%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP667+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 10:11:40 AM UTC 2026
% Result : Theorem 80.91s 10.66s
% Output : CNFRefutation 73.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 103
% Number of leaves : 10
% Syntax : Number of formulae : 741 ( 738 unt; 0 def)
% Number of atoms : 750 ( 749 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 6 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 1395 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c1,conjecture,
( ! [X0,X1,X2] : mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)
| ! [X3,X4,X5] : mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)
| ! [X6,X7,X8] : mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)
| ! [X9,X10,X11] : mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ( ! [X0_2,X1_2,X2_2] : mult(X2_2,mult(X0_2,mult(X2_2,X1_2))) = mult(mult(mult(X2_2,X0_2),X2_2),X1_2)
| ! [X3_2,X4_2,X5_2] : mult(X3_2,mult(X5_2,mult(X4_2,X5_2))) = mult(mult(mult(X3_2,X5_2),X4_2),X5_2)
| ! [X6_2,X7_2,X8_2] : mult(mult(X8_2,X6_2),mult(X7_2,X8_2)) = mult(mult(X8_2,mult(X6_2,X7_2)),X8_2)
| ! [X9_2,X10_2,X11_2] : mult(mult(X11_2,X9_2),mult(X10_2,X11_2)) = mult(X11_2,mult(mult(X9_2,X10_2),X11_2)) ),
inference(negate_conjecture,[status(cth)],[c1]) ).
fof(c3,plain,
( mult(x2,mult(x0,mult(x2,x1))) != mult(mult(mult(x2,x0),x2),x1)
& mult(x3,mult(x5,mult(x4,x5))) != mult(mult(mult(x3,x5),x4),x5)
& mult(mult(x8,x6),mult(x7,x8)) != mult(mult(x8,mult(x6,x7)),x8)
& mult(mult(x11,x9),mult(x10,x11)) != mult(x11,mult(mult(x9,x10),x11)) ),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,plain,
mult(x3,mult(x5,mult(x4,x5))) != mult(mult(mult(x3,x5),x4),x5),
inference(clausify,[status(thm)],[c3]) ).
cnf(c5,axiom,
mult(mult(A,B),A) = mult(A,mult(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
cnf(c6,plain,
mult(mult(X12,X),X12) = mult(X12,mult(X,X12)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
mult(X12,mult(X,X12)) = mult(mult(X12,X),X12),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
rd(mult(X12,mult(X,X12)),X12) = rd(mult(mult(X12,X),X12),X12),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
cnf(c10,plain,
rd(mult(mult(X12,X),X12),X12) = mult(X12,X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
rd(mult(X12,mult(X,X12)),X12) = mult(X12,X),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
rd(mult(X12,mult(rd(X,X12),X12)),X12) = mult(X12,rd(X,X12)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
mult(X12,rd(X,X12)) = rd(mult(X12,mult(rd(X,X12),X12)),X12),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
cnf(c15,plain,
mult(rd(X,X12),X12) = X,
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
mult(X12,mult(rd(X,X12),X12)) = mult(X12,X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
rd(mult(X12,mult(rd(X,X12),X12)),X12) = rd(mult(X12,X),X12),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
mult(X12,rd(X,X12)) = rd(mult(X12,X),X12),
inference(transitivity,[status(thm)],[c13,c17]) ).
cnf(c19,plain,
rd(mult(X12,X),X12) = mult(X12,rd(X,X12)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
ld(X12,rd(mult(X12,X),X12)) = ld(X12,mult(X12,rd(X,X12))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,axiom,
ld(A2,mult(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
cnf(c22,plain,
ld(X12,mult(X12,rd(X,X12))) = rd(X,X12),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
ld(X12,rd(mult(X12,X),X12)) = rd(X,X12),
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
ld(X,rd(mult(X,unit),X)) = rd(unit,X),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
rd(unit,X) = ld(X,rd(mult(X,unit),X)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
cnf(c27,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
rd(mult(X,unit),X) = rd(X,X),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
ld(X,rd(mult(X,unit),X)) = ld(X,rd(X,X)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,axiom,
mult(unit,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
cnf(c31,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
rd(X,X) = rd(mult(unit,X),X),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
rd(mult(unit,X),X) = unit,
inference(substitution,[status(thm)],[c9]) ).
cnf(c35,plain,
rd(X,X) = unit,
inference(transitivity,[status(thm)],[c33,c34]) ).
cnf(c36,plain,
ld(X,rd(X,X)) = ld(X,unit),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
ld(X,rd(mult(X,unit),X)) = ld(X,unit),
inference(transitivity,[status(thm)],[c29,c36]) ).
cnf(c38,plain,
rd(unit,X) = ld(X,unit),
inference(transitivity,[status(thm)],[c25,c37]) ).
cnf(c39,plain,
ld(X,unit) = rd(unit,X),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
rd(X12,ld(X,unit)) = rd(X12,rd(unit,X)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
mult(rd(X12,mult(X,X)),mult(X,X)) = X12,
inference(substitution,[status(thm)],[c14]) ).
cnf(c42,plain,
X12 = mult(rd(X12,mult(X,X)),mult(X,X)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
mult(X12,ld(X,unit)) = mult(mult(rd(X12,mult(X,X)),mult(X,X)),ld(X,unit)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,axiom,
mult(f(A2),f(A2)) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
cnf(c45,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
mult(X,X) = mult(X,mult(f(X),f(X))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
mult(X12,mult(X,X)) = mult(X12,mult(X,mult(f(X),f(X)))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
mult(mult(X12,mult(X,X)),ld(X,unit)) = mult(mult(X12,mult(X,mult(f(X),f(X)))),ld(X,unit)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c26]) ).
cnf(c51,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
mult(mult(X12,X),X) = mult(mult(X12,X),mult(X,unit)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
mult(unit,mult(X,unit)) = mult(X,unit),
inference(substitution,[status(thm)],[c30]) ).
cnf(c54,plain,
mult(X,unit) = mult(unit,mult(X,unit)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
mult(mult(X12,X),mult(X,unit)) = mult(mult(X12,X),mult(unit,mult(X,unit))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
mult(mult(X,X12),X) = mult(X,mult(X12,X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c57,plain,
mult(X12,mult(X,X12)) = mult(mult(X12,X),X12),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
mult(X13,mult(X12,mult(X,X12))) = mult(X13,mult(mult(X12,X),X12)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
mult(mult(X13,mult(X12,mult(X,X12))),X) = mult(mult(X13,mult(mult(X12,X),X12)),X),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,axiom,
mult(mult(A2,B2),mult(mult(C,B2),C)) = mult(mult(A2,mult(mult(B2,C),B2)),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
cnf(c61,plain,
mult(mult(X13,X12),mult(mult(X,X12),X)) = mult(mult(X13,mult(mult(X12,X),X12)),X),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
mult(mult(X13,mult(mult(X12,X),X12)),X) = mult(mult(X13,X12),mult(mult(X,X12),X)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
mult(mult(X,X12),X) = mult(X,mult(X12,X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c64,plain,
mult(mult(X13,X12),mult(mult(X,X12),X)) = mult(mult(X13,X12),mult(X,mult(X12,X))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
mult(mult(X13,mult(mult(X12,X),X12)),X) = mult(mult(X13,X12),mult(X,mult(X12,X))),
inference(transitivity,[status(thm)],[c62,c64]) ).
cnf(c66,plain,
mult(mult(X13,mult(X12,mult(X,X12))),X) = mult(mult(X13,X12),mult(X,mult(X12,X))),
inference(transitivity,[status(thm)],[c59,c65]) ).
cnf(c67,plain,
mult(mult(X12,mult(X,mult(unit,X))),unit) = mult(mult(X12,X),mult(unit,mult(X,unit))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
mult(mult(X12,X),mult(unit,mult(X,unit))) = mult(mult(X12,mult(X,mult(unit,X))),unit),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
mult(mult(X12,mult(X,mult(unit,X))),unit) = mult(X12,mult(X,mult(unit,X))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c70,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c71,plain,
mult(X,mult(unit,X)) = mult(X,X),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
mult(X12,mult(X,mult(unit,X))) = mult(X12,mult(X,X)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
mult(mult(X12,mult(X,mult(unit,X))),unit) = mult(X12,mult(X,X)),
inference(transitivity,[status(thm)],[c69,c72]) ).
cnf(c74,plain,
mult(mult(X12,X),mult(unit,mult(X,unit))) = mult(X12,mult(X,X)),
inference(transitivity,[status(thm)],[c68,c73]) ).
cnf(c75,plain,
mult(mult(X12,X),mult(X,unit)) = mult(X12,mult(X,X)),
inference(transitivity,[status(thm)],[c55,c74]) ).
cnf(c76,plain,
mult(mult(X12,X),X) = mult(X12,mult(X,X)),
inference(transitivity,[status(thm)],[c52,c75]) ).
cnf(c77,plain,
mult(mult(X,f(X)),f(X)) = mult(X,mult(f(X),f(X))),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
mult(X,mult(f(X),f(X))) = mult(mult(X,f(X)),f(X)),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
mult(X12,mult(X,mult(f(X),f(X)))) = mult(X12,mult(mult(X,f(X)),f(X))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
mult(mult(X12,mult(X,mult(f(X),f(X)))),ld(X,unit)) = mult(mult(X12,mult(mult(X,f(X)),f(X))),ld(X,unit)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c82,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
mult(f(X),X) = mult(f(X),mult(f(X),f(X))),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
mult(mult(f(X),f(X)),f(X)) = mult(f(X),mult(f(X),f(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c85,plain,
mult(f(X),mult(f(X),f(X))) = mult(mult(f(X),f(X)),f(X)),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c87,plain,
mult(mult(f(X),f(X)),f(X)) = mult(X,f(X)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
mult(f(X),mult(f(X),f(X))) = mult(X,f(X)),
inference(transitivity,[status(thm)],[c85,c87]) ).
cnf(c89,plain,
mult(f(X),X) = mult(X,f(X)),
inference(transitivity,[status(thm)],[c83,c88]) ).
cnf(c90,plain,
mult(X,f(X)) = mult(f(X),X),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
ld(f(X),mult(X,f(X))) = ld(f(X),mult(f(X),X)),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
ld(f(X),mult(f(X),X)) = X,
inference(substitution,[status(thm)],[c21]) ).
cnf(c93,plain,
ld(f(X),mult(X,f(X))) = X,
inference(transitivity,[status(thm)],[c91,c92]) ).
cnf(c94,plain,
X = ld(f(X),mult(X,f(X))),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
mult(X,f(X)) = mult(ld(f(X),mult(X,f(X))),f(X)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
mult(f(X),mult(X,f(X))) = mult(f(X),mult(ld(f(X),mult(X,f(X))),f(X))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
mult(mult(X12,ld(X12,X)),X12) = mult(X12,mult(ld(X12,X),X12)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c98,plain,
mult(X12,mult(ld(X12,X),X12)) = mult(mult(X12,ld(X12,X)),X12),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
cnf(c100,plain,
mult(X12,ld(X12,X)) = X,
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
mult(mult(X12,ld(X12,X)),X12) = mult(X,X12),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
mult(X12,mult(ld(X12,X),X12)) = mult(X,X12),
inference(transitivity,[status(thm)],[c98,c101]) ).
cnf(c103,plain,
mult(f(X),mult(ld(f(X),mult(X,f(X))),f(X))) = mult(mult(X,f(X)),f(X)),
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
mult(mult(X,f(X)),f(X)) = mult(X,mult(f(X),f(X))),
inference(substitution,[status(thm)],[c76]) ).
cnf(c105,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c106,plain,
mult(X,mult(f(X),f(X))) = mult(X,X),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
mult(mult(X,f(X)),f(X)) = mult(X,X),
inference(transitivity,[status(thm)],[c104,c106]) ).
cnf(c108,plain,
mult(f(X),mult(ld(f(X),mult(X,f(X))),f(X))) = mult(X,X),
inference(transitivity,[status(thm)],[c103,c107]) ).
cnf(c109,plain,
mult(f(X),mult(X,f(X))) = mult(X,X),
inference(transitivity,[status(thm)],[c96,c108]) ).
cnf(c110,plain,
mult(X,X) = mult(f(X),mult(X,f(X))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
ld(mult(X,f(X)),mult(X,X)) = ld(mult(X,f(X)),mult(f(X),mult(X,f(X)))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
mult(X,f(X)) = mult(f(X),X),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c113,plain,
ld(mult(X,f(X)),mult(f(X),mult(X,f(X)))) = ld(mult(f(X),X),mult(f(X),mult(X,f(X)))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
mult(mult(X12,X),X12) = mult(X12,mult(X,X12)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c115,plain,
mult(X12,mult(X,X12)) = mult(mult(X12,X),X12),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
ld(mult(X12,X),mult(X12,mult(X,X12))) = ld(mult(X12,X),mult(mult(X12,X),X12)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
ld(mult(X12,X),mult(mult(X12,X),X12)) = X12,
inference(substitution,[status(thm)],[c21]) ).
cnf(c118,plain,
ld(mult(X12,X),mult(X12,mult(X,X12))) = X12,
inference(transitivity,[status(thm)],[c116,c117]) ).
cnf(c119,plain,
ld(mult(f(X),X),mult(f(X),mult(X,f(X)))) = f(X),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
ld(mult(X,f(X)),mult(f(X),mult(X,f(X)))) = f(X),
inference(transitivity,[status(thm)],[c113,c119]) ).
cnf(c121,plain,
ld(mult(X,f(X)),mult(X,X)) = f(X),
inference(transitivity,[status(thm)],[c111,c120]) ).
cnf(c122,plain,
f(X) = ld(mult(X,f(X)),mult(X,X)),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
ld(ld(X,unit),f(X)) = ld(ld(X,unit),ld(mult(X,f(X)),mult(X,X))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
mult(X,ld(X,f(X))) = f(X),
inference(substitution,[status(thm)],[c99]) ).
cnf(c125,plain,
f(X) = mult(X,ld(X,f(X))),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
ld(mult(X,f(X)),f(X)) = ld(mult(X,f(X)),mult(X,ld(X,f(X)))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
mult(X,f(X)) = mult(f(X),X),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c128,plain,
mult(mult(X,f(X)),ld(X,f(X))) = mult(mult(f(X),X),ld(X,f(X))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
mult(X,mult(ld(X,X12),X)) = mult(X12,X),
inference(substitution,[status(thm)],[c102]) ).
cnf(c130,plain,
mult(X12,X) = mult(X,mult(ld(X,X12),X)),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
mult(mult(X12,X),ld(X,X12)) = mult(mult(X,mult(ld(X,X12),X)),ld(X,X12)),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
mult(unit,mult(X12,mult(X,X12))) = mult(X12,mult(X,X12)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c133,plain,
mult(X12,mult(X,X12)) = mult(unit,mult(X12,mult(X,X12))),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
mult(mult(X12,mult(X,X12)),X) = mult(mult(unit,mult(X12,mult(X,X12))),X),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
mult(mult(unit,mult(X12,mult(X,X12))),X) = mult(mult(unit,X12),mult(X,mult(X12,X))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c136,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c137,plain,
mult(mult(unit,X12),mult(X,mult(X12,X))) = mult(X12,mult(X,mult(X12,X))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
mult(mult(unit,mult(X12,mult(X,X12))),X) = mult(X12,mult(X,mult(X12,X))),
inference(transitivity,[status(thm)],[c135,c137]) ).
cnf(c139,plain,
mult(mult(X12,mult(X,X12)),X) = mult(X12,mult(X,mult(X12,X))),
inference(transitivity,[status(thm)],[c134,c138]) ).
cnf(c140,plain,
mult(mult(X,mult(ld(X,X12),X)),ld(X,X12)) = mult(X,mult(ld(X,X12),mult(X,ld(X,X12)))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
mult(X,ld(X,X12)) = X12,
inference(substitution,[status(thm)],[c99]) ).
cnf(c142,plain,
mult(ld(X,X12),mult(X,ld(X,X12))) = mult(ld(X,X12),X12),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
mult(X,mult(ld(X,X12),mult(X,ld(X,X12)))) = mult(X,mult(ld(X,X12),X12)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
mult(mult(X,mult(ld(X,X12),X)),ld(X,X12)) = mult(X,mult(ld(X,X12),X12)),
inference(transitivity,[status(thm)],[c140,c143]) ).
cnf(c145,plain,
mult(mult(X12,X),ld(X,X12)) = mult(X,mult(ld(X,X12),X12)),
inference(transitivity,[status(thm)],[c131,c144]) ).
cnf(c146,plain,
mult(mult(f(X),X),ld(X,f(X))) = mult(X,mult(ld(X,f(X)),f(X))),
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
ld(X,rd(mult(X,f(X)),X)) = rd(f(X),X),
inference(substitution,[status(thm)],[c23]) ).
cnf(c148,plain,
rd(f(X),X) = ld(X,rd(mult(X,f(X)),X)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
mult(X,f(X)) = mult(f(X),X),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c150,plain,
rd(mult(X,f(X)),X) = rd(mult(f(X),X),X),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
rd(mult(f(X),X),X) = f(X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c152,plain,
rd(mult(X,f(X)),X) = f(X),
inference(transitivity,[status(thm)],[c150,c151]) ).
cnf(c153,plain,
ld(X,rd(mult(X,f(X)),X)) = ld(X,f(X)),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
rd(f(X),X) = ld(X,f(X)),
inference(transitivity,[status(thm)],[c148,c153]) ).
cnf(c155,plain,
ld(X,f(X)) = rd(f(X),X),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
mult(ld(X,f(X)),f(X)) = mult(rd(f(X),X),f(X)),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c158,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
mult(X12,X) = mult(X12,mult(f(X),f(X))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
rd(mult(X12,X),f(X)) = rd(mult(X12,mult(f(X),f(X))),f(X)),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
mult(X12,mult(X,X)) = mult(mult(X12,X),X),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c162,plain,
rd(mult(X12,mult(X,X)),X) = rd(mult(mult(X12,X),X),X),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
rd(mult(mult(X12,X),X),X) = mult(X12,X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c164,plain,
rd(mult(X12,mult(X,X)),X) = mult(X12,X),
inference(transitivity,[status(thm)],[c162,c163]) ).
cnf(c165,plain,
rd(mult(X12,mult(f(X),f(X))),f(X)) = mult(X12,f(X)),
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
rd(mult(X12,X),f(X)) = mult(X12,f(X)),
inference(transitivity,[status(thm)],[c160,c165]) ).
cnf(c167,plain,
rd(mult(rd(X12,X),X),f(X)) = mult(rd(X12,X),f(X)),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
mult(rd(X12,X),f(X)) = rd(mult(rd(X12,X),X),f(X)),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
mult(rd(X12,X),X) = X12,
inference(substitution,[status(thm)],[c14]) ).
cnf(c170,plain,
rd(mult(rd(X12,X),X),f(X)) = rd(X12,f(X)),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
mult(rd(X12,X),f(X)) = rd(X12,f(X)),
inference(transitivity,[status(thm)],[c168,c170]) ).
cnf(c172,plain,
mult(rd(f(X),X),f(X)) = rd(f(X),f(X)),
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
rd(f(X),f(X)) = unit,
inference(substitution,[status(thm)],[c35]) ).
cnf(c174,plain,
mult(rd(f(X),X),f(X)) = unit,
inference(transitivity,[status(thm)],[c172,c173]) ).
cnf(c175,plain,
mult(ld(X,f(X)),f(X)) = unit,
inference(transitivity,[status(thm)],[c156,c174]) ).
cnf(c176,plain,
mult(X,mult(ld(X,f(X)),f(X))) = mult(X,unit),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c26]) ).
cnf(c178,plain,
mult(X,mult(ld(X,f(X)),f(X))) = X,
inference(transitivity,[status(thm)],[c176,c177]) ).
cnf(c179,plain,
mult(mult(f(X),X),ld(X,f(X))) = X,
inference(transitivity,[status(thm)],[c146,c178]) ).
cnf(c180,plain,
mult(mult(X,f(X)),ld(X,f(X))) = X,
inference(transitivity,[status(thm)],[c128,c179]) ).
cnf(c181,plain,
X = mult(mult(X,f(X)),ld(X,f(X))),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
ld(mult(X,f(X)),X) = ld(mult(X,f(X)),mult(mult(X,f(X)),ld(X,f(X)))),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
ld(mult(X,f(X)),mult(mult(X,f(X)),ld(X,f(X)))) = ld(X,f(X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c184,plain,
ld(mult(X,f(X)),X) = ld(X,f(X)),
inference(transitivity,[status(thm)],[c182,c183]) ).
cnf(c185,plain,
ld(X,f(X)) = ld(mult(X,f(X)),X),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
mult(X,ld(X,f(X))) = mult(X,ld(mult(X,f(X)),X)),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
ld(mult(X,f(X)),mult(X,ld(X,f(X)))) = ld(mult(X,f(X)),mult(X,ld(mult(X,f(X)),X))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
ld(X12,mult(X12,mult(ld(X12,X),ld(X12,X)))) = mult(ld(X12,X),ld(X12,X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c189,plain,
mult(ld(X12,X),ld(X12,X)) = ld(X12,mult(X12,mult(ld(X12,X),ld(X12,X)))),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
mult(mult(X12,ld(X12,X)),ld(X12,X)) = mult(X12,mult(ld(X12,X),ld(X12,X))),
inference(substitution,[status(thm)],[c76]) ).
cnf(c191,plain,
mult(X12,mult(ld(X12,X),ld(X12,X))) = mult(mult(X12,ld(X12,X)),ld(X12,X)),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
mult(X12,ld(X12,X)) = X,
inference(substitution,[status(thm)],[c99]) ).
cnf(c193,plain,
mult(mult(X12,ld(X12,X)),ld(X12,X)) = mult(X,ld(X12,X)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
mult(X12,mult(ld(X12,X),ld(X12,X))) = mult(X,ld(X12,X)),
inference(transitivity,[status(thm)],[c191,c193]) ).
cnf(c195,plain,
ld(X12,mult(X12,mult(ld(X12,X),ld(X12,X)))) = ld(X12,mult(X,ld(X12,X))),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
mult(ld(X12,X),ld(X12,X)) = ld(X12,mult(X,ld(X12,X))),
inference(transitivity,[status(thm)],[c189,c195]) ).
cnf(c197,plain,
mult(ld(mult(X,f(X)),X),ld(mult(X,f(X)),X)) = ld(mult(X,f(X)),mult(X,ld(mult(X,f(X)),X))),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
ld(mult(X,f(X)),mult(X,ld(mult(X,f(X)),X))) = mult(ld(mult(X,f(X)),X),ld(mult(X,f(X)),X)),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
mult(ld(mult(X,f(X)),X),ld(mult(X,f(X)),X)) = mult(ld(X,f(X)),ld(mult(X,f(X)),X)),
inference(congruence,[status(thm)],[c184]) ).
cnf(c200,plain,
mult(ld(X,f(X)),ld(mult(X,f(X)),X)) = mult(ld(X,f(X)),ld(X,f(X))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c201,plain,
mult(mult(rd(X12,X),X),X) = mult(rd(X12,X),mult(X,X)),
inference(substitution,[status(thm)],[c76]) ).
cnf(c202,plain,
mult(rd(X12,X),mult(X,X)) = mult(mult(rd(X12,X),X),X),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
mult(rd(X12,X),X) = X12,
inference(substitution,[status(thm)],[c14]) ).
cnf(c204,plain,
mult(mult(rd(X12,X),X),X) = mult(X12,X),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
mult(rd(X12,X),mult(X,X)) = mult(X12,X),
inference(transitivity,[status(thm)],[c202,c204]) ).
cnf(c206,plain,
mult(X12,X) = mult(rd(X12,X),mult(X,X)),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
ld(rd(X12,X),mult(X12,X)) = ld(rd(X12,X),mult(rd(X12,X),mult(X,X))),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
ld(rd(X12,X),mult(rd(X12,X),mult(X,X))) = mult(X,X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c209,plain,
ld(rd(X12,X),mult(X12,X)) = mult(X,X),
inference(transitivity,[status(thm)],[c207,c208]) ).
cnf(c210,plain,
ld(rd(f(X),ld(X,f(X))),mult(f(X),ld(X,f(X)))) = mult(ld(X,f(X)),ld(X,f(X))),
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
mult(ld(X,f(X)),ld(X,f(X))) = ld(rd(f(X),ld(X,f(X))),mult(f(X),ld(X,f(X)))),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
ld(X,f(X)) = rd(f(X),X),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c213,plain,
mult(f(X),ld(X,f(X))) = mult(f(X),rd(f(X),X)),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
mult(X,rd(X12,X)) = rd(mult(X,X12),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c215,plain,
rd(mult(X,X12),X) = mult(X,rd(X12,X)),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
mult(rd(X12,X),rd(mult(X,X12),X)) = mult(rd(X12,X),mult(X,rd(X12,X))),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
mult(mult(rd(X12,X),X),rd(X12,X)) = mult(rd(X12,X),mult(X,rd(X12,X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c218,plain,
mult(rd(X12,X),mult(X,rd(X12,X))) = mult(mult(rd(X12,X),X),rd(X12,X)),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
mult(rd(X12,X),X) = X12,
inference(substitution,[status(thm)],[c14]) ).
cnf(c220,plain,
mult(mult(rd(X12,X),X),rd(X12,X)) = mult(X12,rd(X12,X)),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
mult(rd(X12,X),mult(X,rd(X12,X))) = mult(X12,rd(X12,X)),
inference(transitivity,[status(thm)],[c218,c220]) ).
cnf(c222,plain,
mult(rd(X12,X),rd(mult(X,X12),X)) = mult(X12,rd(X12,X)),
inference(transitivity,[status(thm)],[c216,c221]) ).
cnf(c223,plain,
mult(rd(f(X),X),rd(mult(X,f(X)),X)) = mult(f(X),rd(f(X),X)),
inference(substitution,[status(thm)],[c222]) ).
cnf(c224,plain,
mult(f(X),rd(f(X),X)) = mult(rd(f(X),X),rd(mult(X,f(X)),X)),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
mult(rd(f(X),X),rd(mult(X,f(X)),X)) = mult(rd(f(X),X),f(X)),
inference(congruence,[status(thm)],[c152]) ).
cnf(c226,plain,
mult(rd(f(X),X),f(X)) = rd(f(X),f(X)),
inference(substitution,[status(thm)],[c171]) ).
cnf(c227,plain,
rd(f(X),f(X)) = unit,
inference(substitution,[status(thm)],[c35]) ).
cnf(c228,plain,
mult(rd(f(X),X),f(X)) = unit,
inference(transitivity,[status(thm)],[c226,c227]) ).
cnf(c229,plain,
mult(rd(f(X),X),rd(mult(X,f(X)),X)) = unit,
inference(transitivity,[status(thm)],[c225,c228]) ).
cnf(c230,plain,
mult(f(X),rd(f(X),X)) = unit,
inference(transitivity,[status(thm)],[c224,c229]) ).
cnf(c231,plain,
mult(f(X),ld(X,f(X))) = unit,
inference(transitivity,[status(thm)],[c213,c230]) ).
cnf(c232,plain,
ld(rd(f(X),ld(X,f(X))),mult(f(X),ld(X,f(X)))) = ld(rd(f(X),ld(X,f(X))),unit),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
mult(X,ld(X,X12)) = X12,
inference(substitution,[status(thm)],[c99]) ).
cnf(c234,plain,
X12 = mult(X,ld(X,X12)),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
rd(X12,ld(X,X12)) = rd(mult(X,ld(X,X12)),ld(X,X12)),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
rd(mult(X,ld(X,X12)),ld(X,X12)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c237,plain,
rd(X12,ld(X,X12)) = X,
inference(transitivity,[status(thm)],[c235,c236]) ).
cnf(c238,plain,
rd(f(X),ld(X,f(X))) = X,
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
ld(rd(f(X),ld(X,f(X))),unit) = ld(X,unit),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
ld(rd(f(X),ld(X,f(X))),mult(f(X),ld(X,f(X)))) = ld(X,unit),
inference(transitivity,[status(thm)],[c232,c239]) ).
cnf(c241,plain,
mult(ld(X,f(X)),ld(X,f(X))) = ld(X,unit),
inference(transitivity,[status(thm)],[c211,c240]) ).
cnf(c242,plain,
mult(ld(X,f(X)),ld(mult(X,f(X)),X)) = ld(X,unit),
inference(transitivity,[status(thm)],[c200,c241]) ).
cnf(c243,plain,
mult(ld(mult(X,f(X)),X),ld(mult(X,f(X)),X)) = ld(X,unit),
inference(transitivity,[status(thm)],[c199,c242]) ).
cnf(c244,plain,
ld(mult(X,f(X)),mult(X,ld(mult(X,f(X)),X))) = ld(X,unit),
inference(transitivity,[status(thm)],[c198,c243]) ).
cnf(c245,plain,
ld(mult(X,f(X)),mult(X,ld(X,f(X)))) = ld(X,unit),
inference(transitivity,[status(thm)],[c187,c244]) ).
cnf(c246,plain,
ld(mult(X,f(X)),f(X)) = ld(X,unit),
inference(transitivity,[status(thm)],[c126,c245]) ).
cnf(c247,plain,
ld(X,unit) = ld(mult(X,f(X)),f(X)),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
ld(ld(X,unit),ld(mult(X,f(X)),mult(X,X))) = ld(ld(mult(X,f(X)),f(X)),ld(mult(X,f(X)),mult(X,X))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
mult(X,X) = mult(f(X),mult(X,f(X))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c250,plain,
ld(mult(X,f(X)),mult(X,X)) = ld(mult(X,f(X)),mult(f(X),mult(X,f(X)))),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
ld(ld(mult(X,f(X)),f(X)),ld(mult(X,f(X)),mult(X,X))) = ld(ld(mult(X,f(X)),f(X)),ld(mult(X,f(X)),mult(f(X),mult(X,f(X))))),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
ld(X12,mult(X12,mult(ld(X12,X),X12))) = mult(ld(X12,X),X12),
inference(substitution,[status(thm)],[c21]) ).
cnf(c253,plain,
mult(ld(X12,X),X12) = ld(X12,mult(X12,mult(ld(X12,X),X12))),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
ld(X12,mult(X12,mult(ld(X12,X),X12))) = ld(X12,mult(X,X12)),
inference(congruence,[status(thm)],[c102]) ).
cnf(c255,plain,
mult(ld(X12,X),X12) = ld(X12,mult(X,X12)),
inference(transitivity,[status(thm)],[c253,c254]) ).
cnf(c256,plain,
ld(X12,mult(X,X12)) = mult(ld(X12,X),X12),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c257,plain,
ld(ld(X12,X),ld(X12,mult(X,X12))) = ld(ld(X12,X),mult(ld(X12,X),X12)),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
ld(ld(X12,X),mult(ld(X12,X),X12)) = X12,
inference(substitution,[status(thm)],[c21]) ).
cnf(c259,plain,
ld(ld(X12,X),ld(X12,mult(X,X12))) = X12,
inference(transitivity,[status(thm)],[c257,c258]) ).
cnf(c260,plain,
ld(ld(mult(X,f(X)),f(X)),ld(mult(X,f(X)),mult(f(X),mult(X,f(X))))) = mult(X,f(X)),
inference(substitution,[status(thm)],[c259]) ).
cnf(c261,plain,
ld(ld(mult(X,f(X)),f(X)),ld(mult(X,f(X)),mult(X,X))) = mult(X,f(X)),
inference(transitivity,[status(thm)],[c251,c260]) ).
cnf(c262,plain,
ld(ld(X,unit),ld(mult(X,f(X)),mult(X,X))) = mult(X,f(X)),
inference(transitivity,[status(thm)],[c248,c261]) ).
cnf(c263,plain,
ld(ld(X,unit),f(X)) = mult(X,f(X)),
inference(transitivity,[status(thm)],[c123,c262]) ).
cnf(c264,plain,
mult(X,f(X)) = ld(ld(X,unit),f(X)),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
mult(mult(X,f(X)),f(X)) = mult(ld(ld(X,unit),f(X)),f(X)),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
mult(X12,mult(mult(X,f(X)),f(X))) = mult(X12,mult(ld(ld(X,unit),f(X)),f(X))),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
mult(mult(X12,mult(mult(X,f(X)),f(X))),ld(X,unit)) = mult(mult(X12,mult(ld(ld(X,unit),f(X)),f(X))),ld(X,unit)),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
X12 = ld(ld(X12,X),ld(X12,mult(X,X12))),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c269,plain,
mult(mult(X13,mult(ld(X12,X),X)),X12) = mult(mult(X13,mult(ld(X12,X),X)),ld(ld(X12,X),ld(X12,mult(X,X12)))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
rd(mult(X,X12),X12) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c271,plain,
X = rd(mult(X,X12),X12),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
ld(X12,X) = ld(X12,rd(mult(X,X12),X12)),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
mult(ld(X12,mult(X,X12)),ld(X12,X)) = mult(ld(X12,mult(X,X12)),ld(X12,rd(mult(X,X12),X12))),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
ld(X12,rd(mult(X12,ld(X12,X)),X12)) = rd(ld(X12,X),X12),
inference(substitution,[status(thm)],[c23]) ).
cnf(c275,plain,
rd(ld(X12,X),X12) = ld(X12,rd(mult(X12,ld(X12,X)),X12)),
inference(symmetry,[status(thm)],[c274]) ).
cnf(c276,plain,
mult(X12,ld(X12,X)) = X,
inference(substitution,[status(thm)],[c99]) ).
cnf(c277,plain,
rd(mult(X12,ld(X12,X)),X12) = rd(X,X12),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
ld(X12,rd(mult(X12,ld(X12,X)),X12)) = ld(X12,rd(X,X12)),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
rd(ld(X12,X),X12) = ld(X12,rd(X,X12)),
inference(transitivity,[status(thm)],[c275,c278]) ).
cnf(c280,plain,
rd(ld(X12,mult(X,X12)),X12) = ld(X12,rd(mult(X,X12),X12)),
inference(substitution,[status(thm)],[c279]) ).
cnf(c281,plain,
ld(X12,rd(mult(X,X12),X12)) = rd(ld(X12,mult(X,X12)),X12),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,plain,
mult(ld(X12,mult(X,X12)),ld(X12,rd(mult(X,X12),X12))) = mult(ld(X12,mult(X,X12)),rd(ld(X12,mult(X,X12)),X12)),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
ld(X12,mult(X,X12)) = mult(ld(X12,X),X12),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c284,plain,
mult(ld(X12,mult(X,X12)),rd(ld(X12,mult(X,X12)),X12)) = mult(mult(ld(X12,X),X12),rd(ld(X12,mult(X,X12)),X12)),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
ld(X12,mult(X,X12)) = mult(ld(X12,X),X12),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c286,plain,
rd(ld(X12,mult(X,X12)),X12) = rd(mult(ld(X12,X),X12),X12),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
mult(mult(ld(X12,X),X12),rd(ld(X12,mult(X,X12)),X12)) = mult(mult(ld(X12,X),X12),rd(mult(ld(X12,X),X12),X12)),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
mult(rd(mult(ld(X12,X),X12),X12),rd(mult(X12,mult(ld(X12,X),X12)),X12)) = mult(mult(ld(X12,X),X12),rd(mult(ld(X12,X),X12),X12)),
inference(substitution,[status(thm)],[c222]) ).
cnf(c289,plain,
mult(mult(ld(X12,X),X12),rd(mult(ld(X12,X),X12),X12)) = mult(rd(mult(ld(X12,X),X12),X12),rd(mult(X12,mult(ld(X12,X),X12)),X12)),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
rd(mult(X12,mult(ld(X12,X),X12)),X12) = rd(mult(X,X12),X12),
inference(congruence,[status(thm)],[c102]) ).
cnf(c291,plain,
mult(rd(mult(ld(X12,X),X12),X12),rd(mult(X12,mult(ld(X12,X),X12)),X12)) = mult(rd(mult(ld(X12,X),X12),X12),rd(mult(X,X12),X12)),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
rd(mult(ld(X12,X),X12),X12) = ld(X12,X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c293,plain,
mult(rd(mult(ld(X12,X),X12),X12),rd(mult(X,X12),X12)) = mult(ld(X12,X),rd(mult(X,X12),X12)),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
rd(mult(X,X12),X12) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c295,plain,
mult(ld(X12,X),rd(mult(X,X12),X12)) = mult(ld(X12,X),X),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
mult(rd(mult(ld(X12,X),X12),X12),rd(mult(X,X12),X12)) = mult(ld(X12,X),X),
inference(transitivity,[status(thm)],[c293,c295]) ).
cnf(c297,plain,
mult(rd(mult(ld(X12,X),X12),X12),rd(mult(X12,mult(ld(X12,X),X12)),X12)) = mult(ld(X12,X),X),
inference(transitivity,[status(thm)],[c291,c296]) ).
cnf(c298,plain,
mult(mult(ld(X12,X),X12),rd(mult(ld(X12,X),X12),X12)) = mult(ld(X12,X),X),
inference(transitivity,[status(thm)],[c289,c297]) ).
cnf(c299,plain,
mult(mult(ld(X12,X),X12),rd(ld(X12,mult(X,X12)),X12)) = mult(ld(X12,X),X),
inference(transitivity,[status(thm)],[c287,c298]) ).
cnf(c300,plain,
mult(ld(X12,mult(X,X12)),rd(ld(X12,mult(X,X12)),X12)) = mult(ld(X12,X),X),
inference(transitivity,[status(thm)],[c284,c299]) ).
cnf(c301,plain,
mult(ld(X12,mult(X,X12)),ld(X12,rd(mult(X,X12),X12))) = mult(ld(X12,X),X),
inference(transitivity,[status(thm)],[c282,c300]) ).
cnf(c302,plain,
mult(ld(X12,mult(X,X12)),ld(X12,X)) = mult(ld(X12,X),X),
inference(transitivity,[status(thm)],[c273,c301]) ).
cnf(c303,plain,
mult(ld(X12,X),X) = mult(ld(X12,mult(X,X12)),ld(X12,X)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
mult(X13,mult(ld(X12,X),X)) = mult(X13,mult(ld(X12,mult(X,X12)),ld(X12,X))),
inference(congruence,[status(thm)],[c303]) ).
cnf(c305,plain,
mult(mult(X13,mult(ld(X12,X),X)),ld(ld(X12,X),ld(X12,mult(X,X12)))) = mult(mult(X13,mult(ld(X12,mult(X,X12)),ld(X12,X))),ld(ld(X12,X),ld(X12,mult(X,X12)))),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
mult(X,mult(ld(X,X12),X)) = mult(X12,X),
inference(substitution,[status(thm)],[c102]) ).
cnf(c307,plain,
mult(X12,X) = mult(X,mult(ld(X,X12),X)),
inference(symmetry,[status(thm)],[c306]) ).
cnf(c308,plain,
mult(X13,mult(X12,X)) = mult(X13,mult(X,mult(ld(X,X12),X))),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
mult(mult(X13,mult(X12,X)),ld(X,X12)) = mult(mult(X13,mult(X,mult(ld(X,X12),X))),ld(X,X12)),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
mult(mult(X13,mult(X,mult(ld(X,X12),X))),ld(X,X12)) = mult(mult(X13,X),mult(ld(X,X12),mult(X,ld(X,X12)))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c311,plain,
mult(X,ld(X,X12)) = X12,
inference(substitution,[status(thm)],[c99]) ).
cnf(c312,plain,
mult(ld(X,X12),mult(X,ld(X,X12))) = mult(ld(X,X12),X12),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
mult(mult(X13,X),mult(ld(X,X12),mult(X,ld(X,X12)))) = mult(mult(X13,X),mult(ld(X,X12),X12)),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
mult(mult(X13,mult(X,mult(ld(X,X12),X))),ld(X,X12)) = mult(mult(X13,X),mult(ld(X,X12),X12)),
inference(transitivity,[status(thm)],[c310,c313]) ).
cnf(c315,plain,
mult(mult(X13,mult(X12,X)),ld(X,X12)) = mult(mult(X13,X),mult(ld(X,X12),X12)),
inference(transitivity,[status(thm)],[c309,c314]) ).
cnf(c316,plain,
mult(mult(X13,mult(ld(X12,mult(X,X12)),ld(X12,X))),ld(ld(X12,X),ld(X12,mult(X,X12)))) = mult(mult(X13,ld(X12,X)),mult(ld(ld(X12,X),ld(X12,mult(X,X12))),ld(X12,mult(X,X12)))),
inference(substitution,[status(thm)],[c315]) ).
cnf(c317,plain,
mult(ld(ld(X12,X),ld(X12,mult(X,X12))),ld(X12,mult(X,X12))) = mult(X12,ld(X12,mult(X,X12))),
inference(congruence,[status(thm)],[c259]) ).
cnf(c318,plain,
mult(mult(X13,ld(X12,X)),mult(ld(ld(X12,X),ld(X12,mult(X,X12))),ld(X12,mult(X,X12)))) = mult(mult(X13,ld(X12,X)),mult(X12,ld(X12,mult(X,X12)))),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
mult(X12,ld(X12,mult(X,X12))) = mult(X,X12),
inference(substitution,[status(thm)],[c99]) ).
cnf(c320,plain,
mult(mult(X13,ld(X12,X)),mult(X12,ld(X12,mult(X,X12)))) = mult(mult(X13,ld(X12,X)),mult(X,X12)),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
mult(mult(X13,ld(X12,X)),mult(ld(ld(X12,X),ld(X12,mult(X,X12))),ld(X12,mult(X,X12)))) = mult(mult(X13,ld(X12,X)),mult(X,X12)),
inference(transitivity,[status(thm)],[c318,c320]) ).
cnf(c322,plain,
mult(mult(X13,mult(ld(X12,mult(X,X12)),ld(X12,X))),ld(ld(X12,X),ld(X12,mult(X,X12)))) = mult(mult(X13,ld(X12,X)),mult(X,X12)),
inference(transitivity,[status(thm)],[c316,c321]) ).
cnf(c323,plain,
mult(mult(X13,mult(ld(X12,X),X)),ld(ld(X12,X),ld(X12,mult(X,X12)))) = mult(mult(X13,ld(X12,X)),mult(X,X12)),
inference(transitivity,[status(thm)],[c305,c322]) ).
cnf(c324,plain,
mult(mult(X13,mult(ld(X12,X),X)),X12) = mult(mult(X13,ld(X12,X)),mult(X,X12)),
inference(transitivity,[status(thm)],[c269,c323]) ).
cnf(c325,plain,
mult(mult(X12,mult(ld(ld(X,unit),f(X)),f(X))),ld(X,unit)) = mult(mult(X12,ld(ld(X,unit),f(X))),mult(f(X),ld(X,unit))),
inference(substitution,[status(thm)],[c324]) ).
cnf(c326,plain,
mult(X12,ld(ld(X,unit),f(X))) = mult(X12,mult(X,f(X))),
inference(congruence,[status(thm)],[c263]) ).
cnf(c327,plain,
mult(mult(X12,ld(ld(X,unit),f(X))),mult(f(X),ld(X,unit))) = mult(mult(X12,mult(X,f(X))),mult(f(X),ld(X,unit))),
inference(congruence,[status(thm)],[c326]) ).
cnf(c328,plain,
ld(X,unit) = mult(ld(X,f(X)),ld(X,f(X))),
inference(symmetry,[status(thm)],[c241]) ).
cnf(c329,plain,
mult(f(X),ld(X,unit)) = mult(f(X),mult(ld(X,f(X)),ld(X,f(X)))),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c331,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c330]) ).
cnf(c332,plain,
ld(unit,X) = ld(unit,mult(unit,X)),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
ld(unit,mult(unit,X)) = X,
inference(substitution,[status(thm)],[c21]) ).
cnf(c334,plain,
ld(unit,X) = X,
inference(transitivity,[status(thm)],[c332,c333]) ).
cnf(c335,plain,
ld(unit,mult(f(X),mult(ld(X,f(X)),ld(X,f(X))))) = mult(f(X),mult(ld(X,f(X)),ld(X,f(X)))),
inference(substitution,[status(thm)],[c334]) ).
cnf(c336,plain,
mult(f(X),mult(ld(X,f(X)),ld(X,f(X)))) = ld(unit,mult(f(X),mult(ld(X,f(X)),ld(X,f(X))))),
inference(symmetry,[status(thm)],[c335]) ).
cnf(c337,plain,
unit = mult(f(X),ld(X,f(X))),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c338,plain,
ld(unit,mult(f(X),mult(ld(X,f(X)),ld(X,f(X))))) = ld(mult(f(X),ld(X,f(X))),mult(f(X),mult(ld(X,f(X)),ld(X,f(X))))),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
mult(X12,mult(X,X)) = mult(mult(X12,X),X),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c340,plain,
ld(mult(X12,X),mult(X12,mult(X,X))) = ld(mult(X12,X),mult(mult(X12,X),X)),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
ld(mult(X12,X),mult(mult(X12,X),X)) = X,
inference(substitution,[status(thm)],[c21]) ).
cnf(c342,plain,
ld(mult(X12,X),mult(X12,mult(X,X))) = X,
inference(transitivity,[status(thm)],[c340,c341]) ).
cnf(c343,plain,
ld(mult(f(X),ld(X,f(X))),mult(f(X),mult(ld(X,f(X)),ld(X,f(X))))) = ld(X,f(X)),
inference(substitution,[status(thm)],[c342]) ).
cnf(c344,plain,
ld(unit,mult(f(X),mult(ld(X,f(X)),ld(X,f(X))))) = ld(X,f(X)),
inference(transitivity,[status(thm)],[c338,c343]) ).
cnf(c345,plain,
mult(f(X),mult(ld(X,f(X)),ld(X,f(X)))) = ld(X,f(X)),
inference(transitivity,[status(thm)],[c336,c344]) ).
cnf(c346,plain,
mult(f(X),ld(X,unit)) = ld(X,f(X)),
inference(transitivity,[status(thm)],[c329,c345]) ).
cnf(c347,plain,
mult(mult(X12,mult(X,f(X))),mult(f(X),ld(X,unit))) = mult(mult(X12,mult(X,f(X))),ld(X,f(X))),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
mult(X,f(X)) = mult(f(X),X),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c349,plain,
mult(X12,mult(X,f(X))) = mult(X12,mult(f(X),X)),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
mult(mult(X12,mult(X,f(X))),ld(X,f(X))) = mult(mult(X12,mult(f(X),X)),ld(X,f(X))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
mult(mult(X12,mult(f(X),X)),ld(X,f(X))) = mult(mult(X12,X),mult(ld(X,f(X)),f(X))),
inference(substitution,[status(thm)],[c315]) ).
cnf(c352,plain,
mult(mult(X12,X),mult(ld(X,f(X)),f(X))) = mult(mult(X12,X),unit),
inference(congruence,[status(thm)],[c175]) ).
cnf(c353,plain,
mult(mult(X12,X),unit) = mult(X12,X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c354,plain,
mult(mult(X12,X),mult(ld(X,f(X)),f(X))) = mult(X12,X),
inference(transitivity,[status(thm)],[c352,c353]) ).
cnf(c355,plain,
mult(mult(X12,mult(f(X),X)),ld(X,f(X))) = mult(X12,X),
inference(transitivity,[status(thm)],[c351,c354]) ).
cnf(c356,plain,
mult(mult(X12,mult(X,f(X))),ld(X,f(X))) = mult(X12,X),
inference(transitivity,[status(thm)],[c350,c355]) ).
cnf(c357,plain,
mult(mult(X12,mult(X,f(X))),mult(f(X),ld(X,unit))) = mult(X12,X),
inference(transitivity,[status(thm)],[c347,c356]) ).
cnf(c358,plain,
mult(mult(X12,ld(ld(X,unit),f(X))),mult(f(X),ld(X,unit))) = mult(X12,X),
inference(transitivity,[status(thm)],[c327,c357]) ).
cnf(c359,plain,
mult(mult(X12,mult(ld(ld(X,unit),f(X)),f(X))),ld(X,unit)) = mult(X12,X),
inference(transitivity,[status(thm)],[c325,c358]) ).
cnf(c360,plain,
mult(mult(X12,mult(mult(X,f(X)),f(X))),ld(X,unit)) = mult(X12,X),
inference(transitivity,[status(thm)],[c267,c359]) ).
cnf(c361,plain,
mult(mult(X12,mult(X,mult(f(X),f(X)))),ld(X,unit)) = mult(X12,X),
inference(transitivity,[status(thm)],[c80,c360]) ).
cnf(c362,plain,
mult(mult(X12,mult(X,X)),ld(X,unit)) = mult(X12,X),
inference(transitivity,[status(thm)],[c49,c361]) ).
cnf(c363,plain,
mult(mult(rd(X12,mult(X,X)),mult(X,X)),ld(X,unit)) = mult(rd(X12,mult(X,X)),X),
inference(substitution,[status(thm)],[c362]) ).
cnf(c364,plain,
rd(mult(rd(X12,mult(X,X)),mult(X,X)),X) = mult(rd(X12,mult(X,X)),X),
inference(substitution,[status(thm)],[c164]) ).
cnf(c365,plain,
mult(rd(X12,mult(X,X)),X) = rd(mult(rd(X12,mult(X,X)),mult(X,X)),X),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
mult(rd(X12,mult(X,X)),mult(X,X)) = X12,
inference(substitution,[status(thm)],[c14]) ).
cnf(c367,plain,
rd(mult(rd(X12,mult(X,X)),mult(X,X)),X) = rd(X12,X),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
mult(rd(X12,mult(X,X)),X) = rd(X12,X),
inference(transitivity,[status(thm)],[c365,c367]) ).
cnf(c369,plain,
mult(mult(rd(X12,mult(X,X)),mult(X,X)),ld(X,unit)) = rd(X12,X),
inference(transitivity,[status(thm)],[c363,c368]) ).
cnf(c370,plain,
mult(X12,ld(X,unit)) = rd(X12,X),
inference(transitivity,[status(thm)],[c43,c369]) ).
cnf(c371,plain,
mult(X12,ld(rd(unit,X),unit)) = rd(X12,rd(unit,X)),
inference(substitution,[status(thm)],[c370]) ).
cnf(c372,plain,
rd(X12,rd(unit,X)) = mult(X12,ld(rd(unit,X),unit)),
inference(symmetry,[status(thm)],[c371]) ).
cnf(c373,plain,
mult(rd(X12,X),X) = X12,
inference(substitution,[status(thm)],[c14]) ).
cnf(c374,plain,
X12 = mult(rd(X12,X),X),
inference(symmetry,[status(thm)],[c373]) ).
cnf(c375,plain,
ld(rd(X12,X),X12) = ld(rd(X12,X),mult(rd(X12,X),X)),
inference(congruence,[status(thm)],[c374]) ).
cnf(c376,plain,
ld(rd(X12,X),mult(rd(X12,X),X)) = X,
inference(substitution,[status(thm)],[c21]) ).
cnf(c377,plain,
ld(rd(X12,X),X12) = X,
inference(transitivity,[status(thm)],[c375,c376]) ).
cnf(c378,plain,
ld(rd(unit,X),unit) = X,
inference(substitution,[status(thm)],[c377]) ).
cnf(c379,plain,
mult(X12,ld(rd(unit,X),unit)) = mult(X12,X),
inference(congruence,[status(thm)],[c378]) ).
cnf(c380,plain,
rd(X12,rd(unit,X)) = mult(X12,X),
inference(transitivity,[status(thm)],[c372,c379]) ).
cnf(c381,plain,
rd(X12,ld(X,unit)) = mult(X12,X),
inference(transitivity,[status(thm)],[c40,c380]) ).
cnf(c382,plain,
rd(mult(mult(X13,X12),X),ld(X12,unit)) = mult(mult(mult(X13,X12),X),X12),
inference(substitution,[status(thm)],[c381]) ).
cnf(c383,plain,
mult(mult(mult(X13,X12),X),X12) = rd(mult(mult(X13,X12),X),ld(X12,unit)),
inference(symmetry,[status(thm)],[c382]) ).
cnf(c384,plain,
ld(X12,mult(X12,X)) = X,
inference(substitution,[status(thm)],[c21]) ).
cnf(c385,plain,
X = ld(X12,mult(X12,X)),
inference(symmetry,[status(thm)],[c384]) ).
cnf(c386,plain,
rd(mult(X12,mult(X12,X)),X) = rd(mult(X12,mult(X12,X)),ld(X12,mult(X12,X))),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
ld(mult(X12,X),rd(mult(X12,mult(X12,X)),X)) = ld(mult(X12,X),rd(mult(X12,mult(X12,X)),ld(X12,mult(X12,X)))),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
mult(X,ld(X,X12)) = X12,
inference(substitution,[status(thm)],[c99]) ).
cnf(c389,plain,
X12 = mult(X,ld(X,X12)),
inference(symmetry,[status(thm)],[c388]) ).
cnf(c390,plain,
mult(X12,ld(ld(X,X12),X)) = mult(mult(X,ld(X,X12)),ld(ld(X,X12),X)),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
mult(mult(X,ld(X,X12)),ld(ld(X,X12),X)) = mult(ld(X,X12),mult(ld(ld(X,X12),X),X)),
inference(substitution,[status(thm)],[c145]) ).
cnf(c392,plain,
rd(ld(X12,mult(X,mult(X,X12))),X12) = ld(X12,rd(mult(X,mult(X,X12)),X12)),
inference(substitution,[status(thm)],[c279]) ).
cnf(c393,plain,
ld(X12,rd(mult(X,mult(X,X12)),X12)) = rd(ld(X12,mult(X,mult(X,X12))),X12),
inference(symmetry,[status(thm)],[c392]) ).
cnf(c394,plain,
ld(X12,mult(X12,mult(ld(X12,X),mult(X,X12)))) = mult(ld(X12,X),mult(X,X12)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c395,plain,
mult(ld(X12,X),mult(X,X12)) = ld(X12,mult(X12,mult(ld(X12,X),mult(X,X12)))),
inference(symmetry,[status(thm)],[c394]) ).
cnf(c396,plain,
mult(X,X12) = mult(X12,mult(ld(X12,X),X12)),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c397,plain,
mult(ld(X12,X),mult(X,X12)) = mult(ld(X12,X),mult(X12,mult(ld(X12,X),X12))),
inference(congruence,[status(thm)],[c396]) ).
cnf(c398,plain,
mult(X12,mult(ld(X12,X),mult(X,X12))) = mult(X12,mult(ld(X12,X),mult(X12,mult(ld(X12,X),X12)))),
inference(congruence,[status(thm)],[c397]) ).
cnf(c399,plain,
mult(mult(X12,mult(X,mult(X12,X))),X12) = mult(mult(X12,X),mult(X12,mult(X,X12))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c400,plain,
mult(mult(X12,X),mult(X12,mult(X,X12))) = mult(mult(X12,mult(X,mult(X12,X))),X12),
inference(symmetry,[status(thm)],[c399]) ).
cnf(c401,plain,
mult(mult(X12,mult(X,mult(X12,X))),X12) = mult(X12,mult(mult(X,mult(X12,X)),X12)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c402,plain,
mult(mult(X,mult(X12,X)),X12) = mult(X,mult(X12,mult(X,X12))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c403,plain,
mult(X12,mult(mult(X,mult(X12,X)),X12)) = mult(X12,mult(X,mult(X12,mult(X,X12)))),
inference(congruence,[status(thm)],[c402]) ).
cnf(c404,plain,
mult(mult(X12,mult(X,mult(X12,X))),X12) = mult(X12,mult(X,mult(X12,mult(X,X12)))),
inference(transitivity,[status(thm)],[c401,c403]) ).
cnf(c405,plain,
mult(mult(X12,X),mult(X12,mult(X,X12))) = mult(X12,mult(X,mult(X12,mult(X,X12)))),
inference(transitivity,[status(thm)],[c400,c404]) ).
cnf(c406,plain,
mult(mult(X12,ld(X12,X)),mult(X12,mult(ld(X12,X),X12))) = mult(X12,mult(ld(X12,X),mult(X12,mult(ld(X12,X),X12)))),
inference(substitution,[status(thm)],[c405]) ).
cnf(c407,plain,
mult(X12,mult(ld(X12,X),mult(X12,mult(ld(X12,X),X12)))) = mult(mult(X12,ld(X12,X)),mult(X12,mult(ld(X12,X),X12))),
inference(symmetry,[status(thm)],[c406]) ).
cnf(c408,plain,
mult(X12,ld(X12,X)) = X,
inference(substitution,[status(thm)],[c99]) ).
cnf(c409,plain,
mult(mult(X12,ld(X12,X)),mult(X12,mult(ld(X12,X),X12))) = mult(X,mult(X12,mult(ld(X12,X),X12))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
mult(X,mult(X12,mult(ld(X12,X),X12))) = mult(X,mult(X,X12)),
inference(congruence,[status(thm)],[c102]) ).
cnf(c411,plain,
mult(mult(X12,ld(X12,X)),mult(X12,mult(ld(X12,X),X12))) = mult(X,mult(X,X12)),
inference(transitivity,[status(thm)],[c409,c410]) ).
cnf(c412,plain,
mult(X12,mult(ld(X12,X),mult(X12,mult(ld(X12,X),X12)))) = mult(X,mult(X,X12)),
inference(transitivity,[status(thm)],[c407,c411]) ).
cnf(c413,plain,
mult(X12,mult(ld(X12,X),mult(X,X12))) = mult(X,mult(X,X12)),
inference(transitivity,[status(thm)],[c398,c412]) ).
cnf(c414,plain,
ld(X12,mult(X12,mult(ld(X12,X),mult(X,X12)))) = ld(X12,mult(X,mult(X,X12))),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
mult(ld(X12,X),mult(X,X12)) = ld(X12,mult(X,mult(X,X12))),
inference(transitivity,[status(thm)],[c395,c414]) ).
cnf(c416,plain,
ld(X12,mult(X,mult(X,X12))) = mult(ld(X12,X),mult(X,X12)),
inference(symmetry,[status(thm)],[c415]) ).
cnf(c417,plain,
rd(ld(X12,mult(X,mult(X,X12))),X12) = rd(mult(ld(X12,X),mult(X,X12)),X12),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
mult(X12,ld(X12,X)) = X,
inference(substitution,[status(thm)],[c99]) ).
cnf(c419,plain,
X = mult(X12,ld(X12,X)),
inference(symmetry,[status(thm)],[c418]) ).
cnf(c420,plain,
mult(ld(X12,X),X) = mult(ld(X12,X),mult(X12,ld(X12,X))),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,plain,
mult(mult(ld(X12,X),X),X12) = mult(mult(ld(X12,X),mult(X12,ld(X12,X))),X12),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
mult(mult(ld(X12,X),mult(X12,ld(X12,X))),X12) = mult(ld(X12,X),mult(X12,mult(ld(X12,X),X12))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c423,plain,
mult(ld(X12,X),mult(X12,mult(ld(X12,X),X12))) = mult(ld(X12,X),mult(X,X12)),
inference(congruence,[status(thm)],[c102]) ).
cnf(c424,plain,
mult(mult(ld(X12,X),mult(X12,ld(X12,X))),X12) = mult(ld(X12,X),mult(X,X12)),
inference(transitivity,[status(thm)],[c422,c423]) ).
cnf(c425,plain,
mult(mult(ld(X12,X),X),X12) = mult(ld(X12,X),mult(X,X12)),
inference(transitivity,[status(thm)],[c421,c424]) ).
cnf(c426,plain,
mult(ld(X12,X),mult(X,X12)) = mult(mult(ld(X12,X),X),X12),
inference(symmetry,[status(thm)],[c425]) ).
cnf(c427,plain,
rd(mult(ld(X12,X),mult(X,X12)),X12) = rd(mult(mult(ld(X12,X),X),X12),X12),
inference(congruence,[status(thm)],[c426]) ).
cnf(c428,plain,
rd(mult(mult(ld(X12,X),X),X12),X12) = mult(ld(X12,X),X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c429,plain,
rd(mult(ld(X12,X),mult(X,X12)),X12) = mult(ld(X12,X),X),
inference(transitivity,[status(thm)],[c427,c428]) ).
cnf(c430,plain,
rd(ld(X12,mult(X,mult(X,X12))),X12) = mult(ld(X12,X),X),
inference(transitivity,[status(thm)],[c417,c429]) ).
cnf(c431,plain,
ld(X12,rd(mult(X,mult(X,X12)),X12)) = mult(ld(X12,X),X),
inference(transitivity,[status(thm)],[c393,c430]) ).
cnf(c432,plain,
mult(ld(X12,X),X) = ld(X12,rd(mult(X,mult(X,X12)),X12)),
inference(symmetry,[status(thm)],[c431]) ).
cnf(c433,plain,
mult(X12,mult(ld(X12,X),X)) = mult(X12,ld(X12,rd(mult(X,mult(X,X12)),X12))),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
mult(X12,ld(X12,rd(mult(X,mult(X,X12)),X12))) = rd(mult(X,mult(X,X12)),X12),
inference(substitution,[status(thm)],[c99]) ).
cnf(c435,plain,
mult(X12,mult(ld(X12,X),X)) = rd(mult(X,mult(X,X12)),X12),
inference(transitivity,[status(thm)],[c433,c434]) ).
cnf(c436,plain,
mult(ld(X,X12),mult(ld(ld(X,X12),X),X)) = rd(mult(X,mult(X,ld(X,X12))),ld(X,X12)),
inference(substitution,[status(thm)],[c435]) ).
cnf(c437,plain,
mult(X,ld(X,X12)) = X12,
inference(substitution,[status(thm)],[c99]) ).
cnf(c438,plain,
mult(X,mult(X,ld(X,X12))) = mult(X,X12),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
rd(mult(X,mult(X,ld(X,X12))),ld(X,X12)) = rd(mult(X,X12),ld(X,X12)),
inference(congruence,[status(thm)],[c438]) ).
cnf(c440,plain,
mult(ld(X,X12),mult(ld(ld(X,X12),X),X)) = rd(mult(X,X12),ld(X,X12)),
inference(transitivity,[status(thm)],[c436,c439]) ).
cnf(c441,plain,
mult(mult(X,ld(X,X12)),ld(ld(X,X12),X)) = rd(mult(X,X12),ld(X,X12)),
inference(transitivity,[status(thm)],[c391,c440]) ).
cnf(c442,plain,
mult(X12,ld(ld(X,X12),X)) = rd(mult(X,X12),ld(X,X12)),
inference(transitivity,[status(thm)],[c390,c441]) ).
cnf(c443,plain,
rd(mult(X,X12),ld(X,X12)) = mult(X12,ld(ld(X,X12),X)),
inference(symmetry,[status(thm)],[c442]) ).
cnf(c444,plain,
ld(X12,rd(mult(X,X12),ld(X,X12))) = ld(X12,mult(X12,ld(ld(X,X12),X))),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
ld(X12,mult(X12,ld(ld(X,X12),X))) = ld(ld(X,X12),X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c446,plain,
ld(X12,rd(mult(X,X12),ld(X,X12))) = ld(ld(X,X12),X),
inference(transitivity,[status(thm)],[c444,c445]) ).
cnf(c447,plain,
ld(mult(X12,X),rd(mult(X12,mult(X12,X)),ld(X12,mult(X12,X)))) = ld(ld(X12,mult(X12,X)),X12),
inference(substitution,[status(thm)],[c446]) ).
cnf(c448,plain,
ld(X12,mult(X12,X)) = X,
inference(substitution,[status(thm)],[c21]) ).
cnf(c449,plain,
ld(ld(X12,mult(X12,X)),X12) = ld(X,X12),
inference(congruence,[status(thm)],[c448]) ).
cnf(c450,plain,
ld(mult(X12,X),rd(mult(X12,mult(X12,X)),ld(X12,mult(X12,X)))) = ld(X,X12),
inference(transitivity,[status(thm)],[c447,c449]) ).
cnf(c451,plain,
ld(mult(X12,X),rd(mult(X12,mult(X12,X)),X)) = ld(X,X12),
inference(transitivity,[status(thm)],[c387,c450]) ).
cnf(c452,plain,
ld(mult(X,ld(X12,unit)),rd(mult(X,mult(X,ld(X12,unit))),ld(X12,unit))) = ld(ld(X12,unit),X),
inference(substitution,[status(thm)],[c451]) ).
cnf(c453,plain,
ld(ld(X12,unit),X) = ld(mult(X,ld(X12,unit)),rd(mult(X,mult(X,ld(X12,unit))),ld(X12,unit))),
inference(symmetry,[status(thm)],[c452]) ).
cnf(c454,plain,
rd(mult(X,mult(X,ld(X12,unit))),ld(X12,unit)) = mult(mult(X,mult(X,ld(X12,unit))),X12),
inference(substitution,[status(thm)],[c381]) ).
cnf(c455,plain,
ld(mult(X,ld(X12,unit)),rd(mult(X,mult(X,ld(X12,unit))),ld(X12,unit))) = ld(mult(X,ld(X12,unit)),mult(mult(X,mult(X,ld(X12,unit))),X12)),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
mult(X,ld(X12,unit)) = rd(X,X12),
inference(substitution,[status(thm)],[c370]) ).
cnf(c457,plain,
ld(mult(X,ld(X12,unit)),mult(mult(X,mult(X,ld(X12,unit))),X12)) = ld(rd(X,X12),mult(mult(X,mult(X,ld(X12,unit))),X12)),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
mult(X,ld(X12,unit)) = rd(X,X12),
inference(substitution,[status(thm)],[c370]) ).
cnf(c459,plain,
mult(X,mult(X,ld(X12,unit))) = mult(X,rd(X,X12)),
inference(congruence,[status(thm)],[c458]) ).
cnf(c460,plain,
mult(mult(X,mult(X,ld(X12,unit))),X12) = mult(mult(X,rd(X,X12)),X12),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
ld(rd(X,X12),mult(mult(X,mult(X,ld(X12,unit))),X12)) = ld(rd(X,X12),mult(mult(X,rd(X,X12)),X12)),
inference(congruence,[status(thm)],[c460]) ).
cnf(c462,plain,
mult(X12,rd(X12,X)) = mult(rd(X12,X),rd(mult(X,X12),X)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c463,plain,
mult(mult(X12,rd(X12,X)),X) = mult(mult(rd(X12,X),rd(mult(X,X12),X)),X),
inference(congruence,[status(thm)],[c462]) ).
cnf(c464,plain,
mult(X,rd(X12,X)) = rd(mult(X,X12),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c465,plain,
rd(mult(X,X12),X) = mult(X,rd(X12,X)),
inference(symmetry,[status(thm)],[c464]) ).
cnf(c466,plain,
mult(rd(X12,X),rd(mult(X,X12),X)) = mult(rd(X12,X),mult(X,rd(X12,X))),
inference(congruence,[status(thm)],[c465]) ).
cnf(c467,plain,
mult(mult(rd(X12,X),rd(mult(X,X12),X)),X) = mult(mult(rd(X12,X),mult(X,rd(X12,X))),X),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
mult(mult(rd(X12,X),mult(X,rd(X12,X))),X) = mult(rd(X12,X),mult(X,mult(rd(X12,X),X))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c469,plain,
mult(rd(X12,X),X) = X12,
inference(substitution,[status(thm)],[c14]) ).
cnf(c470,plain,
mult(X,mult(rd(X12,X),X)) = mult(X,X12),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,plain,
mult(rd(X12,X),mult(X,mult(rd(X12,X),X))) = mult(rd(X12,X),mult(X,X12)),
inference(congruence,[status(thm)],[c470]) ).
cnf(c472,plain,
mult(mult(rd(X12,X),mult(X,rd(X12,X))),X) = mult(rd(X12,X),mult(X,X12)),
inference(transitivity,[status(thm)],[c468,c471]) ).
cnf(c473,plain,
mult(mult(rd(X12,X),rd(mult(X,X12),X)),X) = mult(rd(X12,X),mult(X,X12)),
inference(transitivity,[status(thm)],[c467,c472]) ).
cnf(c474,plain,
mult(mult(X12,rd(X12,X)),X) = mult(rd(X12,X),mult(X,X12)),
inference(transitivity,[status(thm)],[c463,c473]) ).
cnf(c475,plain,
mult(mult(X,rd(X,X12)),X12) = mult(rd(X,X12),mult(X12,X)),
inference(substitution,[status(thm)],[c474]) ).
cnf(c476,plain,
ld(rd(X,X12),mult(mult(X,rd(X,X12)),X12)) = ld(rd(X,X12),mult(rd(X,X12),mult(X12,X))),
inference(congruence,[status(thm)],[c475]) ).
cnf(c477,plain,
ld(rd(X,X12),mult(rd(X,X12),mult(X12,X))) = mult(X12,X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c478,plain,
ld(rd(X,X12),mult(mult(X,rd(X,X12)),X12)) = mult(X12,X),
inference(transitivity,[status(thm)],[c476,c477]) ).
cnf(c479,plain,
ld(rd(X,X12),mult(mult(X,mult(X,ld(X12,unit))),X12)) = mult(X12,X),
inference(transitivity,[status(thm)],[c461,c478]) ).
cnf(c480,plain,
ld(mult(X,ld(X12,unit)),mult(mult(X,mult(X,ld(X12,unit))),X12)) = mult(X12,X),
inference(transitivity,[status(thm)],[c457,c479]) ).
cnf(c481,plain,
ld(mult(X,ld(X12,unit)),rd(mult(X,mult(X,ld(X12,unit))),ld(X12,unit))) = mult(X12,X),
inference(transitivity,[status(thm)],[c455,c480]) ).
cnf(c482,plain,
ld(ld(X12,unit),X) = mult(X12,X),
inference(transitivity,[status(thm)],[c453,c481]) ).
cnf(c483,plain,
ld(ld(X,unit),X12) = mult(X,X12),
inference(substitution,[status(thm)],[c482]) ).
cnf(c484,plain,
mult(X,X12) = ld(ld(X,unit),X12),
inference(symmetry,[status(thm)],[c483]) ).
cnf(c485,plain,
rd(X12,mult(X,X12)) = rd(X12,ld(ld(X,unit),X12)),
inference(congruence,[status(thm)],[c484]) ).
cnf(c486,plain,
rd(X12,ld(ld(X,unit),X12)) = ld(X,unit),
inference(substitution,[status(thm)],[c237]) ).
cnf(c487,plain,
rd(X12,mult(X,X12)) = ld(X,unit),
inference(transitivity,[status(thm)],[c485,c486]) ).
cnf(c488,plain,
rd(X,mult(X12,X)) = ld(X12,unit),
inference(substitution,[status(thm)],[c487]) ).
cnf(c489,plain,
ld(X12,unit) = rd(X,mult(X12,X)),
inference(symmetry,[status(thm)],[c488]) ).
cnf(c490,plain,
rd(mult(mult(X13,X12),X),ld(X12,unit)) = rd(mult(mult(X13,X12),X),rd(X,mult(X12,X))),
inference(congruence,[status(thm)],[c489]) ).
cnf(c491,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c492,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c491]) ).
cnf(c493,plain,
mult(X12,X) = mult(X12,mult(f(X),f(X))),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
mult(X13,mult(X12,X)) = mult(X13,mult(X12,mult(f(X),f(X)))),
inference(congruence,[status(thm)],[c493]) ).
cnf(c495,plain,
rd(mult(X13,mult(X12,X)),X12) = rd(mult(X13,mult(X12,mult(f(X),f(X)))),X12),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
mult(X12,mult(X,X)) = mult(mult(X12,X),X),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c497,plain,
mult(X13,mult(X12,mult(X,X))) = mult(X13,mult(mult(X12,X),X)),
inference(congruence,[status(thm)],[c496]) ).
cnf(c498,plain,
rd(mult(X13,mult(X12,mult(X,X))),X12) = rd(mult(X13,mult(mult(X12,X),X)),X12),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,plain,
rd(mult(X12,X),X) = X12,
inference(substitution,[status(thm)],[c9]) ).
cnf(c500,plain,
X12 = rd(mult(X12,X),X),
inference(symmetry,[status(thm)],[c499]) ).
cnf(c501,plain,
rd(mult(X13,mult(mult(X12,X),X)),X12) = rd(mult(X13,mult(mult(X12,X),X)),rd(mult(X12,X),X)),
inference(congruence,[status(thm)],[c500]) ).
cnf(c502,plain,
rd(X,mult(rd(X12,X),X)) = ld(rd(X12,X),unit),
inference(substitution,[status(thm)],[c487]) ).
cnf(c503,plain,
ld(rd(X12,X),unit) = rd(X,mult(rd(X12,X),X)),
inference(symmetry,[status(thm)],[c502]) ).
cnf(c504,plain,
mult(rd(X12,X),X) = X12,
inference(substitution,[status(thm)],[c14]) ).
cnf(c505,plain,
rd(X,mult(rd(X12,X),X)) = rd(X,X12),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
ld(rd(X12,X),unit) = rd(X,X12),
inference(transitivity,[status(thm)],[c503,c505]) ).
cnf(c507,plain,
ld(rd(X,X12),unit) = rd(X12,X),
inference(substitution,[status(thm)],[c506]) ).
cnf(c508,plain,
rd(X12,X) = ld(rd(X,X12),unit),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c509,plain,
mult(X13,rd(X12,X)) = mult(X13,ld(rd(X,X12),unit)),
inference(congruence,[status(thm)],[c508]) ).
cnf(c510,plain,
mult(X13,ld(rd(X,X12),unit)) = rd(X13,rd(X,X12)),
inference(substitution,[status(thm)],[c370]) ).
cnf(c511,plain,
mult(X13,rd(X12,X)) = rd(X13,rd(X,X12)),
inference(transitivity,[status(thm)],[c509,c510]) ).
cnf(c512,plain,
mult(mult(X13,mult(X12,X)),rd(X,X12)) = rd(mult(X13,mult(X12,X)),rd(X12,X)),
inference(substitution,[status(thm)],[c511]) ).
cnf(c513,plain,
rd(mult(X13,mult(X12,X)),rd(X12,X)) = mult(mult(X13,mult(X12,X)),rd(X,X12)),
inference(symmetry,[status(thm)],[c512]) ).
cnf(c514,plain,
mult(rd(X,X12),X12) = X,
inference(substitution,[status(thm)],[c14]) ).
cnf(c515,plain,
X = mult(rd(X,X12),X12),
inference(symmetry,[status(thm)],[c514]) ).
cnf(c516,plain,
mult(X12,X) = mult(X12,mult(rd(X,X12),X12)),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
mult(X13,mult(X12,X)) = mult(X13,mult(X12,mult(rd(X,X12),X12))),
inference(congruence,[status(thm)],[c516]) ).
cnf(c518,plain,
mult(mult(X13,mult(X12,X)),rd(X,X12)) = mult(mult(X13,mult(X12,mult(rd(X,X12),X12))),rd(X,X12)),
inference(congruence,[status(thm)],[c517]) ).
cnf(c519,plain,
mult(mult(X13,mult(X12,mult(rd(X,X12),X12))),rd(X,X12)) = mult(mult(X13,X12),mult(rd(X,X12),mult(X12,rd(X,X12)))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c520,plain,
ld(ld(rd(X13,X12),unit),X) = mult(rd(X13,X12),X),
inference(substitution,[status(thm)],[c482]) ).
cnf(c521,plain,
mult(rd(X13,X12),X) = ld(ld(rd(X13,X12),unit),X),
inference(symmetry,[status(thm)],[c520]) ).
cnf(c522,plain,
ld(ld(rd(X13,X12),unit),X) = ld(rd(X12,X13),X),
inference(congruence,[status(thm)],[c506]) ).
cnf(c523,plain,
mult(rd(X13,X12),X) = ld(rd(X12,X13),X),
inference(transitivity,[status(thm)],[c521,c522]) ).
cnf(c524,plain,
mult(rd(X,X12),mult(X12,rd(X,X12))) = ld(rd(X12,X),mult(X12,rd(X,X12))),
inference(substitution,[status(thm)],[c523]) ).
cnf(c525,plain,
mult(mult(X13,X12),mult(rd(X,X12),mult(X12,rd(X,X12)))) = mult(mult(X13,X12),ld(rd(X12,X),mult(X12,rd(X,X12)))),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
rd(X12,X) = mult(X12,ld(X,unit)),
inference(symmetry,[status(thm)],[c370]) ).
cnf(c527,plain,
ld(X12,rd(X12,X)) = ld(X12,mult(X12,ld(X,unit))),
inference(congruence,[status(thm)],[c526]) ).
cnf(c528,plain,
ld(X12,mult(X12,ld(X,unit))) = ld(X,unit),
inference(substitution,[status(thm)],[c21]) ).
cnf(c529,plain,
ld(X12,rd(X12,X)) = ld(X,unit),
inference(transitivity,[status(thm)],[c527,c528]) ).
cnf(c530,plain,
ld(X,rd(X,ld(X12,X))) = ld(ld(X12,X),unit),
inference(substitution,[status(thm)],[c529]) ).
cnf(c531,plain,
ld(ld(X12,X),unit) = ld(X,rd(X,ld(X12,X))),
inference(symmetry,[status(thm)],[c530]) ).
cnf(c532,plain,
rd(X,ld(X12,X)) = X12,
inference(substitution,[status(thm)],[c237]) ).
cnf(c533,plain,
ld(X,rd(X,ld(X12,X))) = ld(X,X12),
inference(congruence,[status(thm)],[c532]) ).
cnf(c534,plain,
ld(ld(X12,X),unit) = ld(X,X12),
inference(transitivity,[status(thm)],[c531,c533]) ).
cnf(c535,plain,
ld(ld(X,X12),unit) = ld(X12,X),
inference(substitution,[status(thm)],[c534]) ).
cnf(c536,plain,
ld(X12,X) = ld(ld(X,X12),unit),
inference(symmetry,[status(thm)],[c535]) ).
cnf(c537,plain,
mult(X13,ld(X12,X)) = mult(X13,ld(ld(X,X12),unit)),
inference(congruence,[status(thm)],[c536]) ).
cnf(c538,plain,
mult(X13,ld(ld(X,X12),unit)) = rd(X13,ld(X,X12)),
inference(substitution,[status(thm)],[c370]) ).
cnf(c539,plain,
mult(X13,ld(X12,X)) = rd(X13,ld(X,X12)),
inference(transitivity,[status(thm)],[c537,c538]) ).
cnf(c540,plain,
mult(mult(X13,X12),ld(rd(X12,X),mult(X12,rd(X,X12)))) = rd(mult(X13,X12),ld(mult(X12,rd(X,X12)),rd(X12,X))),
inference(substitution,[status(thm)],[c539]) ).
cnf(c541,plain,
ld(mult(X12,rd(X,X12)),rd(X12,X)) = ld(rd(mult(X12,X),X12),rd(X12,X)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c542,plain,
rd(mult(X13,X12),ld(mult(X12,rd(X,X12)),rd(X12,X))) = rd(mult(X13,X12),ld(rd(mult(X12,X),X12),rd(X12,X))),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
mult(X12,X) = rd(X12,ld(X,unit)),
inference(symmetry,[status(thm)],[c381]) ).
cnf(c544,plain,
rd(mult(X12,X),X12) = rd(rd(X12,ld(X,unit)),X12),
inference(congruence,[status(thm)],[c543]) ).
cnf(c545,plain,
mult(X12,ld(X12,rd(rd(X12,X),X12))) = rd(rd(X12,X),X12),
inference(substitution,[status(thm)],[c99]) ).
cnf(c546,plain,
rd(rd(X12,X),X12) = mult(X12,ld(X12,rd(rd(X12,X),X12))),
inference(symmetry,[status(thm)],[c545]) ).
cnf(c547,plain,
rd(X12,X) = mult(X12,ld(X,unit)),
inference(symmetry,[status(thm)],[c370]) ).
cnf(c548,plain,
rd(rd(X12,X),X12) = rd(mult(X12,ld(X,unit)),X12),
inference(congruence,[status(thm)],[c547]) ).
cnf(c549,plain,
ld(X12,rd(rd(X12,X),X12)) = ld(X12,rd(mult(X12,ld(X,unit)),X12)),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
ld(X12,rd(mult(X12,ld(X,unit)),X12)) = rd(ld(X,unit),X12),
inference(substitution,[status(thm)],[c23]) ).
cnf(c551,plain,
mult(ld(X12,unit),ld(X,unit)) = rd(ld(X12,unit),X),
inference(substitution,[status(thm)],[c370]) ).
cnf(c552,plain,
rd(ld(X12,unit),X) = mult(ld(X12,unit),ld(X,unit)),
inference(symmetry,[status(thm)],[c551]) ).
cnf(c553,plain,
ld(X,unit) = rd(unit,X),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c554,plain,
mult(ld(X12,unit),X) = mult(rd(unit,X12),X),
inference(congruence,[status(thm)],[c553]) ).
cnf(c555,plain,
ld(ld(rd(unit,X12),unit),X) = mult(rd(unit,X12),X),
inference(substitution,[status(thm)],[c482]) ).
cnf(c556,plain,
mult(rd(unit,X12),X) = ld(ld(rd(unit,X12),unit),X),
inference(symmetry,[status(thm)],[c555]) ).
cnf(c557,plain,
ld(rd(unit,X),unit) = X,
inference(substitution,[status(thm)],[c377]) ).
cnf(c558,plain,
ld(ld(rd(unit,X12),unit),X) = ld(X12,X),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
mult(rd(unit,X12),X) = ld(X12,X),
inference(transitivity,[status(thm)],[c556,c558]) ).
cnf(c560,plain,
mult(ld(X12,unit),X) = ld(X12,X),
inference(transitivity,[status(thm)],[c554,c559]) ).
cnf(c561,plain,
mult(ld(X12,unit),ld(X,unit)) = ld(X12,ld(X,unit)),
inference(substitution,[status(thm)],[c560]) ).
cnf(c562,plain,
rd(ld(X12,unit),X) = ld(X12,ld(X,unit)),
inference(transitivity,[status(thm)],[c552,c561]) ).
cnf(c563,plain,
rd(ld(X,unit),X12) = ld(X,ld(X12,unit)),
inference(substitution,[status(thm)],[c562]) ).
cnf(c564,plain,
ld(X12,rd(mult(X12,ld(X,unit)),X12)) = ld(X,ld(X12,unit)),
inference(transitivity,[status(thm)],[c550,c563]) ).
cnf(c565,plain,
ld(X12,rd(rd(X12,X),X12)) = ld(X,ld(X12,unit)),
inference(transitivity,[status(thm)],[c549,c564]) ).
cnf(c566,plain,
mult(X12,ld(X12,rd(rd(X12,X),X12))) = mult(X12,ld(X,ld(X12,unit))),
inference(congruence,[status(thm)],[c565]) ).
cnf(c567,plain,
mult(X12,ld(X,ld(X12,unit))) = rd(X12,ld(ld(X12,unit),X)),
inference(substitution,[status(thm)],[c539]) ).
cnf(c568,plain,
rd(X12,ld(ld(X12,unit),X)) = rd(X12,mult(X12,X)),
inference(congruence,[status(thm)],[c482]) ).
cnf(c569,plain,
mult(X12,ld(X,ld(X12,unit))) = rd(X12,mult(X12,X)),
inference(transitivity,[status(thm)],[c567,c568]) ).
cnf(c570,plain,
mult(X12,ld(X12,rd(rd(X12,X),X12))) = rd(X12,mult(X12,X)),
inference(transitivity,[status(thm)],[c566,c569]) ).
cnf(c571,plain,
rd(rd(X12,X),X12) = rd(X12,mult(X12,X)),
inference(transitivity,[status(thm)],[c546,c570]) ).
cnf(c572,plain,
rd(rd(X12,ld(X,unit)),X12) = rd(X12,mult(X12,ld(X,unit))),
inference(substitution,[status(thm)],[c571]) ).
cnf(c573,plain,
rd(X12,mult(X12,ld(X,unit))) = rd(X12,rd(X12,X)),
inference(congruence,[status(thm)],[c370]) ).
cnf(c574,plain,
rd(rd(X12,ld(X,unit)),X12) = rd(X12,rd(X12,X)),
inference(transitivity,[status(thm)],[c572,c573]) ).
cnf(c575,plain,
rd(mult(X12,X),X12) = rd(X12,rd(X12,X)),
inference(transitivity,[status(thm)],[c544,c574]) ).
cnf(c576,plain,
ld(rd(mult(X12,X),X12),rd(X12,X)) = ld(rd(X12,rd(X12,X)),rd(X12,X)),
inference(congruence,[status(thm)],[c575]) ).
cnf(c577,plain,
rd(mult(X13,X12),ld(rd(mult(X12,X),X12),rd(X12,X))) = rd(mult(X13,X12),ld(rd(X12,rd(X12,X)),rd(X12,X))),
inference(congruence,[status(thm)],[c576]) ).
cnf(c578,plain,
rd(mult(X12,X12),ld(ld(rd(X12,rd(X12,X)),rd(X12,X)),mult(X12,X12))) = ld(rd(X12,rd(X12,X)),rd(X12,X)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c579,plain,
ld(rd(X12,rd(X12,X)),rd(X12,X)) = rd(mult(X12,X12),ld(ld(rd(X12,rd(X12,X)),rd(X12,X)),mult(X12,X12))),
inference(symmetry,[status(thm)],[c578]) ).
cnf(c580,plain,
rd(X12,rd(X12,X)) = rd(mult(X12,X),X12),
inference(symmetry,[status(thm)],[c575]) ).
cnf(c581,plain,
ld(rd(X12,rd(X12,X)),rd(X12,X)) = ld(rd(mult(X12,X),X12),rd(X12,X)),
inference(congruence,[status(thm)],[c580]) ).
cnf(c582,plain,
ld(ld(rd(X12,rd(X12,X)),rd(X12,X)),mult(X12,X12)) = ld(ld(rd(mult(X12,X),X12),rd(X12,X)),mult(X12,X12)),
inference(congruence,[status(thm)],[c581]) ).
cnf(c583,plain,
rd(mult(X12,X),X12) = mult(X12,rd(X,X12)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c584,plain,
ld(rd(mult(X12,X),X12),rd(X12,X)) = ld(mult(X12,rd(X,X12)),rd(X12,X)),
inference(congruence,[status(thm)],[c583]) ).
cnf(c585,plain,
ld(ld(rd(mult(X12,X),X12),rd(X12,X)),mult(X12,X12)) = ld(ld(mult(X12,rd(X,X12)),rd(X12,X)),mult(X12,X12)),
inference(congruence,[status(thm)],[c584]) ).
cnf(c586,plain,
ld(ld(ld(X13,X12),unit),X) = mult(ld(X13,X12),X),
inference(substitution,[status(thm)],[c482]) ).
cnf(c587,plain,
mult(ld(X13,X12),X) = ld(ld(ld(X13,X12),unit),X),
inference(symmetry,[status(thm)],[c586]) ).
cnf(c588,plain,
ld(ld(ld(X13,X12),unit),X) = ld(ld(X12,X13),X),
inference(congruence,[status(thm)],[c534]) ).
cnf(c589,plain,
mult(ld(X13,X12),X) = ld(ld(X12,X13),X),
inference(transitivity,[status(thm)],[c587,c588]) ).
cnf(c590,plain,
mult(ld(rd(X12,X),mult(X12,rd(X,X12))),mult(X12,X12)) = ld(ld(mult(X12,rd(X,X12)),rd(X12,X)),mult(X12,X12)),
inference(substitution,[status(thm)],[c589]) ).
cnf(c591,plain,
ld(ld(mult(X12,rd(X,X12)),rd(X12,X)),mult(X12,X12)) = mult(ld(rd(X12,X),mult(X12,rd(X,X12))),mult(X12,X12)),
inference(symmetry,[status(thm)],[c590]) ).
cnf(c592,plain,
mult(rd(X,X12),mult(X12,rd(X,X12))) = ld(rd(X12,X),mult(X12,rd(X,X12))),
inference(substitution,[status(thm)],[c523]) ).
cnf(c593,plain,
ld(rd(X12,X),mult(X12,rd(X,X12))) = mult(rd(X,X12),mult(X12,rd(X,X12))),
inference(symmetry,[status(thm)],[c592]) ).
cnf(c594,plain,
mult(ld(rd(X12,X),mult(X12,rd(X,X12))),mult(X12,X12)) = mult(mult(rd(X,X12),mult(X12,rd(X,X12))),mult(X12,X12)),
inference(congruence,[status(thm)],[c593]) ).
cnf(c595,plain,
mult(X12,mult(X,mult(X12,X))) = mult(mult(X12,mult(X,X12)),X),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c596,plain,
mult(mult(X12,mult(X,mult(X12,X))),X) = mult(mult(mult(X12,mult(X,X12)),X),X),
inference(congruence,[status(thm)],[c595]) ).
cnf(c597,plain,
mult(mult(mult(X12,mult(X,X12)),X),X) = mult(mult(X12,mult(X,X12)),mult(X,X)),
inference(substitution,[status(thm)],[c76]) ).
cnf(c598,plain,
mult(mult(X12,mult(X,mult(X12,X))),X) = mult(mult(X12,mult(X,X12)),mult(X,X)),
inference(transitivity,[status(thm)],[c596,c597]) ).
cnf(c599,plain,
mult(mult(rd(X,X12),mult(X12,mult(rd(X,X12),X12))),X12) = mult(mult(rd(X,X12),mult(X12,rd(X,X12))),mult(X12,X12)),
inference(substitution,[status(thm)],[c598]) ).
cnf(c600,plain,
mult(mult(rd(X,X12),mult(X12,rd(X,X12))),mult(X12,X12)) = mult(mult(rd(X,X12),mult(X12,mult(rd(X,X12),X12))),X12),
inference(symmetry,[status(thm)],[c599]) ).
cnf(c601,plain,
mult(rd(X,X12),X12) = X,
inference(substitution,[status(thm)],[c14]) ).
cnf(c602,plain,
mult(X12,mult(rd(X,X12),X12)) = mult(X12,X),
inference(congruence,[status(thm)],[c601]) ).
cnf(c603,plain,
mult(rd(X,X12),mult(X12,mult(rd(X,X12),X12))) = mult(rd(X,X12),mult(X12,X)),
inference(congruence,[status(thm)],[c602]) ).
cnf(c604,plain,
mult(mult(rd(X,X12),mult(X12,mult(rd(X,X12),X12))),X12) = mult(mult(rd(X,X12),mult(X12,X)),X12),
inference(congruence,[status(thm)],[c603]) ).
cnf(c605,plain,
mult(rd(X,X12),mult(X12,X)) = ld(rd(X12,X),mult(X12,X)),
inference(substitution,[status(thm)],[c523]) ).
cnf(c606,plain,
mult(mult(rd(X,X12),mult(X12,X)),X12) = mult(ld(rd(X12,X),mult(X12,X)),X12),
inference(congruence,[status(thm)],[c605]) ).
cnf(c607,plain,
mult(ld(rd(X12,X),mult(X12,X)),X12) = ld(ld(mult(X12,X),rd(X12,X)),X12),
inference(substitution,[status(thm)],[c589]) ).
cnf(c608,plain,
mult(X12,X) = mult(rd(X12,X),mult(X,X)),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c609,plain,
rd(mult(X12,X),mult(X,X)) = rd(mult(rd(X12,X),mult(X,X)),mult(X,X)),
inference(congruence,[status(thm)],[c608]) ).
cnf(c610,plain,
rd(mult(rd(X12,X),mult(X,X)),mult(X,X)) = rd(X12,X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c611,plain,
rd(mult(X12,X),mult(X,X)) = rd(X12,X),
inference(transitivity,[status(thm)],[c609,c610]) ).
cnf(c612,plain,
rd(X12,X) = rd(mult(X12,X),mult(X,X)),
inference(symmetry,[status(thm)],[c611]) ).
cnf(c613,plain,
ld(mult(X12,X),rd(X12,X)) = ld(mult(X12,X),rd(mult(X12,X),mult(X,X))),
inference(congruence,[status(thm)],[c612]) ).
cnf(c614,plain,
ld(mult(X12,X),rd(mult(X12,X),mult(X,X))) = ld(mult(X,X),unit),
inference(substitution,[status(thm)],[c529]) ).
cnf(c615,plain,
rd(unit,mult(X,X)) = ld(mult(X,X),unit),
inference(substitution,[status(thm)],[c38]) ).
cnf(c616,plain,
ld(mult(X,X),unit) = rd(unit,mult(X,X)),
inference(symmetry,[status(thm)],[c615]) ).
cnf(c617,plain,
rd(X12,X) = mult(rd(X12,mult(X,X)),X),
inference(symmetry,[status(thm)],[c368]) ).
cnf(c618,plain,
rd(rd(X12,X),X) = rd(mult(rd(X12,mult(X,X)),X),X),
inference(congruence,[status(thm)],[c617]) ).
cnf(c619,plain,
rd(mult(rd(X12,mult(X,X)),X),X) = rd(X12,mult(X,X)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c620,plain,
rd(rd(X12,X),X) = rd(X12,mult(X,X)),
inference(transitivity,[status(thm)],[c618,c619]) ).
cnf(c621,plain,
rd(rd(unit,X),X) = rd(unit,mult(X,X)),
inference(substitution,[status(thm)],[c620]) ).
cnf(c622,plain,
rd(unit,mult(X,X)) = rd(rd(unit,X),X),
inference(symmetry,[status(thm)],[c621]) ).
cnf(c623,plain,
rd(rd(unit,X),X) = rd(ld(X,unit),X),
inference(congruence,[status(thm)],[c38]) ).
cnf(c624,plain,
rd(ld(X,unit),X) = ld(X,rd(unit,X)),
inference(substitution,[status(thm)],[c279]) ).
cnf(c625,plain,
ld(X,rd(unit,X)) = ld(X,ld(X,unit)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c626,plain,
rd(ld(X,unit),X) = ld(X,ld(X,unit)),
inference(transitivity,[status(thm)],[c624,c625]) ).
cnf(c627,plain,
rd(rd(unit,X),X) = ld(X,ld(X,unit)),
inference(transitivity,[status(thm)],[c623,c626]) ).
cnf(c628,plain,
rd(unit,mult(X,X)) = ld(X,ld(X,unit)),
inference(transitivity,[status(thm)],[c622,c627]) ).
cnf(c629,plain,
ld(mult(X,X),unit) = ld(X,ld(X,unit)),
inference(transitivity,[status(thm)],[c616,c628]) ).
cnf(c630,plain,
ld(mult(X12,X),rd(mult(X12,X),mult(X,X))) = ld(X,ld(X,unit)),
inference(transitivity,[status(thm)],[c614,c629]) ).
cnf(c631,plain,
ld(mult(X12,X),rd(X12,X)) = ld(X,ld(X,unit)),
inference(transitivity,[status(thm)],[c613,c630]) ).
cnf(c632,plain,
ld(ld(mult(X12,X),rd(X12,X)),X12) = ld(ld(X,ld(X,unit)),X12),
inference(congruence,[status(thm)],[c631]) ).
cnf(c633,plain,
ld(mult(X,ld(X12,ld(X12,unit))),rd(mult(X,mult(X,ld(X12,ld(X12,unit)))),ld(X12,ld(X12,unit)))) = ld(ld(X12,ld(X12,unit)),X),
inference(substitution,[status(thm)],[c451]) ).
cnf(c634,plain,
ld(ld(X12,ld(X12,unit)),X) = ld(mult(X,ld(X12,ld(X12,unit))),rd(mult(X,mult(X,ld(X12,ld(X12,unit)))),ld(X12,ld(X12,unit)))),
inference(symmetry,[status(thm)],[c633]) ).
cnf(c635,plain,
mult(X12,ld(ld(X,ld(X,unit)),unit)) = rd(X12,ld(X,ld(X,unit))),
inference(substitution,[status(thm)],[c370]) ).
cnf(c636,plain,
rd(X12,ld(X,ld(X,unit))) = mult(X12,ld(ld(X,ld(X,unit)),unit)),
inference(symmetry,[status(thm)],[c635]) ).
cnf(c637,plain,
rd(unit,ld(X,ld(X,unit))) = ld(ld(X,ld(X,unit)),unit),
inference(substitution,[status(thm)],[c38]) ).
cnf(c638,plain,
ld(ld(X,ld(X,unit)),unit) = rd(unit,ld(X,ld(X,unit))),
inference(symmetry,[status(thm)],[c637]) ).
cnf(c639,plain,
mult(unit,ld(X,unit)) = ld(X,unit),
inference(substitution,[status(thm)],[c30]) ).
cnf(c640,plain,
ld(X,unit) = mult(unit,ld(X,unit)),
inference(symmetry,[status(thm)],[c639]) ).
cnf(c641,plain,
ld(X,ld(X,unit)) = ld(X,mult(unit,ld(X,unit))),
inference(congruence,[status(thm)],[c640]) ).
cnf(c642,plain,
rd(unit,ld(X,ld(X,unit))) = rd(unit,ld(X,mult(unit,ld(X,unit)))),
inference(congruence,[status(thm)],[c641]) ).
cnf(c643,plain,
mult(ld(X,X12),ld(X,X12)) = ld(X,mult(X12,ld(X,X12))),
inference(substitution,[status(thm)],[c196]) ).
cnf(c644,plain,
ld(X,mult(X12,ld(X,X12))) = mult(ld(X,X12),ld(X,X12)),
inference(symmetry,[status(thm)],[c643]) ).
cnf(c645,plain,
rd(X12,ld(X,mult(X12,ld(X,X12)))) = rd(X12,mult(ld(X,X12),ld(X,X12))),
inference(congruence,[status(thm)],[c644]) ).
cnf(c646,plain,
mult(X,ld(X,X12)) = X12,
inference(substitution,[status(thm)],[c99]) ).
cnf(c647,plain,
X12 = mult(X,ld(X,X12)),
inference(symmetry,[status(thm)],[c646]) ).
cnf(c648,plain,
rd(X12,mult(ld(X,X12),ld(X,X12))) = rd(mult(X,ld(X,X12)),mult(ld(X,X12),ld(X,X12))),
inference(congruence,[status(thm)],[c647]) ).
cnf(c649,plain,
rd(mult(X,ld(X,X12)),mult(ld(X,X12),ld(X,X12))) = rd(X,ld(X,X12)),
inference(substitution,[status(thm)],[c611]) ).
cnf(c650,plain,
rd(X12,mult(ld(X,X12),ld(X,X12))) = rd(X,ld(X,X12)),
inference(transitivity,[status(thm)],[c648,c649]) ).
cnf(c651,plain,
rd(X12,ld(X,mult(X12,ld(X,X12)))) = rd(X,ld(X,X12)),
inference(transitivity,[status(thm)],[c645,c650]) ).
cnf(c652,plain,
rd(unit,ld(X,mult(unit,ld(X,unit)))) = rd(X,ld(X,unit)),
inference(substitution,[status(thm)],[c651]) ).
cnf(c653,plain,
rd(X,ld(X,unit)) = mult(X,X),
inference(substitution,[status(thm)],[c381]) ).
cnf(c654,plain,
rd(unit,ld(X,mult(unit,ld(X,unit)))) = mult(X,X),
inference(transitivity,[status(thm)],[c652,c653]) ).
cnf(c655,plain,
rd(unit,ld(X,ld(X,unit))) = mult(X,X),
inference(transitivity,[status(thm)],[c642,c654]) ).
cnf(c656,plain,
ld(ld(X,ld(X,unit)),unit) = mult(X,X),
inference(transitivity,[status(thm)],[c638,c655]) ).
cnf(c657,plain,
mult(X12,ld(ld(X,ld(X,unit)),unit)) = mult(X12,mult(X,X)),
inference(congruence,[status(thm)],[c656]) ).
cnf(c658,plain,
rd(X12,ld(X,ld(X,unit))) = mult(X12,mult(X,X)),
inference(transitivity,[status(thm)],[c636,c657]) ).
cnf(c659,plain,
rd(mult(X,mult(X,ld(X12,ld(X12,unit)))),ld(X12,ld(X12,unit))) = mult(mult(X,mult(X,ld(X12,ld(X12,unit)))),mult(X12,X12)),
inference(substitution,[status(thm)],[c658]) ).
cnf(c660,plain,
ld(mult(X,ld(X12,ld(X12,unit))),rd(mult(X,mult(X,ld(X12,ld(X12,unit)))),ld(X12,ld(X12,unit)))) = ld(mult(X,ld(X12,ld(X12,unit))),mult(mult(X,mult(X,ld(X12,ld(X12,unit)))),mult(X12,X12))),
inference(congruence,[status(thm)],[c659]) ).
cnf(c661,plain,
mult(X,ld(X12,ld(X12,unit))) = rd(X,ld(ld(X12,unit),X12)),
inference(substitution,[status(thm)],[c539]) ).
cnf(c662,plain,
ld(mult(X,ld(X12,ld(X12,unit))),mult(mult(X,mult(X,ld(X12,ld(X12,unit)))),mult(X12,X12))) = ld(rd(X,ld(ld(X12,unit),X12)),mult(mult(X,mult(X,ld(X12,ld(X12,unit)))),mult(X12,X12))),
inference(congruence,[status(thm)],[c661]) ).
cnf(c663,plain,
mult(X,ld(X12,ld(X12,unit))) = rd(X,ld(ld(X12,unit),X12)),
inference(substitution,[status(thm)],[c539]) ).
cnf(c664,plain,
mult(X,mult(X,ld(X12,ld(X12,unit)))) = mult(X,rd(X,ld(ld(X12,unit),X12))),
inference(congruence,[status(thm)],[c663]) ).
cnf(c665,plain,
mult(mult(X,mult(X,ld(X12,ld(X12,unit)))),mult(X12,X12)) = mult(mult(X,rd(X,ld(ld(X12,unit),X12))),mult(X12,X12)),
inference(congruence,[status(thm)],[c664]) ).
cnf(c666,plain,
ld(rd(X,ld(ld(X12,unit),X12)),mult(mult(X,mult(X,ld(X12,ld(X12,unit)))),mult(X12,X12))) = ld(rd(X,ld(ld(X12,unit),X12)),mult(mult(X,rd(X,ld(ld(X12,unit),X12))),mult(X12,X12))),
inference(congruence,[status(thm)],[c665]) ).
cnf(c667,plain,
ld(ld(X,unit),X) = mult(X,X),
inference(substitution,[status(thm)],[c482]) ).
cnf(c668,plain,
rd(X,ld(ld(X12,unit),X12)) = rd(X,mult(X12,X12)),
inference(congruence,[status(thm)],[c667]) ).
cnf(c669,plain,
ld(rd(X,ld(ld(X12,unit),X12)),mult(mult(X,rd(X,ld(ld(X12,unit),X12))),mult(X12,X12))) = ld(rd(X,mult(X12,X12)),mult(mult(X,rd(X,ld(ld(X12,unit),X12))),mult(X12,X12))),
inference(congruence,[status(thm)],[c668]) ).
cnf(c670,plain,
ld(ld(X,unit),X) = mult(X,X),
inference(substitution,[status(thm)],[c482]) ).
cnf(c671,plain,
rd(X,ld(ld(X12,unit),X12)) = rd(X,mult(X12,X12)),
inference(congruence,[status(thm)],[c670]) ).
cnf(c672,plain,
mult(X,rd(X,ld(ld(X12,unit),X12))) = mult(X,rd(X,mult(X12,X12))),
inference(congruence,[status(thm)],[c671]) ).
cnf(c673,plain,
mult(mult(X,rd(X,ld(ld(X12,unit),X12))),mult(X12,X12)) = mult(mult(X,rd(X,mult(X12,X12))),mult(X12,X12)),
inference(congruence,[status(thm)],[c672]) ).
cnf(c674,plain,
ld(rd(X,mult(X12,X12)),mult(mult(X,rd(X,ld(ld(X12,unit),X12))),mult(X12,X12))) = ld(rd(X,mult(X12,X12)),mult(mult(X,rd(X,mult(X12,X12))),mult(X12,X12))),
inference(congruence,[status(thm)],[c673]) ).
cnf(c675,plain,
mult(mult(X,rd(X,mult(X12,X12))),mult(X12,X12)) = mult(rd(X,mult(X12,X12)),mult(mult(X12,X12),X)),
inference(substitution,[status(thm)],[c474]) ).
cnf(c676,plain,
ld(rd(X,mult(X12,X12)),mult(mult(X,rd(X,mult(X12,X12))),mult(X12,X12))) = ld(rd(X,mult(X12,X12)),mult(rd(X,mult(X12,X12)),mult(mult(X12,X12),X))),
inference(congruence,[status(thm)],[c675]) ).
cnf(c677,plain,
ld(rd(X,mult(X12,X12)),mult(rd(X,mult(X12,X12)),mult(mult(X12,X12),X))) = mult(mult(X12,X12),X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c678,plain,
ld(rd(X,mult(X12,X12)),mult(mult(X,rd(X,mult(X12,X12))),mult(X12,X12))) = mult(mult(X12,X12),X),
inference(transitivity,[status(thm)],[c676,c677]) ).
cnf(c679,plain,
ld(rd(X,mult(X12,X12)),mult(mult(X,rd(X,ld(ld(X12,unit),X12))),mult(X12,X12))) = mult(mult(X12,X12),X),
inference(transitivity,[status(thm)],[c674,c678]) ).
cnf(c680,plain,
ld(rd(X,ld(ld(X12,unit),X12)),mult(mult(X,rd(X,ld(ld(X12,unit),X12))),mult(X12,X12))) = mult(mult(X12,X12),X),
inference(transitivity,[status(thm)],[c669,c679]) ).
cnf(c681,plain,
ld(rd(X,ld(ld(X12,unit),X12)),mult(mult(X,mult(X,ld(X12,ld(X12,unit)))),mult(X12,X12))) = mult(mult(X12,X12),X),
inference(transitivity,[status(thm)],[c666,c680]) ).
cnf(c682,plain,
ld(mult(X,ld(X12,ld(X12,unit))),mult(mult(X,mult(X,ld(X12,ld(X12,unit)))),mult(X12,X12))) = mult(mult(X12,X12),X),
inference(transitivity,[status(thm)],[c662,c681]) ).
cnf(c683,plain,
ld(mult(X,ld(X12,ld(X12,unit))),rd(mult(X,mult(X,ld(X12,ld(X12,unit)))),ld(X12,ld(X12,unit)))) = mult(mult(X12,X12),X),
inference(transitivity,[status(thm)],[c660,c682]) ).
cnf(c684,plain,
ld(ld(X12,ld(X12,unit)),X) = mult(mult(X12,X12),X),
inference(transitivity,[status(thm)],[c634,c683]) ).
cnf(c685,plain,
ld(ld(X,ld(X,unit)),X12) = mult(mult(X,X),X12),
inference(substitution,[status(thm)],[c684]) ).
cnf(c686,plain,
ld(ld(mult(X12,X),rd(X12,X)),X12) = mult(mult(X,X),X12),
inference(transitivity,[status(thm)],[c632,c685]) ).
cnf(c687,plain,
mult(ld(rd(X12,X),mult(X12,X)),X12) = mult(mult(X,X),X12),
inference(transitivity,[status(thm)],[c607,c686]) ).
cnf(c688,plain,
mult(mult(rd(X,X12),mult(X12,X)),X12) = mult(mult(X,X),X12),
inference(transitivity,[status(thm)],[c606,c687]) ).
cnf(c689,plain,
mult(mult(rd(X,X12),mult(X12,mult(rd(X,X12),X12))),X12) = mult(mult(X,X),X12),
inference(transitivity,[status(thm)],[c604,c688]) ).
cnf(c690,plain,
mult(mult(rd(X,X12),mult(X12,rd(X,X12))),mult(X12,X12)) = mult(mult(X,X),X12),
inference(transitivity,[status(thm)],[c600,c689]) ).
cnf(c691,plain,
mult(ld(rd(X12,X),mult(X12,rd(X,X12))),mult(X12,X12)) = mult(mult(X,X),X12),
inference(transitivity,[status(thm)],[c594,c690]) ).
cnf(c692,plain,
ld(ld(mult(X12,rd(X,X12)),rd(X12,X)),mult(X12,X12)) = mult(mult(X,X),X12),
inference(transitivity,[status(thm)],[c591,c691]) ).
cnf(c693,plain,
ld(ld(rd(mult(X12,X),X12),rd(X12,X)),mult(X12,X12)) = mult(mult(X,X),X12),
inference(transitivity,[status(thm)],[c585,c692]) ).
cnf(c694,plain,
ld(ld(rd(X12,rd(X12,X)),rd(X12,X)),mult(X12,X12)) = mult(mult(X,X),X12),
inference(transitivity,[status(thm)],[c582,c693]) ).
cnf(c695,plain,
rd(mult(X12,X12),ld(ld(rd(X12,rd(X12,X)),rd(X12,X)),mult(X12,X12))) = rd(mult(X12,X12),mult(mult(X,X),X12)),
inference(congruence,[status(thm)],[c694]) ).
cnf(c696,plain,
ld(rd(X,mult(X12,X12)),unit) = rd(mult(X12,X12),X),
inference(substitution,[status(thm)],[c506]) ).
cnf(c697,plain,
rd(mult(X12,X12),X) = ld(rd(X,mult(X12,X12)),unit),
inference(symmetry,[status(thm)],[c696]) ).
cnf(c698,plain,
rd(rd(X,X12),X12) = rd(X,mult(X12,X12)),
inference(substitution,[status(thm)],[c620]) ).
cnf(c699,plain,
rd(X,mult(X12,X12)) = rd(rd(X,X12),X12),
inference(symmetry,[status(thm)],[c698]) ).
cnf(c700,plain,
ld(rd(X,mult(X12,X12)),unit) = ld(rd(rd(X,X12),X12),unit),
inference(congruence,[status(thm)],[c699]) ).
cnf(c701,plain,
ld(rd(rd(X,X12),X12),unit) = rd(X12,rd(X,X12)),
inference(substitution,[status(thm)],[c506]) ).
cnf(c702,plain,
ld(rd(X,mult(X12,X12)),unit) = rd(X12,rd(X,X12)),
inference(transitivity,[status(thm)],[c700,c701]) ).
cnf(c703,plain,
rd(mult(X12,X12),X) = rd(X12,rd(X,X12)),
inference(transitivity,[status(thm)],[c697,c702]) ).
cnf(c704,plain,
rd(mult(X12,X12),mult(mult(X,X),X12)) = rd(X12,rd(mult(mult(X,X),X12),X12)),
inference(substitution,[status(thm)],[c703]) ).
cnf(c705,plain,
rd(mult(mult(X,X),X12),X12) = mult(X,X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c706,plain,
rd(X12,rd(mult(mult(X,X),X12),X12)) = rd(X12,mult(X,X)),
inference(congruence,[status(thm)],[c705]) ).
cnf(c707,plain,
rd(mult(X12,X12),mult(mult(X,X),X12)) = rd(X12,mult(X,X)),
inference(transitivity,[status(thm)],[c704,c706]) ).
cnf(c708,plain,
rd(mult(X12,X12),ld(ld(rd(X12,rd(X12,X)),rd(X12,X)),mult(X12,X12))) = rd(X12,mult(X,X)),
inference(transitivity,[status(thm)],[c695,c707]) ).
cnf(c709,plain,
ld(rd(X12,rd(X12,X)),rd(X12,X)) = rd(X12,mult(X,X)),
inference(transitivity,[status(thm)],[c579,c708]) ).
cnf(c710,plain,
rd(mult(X13,X12),ld(rd(X12,rd(X12,X)),rd(X12,X))) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(congruence,[status(thm)],[c709]) ).
cnf(c711,plain,
rd(mult(X13,X12),ld(rd(mult(X12,X),X12),rd(X12,X))) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c577,c710]) ).
cnf(c712,plain,
rd(mult(X13,X12),ld(mult(X12,rd(X,X12)),rd(X12,X))) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c542,c711]) ).
cnf(c713,plain,
mult(mult(X13,X12),ld(rd(X12,X),mult(X12,rd(X,X12)))) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c540,c712]) ).
cnf(c714,plain,
mult(mult(X13,X12),mult(rd(X,X12),mult(X12,rd(X,X12)))) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c525,c713]) ).
cnf(c715,plain,
mult(mult(X13,mult(X12,mult(rd(X,X12),X12))),rd(X,X12)) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c519,c714]) ).
cnf(c716,plain,
mult(mult(X13,mult(X12,X)),rd(X,X12)) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c518,c715]) ).
cnf(c717,plain,
rd(mult(X13,mult(X12,X)),rd(X12,X)) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c513,c716]) ).
cnf(c718,plain,
rd(mult(X13,mult(mult(X12,X),X)),rd(mult(X12,X),X)) = rd(mult(X13,mult(X12,X)),rd(mult(X12,X),mult(X,X))),
inference(substitution,[status(thm)],[c717]) ).
cnf(c719,plain,
rd(mult(X13,mult(X12,X)),rd(mult(X12,X),mult(X,X))) = rd(mult(X13,mult(X12,X)),rd(X12,X)),
inference(congruence,[status(thm)],[c611]) ).
cnf(c720,plain,
rd(mult(X13,mult(X12,X)),rd(mult(X12,X),mult(X,X))) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c719,c717]) ).
cnf(c721,plain,
rd(mult(X13,mult(mult(X12,X),X)),rd(mult(X12,X),X)) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c718,c720]) ).
cnf(c722,plain,
rd(mult(X13,mult(mult(X12,X),X)),X12) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c501,c721]) ).
cnf(c723,plain,
rd(mult(X13,mult(X12,mult(X,X))),X12) = rd(mult(X13,X12),rd(X12,mult(X,X))),
inference(transitivity,[status(thm)],[c498,c722]) ).
cnf(c724,plain,
rd(mult(X13,mult(X12,mult(f(X),f(X)))),X12) = rd(mult(X13,X12),rd(X12,mult(f(X),f(X)))),
inference(substitution,[status(thm)],[c723]) ).
cnf(c725,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c726,plain,
rd(X12,mult(f(X),f(X))) = rd(X12,X),
inference(congruence,[status(thm)],[c725]) ).
cnf(c727,plain,
rd(mult(X13,X12),rd(X12,mult(f(X),f(X)))) = rd(mult(X13,X12),rd(X12,X)),
inference(congruence,[status(thm)],[c726]) ).
cnf(c728,plain,
rd(mult(X13,mult(X12,mult(f(X),f(X)))),X12) = rd(mult(X13,X12),rd(X12,X)),
inference(transitivity,[status(thm)],[c724,c727]) ).
cnf(c729,plain,
rd(mult(X13,mult(X12,X)),X12) = rd(mult(X13,X12),rd(X12,X)),
inference(transitivity,[status(thm)],[c495,c728]) ).
cnf(c730,plain,
rd(mult(mult(X13,X12),mult(X,mult(X12,X))),X) = rd(mult(mult(X13,X12),X),rd(X,mult(X12,X))),
inference(substitution,[status(thm)],[c729]) ).
cnf(c731,plain,
rd(mult(mult(X13,X12),X),rd(X,mult(X12,X))) = rd(mult(mult(X13,X12),mult(X,mult(X12,X))),X),
inference(symmetry,[status(thm)],[c730]) ).
cnf(c732,plain,
mult(mult(X13,X12),mult(X,mult(X12,X))) = mult(mult(X13,mult(X12,mult(X,X12))),X),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c733,plain,
rd(mult(mult(X13,X12),mult(X,mult(X12,X))),X) = rd(mult(mult(X13,mult(X12,mult(X,X12))),X),X),
inference(congruence,[status(thm)],[c732]) ).
cnf(c734,plain,
rd(mult(mult(X13,mult(X12,mult(X,X12))),X),X) = mult(X13,mult(X12,mult(X,X12))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c735,plain,
rd(mult(mult(X13,X12),mult(X,mult(X12,X))),X) = mult(X13,mult(X12,mult(X,X12))),
inference(transitivity,[status(thm)],[c733,c734]) ).
cnf(c736,plain,
rd(mult(mult(X13,X12),X),rd(X,mult(X12,X))) = mult(X13,mult(X12,mult(X,X12))),
inference(transitivity,[status(thm)],[c731,c735]) ).
cnf(c737,plain,
rd(mult(mult(X13,X12),X),ld(X12,unit)) = mult(X13,mult(X12,mult(X,X12))),
inference(transitivity,[status(thm)],[c490,c736]) ).
cnf(c738,plain,
mult(mult(mult(X13,X12),X),X12) = mult(X13,mult(X12,mult(X,X12))),
inference(transitivity,[status(thm)],[c383,c737]) ).
cnf(c739,plain,
mult(mult(mult(x3,x5),x4),x5) = mult(x3,mult(x5,mult(x4,x5))),
inference(substitution,[status(thm)],[c738]) ).
cnf(c740,plain,
mult(x3,mult(x5,mult(x4,x5))) = mult(mult(mult(x3,x5),x4),x5),
inference(symmetry,[status(thm)],[c739]) ).
cnf(c741,plain,
$false,
inference(resolution,[status(thm)],[c4,c740]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP667+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.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 10:36:23 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 80.91/10.66 Command-line arguments: --no-flatten-goal
% 80.91/10.66
% 80.91/10.66 % SZS status Theorem
% 80.91/10.66
% 81.72/10.72 % SZS output start CNFRefutation
% See solution above
% 73.94/11.11
% 73.94/11.11 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------