%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP668-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:11:40 AM UTC 2026
% Result : Unsatisfiable 20.40s 3.02s
% Output : CNFRefutation 22.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 9
% Syntax : Number of clauses : 456 ( 456 unt; 0 nHn; 4 RR)
% Number of literals : 456 ( 455 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 1011 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c3,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
mult(ld(X2,unit),X) = mult(ld(X2,unit),mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
mult(mult(A2,B2),A2) = mult(A2,mult(B2,A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
cnf(c7,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
mult(X2,mult(X,X2)) = mult(mult(X2,X),X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
rd(mult(X2,mult(X,X2)),X2) = rd(mult(mult(X2,X),X2),X2),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c11,plain,
rd(mult(mult(X2,X),X2),X2) = mult(X2,X),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
rd(mult(X2,mult(X,X2)),X2) = mult(X2,X),
inference(transitivity,[status(thm)],[c9,c11]) ).
cnf(c13,plain,
rd(mult(X2,mult(rd(X,X2),X2)),X2) = mult(X2,rd(X,X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
mult(X2,rd(X,X2)) = rd(mult(X2,mult(rd(X,X2),X2)),X2),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c16,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
mult(X2,mult(rd(X,X2),X2)) = mult(X2,X),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
rd(mult(X2,mult(rd(X,X2),X2)),X2) = rd(mult(X2,X),X2),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
mult(X2,rd(X,X2)) = rd(mult(X2,X),X2),
inference(transitivity,[status(thm)],[c14,c18]) ).
cnf(c20,plain,
rd(mult(X2,X),X2) = mult(X2,rd(X,X2)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
ld(X2,rd(mult(X2,X),X2)) = ld(X2,mult(X2,rd(X,X2))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,axiom,
ld(A2,mult(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c23,plain,
ld(X2,mult(X2,rd(X,X2))) = rd(X,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
ld(X2,rd(mult(X2,X),X2)) = rd(X,X2),
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
ld(X,rd(mult(X,unit),X)) = rd(unit,X),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
rd(unit,X) = ld(X,rd(mult(X,unit),X)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c28,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
rd(mult(X,unit),X) = rd(X,X),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
ld(X,rd(mult(X,unit),X)) = ld(X,rd(X,X)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,axiom,
mult(unit,A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c32,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
rd(X,X) = rd(mult(unit,X),X),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
rd(mult(unit,X),X) = unit,
inference(substitution,[status(thm)],[c10]) ).
cnf(c36,plain,
rd(X,X) = unit,
inference(transitivity,[status(thm)],[c34,c35]) ).
cnf(c37,plain,
ld(X,rd(X,X)) = ld(X,unit),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
ld(X,rd(mult(X,unit),X)) = ld(X,unit),
inference(transitivity,[status(thm)],[c30,c37]) ).
cnf(c39,plain,
rd(unit,X) = ld(X,unit),
inference(transitivity,[status(thm)],[c26,c38]) ).
cnf(c40,plain,
ld(X,unit) = rd(unit,X),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
mult(ld(X2,unit),mult(X2,X)) = mult(rd(unit,X2),mult(X2,X)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,axiom,
mult(A2,mult(B2,mult(B2,C))) = mult(mult(mult(A2,B2),B2),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c43,plain,
mult(rd(X2,X),mult(X,mult(X,X3))) = mult(mult(mult(rd(X2,X),X),X),X3),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c45,plain,
mult(mult(rd(X2,X),X),X) = mult(X2,X),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
mult(mult(mult(rd(X3,X2),X2),X2),X) = mult(mult(X3,X2),X),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
mult(rd(X3,X2),mult(X2,mult(X2,X))) = mult(mult(X3,X2),X),
inference(transitivity,[status(thm)],[c43,c46]) ).
cnf(c48,plain,
mult(rd(X3,X2),mult(X2,mult(X2,ld(X2,X)))) = mult(mult(X3,X2),ld(X2,X)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
mult(mult(X3,X2),ld(X2,X)) = mult(rd(X3,X2),mult(X2,mult(X2,ld(X2,X)))),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c51,plain,
mult(X2,mult(X2,ld(X2,X))) = mult(X2,X),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
mult(rd(X3,X2),mult(X2,mult(X2,ld(X2,X)))) = mult(rd(X3,X2),mult(X2,X)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
mult(mult(X3,X2),ld(X2,X)) = mult(rd(X3,X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c49,c52]) ).
cnf(c54,plain,
mult(mult(unit,X2),ld(X2,X)) = mult(rd(unit,X2),mult(X2,X)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
mult(rd(unit,X2),mult(X2,X)) = mult(mult(unit,X2),ld(X2,X)),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c31]) ).
cnf(c57,plain,
mult(mult(unit,X2),ld(X2,X)) = mult(X2,ld(X2,X)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
mult(mult(unit,X2),ld(X2,X)) = X,
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
mult(rd(unit,X2),mult(X2,X)) = X,
inference(transitivity,[status(thm)],[c55,c59]) ).
cnf(c61,plain,
mult(ld(X2,unit),mult(X2,X)) = X,
inference(transitivity,[status(thm)],[c41,c60]) ).
cnf(c62,plain,
mult(ld(X2,unit),mult(X2,ld(X2,X))) = ld(X2,X),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
mult(ld(X2,unit),X) = ld(X2,X),
inference(transitivity,[status(thm)],[c5,c62]) ).
cnf(c64,plain,
mult(ld(X,unit),mult(X2,X2)) = ld(X,mult(X2,X2)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
ld(X,mult(X2,X2)) = mult(ld(X,unit),mult(X2,X2)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
rd(X2,ld(X,mult(X2,X2))) = rd(X2,mult(ld(X,unit),mult(X2,X2))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
mult(mult(mult(X2,X),X),unit) = mult(mult(X2,X),X),
inference(substitution,[status(thm)],[c27]) ).
cnf(c68,plain,
mult(mult(X2,X),X) = mult(mult(mult(X2,X),X),unit),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
mult(X2,mult(X,mult(X,unit))) = mult(mult(mult(X2,X),X),unit),
inference(substitution,[status(thm)],[c42]) ).
cnf(c70,plain,
mult(mult(mult(X2,X),X),unit) = mult(X2,mult(X,mult(X,unit))),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c27]) ).
cnf(c72,plain,
mult(X,mult(X,unit)) = mult(X,X),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
mult(X2,mult(X,mult(X,unit))) = mult(X2,mult(X,X)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
mult(mult(mult(X2,X),X),unit) = mult(X2,mult(X,X)),
inference(transitivity,[status(thm)],[c70,c73]) ).
cnf(c75,plain,
mult(mult(X2,X),X) = mult(X2,mult(X,X)),
inference(transitivity,[status(thm)],[c68,c74]) ).
cnf(c76,plain,
mult(mult(X,X2),X2) = mult(X,mult(X2,X2)),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
mult(X,mult(X2,X2)) = mult(mult(X,X2),X2),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
rd(X2,mult(X,mult(X2,X2))) = rd(X2,mult(mult(X,X2),X2)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
mult(ld(X,unit),mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c61]) ).
cnf(c80,plain,
X2 = mult(ld(X,unit),mult(X,X2)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
rd(X2,mult(X,X2)) = rd(mult(ld(X,unit),mult(X,X2)),mult(X,X2)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
rd(mult(ld(X,unit),mult(X,X2)),mult(X,X2)) = ld(X,unit),
inference(substitution,[status(thm)],[c10]) ).
cnf(c83,plain,
rd(X2,mult(X,X2)) = ld(X,unit),
inference(transitivity,[status(thm)],[c81,c82]) ).
cnf(c84,plain,
rd(X2,mult(mult(X,X2),X2)) = ld(mult(X,X2),unit),
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
rd(unit,ld(X,unit)) = ld(ld(X,unit),unit),
inference(substitution,[status(thm)],[c39]) ).
cnf(c86,plain,
ld(ld(X,unit),unit) = rd(unit,ld(X,unit)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c88,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
rd(X2,ld(X,X2)) = rd(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
rd(mult(X,ld(X,X2)),ld(X,X2)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c91,plain,
rd(X2,ld(X,X2)) = X,
inference(transitivity,[status(thm)],[c89,c90]) ).
cnf(c92,plain,
rd(unit,ld(X,unit)) = X,
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
ld(ld(X,unit),unit) = X,
inference(transitivity,[status(thm)],[c86,c92]) ).
cnf(c94,plain,
X = ld(ld(X,unit),unit),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
mult(mult(X2,ld(X,unit)),X) = mult(mult(X2,ld(X,unit)),ld(ld(X,unit),unit)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
mult(mult(X2,ld(X,unit)),ld(ld(X,unit),unit)) = mult(rd(X2,ld(X,unit)),mult(ld(X,unit),unit)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c97,plain,
X = mult(ld(X2,unit),mult(X2,X)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c98,plain,
ld(ld(X2,unit),X) = ld(ld(X2,unit),mult(ld(X2,unit),mult(X2,X))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
ld(ld(X2,unit),mult(ld(X2,unit),mult(X2,X))) = mult(X2,X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c100,plain,
ld(ld(X2,unit),X) = mult(X2,X),
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
ld(ld(rd(X3,X2),unit),X) = mult(rd(X3,X2),X),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
mult(rd(X3,X2),X) = ld(ld(rd(X3,X2),unit),X),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
rd(X,mult(rd(X2,X),X)) = ld(rd(X2,X),unit),
inference(substitution,[status(thm)],[c83]) ).
cnf(c104,plain,
ld(rd(X2,X),unit) = rd(X,mult(rd(X2,X),X)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c106,plain,
rd(X,mult(rd(X2,X),X)) = rd(X,X2),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
ld(rd(X2,X),unit) = rd(X,X2),
inference(transitivity,[status(thm)],[c104,c106]) ).
cnf(c108,plain,
ld(ld(rd(X3,X2),unit),X) = ld(rd(X2,X3),X),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
mult(rd(X3,X2),X) = ld(rd(X2,X3),X),
inference(transitivity,[status(thm)],[c102,c108]) ).
cnf(c110,plain,
mult(rd(X2,ld(X,unit)),mult(ld(X,unit),unit)) = ld(rd(ld(X,unit),X2),mult(ld(X,unit),unit)),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
mult(ld(X,unit),unit) = ld(X,unit),
inference(substitution,[status(thm)],[c63]) ).
cnf(c112,plain,
ld(rd(ld(X,unit),X2),mult(ld(X,unit),unit)) = ld(rd(ld(X,unit),X2),ld(X,unit)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c114,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
ld(rd(X2,X),X2) = ld(rd(X2,X),mult(rd(X2,X),X)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
ld(rd(X2,X),mult(rd(X2,X),X)) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c117,plain,
ld(rd(X2,X),X2) = X,
inference(transitivity,[status(thm)],[c115,c116]) ).
cnf(c118,plain,
ld(rd(ld(X,unit),X2),ld(X,unit)) = X2,
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
ld(rd(ld(X,unit),X2),mult(ld(X,unit),unit)) = X2,
inference(transitivity,[status(thm)],[c112,c118]) ).
cnf(c120,plain,
mult(rd(X2,ld(X,unit)),mult(ld(X,unit),unit)) = X2,
inference(transitivity,[status(thm)],[c110,c119]) ).
cnf(c121,plain,
mult(mult(X2,ld(X,unit)),ld(ld(X,unit),unit)) = X2,
inference(transitivity,[status(thm)],[c96,c120]) ).
cnf(c122,plain,
mult(mult(X2,ld(X,unit)),X) = X2,
inference(transitivity,[status(thm)],[c95,c121]) ).
cnf(c123,plain,
mult(mult(rd(X2,ld(X,unit)),ld(X,unit)),X) = rd(X2,ld(X,unit)),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
rd(X2,ld(X,unit)) = mult(mult(rd(X2,ld(X,unit)),ld(X,unit)),X),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
mult(rd(X2,ld(X,unit)),ld(X,unit)) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c126,plain,
mult(mult(rd(X2,ld(X,unit)),ld(X,unit)),X) = mult(X2,X),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
rd(X2,ld(X,unit)) = mult(X2,X),
inference(transitivity,[status(thm)],[c124,c126]) ).
cnf(c128,plain,
mult(X2,X) = rd(X2,ld(X,unit)),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
ld(mult(X2,X),unit) = ld(rd(X2,ld(X,unit)),unit),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
ld(rd(X2,ld(X,unit)),unit) = rd(ld(X,unit),X2),
inference(substitution,[status(thm)],[c107]) ).
cnf(c131,plain,
rd(mult(mult(X2,ld(X,unit)),X),X) = mult(X2,ld(X,unit)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c132,plain,
mult(X2,ld(X,unit)) = rd(mult(mult(X2,ld(X,unit)),X),X),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
rd(mult(mult(X2,ld(X,unit)),X),X) = rd(X2,X),
inference(congruence,[status(thm)],[c122]) ).
cnf(c134,plain,
mult(X2,ld(X,unit)) = rd(X2,X),
inference(transitivity,[status(thm)],[c132,c133]) ).
cnf(c135,plain,
mult(ld(X2,unit),ld(X,unit)) = rd(ld(X2,unit),X),
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
rd(ld(X2,unit),X) = mult(ld(X2,unit),ld(X,unit)),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
mult(ld(X2,unit),ld(X,unit)) = ld(X2,ld(X,unit)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c138,plain,
rd(ld(X2,unit),X) = ld(X2,ld(X,unit)),
inference(transitivity,[status(thm)],[c136,c137]) ).
cnf(c139,plain,
rd(ld(X,unit),X2) = ld(X,ld(X2,unit)),
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
ld(rd(X2,ld(X,unit)),unit) = ld(X,ld(X2,unit)),
inference(transitivity,[status(thm)],[c130,c139]) ).
cnf(c141,plain,
ld(mult(X2,X),unit) = ld(X,ld(X2,unit)),
inference(transitivity,[status(thm)],[c129,c140]) ).
cnf(c142,plain,
ld(mult(X,X2),unit) = ld(X2,ld(X,unit)),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
rd(X2,mult(mult(X,X2),X2)) = ld(X2,ld(X,unit)),
inference(transitivity,[status(thm)],[c84,c142]) ).
cnf(c144,plain,
rd(X2,mult(X,mult(X2,X2))) = ld(X2,ld(X,unit)),
inference(transitivity,[status(thm)],[c78,c143]) ).
cnf(c145,plain,
rd(X2,mult(ld(X,unit),mult(X2,X2))) = ld(X2,ld(ld(X,unit),unit)),
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
ld(X2,ld(ld(X,unit),unit)) = ld(X2,X),
inference(congruence,[status(thm)],[c93]) ).
cnf(c147,plain,
rd(X2,mult(ld(X,unit),mult(X2,X2))) = ld(X2,X),
inference(transitivity,[status(thm)],[c145,c146]) ).
cnf(c148,plain,
rd(X2,ld(X,mult(X2,X2))) = ld(X2,X),
inference(transitivity,[status(thm)],[c66,c147]) ).
cnf(c149,plain,
ld(X2,X) = rd(X2,ld(X,mult(X2,X2))),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
mult(X3,ld(X2,X)) = mult(X3,rd(X2,ld(X,mult(X2,X2)))),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
ld(rd(X,X2),unit) = rd(X2,X),
inference(substitution,[status(thm)],[c107]) ).
cnf(c152,plain,
rd(X2,X) = ld(rd(X,X2),unit),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
mult(X3,rd(X2,X)) = mult(X3,ld(rd(X,X2),unit)),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
mult(X3,ld(rd(X,X2),unit)) = rd(X3,rd(X,X2)),
inference(substitution,[status(thm)],[c134]) ).
cnf(c155,plain,
mult(X3,rd(X2,X)) = rd(X3,rd(X,X2)),
inference(transitivity,[status(thm)],[c153,c154]) ).
cnf(c156,plain,
mult(X3,rd(X2,ld(X,mult(X2,X2)))) = rd(X3,rd(ld(X,mult(X2,X2)),X2)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
mult(ld(X2,unit),mult(X,X)) = ld(X2,mult(X,X)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c158,plain,
ld(X2,mult(X,X)) = mult(ld(X2,unit),mult(X,X)),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
rd(ld(X2,mult(X,X)),X) = rd(mult(ld(X2,unit),mult(X,X)),X),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
mult(X2,mult(X,X)) = mult(mult(X2,X),X),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c161,plain,
rd(mult(X2,mult(X,X)),X) = rd(mult(mult(X2,X),X),X),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
rd(mult(mult(X2,X),X),X) = mult(X2,X),
inference(substitution,[status(thm)],[c10]) ).
cnf(c163,plain,
rd(mult(X2,mult(X,X)),X) = mult(X2,X),
inference(transitivity,[status(thm)],[c161,c162]) ).
cnf(c164,plain,
rd(mult(ld(X2,unit),mult(X,X)),X) = mult(ld(X2,unit),X),
inference(substitution,[status(thm)],[c163]) ).
cnf(c165,plain,
rd(mult(ld(X2,unit),mult(X,X)),X) = ld(X2,X),
inference(transitivity,[status(thm)],[c164,c63]) ).
cnf(c166,plain,
rd(ld(X2,mult(X,X)),X) = ld(X2,X),
inference(transitivity,[status(thm)],[c159,c165]) ).
cnf(c167,plain,
rd(ld(X,mult(X2,X2)),X2) = ld(X,X2),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
rd(X3,rd(ld(X,mult(X2,X2)),X2)) = rd(X3,ld(X,X2)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
mult(X3,rd(X2,ld(X,mult(X2,X2)))) = rd(X3,ld(X,X2)),
inference(transitivity,[status(thm)],[c156,c168]) ).
cnf(c170,plain,
mult(X3,ld(X2,X)) = rd(X3,ld(X,X2)),
inference(transitivity,[status(thm)],[c150,c169]) ).
cnf(c171,plain,
mult(X3,ld(X4,mult(mult(X4,X2),mult(mult(X,X2),X)))) = rd(X3,ld(mult(mult(X4,X2),mult(mult(X,X2),X)),X4)),
inference(substitution,[status(thm)],[c170]) ).
cnf(c172,plain,
rd(X4,ld(mult(mult(X,X3),mult(mult(X2,X3),X2)),X)) = mult(X4,ld(X,mult(mult(X,X3),mult(mult(X2,X3),X2)))),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
mult(rd(X2,X3),mult(X3,mult(X3,X))) = ld(rd(X3,X2),mult(X3,mult(X3,X))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c174,plain,
ld(rd(X3,X2),mult(X3,mult(X3,X))) = mult(rd(X2,X3),mult(X3,mult(X3,X))),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
mult(rd(X2,X3),mult(X3,mult(X3,X))) = mult(mult(X2,X3),X),
inference(substitution,[status(thm)],[c47]) ).
cnf(c176,plain,
ld(rd(X3,X2),mult(X3,mult(X3,X))) = mult(mult(X2,X3),X),
inference(transitivity,[status(thm)],[c174,c175]) ).
cnf(c177,plain,
ld(rd(X2,mult(X2,X)),mult(X2,mult(X2,X))) = mult(mult(mult(X2,X),X2),X),
inference(substitution,[status(thm)],[c176]) ).
cnf(c178,plain,
mult(mult(mult(X2,X),X2),X) = ld(rd(X2,mult(X2,X)),mult(X2,mult(X2,X))),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
mult(mult(rd(X2,X),X),X) = mult(rd(X2,X),mult(X,X)),
inference(substitution,[status(thm)],[c75]) ).
cnf(c180,plain,
mult(rd(X2,X),mult(X,X)) = mult(mult(rd(X2,X),X),X),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c182,plain,
mult(mult(rd(X2,X),X),X) = mult(X2,X),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
mult(rd(X2,X),mult(X,X)) = mult(X2,X),
inference(transitivity,[status(thm)],[c180,c182]) ).
cnf(c184,plain,
mult(X2,X) = mult(rd(X2,X),mult(X,X)),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
ld(rd(X2,X),mult(X2,X)) = ld(rd(X2,X),mult(rd(X2,X),mult(X,X))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
ld(rd(X2,X),mult(rd(X2,X),mult(X,X))) = mult(X,X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c187,plain,
ld(rd(X2,X),mult(X2,X)) = mult(X,X),
inference(transitivity,[status(thm)],[c185,c186]) ).
cnf(c188,plain,
ld(rd(X2,mult(X2,X)),mult(X2,mult(X2,X))) = mult(mult(X2,X),mult(X2,X)),
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
mult(mult(mult(X2,X),X2),X) = mult(mult(X2,X),mult(X2,X)),
inference(transitivity,[status(thm)],[c178,c188]) ).
cnf(c190,plain,
rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(mult(mult(X2,X),X2),X)) = rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(mult(X2,X),mult(X2,X))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
rd(mult(rd(X2,mult(X,X)),mult(X,X)),X) = mult(rd(X2,mult(X,X)),X),
inference(substitution,[status(thm)],[c163]) ).
cnf(c192,plain,
mult(rd(X2,mult(X,X)),X) = rd(mult(rd(X2,mult(X,X)),mult(X,X)),X),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
mult(rd(X2,mult(X,X)),mult(X,X)) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c194,plain,
rd(mult(rd(X2,mult(X,X)),mult(X,X)),X) = rd(X2,X),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
mult(rd(X2,mult(X,X)),X) = rd(X2,X),
inference(transitivity,[status(thm)],[c192,c194]) ).
cnf(c196,plain,
rd(X2,X) = mult(rd(X2,mult(X,X)),X),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
rd(rd(X2,X),X) = rd(mult(rd(X2,mult(X,X)),X),X),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
rd(mult(rd(X2,mult(X,X)),X),X) = rd(X2,mult(X,X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c199,plain,
rd(rd(X2,X),X) = rd(X2,mult(X,X)),
inference(transitivity,[status(thm)],[c197,c198]) ).
cnf(c200,plain,
rd(rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(X2,X)),mult(X2,X)) = rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(mult(X2,X),mult(X2,X))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(mult(X2,X),mult(X2,X))) = rd(rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(X2,X)),mult(X2,X)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
ld(rd(mult(X2,X),rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(X2,X))),unit) = rd(rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(X2,X)),mult(X2,X)),
inference(substitution,[status(thm)],[c107]) ).
cnf(c203,plain,
rd(rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(X2,X)),mult(X2,X)) = ld(rd(mult(X2,X),rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(X2,X))),unit),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
mult(mult(X3,X),rd(mult(X3,X),X2)) = rd(mult(X3,X),rd(X2,mult(X3,X))),
inference(substitution,[status(thm)],[c155]) ).
cnf(c205,plain,
rd(mult(X3,X),rd(X2,mult(X3,X))) = mult(mult(X3,X),rd(mult(X3,X),X2)),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
mult(mult(X3,X),ld(X2,unit)) = rd(mult(X3,X),X2),
inference(substitution,[status(thm)],[c134]) ).
cnf(c207,plain,
rd(mult(X3,X),X2) = mult(mult(X3,X),ld(X2,unit)),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
mult(mult(X3,X),rd(mult(X3,X),X2)) = mult(mult(X3,X),mult(mult(X3,X),ld(X2,unit))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
mult(X3,ld(X3,mult(mult(X3,X2),mult(mult(X3,X2),X)))) = mult(mult(X3,X2),mult(mult(X3,X2),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c210,plain,
mult(mult(X3,X2),mult(mult(X3,X2),X)) = mult(X3,ld(X3,mult(mult(X3,X2),mult(mult(X3,X2),X)))),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c212,plain,
mult(mult(mult(X3,X2),X3),ld(mult(X2,X3),X)) = mult(mult(X3,mult(X2,X3)),ld(mult(X2,X3),X)),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
mult(mult(X3,mult(X2,X3)),ld(mult(X2,X3),X)) = mult(rd(X3,mult(X2,X3)),mult(mult(X2,X3),X)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c214,plain,
mult(rd(X3,mult(X2,X3)),mult(mult(X2,X3),X)) = ld(rd(mult(X2,X3),X3),mult(mult(X2,X3),X)),
inference(substitution,[status(thm)],[c109]) ).
cnf(c215,plain,
rd(mult(X,X2),X2) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c216,plain,
ld(rd(mult(X2,X3),X3),mult(mult(X2,X3),X)) = ld(X2,mult(mult(X2,X3),X)),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
mult(rd(X3,mult(X2,X3)),mult(mult(X2,X3),X)) = ld(X2,mult(mult(X2,X3),X)),
inference(transitivity,[status(thm)],[c214,c216]) ).
cnf(c218,plain,
mult(mult(X3,mult(X2,X3)),ld(mult(X2,X3),X)) = ld(X2,mult(mult(X2,X3),X)),
inference(transitivity,[status(thm)],[c213,c217]) ).
cnf(c219,plain,
mult(mult(mult(X3,X2),X3),ld(mult(X2,X3),X)) = ld(X2,mult(mult(X2,X3),X)),
inference(transitivity,[status(thm)],[c212,c218]) ).
cnf(c220,plain,
mult(mult(mult(X2,X3),X2),ld(mult(X3,X2),mult(mult(X3,X2),X))) = ld(X3,mult(mult(X3,X2),mult(mult(X3,X2),X))),
inference(substitution,[status(thm)],[c219]) ).
cnf(c221,plain,
ld(X3,mult(mult(X3,X2),mult(mult(X3,X2),X))) = mult(mult(mult(X2,X3),X2),ld(mult(X3,X2),mult(mult(X3,X2),X))),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
ld(mult(X3,X2),mult(mult(X3,X2),X)) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c223,plain,
mult(mult(mult(X2,X3),X2),ld(mult(X3,X2),mult(mult(X3,X2),X))) = mult(mult(mult(X2,X3),X2),X),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
ld(X3,mult(mult(X3,X2),mult(mult(X3,X2),X))) = mult(mult(mult(X2,X3),X2),X),
inference(transitivity,[status(thm)],[c221,c223]) ).
cnf(c225,plain,
mult(X3,ld(X3,mult(mult(X3,X2),mult(mult(X3,X2),X)))) = mult(X3,mult(mult(mult(X2,X3),X2),X)),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
mult(mult(X3,X2),mult(mult(X3,X2),X)) = mult(X3,mult(mult(mult(X2,X3),X2),X)),
inference(transitivity,[status(thm)],[c210,c225]) ).
cnf(c227,plain,
mult(mult(X3,X),mult(mult(X3,X),ld(X2,unit))) = mult(X3,mult(mult(mult(X,X3),X),ld(X2,unit))),
inference(substitution,[status(thm)],[c226]) ).
cnf(c228,plain,
mult(mult(mult(X,X3),X),ld(X2,unit)) = rd(mult(mult(X,X3),X),X2),
inference(substitution,[status(thm)],[c134]) ).
cnf(c229,plain,
mult(X3,mult(mult(mult(X,X3),X),ld(X2,unit))) = mult(X3,rd(mult(mult(X,X3),X),X2)),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
mult(X3,rd(mult(mult(X,X3),X),X2)) = rd(X3,rd(X2,mult(mult(X,X3),X))),
inference(substitution,[status(thm)],[c155]) ).
cnf(c231,plain,
mult(X3,mult(mult(mult(X,X3),X),ld(X2,unit))) = rd(X3,rd(X2,mult(mult(X,X3),X))),
inference(transitivity,[status(thm)],[c229,c230]) ).
cnf(c232,plain,
mult(mult(X3,X),mult(mult(X3,X),ld(X2,unit))) = rd(X3,rd(X2,mult(mult(X,X3),X))),
inference(transitivity,[status(thm)],[c227,c231]) ).
cnf(c233,plain,
mult(mult(X3,X),rd(mult(X3,X),X2)) = rd(X3,rd(X2,mult(mult(X,X3),X))),
inference(transitivity,[status(thm)],[c208,c232]) ).
cnf(c234,plain,
rd(mult(X3,X),rd(X2,mult(X3,X))) = rd(X3,rd(X2,mult(mult(X,X3),X))),
inference(transitivity,[status(thm)],[c205,c233]) ).
cnf(c235,plain,
rd(mult(X3,X2),rd(mult(mult(X,X3),mult(mult(X2,X3),X2)),mult(X3,X2))) = rd(X3,rd(mult(mult(X,X3),mult(mult(X2,X3),X2)),mult(mult(X2,X3),X2))),
inference(substitution,[status(thm)],[c234]) ).
cnf(c236,plain,
rd(mult(mult(X,X3),mult(mult(X2,X3),X2)),mult(mult(X2,X3),X2)) = mult(X,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c237,plain,
rd(X3,rd(mult(mult(X,X3),mult(mult(X2,X3),X2)),mult(mult(X2,X3),X2))) = rd(X3,mult(X,X3)),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
rd(X3,rd(mult(mult(X,X3),mult(mult(X2,X3),X2)),mult(mult(X2,X3),X2))) = ld(X,unit),
inference(transitivity,[status(thm)],[c237,c83]) ).
cnf(c239,plain,
rd(mult(X3,X2),rd(mult(mult(X,X3),mult(mult(X2,X3),X2)),mult(X3,X2))) = ld(X,unit),
inference(transitivity,[status(thm)],[c235,c238]) ).
cnf(c240,plain,
rd(mult(X2,X),rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(X2,X))) = ld(X3,unit),
inference(substitution,[status(thm)],[c239]) ).
cnf(c241,plain,
ld(rd(mult(X2,X),rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(X2,X))),unit) = ld(ld(X3,unit),unit),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
ld(rd(mult(X2,X),rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(X2,X))),unit) = X3,
inference(transitivity,[status(thm)],[c241,c93]) ).
cnf(c243,plain,
rd(rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(X2,X)),mult(X2,X)) = X3,
inference(transitivity,[status(thm)],[c203,c242]) ).
cnf(c244,plain,
rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(mult(X2,X),mult(X2,X))) = X3,
inference(transitivity,[status(thm)],[c201,c243]) ).
cnf(c245,plain,
rd(mult(mult(X3,X2),mult(mult(X,X2),X)),mult(mult(mult(X2,X),X2),X)) = X3,
inference(transitivity,[status(thm)],[c190,c244]) ).
cnf(c246,plain,
rd(mult(mult(X,X3),mult(mult(X2,X3),X2)),mult(mult(mult(X3,X2),X3),X2)) = X,
inference(substitution,[status(thm)],[c245]) ).
cnf(c247,plain,
X = rd(mult(mult(X,X3),mult(mult(X2,X3),X2)),mult(mult(mult(X3,X2),X3),X2)),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
ld(X,mult(mult(X,X3),mult(mult(X2,X3),X2))) = ld(rd(mult(mult(X,X3),mult(mult(X2,X3),X2)),mult(mult(mult(X3,X2),X3),X2)),mult(mult(X,X3),mult(mult(X2,X3),X2))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
ld(rd(mult(mult(X,X3),mult(mult(X2,X3),X2)),mult(mult(mult(X3,X2),X3),X2)),mult(mult(X,X3),mult(mult(X2,X3),X2))) = mult(mult(mult(X3,X2),X3),X2),
inference(substitution,[status(thm)],[c117]) ).
cnf(c250,plain,
ld(X,mult(mult(X,X3),mult(mult(X2,X3),X2))) = mult(mult(mult(X3,X2),X3),X2),
inference(transitivity,[status(thm)],[c248,c249]) ).
cnf(c251,plain,
mult(X4,ld(X,mult(mult(X,X3),mult(mult(X2,X3),X2)))) = mult(X4,mult(mult(mult(X3,X2),X3),X2)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
mult(X3,mult(mult(mult(X2,X),X2),X)) = mult(X3,mult(mult(X2,X),mult(X2,X))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c253,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c254,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c253]) ).
cnf(c255,plain,
mult(X2,X) = mult(X2,mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
mult(X3,mult(X2,X)) = mult(X3,mult(X2,mult(X2,ld(X2,X)))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
rd(mult(X3,mult(X2,X)),ld(X2,X)) = rd(mult(X3,mult(X2,mult(X2,ld(X2,X)))),ld(X2,X)),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
mult(X3,mult(X2,mult(X2,X))) = mult(mult(mult(X3,X2),X2),X),
inference(substitution,[status(thm)],[c42]) ).
cnf(c259,plain,
rd(mult(X3,mult(X2,mult(X2,X))),X) = rd(mult(mult(mult(X3,X2),X2),X),X),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
rd(mult(mult(mult(X3,X2),X2),X),X) = mult(mult(X3,X2),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c261,plain,
rd(mult(mult(mult(X3,X2),X2),X),X) = mult(X3,mult(X2,X2)),
inference(transitivity,[status(thm)],[c260,c75]) ).
cnf(c262,plain,
rd(mult(X3,mult(X2,mult(X2,X))),X) = mult(X3,mult(X2,X2)),
inference(transitivity,[status(thm)],[c259,c261]) ).
cnf(c263,plain,
rd(mult(X3,mult(X2,mult(X2,ld(X2,X)))),ld(X2,X)) = mult(X3,mult(X2,X2)),
inference(substitution,[status(thm)],[c262]) ).
cnf(c264,plain,
rd(mult(X3,mult(X2,X)),ld(X2,X)) = mult(X3,mult(X2,X2)),
inference(transitivity,[status(thm)],[c257,c263]) ).
cnf(c265,plain,
rd(mult(X3,mult(mult(X2,X),X2)),ld(mult(X2,X),X2)) = mult(X3,mult(mult(X2,X),mult(X2,X))),
inference(substitution,[status(thm)],[c264]) ).
cnf(c266,plain,
mult(X3,mult(mult(X2,X),mult(X2,X))) = rd(mult(X3,mult(mult(X2,X),X2)),ld(mult(X2,X),X2)),
inference(symmetry,[status(thm)],[c265]) ).
cnf(c267,plain,
mult(X3,ld(ld(mult(X2,X),X2),unit)) = rd(X3,ld(mult(X2,X),X2)),
inference(substitution,[status(thm)],[c134]) ).
cnf(c268,plain,
rd(X3,ld(mult(X2,X),X2)) = mult(X3,ld(ld(mult(X2,X),X2),unit)),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c269,plain,
rd(mult(mult(X2,X),X2),mult(ld(mult(X3,X2),X3),mult(mult(X2,X),X2))) = ld(ld(mult(X3,X2),X3),unit),
inference(substitution,[status(thm)],[c83]) ).
cnf(c270,plain,
ld(ld(mult(X3,X2),X3),unit) = rd(mult(mult(X2,X),X2),mult(ld(mult(X3,X2),X3),mult(mult(X2,X),X2))),
inference(symmetry,[status(thm)],[c269]) ).
cnf(c271,plain,
ld(mult(X,X3),mult(mult(X,X3),ld(mult(mult(X3,X2),X3),mult(X3,X2)))) = ld(mult(mult(X3,X2),X3),mult(X3,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c272,plain,
ld(mult(mult(X3,X2),X3),mult(X3,X2)) = ld(mult(X,X3),mult(mult(X,X3),ld(mult(mult(X3,X2),X3),mult(X3,X2)))),
inference(symmetry,[status(thm)],[c271]) ).
cnf(c273,plain,
ld(mult(mult(X,X2),X),rd(mult(mult(mult(X,X2),X),mult(X2,X)),mult(mult(X,X2),X))) = rd(mult(X2,X),mult(mult(X,X2),X)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c274,plain,
rd(mult(X2,X),mult(mult(X,X2),X)) = ld(mult(mult(X,X2),X),rd(mult(mult(mult(X,X2),X),mult(X2,X)),mult(mult(X,X2),X))),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c276,plain,
mult(ld(X2,unit),mult(mult(X2,X),X2)) = mult(ld(X2,unit),mult(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
mult(ld(X2,unit),mult(X2,mult(X,X2))) = mult(X,X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c278,plain,
mult(ld(X2,unit),mult(mult(X2,X),X2)) = mult(X,X2),
inference(transitivity,[status(thm)],[c276,c277]) ).
cnf(c279,plain,
mult(X,X2) = mult(ld(X2,unit),mult(mult(X2,X),X2)),
inference(symmetry,[status(thm)],[c278]) ).
cnf(c280,plain,
mult(mult(mult(X2,X),X2),mult(X,X2)) = mult(mult(mult(X2,X),X2),mult(ld(X2,unit),mult(mult(X2,X),X2))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
rd(mult(mult(mult(X2,X),X2),mult(X,X2)),mult(mult(X2,X),X2)) = rd(mult(mult(mult(X2,X),X2),mult(ld(X2,unit),mult(mult(X2,X),X2))),mult(mult(X2,X),X2)),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
rd(mult(mult(mult(X2,X),X2),mult(ld(X2,unit),mult(mult(X2,X),X2))),mult(mult(X2,X),X2)) = mult(mult(mult(X2,X),X2),ld(X2,unit)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c283,plain,
rd(mult(mult(mult(X2,X),X2),mult(X,X2)),mult(mult(X2,X),X2)) = mult(mult(mult(X2,X),X2),ld(X2,unit)),
inference(transitivity,[status(thm)],[c281,c282]) ).
cnf(c284,plain,
mult(rd(mult(mult(X2,X),X2),ld(X2,unit)),mult(ld(X2,unit),ld(X2,unit))) = mult(mult(mult(X2,X),X2),ld(X2,unit)),
inference(substitution,[status(thm)],[c183]) ).
cnf(c285,plain,
mult(mult(mult(X2,X),X2),ld(X2,unit)) = mult(rd(mult(mult(X2,X),X2),ld(X2,unit)),mult(ld(X2,unit),ld(X2,unit))),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
mult(ld(X,unit),mult(mult(X,X2),X)) = mult(X2,X),
inference(substitution,[status(thm)],[c278]) ).
cnf(c287,plain,
mult(X2,X) = mult(ld(X,unit),mult(mult(X,X2),X)),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
rd(mult(X2,X),mult(mult(X,X2),X)) = rd(mult(ld(X,unit),mult(mult(X,X2),X)),mult(mult(X,X2),X)),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
rd(mult(ld(X,unit),mult(mult(X,X2),X)),mult(mult(X,X2),X)) = ld(X,unit),
inference(substitution,[status(thm)],[c10]) ).
cnf(c290,plain,
rd(mult(X2,X),mult(mult(X,X2),X)) = ld(X,unit),
inference(transitivity,[status(thm)],[c288,c289]) ).
cnf(c291,plain,
rd(mult(X,X2),mult(mult(X2,X),X2)) = ld(X2,unit),
inference(substitution,[status(thm)],[c290]) ).
cnf(c292,plain,
ld(X2,unit) = rd(mult(X,X2),mult(mult(X2,X),X2)),
inference(symmetry,[status(thm)],[c291]) ).
cnf(c293,plain,
rd(mult(mult(X2,X),X2),ld(X2,unit)) = rd(mult(mult(X2,X),X2),rd(mult(X,X2),mult(mult(X2,X),X2))),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
ld(rd(X,mult(X2,X2)),unit) = rd(mult(X2,X2),X),
inference(substitution,[status(thm)],[c107]) ).
cnf(c295,plain,
rd(mult(X2,X2),X) = ld(rd(X,mult(X2,X2)),unit),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c296,plain,
rd(rd(X,X2),X2) = rd(X,mult(X2,X2)),
inference(substitution,[status(thm)],[c199]) ).
cnf(c297,plain,
rd(X,mult(X2,X2)) = rd(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
ld(rd(X,mult(X2,X2)),unit) = ld(rd(rd(X,X2),X2),unit),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
ld(rd(rd(X,X2),X2),unit) = rd(X2,rd(X,X2)),
inference(substitution,[status(thm)],[c107]) ).
cnf(c300,plain,
ld(rd(X,mult(X2,X2)),unit) = rd(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c298,c299]) ).
cnf(c301,plain,
rd(mult(X2,X2),X) = rd(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c295,c300]) ).
cnf(c302,plain,
rd(mult(mult(mult(X2,X),X2),mult(mult(X2,X),X2)),mult(X,X2)) = rd(mult(mult(X2,X),X2),rd(mult(X,X2),mult(mult(X2,X),X2))),
inference(substitution,[status(thm)],[c301]) ).
cnf(c303,plain,
rd(mult(mult(X2,X),X2),rd(mult(X,X2),mult(mult(X2,X),X2))) = rd(mult(mult(mult(X2,X),X2),mult(mult(X2,X),X2)),mult(X,X2)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
mult(rd(X2,X3),mult(X3,mult(mult(X3,X),X3))) = ld(rd(X3,X2),mult(X3,mult(mult(X3,X),X3))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c305,plain,
ld(rd(X3,X2),mult(X3,mult(mult(X3,X),X3))) = mult(rd(X2,X3),mult(X3,mult(mult(X3,X),X3))),
inference(symmetry,[status(thm)],[c304]) ).
cnf(c306,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c307,plain,
mult(X2,mult(mult(X2,X),X2)) = mult(X2,mult(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
mult(rd(X2,X3),mult(X3,mult(mult(X3,X),X3))) = mult(rd(X2,X3),mult(X3,mult(X3,mult(X,X3)))),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
mult(rd(X2,X3),mult(X3,mult(X3,mult(X,X3)))) = mult(mult(X2,X3),mult(X,X3)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c310,plain,
mult(rd(X2,X3),mult(X3,mult(mult(X3,X),X3))) = mult(mult(X2,X3),mult(X,X3)),
inference(transitivity,[status(thm)],[c308,c309]) ).
cnf(c311,plain,
ld(rd(X3,X2),mult(X3,mult(mult(X3,X),X3))) = mult(mult(X2,X3),mult(X,X3)),
inference(transitivity,[status(thm)],[c305,c310]) ).
cnf(c312,plain,
ld(rd(X2,mult(mult(X2,X),X2)),mult(X2,mult(mult(X2,X),X2))) = mult(mult(mult(mult(X2,X),X2),X2),mult(X,X2)),
inference(substitution,[status(thm)],[c311]) ).
cnf(c313,plain,
mult(mult(mult(mult(X2,X),X2),X2),mult(X,X2)) = ld(rd(X2,mult(mult(X2,X),X2)),mult(X2,mult(mult(X2,X),X2))),
inference(symmetry,[status(thm)],[c312]) ).
cnf(c314,plain,
ld(rd(X2,mult(mult(X2,X),X2)),mult(X2,mult(mult(X2,X),X2))) = mult(mult(mult(X2,X),X2),mult(mult(X2,X),X2)),
inference(substitution,[status(thm)],[c187]) ).
cnf(c315,plain,
mult(mult(mult(mult(X2,X),X2),X2),mult(X,X2)) = mult(mult(mult(X2,X),X2),mult(mult(X2,X),X2)),
inference(transitivity,[status(thm)],[c313,c314]) ).
cnf(c316,plain,
mult(mult(mult(X2,X),X2),mult(mult(X2,X),X2)) = mult(mult(mult(mult(X2,X),X2),X2),mult(X,X2)),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
rd(mult(mult(mult(X2,X),X2),mult(mult(X2,X),X2)),mult(X,X2)) = rd(mult(mult(mult(mult(X2,X),X2),X2),mult(X,X2)),mult(X,X2)),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
rd(mult(mult(mult(mult(X2,X),X2),X2),mult(X,X2)),mult(X,X2)) = mult(mult(mult(X2,X),X2),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c319,plain,
rd(mult(mult(mult(X2,X),X2),mult(mult(X2,X),X2)),mult(X,X2)) = mult(mult(mult(X2,X),X2),X2),
inference(transitivity,[status(thm)],[c317,c318]) ).
cnf(c320,plain,
rd(mult(mult(X2,X),X2),rd(mult(X,X2),mult(mult(X2,X),X2))) = mult(mult(mult(X2,X),X2),X2),
inference(transitivity,[status(thm)],[c303,c319]) ).
cnf(c321,plain,
rd(mult(mult(X2,X),X2),ld(X2,unit)) = mult(mult(mult(X2,X),X2),X2),
inference(transitivity,[status(thm)],[c293,c320]) ).
cnf(c322,plain,
mult(rd(mult(mult(X2,X),X2),ld(X2,unit)),mult(ld(X2,unit),ld(X2,unit))) = mult(mult(mult(mult(X2,X),X2),X2),mult(ld(X2,unit),ld(X2,unit))),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
mult(ld(X,unit),ld(X,unit)) = ld(X,ld(X,unit)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c324,plain,
mult(mult(mult(mult(X2,X),X2),X2),mult(ld(X2,unit),ld(X2,unit))) = mult(mult(mult(mult(X2,X),X2),X2),ld(X2,ld(X2,unit))),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
mult(X3,mult(X2,mult(X2,ld(X2,X)))) = mult(mult(mult(X3,X2),X2),ld(X2,X)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c326,plain,
mult(mult(mult(X3,X2),X2),ld(X2,X)) = mult(X3,mult(X2,mult(X2,ld(X2,X)))),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c328,plain,
mult(X2,mult(X2,ld(X2,X))) = mult(X2,X),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
mult(X3,mult(X2,mult(X2,ld(X2,X)))) = mult(X3,mult(X2,X)),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
mult(mult(mult(X3,X2),X2),ld(X2,X)) = mult(X3,mult(X2,X)),
inference(transitivity,[status(thm)],[c326,c329]) ).
cnf(c331,plain,
mult(mult(mult(mult(X2,X),X2),X2),ld(X2,ld(X2,unit))) = mult(mult(X2,X),mult(X2,ld(X2,unit))),
inference(substitution,[status(thm)],[c330]) ).
cnf(c332,plain,
mult(X,ld(X,unit)) = unit,
inference(substitution,[status(thm)],[c2]) ).
cnf(c333,plain,
mult(mult(X2,X),mult(X2,ld(X2,unit))) = mult(mult(X2,X),unit),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
mult(mult(X2,X),unit) = mult(X2,X),
inference(substitution,[status(thm)],[c27]) ).
cnf(c335,plain,
mult(mult(X2,X),mult(X2,ld(X2,unit))) = mult(X2,X),
inference(transitivity,[status(thm)],[c333,c334]) ).
cnf(c336,plain,
mult(mult(mult(mult(X2,X),X2),X2),ld(X2,ld(X2,unit))) = mult(X2,X),
inference(transitivity,[status(thm)],[c331,c335]) ).
cnf(c337,plain,
mult(mult(mult(mult(X2,X),X2),X2),mult(ld(X2,unit),ld(X2,unit))) = mult(X2,X),
inference(transitivity,[status(thm)],[c324,c336]) ).
cnf(c338,plain,
mult(rd(mult(mult(X2,X),X2),ld(X2,unit)),mult(ld(X2,unit),ld(X2,unit))) = mult(X2,X),
inference(transitivity,[status(thm)],[c322,c337]) ).
cnf(c339,plain,
mult(mult(mult(X2,X),X2),ld(X2,unit)) = mult(X2,X),
inference(transitivity,[status(thm)],[c285,c338]) ).
cnf(c340,plain,
rd(mult(mult(mult(X2,X),X2),mult(X,X2)),mult(mult(X2,X),X2)) = mult(X2,X),
inference(transitivity,[status(thm)],[c283,c339]) ).
cnf(c341,plain,
rd(mult(mult(mult(X,X2),X),mult(X2,X)),mult(mult(X,X2),X)) = mult(X,X2),
inference(substitution,[status(thm)],[c340]) ).
cnf(c342,plain,
ld(mult(mult(X,X2),X),rd(mult(mult(mult(X,X2),X),mult(X2,X)),mult(mult(X,X2),X))) = ld(mult(mult(X,X2),X),mult(X,X2)),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
rd(mult(X2,X),mult(mult(X,X2),X)) = ld(mult(mult(X,X2),X),mult(X,X2)),
inference(transitivity,[status(thm)],[c274,c342]) ).
cnf(c344,plain,
rd(mult(X,X2),mult(mult(X2,X),X2)) = ld(mult(mult(X2,X),X2),mult(X2,X)),
inference(substitution,[status(thm)],[c343]) ).
cnf(c345,plain,
ld(mult(mult(X2,X),X2),mult(X2,X)) = rd(mult(X,X2),mult(mult(X2,X),X2)),
inference(symmetry,[status(thm)],[c344]) ).
cnf(c346,plain,
rd(mult(X,X2),mult(mult(X2,X),X2)) = ld(X2,unit),
inference(substitution,[status(thm)],[c290]) ).
cnf(c347,plain,
ld(mult(mult(X2,X),X2),mult(X2,X)) = ld(X2,unit),
inference(transitivity,[status(thm)],[c345,c346]) ).
cnf(c348,plain,
mult(mult(X3,X2),ld(mult(mult(X2,X),X2),mult(X2,X))) = mult(mult(X3,X2),ld(X2,unit)),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
mult(mult(X2,X3),ld(X3,X)) = mult(rd(X2,X3),mult(X3,X)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c350,plain,
mult(rd(X2,X3),mult(X3,X)) = ld(rd(X3,X2),mult(X3,X)),
inference(substitution,[status(thm)],[c109]) ).
cnf(c351,plain,
mult(mult(X2,X3),ld(X3,X)) = ld(rd(X3,X2),mult(X3,X)),
inference(transitivity,[status(thm)],[c349,c350]) ).
cnf(c352,plain,
mult(mult(X2,X),ld(X,unit)) = ld(rd(X,X2),mult(X,unit)),
inference(substitution,[status(thm)],[c351]) ).
cnf(c353,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c27]) ).
cnf(c354,plain,
ld(rd(X,X2),mult(X,unit)) = ld(rd(X,X2),X),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
ld(rd(X,X2),X) = X2,
inference(substitution,[status(thm)],[c117]) ).
cnf(c356,plain,
ld(rd(X,X2),mult(X,unit)) = X2,
inference(transitivity,[status(thm)],[c354,c355]) ).
cnf(c357,plain,
mult(mult(X2,X),ld(X,unit)) = X2,
inference(transitivity,[status(thm)],[c352,c356]) ).
cnf(c358,plain,
mult(mult(X3,X2),ld(mult(mult(X2,X),X2),mult(X2,X))) = X3,
inference(transitivity,[status(thm)],[c348,c357]) ).
cnf(c359,plain,
mult(mult(X,X3),ld(mult(mult(X3,X2),X3),mult(X3,X2))) = X,
inference(substitution,[status(thm)],[c358]) ).
cnf(c360,plain,
ld(mult(X,X3),mult(mult(X,X3),ld(mult(mult(X3,X2),X3),mult(X3,X2)))) = ld(mult(X,X3),X),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
ld(mult(mult(X3,X2),X3),mult(X3,X2)) = ld(mult(X,X3),X),
inference(transitivity,[status(thm)],[c272,c360]) ).
cnf(c362,plain,
ld(mult(mult(X2,X),X2),mult(X2,X)) = ld(mult(X3,X2),X3),
inference(substitution,[status(thm)],[c361]) ).
cnf(c363,plain,
ld(mult(X3,X2),X3) = ld(mult(mult(X2,X),X2),mult(X2,X)),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
mult(ld(mult(X3,X2),X3),mult(mult(X2,X),X2)) = mult(ld(mult(mult(X2,X),X2),mult(X2,X)),mult(mult(X2,X),X2)),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
ld(X2,mult(X2,mult(ld(X2,X),X2))) = mult(ld(X2,X),X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c366,plain,
mult(ld(X2,X),X2) = ld(X2,mult(X2,mult(ld(X2,X),X2))),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c367,plain,
mult(mult(X2,ld(X2,X)),X2) = mult(X2,mult(ld(X2,X),X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c368,plain,
mult(X2,mult(ld(X2,X),X2)) = mult(mult(X2,ld(X2,X)),X2),
inference(symmetry,[status(thm)],[c367]) ).
cnf(c369,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c370,plain,
mult(mult(X2,ld(X2,X)),X2) = mult(X,X2),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
mult(X2,mult(ld(X2,X),X2)) = mult(X,X2),
inference(transitivity,[status(thm)],[c368,c370]) ).
cnf(c372,plain,
ld(X2,mult(X2,mult(ld(X2,X),X2))) = ld(X2,mult(X,X2)),
inference(congruence,[status(thm)],[c371]) ).
cnf(c373,plain,
mult(ld(X2,X),X2) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c366,c372]) ).
cnf(c374,plain,
mult(ld(mult(mult(X2,X),X2),mult(X2,X)),mult(mult(X2,X),X2)) = ld(mult(mult(X2,X),X2),mult(mult(X2,X),mult(mult(X2,X),X2))),
inference(substitution,[status(thm)],[c373]) ).
cnf(c375,plain,
mult(rd(mult(mult(mult(X2,X),X2),mult(X,X2)),X2),X2) = mult(mult(mult(X2,X),X2),mult(X,X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c376,plain,
mult(mult(mult(X2,X),X2),mult(X,X2)) = mult(rd(mult(mult(mult(X2,X),X2),mult(X,X2)),X2),X2),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c378,plain,
mult(mult(mult(X2,X),X2),mult(X,X2)) = mult(mult(X2,mult(X,X2)),mult(X,X2)),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
mult(mult(X2,mult(X,X2)),mult(X,X2)) = mult(X2,mult(mult(X,X2),mult(X,X2))),
inference(substitution,[status(thm)],[c75]) ).
cnf(c380,plain,
mult(mult(mult(X2,X),X2),mult(X,X2)) = mult(X2,mult(mult(X,X2),mult(X,X2))),
inference(transitivity,[status(thm)],[c378,c379]) ).
cnf(c381,plain,
mult(mult(mult(X,X2),X),X2) = mult(mult(X,X2),mult(X,X2)),
inference(substitution,[status(thm)],[c189]) ).
cnf(c382,plain,
mult(mult(X,X2),mult(X,X2)) = mult(mult(mult(X,X2),X),X2),
inference(symmetry,[status(thm)],[c381]) ).
cnf(c383,plain,
mult(X2,mult(mult(X,X2),mult(X,X2))) = mult(X2,mult(mult(mult(X,X2),X),X2)),
inference(congruence,[status(thm)],[c382]) ).
cnf(c384,plain,
mult(mult(mult(X2,X),X2),mult(X,X2)) = mult(X2,mult(mult(mult(X,X2),X),X2)),
inference(transitivity,[status(thm)],[c380,c383]) ).
cnf(c385,plain,
rd(mult(mult(mult(X2,X),X2),mult(X,X2)),X2) = rd(mult(X2,mult(mult(mult(X,X2),X),X2)),X2),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
rd(mult(X2,mult(mult(mult(X,X2),X),X2)),X2) = mult(X2,mult(mult(X,X2),X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c387,plain,
mult(rd(mult(mult(X2,X),mult(X2,X)),mult(mult(X,X2),X)),mult(mult(X,X2),X)) = mult(mult(X2,X),mult(X2,X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c388,plain,
mult(mult(X2,X),mult(X2,X)) = mult(rd(mult(mult(X2,X),mult(X2,X)),mult(mult(X,X2),X)),mult(mult(X,X2),X)),
inference(symmetry,[status(thm)],[c387]) ).
cnf(c389,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c390,plain,
ld(rd(X2,mult(X,X2)),mult(mult(X2,X),X2)) = ld(rd(X2,mult(X,X2)),mult(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
ld(rd(X2,mult(X,X2)),mult(X2,mult(X,X2))) = mult(mult(X,X2),mult(X,X2)),
inference(substitution,[status(thm)],[c187]) ).
cnf(c392,plain,
ld(rd(X2,mult(X,X2)),mult(mult(X2,X),X2)) = mult(mult(X,X2),mult(X,X2)),
inference(transitivity,[status(thm)],[c390,c391]) ).
cnf(c393,plain,
ld(rd(X,mult(X2,X)),mult(mult(X,X2),X)) = mult(mult(X2,X),mult(X2,X)),
inference(substitution,[status(thm)],[c392]) ).
cnf(c394,plain,
mult(mult(X2,X),mult(X2,X)) = ld(rd(X,mult(X2,X)),mult(mult(X,X2),X)),
inference(symmetry,[status(thm)],[c393]) ).
cnf(c395,plain,
rd(mult(mult(X2,X),mult(X2,X)),mult(mult(X,X2),X)) = rd(ld(rd(X,mult(X2,X)),mult(mult(X,X2),X)),mult(mult(X,X2),X)),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c397,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c396]) ).
cnf(c398,plain,
rd(ld(X2,X),X) = rd(ld(X2,X),mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c397]) ).
cnf(c399,plain,
rd(ld(X2,X),mult(X2,ld(X2,X))) = ld(X2,unit),
inference(substitution,[status(thm)],[c83]) ).
cnf(c400,plain,
rd(ld(X2,X),X) = ld(X2,unit),
inference(transitivity,[status(thm)],[c398,c399]) ).
cnf(c401,plain,
rd(ld(rd(X,mult(X2,X)),mult(mult(X,X2),X)),mult(mult(X,X2),X)) = ld(rd(X,mult(X2,X)),unit),
inference(substitution,[status(thm)],[c400]) ).
cnf(c402,plain,
ld(rd(X,mult(X2,X)),unit) = rd(mult(X2,X),X),
inference(substitution,[status(thm)],[c107]) ).
cnf(c403,plain,
rd(mult(X2,X),X) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c404,plain,
ld(rd(X,mult(X2,X)),unit) = X2,
inference(transitivity,[status(thm)],[c402,c403]) ).
cnf(c405,plain,
rd(ld(rd(X,mult(X2,X)),mult(mult(X,X2),X)),mult(mult(X,X2),X)) = X2,
inference(transitivity,[status(thm)],[c401,c404]) ).
cnf(c406,plain,
rd(mult(mult(X2,X),mult(X2,X)),mult(mult(X,X2),X)) = X2,
inference(transitivity,[status(thm)],[c395,c405]) ).
cnf(c407,plain,
mult(rd(mult(mult(X2,X),mult(X2,X)),mult(mult(X,X2),X)),mult(mult(X,X2),X)) = mult(X2,mult(mult(X,X2),X)),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
mult(mult(X2,X),mult(X2,X)) = mult(X2,mult(mult(X,X2),X)),
inference(transitivity,[status(thm)],[c388,c407]) ).
cnf(c409,plain,
mult(X2,mult(mult(X,X2),X)) = mult(mult(X2,X),mult(X2,X)),
inference(symmetry,[status(thm)],[c408]) ).
cnf(c410,plain,
mult(mult(X2,X),mult(X2,X)) = mult(mult(mult(X2,X),X2),X),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c411,plain,
mult(X2,mult(mult(X,X2),X)) = mult(mult(mult(X2,X),X2),X),
inference(transitivity,[status(thm)],[c409,c410]) ).
cnf(c412,plain,
rd(mult(X2,mult(mult(mult(X,X2),X),X2)),X2) = mult(mult(mult(X2,X),X2),X),
inference(transitivity,[status(thm)],[c386,c411]) ).
cnf(c413,plain,
rd(mult(mult(mult(X2,X),X2),mult(X,X2)),X2) = mult(mult(mult(X2,X),X2),X),
inference(transitivity,[status(thm)],[c385,c412]) ).
cnf(c414,plain,
mult(rd(mult(mult(mult(X2,X),X2),mult(X,X2)),X2),X2) = mult(mult(mult(mult(X2,X),X2),X),X2),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
mult(mult(mult(mult(X3,X2),X3),X2),X) = mult(mult(mult(X3,X2),mult(X3,X2)),X),
inference(congruence,[status(thm)],[c189]) ).
cnf(c416,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c31]) ).
cnf(c417,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c416]) ).
cnf(c418,plain,
mult(X,X) = mult(mult(unit,X),X),
inference(congruence,[status(thm)],[c417]) ).
cnf(c419,plain,
mult(mult(X2,X2),X) = mult(mult(mult(unit,X2),X2),X),
inference(congruence,[status(thm)],[c418]) ).
cnf(c420,plain,
mult(unit,mult(X2,mult(X2,X))) = mult(mult(mult(unit,X2),X2),X),
inference(substitution,[status(thm)],[c42]) ).
cnf(c421,plain,
mult(mult(mult(unit,X2),X2),X) = mult(unit,mult(X2,mult(X2,X))),
inference(symmetry,[status(thm)],[c420]) ).
cnf(c422,plain,
mult(unit,mult(X2,mult(X2,X))) = mult(X2,mult(X2,X)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c423,plain,
mult(mult(mult(unit,X2),X2),X) = mult(X2,mult(X2,X)),
inference(transitivity,[status(thm)],[c421,c422]) ).
cnf(c424,plain,
mult(mult(X2,X2),X) = mult(X2,mult(X2,X)),
inference(transitivity,[status(thm)],[c419,c423]) ).
cnf(c425,plain,
mult(mult(mult(X3,X2),mult(X3,X2)),X) = mult(mult(X3,X2),mult(mult(X3,X2),X)),
inference(substitution,[status(thm)],[c424]) ).
cnf(c426,plain,
mult(mult(mult(mult(X3,X2),X3),X2),X) = mult(mult(X3,X2),mult(mult(X3,X2),X)),
inference(transitivity,[status(thm)],[c415,c425]) ).
cnf(c427,plain,
mult(mult(mult(mult(X2,X),X2),X),X2) = mult(mult(X2,X),mult(mult(X2,X),X2)),
inference(substitution,[status(thm)],[c426]) ).
cnf(c428,plain,
mult(rd(mult(mult(mult(X2,X),X2),mult(X,X2)),X2),X2) = mult(mult(X2,X),mult(mult(X2,X),X2)),
inference(transitivity,[status(thm)],[c414,c427]) ).
cnf(c429,plain,
mult(mult(mult(X2,X),X2),mult(X,X2)) = mult(mult(X2,X),mult(mult(X2,X),X2)),
inference(transitivity,[status(thm)],[c376,c428]) ).
cnf(c430,plain,
mult(mult(X2,X),mult(mult(X2,X),X2)) = mult(mult(mult(X2,X),X2),mult(X,X2)),
inference(symmetry,[status(thm)],[c429]) ).
cnf(c431,plain,
ld(mult(mult(X2,X),X2),mult(mult(X2,X),mult(mult(X2,X),X2))) = ld(mult(mult(X2,X),X2),mult(mult(mult(X2,X),X2),mult(X,X2))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
ld(mult(mult(X2,X),X2),mult(mult(mult(X2,X),X2),mult(X,X2))) = mult(X,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c433,plain,
ld(mult(mult(X2,X),X2),mult(mult(X2,X),mult(mult(X2,X),X2))) = mult(X,X2),
inference(transitivity,[status(thm)],[c431,c432]) ).
cnf(c434,plain,
mult(ld(mult(mult(X2,X),X2),mult(X2,X)),mult(mult(X2,X),X2)) = mult(X,X2),
inference(transitivity,[status(thm)],[c374,c433]) ).
cnf(c435,plain,
mult(ld(mult(X3,X2),X3),mult(mult(X2,X),X2)) = mult(X,X2),
inference(transitivity,[status(thm)],[c364,c434]) ).
cnf(c436,plain,
rd(mult(mult(X2,X),X2),mult(ld(mult(X3,X2),X3),mult(mult(X2,X),X2))) = rd(mult(mult(X2,X),X2),mult(X,X2)),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c438,plain,
rd(mult(mult(X2,X),X2),mult(X,X2)) = rd(mult(X2,mult(X,X2)),mult(X,X2)),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
rd(mult(X2,mult(X,X2)),mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c440,plain,
rd(mult(mult(X2,X),X2),mult(X,X2)) = X2,
inference(transitivity,[status(thm)],[c438,c439]) ).
cnf(c441,plain,
rd(mult(mult(X2,X),X2),mult(ld(mult(X3,X2),X3),mult(mult(X2,X),X2))) = X2,
inference(transitivity,[status(thm)],[c436,c440]) ).
cnf(c442,plain,
ld(ld(mult(X2,X),X2),unit) = X,
inference(transitivity,[status(thm)],[c270,c441]) ).
cnf(c443,plain,
mult(X3,ld(ld(mult(X2,X),X2),unit)) = mult(X3,X),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
rd(X3,ld(mult(X2,X),X2)) = mult(X3,X),
inference(transitivity,[status(thm)],[c268,c443]) ).
cnf(c445,plain,
rd(mult(X3,mult(mult(X2,X),X2)),ld(mult(X2,X),X2)) = mult(mult(X3,mult(mult(X2,X),X2)),X),
inference(substitution,[status(thm)],[c444]) ).
cnf(c446,plain,
mult(X3,mult(mult(X2,X),mult(X2,X))) = mult(mult(X3,mult(mult(X2,X),X2)),X),
inference(transitivity,[status(thm)],[c266,c445]) ).
cnf(c447,plain,
mult(X3,mult(mult(mult(X2,X),X2),X)) = mult(mult(X3,mult(mult(X2,X),X2)),X),
inference(transitivity,[status(thm)],[c252,c446]) ).
cnf(c448,plain,
mult(X4,ld(X,mult(mult(X,X3),mult(mult(X2,X3),X2)))) = mult(mult(X4,mult(mult(X3,X2),X3)),X2),
inference(transitivity,[status(thm)],[c251,c447]) ).
cnf(c449,plain,
rd(X4,ld(mult(mult(X,X3),mult(mult(X2,X3),X2)),X)) = mult(mult(X4,mult(mult(X3,X2),X3)),X2),
inference(transitivity,[status(thm)],[c172,c448]) ).
cnf(c450,plain,
rd(X3,ld(mult(mult(X3,X2),mult(mult(X,X2),X)),X3)) = mult(mult(X3,mult(mult(X2,X),X2)),X),
inference(substitution,[status(thm)],[c449]) ).
cnf(c451,plain,
mult(mult(X3,mult(mult(X2,X),X2)),X) = rd(X3,ld(mult(mult(X3,X2),mult(mult(X,X2),X)),X3)),
inference(symmetry,[status(thm)],[c450]) ).
cnf(c452,plain,
rd(X3,ld(mult(mult(X3,X2),mult(mult(X,X2),X)),X3)) = mult(mult(X3,X2),mult(mult(X,X2),X)),
inference(substitution,[status(thm)],[c91]) ).
cnf(c453,plain,
mult(mult(X3,mult(mult(X2,X),X2)),X) = mult(mult(X3,X2),mult(mult(X,X2),X)),
inference(transitivity,[status(thm)],[c451,c452]) ).
cnf(c454,plain,
mult(mult(a,mult(mult(b,c),b)),c) = mult(mult(a,b),mult(mult(c,b),c)),
inference(substitution,[status(thm)],[c453]) ).
cnf(c455,plain,
mult(mult(a,b),mult(mult(c,b),c)) = mult(mult(a,mult(mult(b,c),b)),c),
inference(symmetry,[status(thm)],[c454]) ).
cnf(c456,plain,
$false,
inference(resolution,[status(thm)],[c1,c455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP668-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:33:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.40/3.02 Command-line arguments: --flatten --complete-subsets
% 20.40/3.02
% 20.40/3.02 % SZS status Unsatisfiable
% 20.40/3.02
% 20.40/3.07 % SZS output start CNFRefutation
% See solution above
% 22.64/3.32
% 22.64/3.32 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------