
mult(rd(ld(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)),mult(ld(X2,X2),X)) = mult(mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)),mult(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)) = mult(ld(X2,X2),mult(rd(X,ld(X2,X2)),ld(X2,X2))),
inference(substitution,[status(thm)],[c346]) ).
cnf(c410,plain,
mult(mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)),mult(ld(X2,X2),X)) = mult(mult(ld(X2,X2),mult(rd(X,ld(X2,X2)),ld(X2,X2))),mult(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
mult(rd(X,ld(X2,X2)),ld(X2,X2)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c412,plain,
mult(ld(X2,X2),mult(rd(X,ld(X2,X2)),ld(X2,X2))) = mult(ld(X2,X2),X),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
mult(mult(ld(X2,X2),mult(rd(X,ld(X2,X2)),ld(X2,X2))),mult(ld(X2,X2),X)) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
mult(mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)),mult(ld(X2,X2),X)) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c410,c413]) ).
cnf(c415,plain,
mult(rd(ld(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)),mult(ld(X2,X2),X)) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c408,c414]) ).
cnf(c416,plain,
mult(mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),rd(X,ld(X2,X2))),ld(X2,X2)) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c406,c415]) ).
cnf(c417,plain,
mult(ld(X2,X2),mult(mult(ld(X2,X2),mult(ld(ld(X2,X2),rd(X,ld(X2,X2))),rd(X,ld(X2,X2)))),ld(X2,X2))) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c405,c416]) ).
cnf(c418,plain,
mult(ld(X2,X2),mult(mult(X,ld(ld(X2,X2),rd(X,ld(X2,X2)))),ld(X2,X2))) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c397,c417]) ).
cnf(c419,plain,
mult(ld(X2,X2),mult(mult(X,ld(ld(X2,X2),mult(X,ld(X2,X2)))),ld(X2,X2))) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c388,c418]) ).
cnf(c420,plain,
mult(ld(X2,X2),mult(mult(X,mult(mult(ld(X2,X2),X),ld(X2,X2))),ld(X2,X2))) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c382,c419]) ).
cnf(c421,plain,
mult(ld(X2,X2),mult(mult(X,ld(X2,X2)),mult(ld(X2,X2),mult(ld(X2,X2),X)))) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c377,c420]) ).
cnf(c422,plain,
mult(ld(X2,X2),mult(mult(X,ld(X2,X2)),ld(ld(X2,X2),X))) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c374,c421]) ).
cnf(c423,plain,
mult(ld(X2,X2),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),X))) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c371,c422]) ).
cnf(c424,plain,
ld(ld(X2,X2),mult(ld(ld(X2,X2),X),X)) = mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c362,c423]) ).
cnf(c425,plain,
ld(ld(X2,X2),mult(ld(ld(X2,X2),mult(X,ld(X2,X2))),mult(X,ld(X2,X2)))) = mult(mult(ld(X2,X2),mult(X,ld(X2,X2))),mult(ld(X2,X2),mult(X,ld(X2,X2)))),
inference(substitution,[status(thm)],[c424]) ).
cnf(c426,plain,
mult(mult(ld(X2,X2),mult(X,ld(X2,X2))),mult(ld(X2,X2),mult(X,ld(X2,X2)))) = ld(ld(X2,X2),mult(ld(ld(X2,X2),mult(X,ld(X2,X2))),mult(X,ld(X2,X2)))),
inference(symmetry,[status(thm)],[c425]) ).
cnf(c427,plain,
mult(ld(X,X),mult(ld(X,X),ld(X,X))) = ld(X,X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c428,plain,
ld(X,X) = mult(ld(X,X),mult(ld(X,X),ld(X,X))),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
ld(X,ld(X2,X2)) = ld(X,mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2)))),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
mult(ld(X2,X2),ld(X,ld(X2,X2))) = mult(ld(X2,X2),ld(X,mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))))),
inference(congruence,[status(thm)],[c429]) ).
cnf(c431,plain,
ld(mult(ld(X2,X2),ld(X,ld(X2,X2))),X) = ld(mult(ld(X2,X2),ld(X,mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))))),X),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
ld(rd(X3,ld(mult(X3,X2),X)),mult(mult(X3,X2),ld(mult(X3,X2),X))) = mult(ld(mult(X3,X2),X),mult(X2,ld(mult(X3,X2),X))),
inference(substitution,[status(thm)],[c52]) ).
cnf(c433,plain,
mult(ld(mult(X3,X2),X),mult(X2,ld(mult(X3,X2),X))) = ld(rd(X3,ld(mult(X3,X2),X)),mult(mult(X3,X2),ld(mult(X3,X2),X))),
inference(symmetry,[status(thm)],[c432]) ).
cnf(c434,plain,
mult(mult(X3,X2),ld(mult(X3,X2),X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c435,plain,
ld(rd(X3,ld(mult(X3,X2),X)),mult(mult(X3,X2),ld(mult(X3,X2),X))) = ld(rd(X3,ld(mult(X3,X2),X)),X),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
rd(X3,ld(mult(X3,X2),X)) = mult(X3,ld(X,mult(X3,X2))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c437,plain,
ld(rd(X3,ld(mult(X3,X2),X)),X) = ld(mult(X3,ld(X,mult(X3,X2))),X),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
ld(rd(X3,ld(mult(X3,X2),X)),mult(mult(X3,X2),ld(mult(X3,X2),X))) = ld(mult(X3,ld(X,mult(X3,X2))),X),
inference(transitivity,[status(thm)],[c435,c437]) ).
cnf(c439,plain,
mult(ld(mult(X3,X2),X),mult(X2,ld(mult(X3,X2),X))) = ld(mult(X3,ld(X,mult(X3,X2))),X),
inference(transitivity,[status(thm)],[c433,c438]) ).
cnf(c440,plain,
mult(ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X),mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X))) = ld(mult(ld(X2,X2),ld(X,mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))))),X),
inference(substitution,[status(thm)],[c439]) ).
cnf(c441,plain,
ld(mult(ld(X2,X2),ld(X,mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))))),X) = mult(ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X),mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X))),
inference(symmetry,[status(thm)],[c440]) ).
cnf(c442,plain,
mult(ld(X,X),mult(ld(X,X),ld(X,X))) = ld(X,X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c443,plain,
ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X) = ld(ld(X2,X2),X),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
mult(ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X),mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X))) = mult(ld(ld(X2,X2),X),mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X))),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X)) = mult(ld(X2,X2),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X)),
inference(congruence,[status(thm)],[c200]) ).
cnf(c446,plain,
mult(ld(ld(X2,X2),X),mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X))) = mult(ld(ld(X2,X2),X),mult(ld(X2,X2),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X))),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
mult(ld(X,X),mult(ld(X,X),ld(X,X))) = mult(ld(X,X),ld(X,X)),
inference(congruence,[status(thm)],[c200]) ).
cnf(c448,plain,
ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X) = ld(mult(ld(X2,X2),ld(X2,X2)),X),
inference(congruence,[status(thm)],[c447]) ).
cnf(c449,plain,
mult(ld(X2,X2),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X)) = mult(ld(X2,X2),ld(mult(ld(X2,X2),ld(X2,X2)),X)),
inference(congruence,[status(thm)],[c448]) ).
cnf(c450,plain,
mult(ld(ld(X2,X2),X),mult(ld(X2,X2),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X))) = mult(ld(ld(X2,X2),X),mult(ld(X2,X2),ld(mult(ld(X2,X2),ld(X2,X2)),X))),
inference(congruence,[status(thm)],[c449]) ).
cnf(c451,plain,
ld(mult(ld(X2,X2),ld(X2,X2)),X) = ld(ld(X2,X2),X),
inference(congruence,[status(thm)],[c200]) ).
cnf(c452,plain,
mult(ld(X2,X2),ld(mult(ld(X2,X2),ld(X2,X2)),X)) = mult(ld(X2,X2),ld(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
mult(ld(ld(X2,X2),X),mult(ld(X2,X2),ld(mult(ld(X2,X2),ld(X2,X2)),X))) = mult(ld(ld(X2,X2),X),mult(ld(X2,X2),ld(ld(X2,X2),X))),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
mult(ld(X2,X2),ld(ld(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c455,plain,
mult(ld(ld(X2,X2),X),mult(ld(X2,X2),ld(ld(X2,X2),X))) = mult(ld(ld(X2,X2),X),X),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
mult(ld(ld(X2,X2),X),mult(ld(X2,X2),ld(mult(ld(X2,X2),ld(X2,X2)),X))) = mult(ld(ld(X2,X2),X),X),
inference(transitivity,[status(thm)],[c453,c455]) ).
cnf(c457,plain,
mult(ld(ld(X2,X2),X),mult(ld(X2,X2),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X))) = mult(ld(ld(X2,X2),X),X),
inference(transitivity,[status(thm)],[c450,c456]) ).
cnf(c458,plain,
mult(ld(ld(X2,X2),X),mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X))) = mult(ld(ld(X2,X2),X),X),
inference(transitivity,[status(thm)],[c446,c457]) ).
cnf(c459,plain,
mult(ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X),mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))),X))) = mult(ld(ld(X2,X2),X),X),
inference(transitivity,[status(thm)],[c444,c458]) ).
cnf(c460,plain,
ld(mult(ld(X2,X2),ld(X,mult(ld(X2,X2),mult(ld(X2,X2),ld(X2,X2))))),X) = mult(ld(ld(X2,X2),X),X),
inference(transitivity,[status(thm)],[c441,c459]) ).
cnf(c461,plain,
ld(mult(ld(X2,X2),ld(X,ld(X2,X2))),X) = mult(ld(ld(X2,X2),X),X),
inference(transitivity,[status(thm)],[c431,c460]) ).
cnf(c462,plain,
ld(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),mult(X,ld(X2,X2))) = mult(ld(ld(X2,X2),mult(X,ld(X2,X2))),mult(X,ld(X2,X2))),
inference(substitution,[status(thm)],[c461]) ).
cnf(c463,plain,
mult(ld(ld(X2,X2),mult(X,ld(X2,X2))),mult(X,ld(X2,X2))) = ld(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),mult(X,ld(X2,X2))),
inference(symmetry,[status(thm)],[c462]) ).
cnf(c464,plain,
ld(ld(X2,X2),mult(ld(ld(X2,X2),mult(X,ld(X2,X2))),mult(X,ld(X2,X2)))) = ld(ld(X2,X2),ld(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),mult(X,ld(X2,X2)))),
inference(congruence,[status(thm)],[c463]) ).
cnf(c465,plain,
ld(ld(X2,X2),ld(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),mult(X,ld(X2,X2)))) = mult(ld(mult(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),ld(X2,X2)),X),ld(X2,X2)),
inference(substitution,[status(thm)],[c290]) ).
cnf(c466,plain,
rd(ld(X2,X2),ld(ld(X2,X2),X)) = mult(ld(X2,X2),ld(X,ld(X2,X2))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c467,plain,
mult(ld(X2,X2),ld(X,ld(X2,X2))) = rd(ld(X2,X2),ld(ld(X2,X2),X)),
inference(symmetry,[status(thm)],[c466]) ).
cnf(c468,plain,
mult(mult(ld(X2,X2),ld(X,ld(X2,X2))),ld(X2,X2)) = mult(rd(ld(X2,X2),ld(ld(X2,X2),X)),ld(X2,X2)),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
rd(ld(X2,X2),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = mult(rd(ld(X2,X2),ld(ld(X2,X2),X)),ld(X2,X2)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c470,plain,
mult(rd(ld(X2,X2),ld(ld(X2,X2),X)),ld(X2,X2)) = rd(ld(X2,X2),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))),
inference(symmetry,[status(thm)],[c469]) ).
cnf(c471,plain,
mult(ld(ld(X2,X2),X),ld(X2,X2)) = mult(ld(X2,X2),mult(X,ld(X2,X2))),
inference(substitution,[status(thm)],[c346]) ).
cnf(c472,plain,
mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2))) = mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
rd(ld(X2,X2),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = rd(ld(X2,X2),mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2))))),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))) = ld(ld(X2,X2),mult(X,ld(X2,X2))),
inference(substitution,[status(thm)],[c319]) ).
cnf(c475,plain,
rd(ld(X2,X2),mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2))))) = rd(ld(X2,X2),ld(ld(X2,X2),mult(X,ld(X2,X2)))),
inference(congruence,[status(thm)],[c474]) ).
cnf(c476,plain,
rd(ld(X2,X2),ld(ld(X2,X2),mult(X,ld(X2,X2)))) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c477,plain,
rd(ld(X2,X2),mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2))))) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),
inference(transitivity,[status(thm)],[c475,c476]) ).
cnf(c478,plain,
rd(ld(X2,X2),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),
inference(transitivity,[status(thm)],[c473,c477]) ).
cnf(c479,plain,
mult(rd(ld(X2,X2),ld(ld(X2,X2),X)),ld(X2,X2)) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),
inference(transitivity,[status(thm)],[c470,c478]) ).
cnf(c480,plain,
mult(mult(ld(X2,X2),ld(X,ld(X2,X2))),ld(X2,X2)) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),
inference(transitivity,[status(thm)],[c468,c479]) ).
cnf(c481,plain,
mult(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),ld(X2,X2)) = mult(ld(X2,X2),ld(mult(mult(X,ld(X2,X2)),ld(X2,X2)),ld(X2,X2))),
inference(substitution,[status(thm)],[c480]) ).
cnf(c482,plain,
ld(mult(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),ld(X2,X2)),X) = ld(mult(ld(X2,X2),ld(mult(mult(X,ld(X2,X2)),ld(X2,X2)),ld(X2,X2))),X),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
mult(ld(mult(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),ld(X2,X2)),X),ld(X2,X2)) = mult(ld(mult(ld(X2,X2),ld(mult(mult(X,ld(X2,X2)),ld(X2,X2)),ld(X2,X2))),X),ld(X2,X2)),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
mult(mult(X,ld(X2,X2)),ld(X2,X2)) = X,
inference(substitution,[status(thm)],[c32]) ).
cnf(c485,plain,
ld(mult(mult(X,ld(X2,X2)),ld(X2,X2)),ld(X2,X2)) = ld(X,ld(X2,X2)),
inference(congruence,[status(thm)],[c484]) ).
cnf(c486,plain,
mult(ld(X2,X2),ld(mult(mult(X,ld(X2,X2)),ld(X2,X2)),ld(X2,X2))) = mult(ld(X2,X2),ld(X,ld(X2,X2))),
inference(congruence,[status(thm)],[c485]) ).
cnf(c487,plain,
ld(mult(ld(X2,X2),ld(mult(mult(X,ld(X2,X2)),ld(X2,X2)),ld(X2,X2))),X) = ld(mult(ld(X2,X2),ld(X,ld(X2,X2))),X),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,plain,
mult(ld(mult(ld(X2,X2),ld(mult(mult(X,ld(X2,X2)),ld(X2,X2)),ld(X2,X2))),X),ld(X2,X2)) = mult(ld(mult(ld(X2,X2),ld(X,ld(X2,X2))),X),ld(X2,X2)),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
mult(ld(mult(ld(X2,X2),ld(X,ld(X2,X2))),X),ld(X2,X2)) = mult(mult(ld(ld(X2,X2),X),X),ld(X2,X2)),
inference(congruence,[status(thm)],[c461]) ).
cnf(c490,plain,
mult(ld(mult(ld(X2,X2),ld(mult(mult(X,ld(X2,X2)),ld(X2,X2)),ld(X2,X2))),X),ld(X2,X2)) = mult(mult(ld(ld(X2,X2),X),X),ld(X2,X2)),
inference(transitivity,[status(thm)],[c488,c489]) ).
cnf(c491,plain,
mult(ld(mult(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),ld(X2,X2)),X),ld(X2,X2)) = mult(mult(ld(ld(X2,X2),X),X),ld(X2,X2)),
inference(transitivity,[status(thm)],[c483,c490]) ).
cnf(c492,plain,
ld(ld(X2,X2),ld(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),ld(X2,X2))),mult(X,ld(X2,X2)))) = mult(mult(ld(ld(X2,X2),X),X),ld(X2,X2)),
inference(transitivity,[status(thm)],[c465,c491]) ).
cnf(c493,plain,
ld(ld(X2,X2),mult(ld(ld(X2,X2),mult(X,ld(X2,X2))),mult(X,ld(X2,X2)))) = mult(mult(ld(ld(X2,X2),X),X),ld(X2,X2)),
inference(transitivity,[status(thm)],[c464,c492]) ).
cnf(c494,plain,
mult(mult(ld(X2,X2),mult(X,ld(X2,X2))),mult(ld(X2,X2),mult(X,ld(X2,X2)))) = mult(mult(ld(ld(X2,X2),X),X),ld(X2,X2)),
inference(transitivity,[status(thm)],[c426,c493]) ).
cnf(c495,plain,
mult(mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2))),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = mult(mult(ld(ld(X2,X2),ld(ld(X2,X2),X)),ld(ld(X2,X2),X)),ld(X2,X2)),
inference(substitution,[status(thm)],[c494]) ).
cnf(c496,plain,
mult(mult(ld(X2,X3),ld(X2,X3)),mult(ld(X3,X2),ld(ld(X3,X2),X))) = ld(ld(X3,X2),ld(ld(X3,X2),X)),
inference(substitution,[status(thm)],[c182]) ).
cnf(c497,plain,
ld(ld(X3,X2),ld(ld(X3,X2),X)) = mult(mult(ld(X2,X3),ld(X2,X3)),mult(ld(X3,X2),ld(ld(X3,X2),X))),
inference(symmetry,[status(thm)],[c496]) ).
cnf(c498,plain,
mult(ld(X3,X2),ld(ld(X3,X2),X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c499,plain,
mult(mult(ld(X2,X3),ld(X2,X3)),mult(ld(X3,X2),ld(ld(X3,X2),X))) = mult(mult(ld(X2,X3),ld(X2,X3)),X),
inference(congruence,[status(thm)],[c498]) ).
cnf(c500,plain,
ld(ld(X3,X2),ld(ld(X3,X2),X)) = mult(mult(ld(X2,X3),ld(X2,X3)),X),
inference(transitivity,[status(thm)],[c497,c499]) ).
cnf(c501,plain,
ld(ld(X2,X2),ld(ld(X2,X2),X)) = mult(mult(ld(X2,X2),ld(X2,X2)),X),
inference(substitution,[status(thm)],[c500]) ).
cnf(c502,plain,
mult(ld(ld(X2,X2),ld(ld(X2,X2),X)),ld(ld(X2,X2),X)) = mult(mult(mult(ld(X2,X2),ld(X2,X2)),X),ld(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c501]) ).
cnf(c503,plain,
mult(mult(ld(ld(X2,X2),ld(ld(X2,X2),X)),ld(ld(X2,X2),X)),ld(X2,X2)) = mult(mult(mult(mult(ld(X2,X2),ld(X2,X2)),X),ld(ld(X2,X2),X)),ld(X2,X2)),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
mult(mult(ld(X2,X2),ld(X2,X2)),X) = mult(ld(X2,X2),X),
inference(congruence,[status(thm)],[c200]) ).
cnf(c505,plain,
mult(mult(mult(ld(X2,X2),ld(X2,X2)),X),ld(ld(X2,X2),X)) = mult(mult(ld(X2,X2),X),ld(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
mult(mult(mult(mult(ld(X2,X2),ld(X2,X2)),X),ld(ld(X2,X2),X)),ld(X2,X2)) = mult(mult(mult(ld(X2,X2),X),ld(ld(X2,X2),X)),ld(X2,X2)),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
ld(X,X) = mult(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c508,plain,
mult(ld(X2,X2),X) = mult(mult(ld(X2,X2),ld(X2,X2)),X),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
mult(mult(ld(X2,X2),X),ld(ld(X2,X2),X)) = mult(mult(mult(ld(X2,X2),ld(X2,X2)),X),ld(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c508]) ).
cnf(c510,plain,
ld(ld(X2,X2),ld(ld(X2,X2),X)) = mult(mult(ld(X2,X2),ld(X2,X2)),X),
inference(substitution,[status(thm)],[c500]) ).
cnf(c511,plain,
mult(mult(ld(X2,X2),ld(X2,X2)),X) = ld(ld(X2,X2),ld(ld(X2,X2),X)),
inference(symmetry,[status(thm)],[c510]) ).
cnf(c512,plain,
mult(mult(mult(ld(X2,X2),ld(X2,X2)),X),ld(ld(X2,X2),X)) = mult(ld(ld(X2,X2),ld(ld(X2,X2),X)),ld(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X)) = ld(ld(X2,X2),mult(ld(ld(X2,X2),X),X)),
inference(symmetry,[status(thm)],[c424]) ).
cnf(c514,plain,
mult(ld(X2,X2),mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X))) = mult(ld(X2,X2),ld(ld(X2,X2),mult(ld(ld(X2,X2),X),X))),
inference(congruence,[status(thm)],[c513]) ).
cnf(c515,plain,
mult(ld(X2,X2),ld(ld(X2,X2),mult(ld(ld(X2,X2),X),X))) = mult(ld(ld(X2,X2),X),X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c516,plain,
mult(ld(X2,X2),mult(mult(ld(X2,X2),X),mult(ld(X2,X2),X))) = mult(ld(ld(X2,X2),X),X),
inference(transitivity,[status(thm)],[c514,c515]) ).
cnf(c517,plain,
mult(ld(X2,X2),mult(mult(ld(X2,X2),ld(ld(X2,X2),X)),mult(ld(X2,X2),ld(ld(X2,X2),X)))) = mult(ld(ld(X2,X2),ld(ld(X2,X2),X)),ld(ld(X2,X2),X)),
inference(substitution,[status(thm)],[c516]) ).
cnf(c518,plain,
mult(ld(ld(X2,X2),ld(ld(X2,X2),X)),ld(ld(X2,X2),X)) = mult(ld(X2,X2),mult(mult(ld(X2,X2),ld(ld(X2,X2),X)),mult(ld(X2,X2),ld(ld(X2,X2),X)))),
inference(symmetry,[status(thm)],[c517]) ).
cnf(c519,plain,
mult(ld(X2,X2),ld(ld(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c520,plain,
mult(mult(ld(X2,X2),ld(ld(X2,X2),X)),mult(ld(X2,X2),ld(ld(X2,X2),X))) = mult(X,mult(ld(X2,X2),ld(ld(X2,X2),X))),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
mult(ld(X2,X2),mult(mult(ld(X2,X2),ld(ld(X2,X2),X)),mult(ld(X2,X2),ld(ld(X2,X2),X)))) = mult(ld(X2,X2),mult(X,mult(ld(X2,X2),ld(ld(X2,X2),X)))),
inference(congruence,[status(thm)],[c520]) ).
cnf(c522,plain,
mult(ld(X2,X2),ld(ld(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c523,plain,
mult(X,mult(ld(X2,X2),ld(ld(X2,X2),X))) = mult(X,X),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
mult(ld(X2,X2),mult(X,mult(ld(X2,X2),ld(ld(X2,X2),X)))) = mult(ld(X2,X2),mult(X,X)),
inference(congruence,[status(thm)],[c523]) ).
cnf(c525,plain,
mult(ld(X2,X2),mult(mult(ld(X2,X2),ld(ld(X2,X2),X)),mult(ld(X2,X2),ld(ld(X2,X2),X)))) = mult(ld(X2,X2),mult(X,X)),
inference(transitivity,[status(thm)],[c521,c524]) ).
cnf(c526,plain,
mult(ld(ld(X2,X2),ld(ld(X2,X2),X)),ld(ld(X2,X2),X)) = mult(ld(X2,X2),mult(X,X)),
inference(transitivity,[status(thm)],[c518,c525]) ).
cnf(c527,plain,
mult(mult(mult(ld(X2,X2),ld(X2,X2)),X),ld(ld(X2,X2),X)) = mult(ld(X2,X2),mult(X,X)),
inference(transitivity,[status(thm)],[c512,c526]) ).
cnf(c528,plain,
mult(mult(ld(X2,X2),X),ld(ld(X2,X2),X)) = mult(ld(X2,X2),mult(X,X)),
inference(transitivity,[status(thm)],[c509,c527]) ).
cnf(c529,plain,
mult(mult(mult(ld(X2,X2),X),ld(ld(X2,X2),X)),ld(X2,X2)) = mult(mult(ld(X2,X2),mult(X,X)),ld(X2,X2)),
inference(congruence,[status(thm)],[c528]) ).
cnf(c530,plain,
mult(mult(mult(mult(ld(X2,X2),ld(X2,X2)),X),ld(ld(X2,X2),X)),ld(X2,X2)) = mult(mult(ld(X2,X2),mult(X,X)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c506,c529]) ).
cnf(c531,plain,
mult(mult(ld(ld(X2,X2),ld(ld(X2,X2),X)),ld(ld(X2,X2),X)),ld(X2,X2)) = mult(mult(ld(X2,X2),mult(X,X)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c503,c530]) ).
cnf(c532,plain,
mult(mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2))),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = mult(mult(ld(X2,X2),mult(X,X)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c495,c531]) ).
cnf(c533,plain,
mult(mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2)))),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = mult(mult(ld(X2,X2),mult(X,X)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c360,c532]) ).
cnf(c534,plain,
mult(ld(ld(X2,X2),mult(X,ld(X2,X2))),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = mult(mult(ld(X2,X2),mult(X,X)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c356,c533]) ).
cnf(c535,plain,
mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2)))) = mult(mult(ld(X2,X2),mult(X,X)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c353,c534]) ).
cnf(c536,plain,
mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),mult(ld(X2,X2),mult(ld(X2,X2),mult(X,ld(X2,X2))))) = mult(mult(ld(X2,X2),mult(X,X)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c350,c535]) ).
cnf(c537,plain,
mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),ld(ld(X2,X2),mult(X,ld(X2,X2)))) = mult(mult(ld(X2,X2),mult(X,X)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c322,c536]) ).
cnf(c538,plain,
mult(mult(mult(ld(X2,X2),X),ld(X2,X2)),mult(mult(ld(X2,X2),X),ld(X2,X2))) = mult(mult(ld(X2,X2),mult(X,X)),ld(X2,X2)),
inference(transitivity,[status(thm)],[c315,c537]) ).
cnf(c539,plain,
mult(mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2)),mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2))) = mult(mult(ld(X2,X2),mult(ld(X,X),ld(X,X))),ld(X2,X2)),
inference(substitution,[status(thm)],[c538]) ).
cnf(c540,plain,
mult(ld(X2,X2),mult(ld(X,X),ld(X,X))) = mult(ld(X2,X2),ld(X,X)),
inference(congruence,[status(thm)],[c200]) ).
cnf(c541,plain,
mult(mult(ld(X2,X2),mult(ld(X,X),ld(X,X))),ld(X2,X2)) = mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2)),
inference(congruence,[status(thm)],[c540]) ).
cnf(c542,plain,
mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))) = mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2)),
inference(substitution,[status(thm)],[c267]) ).
cnf(c543,plain,
mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2)) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),
inference(symmetry,[status(thm)],[c542]) ).
cnf(c544,plain,
mult(mult(ld(X2,X2),mult(ld(X,X),ld(X,X))),ld(X2,X2)) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),
inference(transitivity,[status(thm)],[c541,c543]) ).
cnf(c545,plain,
mult(mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2)),mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2))) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),
inference(transitivity,[status(thm)],[c539,c544]) ).
cnf(c546,plain,
mult(mult(mult(ld(X2,X2),ld(X2,X2)),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2))) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),
inference(transitivity,[status(thm)],[c312,c545]) ).
cnf(c547,plain,
mult(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),ld(X,X)),ld(X2,X2))) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),
inference(transitivity,[status(thm)],[c272,c546]) ).
cnf(c548,plain,
mult(mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2))))) = mult(ld(X2,X2),ld(mult(X,ld(X2,X2)),mult(X,ld(X2,X2)))),
inference(transitivity,[status(thm)],[c269,c547]) ).
cnf(c549,plain,
mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))))) = mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),
inference(substitution,[status(thm)],[c548]) ).
cnf(c550,plain,
mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))) = mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))))),
inference(symmetry,[status(thm)],[c549]) ).
cnf(c551,plain,
mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))) = mult(mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),
inference(congruence,[status(thm)],[c550]) ).
cnf(c552,plain,
mult(ld(X,X),mult(ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))),mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))))) = mult(mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c553,plain,
mult(mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))) = mult(ld(X,X),mult(ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))),mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))))),
inference(symmetry,[status(thm)],[c552]) ).
cnf(c554,plain,
mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))) = ld(X,X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c555,plain,
mult(ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))),mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))))) = mult(ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))),ld(X,X)),
inference(congruence,[status(thm)],[c554]) ).
cnf(c556,plain,
mult(ld(X,X),mult(ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))),mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))))) = mult(ld(X,X),mult(ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))),ld(X,X))),
inference(congruence,[status(thm)],[c555]) ).
cnf(c557,plain,
mult(ld(X,X),mult(ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))),ld(X,X))) = ld(X2,mult(mult(X2,ld(X,X)),ld(X,X))),
inference(substitution,[status(thm)],[c286]) ).
cnf(c558,plain,
mult(mult(X2,ld(X,X)),ld(X,X)) = X2,
inference(substitution,[status(thm)],[c32]) ).
cnf(c559,plain,
ld(X2,mult(mult(X2,ld(X,X)),ld(X,X))) = ld(X2,X2),
inference(congruence,[status(thm)],[c558]) ).
cnf(c560,plain,
mult(ld(X,X),mult(ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))),ld(X,X))) = ld(X2,X2),
inference(transitivity,[status(thm)],[c557,c559]) ).
cnf(c561,plain,
mult(ld(X,X),mult(ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))),mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))))) = ld(X2,X2),
inference(transitivity,[status(thm)],[c556,c560]) ).
cnf(c562,plain,
mult(mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X))))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))) = ld(X2,X2),
inference(transitivity,[status(thm)],[c553,c561]) ).
cnf(c563,plain,
mult(mult(ld(X,X),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))),ld(mult(X2,ld(X,X)),mult(X2,ld(X,X)))) = ld(X2,X2),
inference(transitivity,[status(thm)],[c551,c562]) ).
cnf(c564,plain,
ld(X,X) = ld(X2,X2),
inference(transitivity,[status(thm)],[c34,c563]) ).
cnf(c565,plain,
mult(X2,ld(X,X)) = mult(X2,ld(X2,X2)),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
mult(X,ld(X,X)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c567,plain,
mult(X2,ld(X,X)) = X2,
inference(transitivity,[status(thm)],[c565,c566]) ).
cnf(c568,plain,
mult(x0,ld(x1,x1)) = x0,
inference(substitution,[status(thm)],[c567]) ).
cnf(c569,plain,
$false,
inference(resolution,[status(thm)],[c1,c568]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP655-13 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 10:27:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.90/0.99 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.90/0.99
% 3.90/0.99 % SZS status Unsatisfiable
% 3.90/0.99
% 3.90/1.02 % SZS output start CNFRefutation
% See solution above
% 6.23/1.22
% 6.23/1.22 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------