%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP667-4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:11:39 AM UTC 2026
% Result : Unsatisfiable 159.68s 20.65s
% Output : CNFRefutation 161.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 10
% Syntax : Number of clauses : 411 ( 411 unt; 0 nHn; 4 RR)
% Number of literals : 411 ( 410 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 871 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(mult(a,b),mult(c,a)) != mult(mult(a,mult(b,c)),a),
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(mult(X3,X2),ld(mult(X3,X2),mult(mult(X3,mult(X2,X)),X3))) = mult(mult(X3,mult(X2,X)),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
mult(mult(X3,mult(X2,X)),X3) = mult(mult(X3,X2),ld(mult(X3,X2),mult(mult(X3,mult(X2,X)),X3))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
mult(ld(X2,unit),X) = mult(ld(X2,unit),mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
mult(mult(A2,B2),A2) = mult(A2,mult(B2,A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
cnf(c9,plain,
mult(mult(rd(X2,X),X),rd(X2,X)) = mult(rd(X2,X),mult(X,rd(X2,X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
mult(rd(X2,X),mult(X,rd(X2,X))) = mult(mult(rd(X2,X),X),rd(X2,X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c12,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
mult(mult(rd(X2,X),X),rd(X2,X)) = mult(X2,rd(X2,X)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
mult(rd(X2,X),mult(X,rd(X2,X))) = mult(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c10,c13]) ).
cnf(c15,plain,
mult(rd(X,X2),mult(X2,rd(X,X2))) = mult(X,rd(X,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
mult(X,rd(X,X2)) = mult(rd(X,X2),mult(X2,rd(X,X2))),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
mult(mult(X3,X2),mult(X,rd(X,X2))) = mult(mult(X3,X2),mult(rd(X,X2),mult(X2,rd(X,X2)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
rd(mult(mult(X3,X2),mult(X,rd(X,X2))),rd(X,X2)) = rd(mult(mult(X3,X2),mult(rd(X,X2),mult(X2,rd(X,X2)))),rd(X,X2)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c20,plain,
mult(X2,mult(X,X2)) = mult(mult(X2,X),X2),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
mult(X3,mult(X2,mult(X,X2))) = mult(X3,mult(mult(X2,X),X2)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
mult(mult(X3,mult(X2,mult(X,X2))),X) = mult(mult(X3,mult(mult(X2,X),X2)),X),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,axiom,
mult(mult(A2,B2),mult(mult(C,B2),C)) = mult(mult(A2,mult(mult(B2,C),B2)),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c24,plain,
mult(mult(X3,X2),mult(mult(X,X2),X)) = mult(mult(X3,mult(mult(X2,X),X2)),X),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
mult(mult(X3,mult(mult(X2,X),X2)),X) = mult(mult(X3,X2),mult(mult(X,X2),X)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
mult(mult(X,X2),X) = mult(X,mult(X2,X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c27,plain,
mult(mult(X3,X2),mult(mult(X,X2),X)) = mult(mult(X3,X2),mult(X,mult(X2,X))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
mult(mult(X3,mult(mult(X2,X),X2)),X) = mult(mult(X3,X2),mult(X,mult(X2,X))),
inference(transitivity,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
mult(mult(X3,mult(X2,mult(X,X2))),X) = mult(mult(X3,X2),mult(X,mult(X2,X))),
inference(transitivity,[status(thm)],[c22,c28]) ).
cnf(c30,plain,
mult(mult(X3,X2),mult(X,mult(X2,X))) = mult(mult(X3,mult(X2,mult(X,X2))),X),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
rd(mult(mult(X3,X2),mult(X,mult(X2,X))),X) = rd(mult(mult(X3,mult(X2,mult(X,X2))),X),X),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c33,plain,
rd(mult(mult(X3,mult(X2,mult(X,X2))),X),X) = mult(X3,mult(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
rd(mult(mult(X3,X2),mult(X,mult(X2,X))),X) = mult(X3,mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c31,c33]) ).
cnf(c35,plain,
rd(mult(mult(X3,X2),mult(rd(X,X2),mult(X2,rd(X,X2)))),rd(X,X2)) = mult(X3,mult(X2,mult(rd(X,X2),X2))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c37,plain,
mult(X2,mult(rd(X,X2),X2)) = mult(X2,X),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
mult(X3,mult(X2,mult(rd(X,X2),X2))) = mult(X3,mult(X2,X)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
rd(mult(mult(X3,X2),mult(rd(X,X2),mult(X2,rd(X,X2)))),rd(X,X2)) = mult(X3,mult(X2,X)),
inference(transitivity,[status(thm)],[c35,c38]) ).
cnf(c40,plain,
rd(mult(mult(X3,X2),mult(X,rd(X,X2))),rd(X,X2)) = mult(X3,mult(X2,X)),
inference(transitivity,[status(thm)],[c18,c39]) ).
cnf(c41,plain,
rd(mult(mult(ld(X2,unit),X2),mult(X,rd(X,X2))),rd(X,X2)) = mult(ld(X2,unit),mult(X2,X)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
mult(ld(X2,unit),mult(X2,X)) = rd(mult(mult(ld(X2,unit),X2),mult(X,rd(X,X2))),rd(X,X2)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
mult(mult(X2,ld(X2,X)),X2) = mult(X2,mult(ld(X2,X),X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c44,plain,
mult(X2,mult(ld(X2,X),X2)) = mult(mult(X2,ld(X2,X)),X2),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c46,plain,
mult(mult(X2,ld(X2,X)),X2) = mult(X,X2),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
mult(X2,mult(ld(X2,X),X2)) = mult(X,X2),
inference(transitivity,[status(thm)],[c44,c46]) ).
cnf(c48,plain,
mult(X,X2) = mult(X2,mult(ld(X2,X),X2)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
ld(X2,mult(X,X2)) = ld(X2,mult(X2,mult(ld(X2,X),X2))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,axiom,
ld(A2,mult(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c51,plain,
ld(X2,mult(X2,mult(ld(X2,X),X2))) = mult(ld(X2,X),X2),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
ld(X2,mult(X,X2)) = mult(ld(X2,X),X2),
inference(transitivity,[status(thm)],[c49,c51]) ).
cnf(c53,plain,
ld(X,mult(unit,X)) = mult(ld(X,unit),X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
mult(ld(X,unit),X) = ld(X,mult(unit,X)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,axiom,
mult(unit,A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c56,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
ld(X,mult(unit,X)) = ld(X,X),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c59,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
ld(X,X) = ld(X,mult(X,unit)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
ld(X,mult(X,unit)) = unit,
inference(substitution,[status(thm)],[c50]) ).
cnf(c63,plain,
ld(X,X) = unit,
inference(transitivity,[status(thm)],[c61,c62]) ).
cnf(c64,plain,
ld(X,mult(unit,X)) = unit,
inference(transitivity,[status(thm)],[c57,c63]) ).
cnf(c65,plain,
mult(ld(X,unit),X) = unit,
inference(transitivity,[status(thm)],[c54,c64]) ).
cnf(c66,plain,
mult(mult(ld(X2,unit),X2),mult(X,rd(X,X2))) = mult(unit,mult(X,rd(X,X2))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
rd(mult(mult(ld(X2,unit),X2),mult(X,rd(X,X2))),rd(X,X2)) = rd(mult(unit,mult(X,rd(X,X2))),rd(X,X2)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
mult(unit,mult(X,rd(X,X2))) = mult(X,rd(X,X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c69,plain,
rd(mult(unit,mult(X,rd(X,X2))),rd(X,X2)) = rd(mult(X,rd(X,X2)),rd(X,X2)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
rd(mult(X,rd(X,X2)),rd(X,X2)) = X,
inference(substitution,[status(thm)],[c32]) ).
cnf(c71,plain,
rd(mult(unit,mult(X,rd(X,X2))),rd(X,X2)) = X,
inference(transitivity,[status(thm)],[c69,c70]) ).
cnf(c72,plain,
rd(mult(mult(ld(X2,unit),X2),mult(X,rd(X,X2))),rd(X,X2)) = X,
inference(transitivity,[status(thm)],[c67,c71]) ).
cnf(c73,plain,
mult(ld(X2,unit),mult(X2,X)) = X,
inference(transitivity,[status(thm)],[c42,c72]) ).
cnf(c74,plain,
mult(ld(X2,unit),mult(X2,ld(X2,X))) = ld(X2,X),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
mult(ld(X2,unit),X) = ld(X2,X),
inference(transitivity,[status(thm)],[c7,c74]) ).
cnf(c76,plain,
mult(ld(mult(X3,X2),unit),mult(mult(X3,mult(X2,X)),X3)) = ld(mult(X3,X2),mult(mult(X3,mult(X2,X)),X3)),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
ld(mult(X3,X2),mult(mult(X3,mult(X2,X)),X3)) = mult(ld(mult(X3,X2),unit),mult(mult(X3,mult(X2,X)),X3)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
rd(mult(mult(X2,ld(mult(mult(X2,X),X2),X2)),mult(X,mult(X2,X))),mult(X,mult(X2,X))) = mult(X2,ld(mult(mult(X2,X),X2),X2)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c79,plain,
mult(X2,ld(mult(mult(X2,X),X2),X2)) = rd(mult(mult(X2,ld(mult(mult(X2,X),X2),X2)),mult(X,mult(X2,X))),mult(X,mult(X2,X))),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c81,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
mult(X2,X) = mult(X2,mult(rd(X,X2),X2)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
rd(mult(X2,X),X2) = rd(mult(X2,mult(rd(X,X2),X2)),X2),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c85,plain,
mult(X2,mult(X,X2)) = mult(mult(X2,X),X2),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
rd(mult(X2,mult(X,X2)),X2) = rd(mult(mult(X2,X),X2),X2),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
rd(mult(mult(X2,X),X2),X2) = mult(X2,X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c88,plain,
rd(mult(X2,mult(X,X2)),X2) = mult(X2,X),
inference(transitivity,[status(thm)],[c86,c87]) ).
cnf(c89,plain,
rd(mult(X2,mult(rd(X,X2),X2)),X2) = mult(X2,rd(X,X2)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
rd(mult(X2,X),X2) = mult(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c83,c89]) ).
cnf(c91,plain,
rd(mult(X2,ld(X2,X)),X2) = mult(X2,rd(ld(X2,X),X2)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
mult(X2,rd(ld(X2,X),X2)) = rd(mult(X2,ld(X2,X)),X2),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c94,plain,
rd(mult(X2,ld(X2,X)),X2) = rd(X,X2),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
mult(X2,rd(ld(X2,X),X2)) = rd(X,X2),
inference(transitivity,[status(thm)],[c92,c94]) ).
cnf(c96,plain,
mult(X,rd(ld(X,X2),X)) = rd(X2,X),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
rd(X2,X) = mult(X,rd(ld(X,X2),X)),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
mult(rd(X2,X),X2) = mult(mult(X,rd(ld(X,X2),X)),X2),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c100,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
mult(mult(X,rd(ld(X,X2),X)),X2) = mult(mult(X,rd(ld(X,X2),X)),mult(X,ld(X,X2))),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c103,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
mult(X2,X) = mult(X2,mult(rd(X,X2),X2)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
mult(mult(X2,rd(X,X2)),mult(X2,X)) = mult(mult(X2,rd(X,X2)),mult(X2,mult(rd(X,X2),X2))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
mult(mult(X2,mult(X,mult(X2,X))),X2) = mult(mult(X2,X),mult(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c107,plain,
mult(mult(X2,X),mult(X2,mult(X,X2))) = mult(mult(X2,mult(X,mult(X2,X))),X2),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
mult(mult(X2,mult(X,mult(X2,X))),X2) = mult(X2,mult(mult(X,mult(X2,X)),X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c109,plain,
mult(unit,mult(X2,mult(X,X2))) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c110,plain,
mult(X2,mult(X,X2)) = mult(unit,mult(X2,mult(X,X2))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
mult(mult(X2,mult(X,X2)),X) = mult(mult(unit,mult(X2,mult(X,X2))),X),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
mult(mult(unit,mult(X2,mult(X,X2))),X) = mult(mult(unit,X2),mult(X,mult(X2,X))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c113,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c55]) ).
cnf(c114,plain,
mult(mult(unit,X2),mult(X,mult(X2,X))) = mult(X2,mult(X,mult(X2,X))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
mult(mult(unit,mult(X2,mult(X,X2))),X) = mult(X2,mult(X,mult(X2,X))),
inference(transitivity,[status(thm)],[c112,c114]) ).
cnf(c116,plain,
mult(mult(X2,mult(X,X2)),X) = mult(X2,mult(X,mult(X2,X))),
inference(transitivity,[status(thm)],[c111,c115]) ).
cnf(c117,plain,
mult(mult(X,mult(X2,X)),X2) = mult(X,mult(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
mult(X2,mult(mult(X,mult(X2,X)),X2)) = mult(X2,mult(X,mult(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
mult(mult(X2,mult(X,mult(X2,X))),X2) = mult(X2,mult(X,mult(X2,mult(X,X2)))),
inference(transitivity,[status(thm)],[c108,c118]) ).
cnf(c120,plain,
mult(mult(X2,X),mult(X2,mult(X,X2))) = mult(X2,mult(X,mult(X2,mult(X,X2)))),
inference(transitivity,[status(thm)],[c107,c119]) ).
cnf(c121,plain,
mult(mult(X2,rd(X,X2)),mult(X2,mult(rd(X,X2),X2))) = mult(X2,mult(rd(X,X2),mult(X2,mult(rd(X,X2),X2)))),
inference(substitution,[status(thm)],[c120]) ).
cnf(c122,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c123,plain,
mult(X2,mult(rd(X,X2),X2)) = mult(X2,X),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
mult(rd(X,X2),mult(X2,mult(rd(X,X2),X2))) = mult(rd(X,X2),mult(X2,X)),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
mult(X2,mult(rd(X,X2),mult(X2,mult(rd(X,X2),X2)))) = mult(X2,mult(rd(X,X2),mult(X2,X))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
mult(ld(X,unit),mult(X,mult(X2,X2))) = mult(X2,X2),
inference(substitution,[status(thm)],[c73]) ).
cnf(c127,plain,
mult(X2,X2) = mult(ld(X,unit),mult(X,mult(X2,X2))),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
rd(mult(X2,X2),mult(X,X2)) = rd(mult(ld(X,unit),mult(X,mult(X2,X2))),mult(X,X2)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
mult(ld(X,unit),mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c73]) ).
cnf(c130,plain,
X2 = mult(ld(X,unit),mult(X,X2)),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
rd(X2,mult(X,X2)) = rd(mult(ld(X,unit),mult(X,X2)),mult(X,X2)),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
rd(mult(ld(X,unit),mult(X,X2)),mult(X,X2)) = ld(X,unit),
inference(substitution,[status(thm)],[c32]) ).
cnf(c133,plain,
rd(X2,mult(X,X2)) = ld(X,unit),
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
ld(X,unit) = rd(X2,mult(X,X2)),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
mult(ld(X,unit),mult(X,mult(X2,X2))) = mult(rd(X2,mult(X,X2)),mult(X,mult(X2,X2))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
rd(mult(ld(X,unit),mult(X,mult(X2,X2))),mult(X,X2)) = rd(mult(rd(X2,mult(X,X2)),mult(X,mult(X2,X2))),mult(X,X2)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c58]) ).
cnf(c138,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
mult(mult(X2,X),X) = mult(mult(X2,X),mult(X,unit)),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
mult(unit,mult(X,unit)) = mult(X,unit),
inference(substitution,[status(thm)],[c55]) ).
cnf(c141,plain,
mult(X,unit) = mult(unit,mult(X,unit)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
mult(mult(X2,X),mult(X,unit)) = mult(mult(X2,X),mult(unit,mult(X,unit))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
mult(mult(X2,mult(X,mult(unit,X))),unit) = mult(mult(X2,X),mult(unit,mult(X,unit))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c144,plain,
mult(mult(X2,X),mult(unit,mult(X,unit))) = mult(mult(X2,mult(X,mult(unit,X))),unit),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
mult(mult(X2,mult(X,mult(unit,X))),unit) = mult(X2,mult(X,mult(unit,X))),
inference(substitution,[status(thm)],[c58]) ).
cnf(c146,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c55]) ).
cnf(c147,plain,
mult(X,mult(unit,X)) = mult(X,X),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
mult(X2,mult(X,mult(unit,X))) = mult(X2,mult(X,X)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
mult(mult(X2,mult(X,mult(unit,X))),unit) = mult(X2,mult(X,X)),
inference(transitivity,[status(thm)],[c145,c148]) ).
cnf(c150,plain,
mult(mult(X2,X),mult(unit,mult(X,unit))) = mult(X2,mult(X,X)),
inference(transitivity,[status(thm)],[c144,c149]) ).
cnf(c151,plain,
mult(mult(X2,X),mult(X,unit)) = mult(X2,mult(X,X)),
inference(transitivity,[status(thm)],[c142,c150]) ).
cnf(c152,plain,
mult(mult(X2,X),X) = mult(X2,mult(X,X)),
inference(transitivity,[status(thm)],[c139,c151]) ).
cnf(c153,plain,
mult(mult(X,X2),X2) = mult(X,mult(X2,X2)),
inference(substitution,[status(thm)],[c152]) ).
cnf(c154,plain,
mult(X,mult(X2,X2)) = mult(mult(X,X2),X2),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
mult(rd(X2,mult(X,X2)),mult(X,mult(X2,X2))) = mult(rd(X2,mult(X,X2)),mult(mult(X,X2),X2)),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
rd(mult(rd(X2,mult(X,X2)),mult(X,mult(X2,X2))),mult(X,X2)) = rd(mult(rd(X2,mult(X,X2)),mult(mult(X,X2),X2)),mult(X,X2)),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c158,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
mult(X,X2) = mult(X,mult(rd(X2,X),X)),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
mult(rd(X2,X),mult(X,X2)) = mult(rd(X2,X),mult(X,mult(rd(X2,X),X))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
rd(mult(rd(X2,X),mult(X,X2)),X) = rd(mult(rd(X2,X),mult(X,mult(rd(X2,X),X))),X),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
mult(X2,mult(X,mult(X2,X))) = mult(mult(X2,mult(X,X2)),X),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c163,plain,
rd(mult(X2,mult(X,mult(X2,X))),X) = rd(mult(mult(X2,mult(X,X2)),X),X),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
rd(mult(mult(X2,mult(X,X2)),X),X) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c165,plain,
rd(mult(X2,mult(X,mult(X2,X))),X) = mult(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c163,c164]) ).
cnf(c166,plain,
rd(mult(rd(X2,X),mult(X,mult(rd(X2,X),X))),X) = mult(rd(X2,X),mult(X,rd(X2,X))),
inference(substitution,[status(thm)],[c165]) ).
cnf(c167,plain,
rd(mult(rd(X2,X),mult(X,mult(rd(X2,X),X))),X) = mult(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c166,c14]) ).
cnf(c168,plain,
rd(mult(rd(X2,X),mult(X,X2)),X) = mult(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c161,c167]) ).
cnf(c169,plain,
rd(mult(rd(X2,mult(X,X2)),mult(mult(X,X2),X2)),mult(X,X2)) = mult(X2,rd(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
mult(X2,rd(X2,mult(X,X2))) = mult(X2,ld(X,unit)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c171,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c172,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
ld(X,unit) = ld(mult(rd(X,X2),X2),unit),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
mult(X2,ld(X,unit)) = mult(X2,ld(mult(rd(X,X2),X2),unit)),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
mult(ld(X,unit),mult(X,mult(X2,X2))) = mult(X2,X2),
inference(substitution,[status(thm)],[c73]) ).
cnf(c176,plain,
mult(X2,X2) = mult(ld(X,unit),mult(X,mult(X2,X2))),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
rd(mult(X2,X2),mult(X,X2)) = rd(mult(ld(X,unit),mult(X,mult(X2,X2))),mult(X,X2)),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
ld(X,unit) = rd(X2,mult(X,X2)),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c179,plain,
mult(ld(X,unit),mult(X,mult(X2,X2))) = mult(rd(X2,mult(X,X2)),mult(X,mult(X2,X2))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
rd(mult(ld(X,unit),mult(X,mult(X2,X2))),mult(X,X2)) = rd(mult(rd(X2,mult(X,X2)),mult(X,mult(X2,X2))),mult(X,X2)),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
mult(mult(X,X2),X2) = mult(X,mult(X2,X2)),
inference(substitution,[status(thm)],[c152]) ).
cnf(c182,plain,
mult(X,mult(X2,X2)) = mult(mult(X,X2),X2),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
mult(rd(X2,mult(X,X2)),mult(X,mult(X2,X2))) = mult(rd(X2,mult(X,X2)),mult(mult(X,X2),X2)),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
rd(mult(rd(X2,mult(X,X2)),mult(X,mult(X2,X2))),mult(X,X2)) = rd(mult(rd(X2,mult(X,X2)),mult(mult(X,X2),X2)),mult(X,X2)),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
rd(mult(rd(X2,mult(X,X2)),mult(mult(X,X2),X2)),mult(X,X2)) = mult(X2,rd(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c168]) ).
cnf(c186,plain,
mult(X2,rd(X2,mult(X,X2))) = mult(X2,ld(X,unit)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c187,plain,
rd(mult(rd(X2,mult(X,X2)),mult(mult(X,X2),X2)),mult(X,X2)) = mult(X2,ld(X,unit)),
inference(transitivity,[status(thm)],[c185,c186]) ).
cnf(c188,plain,
rd(mult(rd(X2,mult(X,X2)),mult(X,mult(X2,X2))),mult(X,X2)) = mult(X2,ld(X,unit)),
inference(transitivity,[status(thm)],[c184,c187]) ).
cnf(c189,plain,
rd(mult(ld(X,unit),mult(X,mult(X2,X2))),mult(X,X2)) = mult(X2,ld(X,unit)),
inference(transitivity,[status(thm)],[c180,c188]) ).
cnf(c190,plain,
rd(mult(X2,X2),mult(X,X2)) = mult(X2,ld(X,unit)),
inference(transitivity,[status(thm)],[c177,c189]) ).
cnf(c191,plain,
rd(mult(X2,X2),mult(mult(X,X2),X2)) = mult(X2,ld(mult(X,X2),unit)),
inference(substitution,[status(thm)],[c190]) ).
cnf(c192,plain,
mult(X2,ld(mult(X,X2),unit)) = rd(mult(X2,X2),mult(mult(X,X2),X2)),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
mult(mult(X,X2),X2) = mult(X,mult(X2,X2)),
inference(substitution,[status(thm)],[c152]) ).
cnf(c194,plain,
rd(mult(X2,X2),mult(mult(X,X2),X2)) = rd(mult(X2,X2),mult(X,mult(X2,X2))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
rd(mult(X2,X2),mult(X,mult(X2,X2))) = ld(X,unit),
inference(substitution,[status(thm)],[c133]) ).
cnf(c196,plain,
rd(mult(X2,X2),mult(mult(X,X2),X2)) = ld(X,unit),
inference(transitivity,[status(thm)],[c194,c195]) ).
cnf(c197,plain,
mult(X2,ld(mult(X,X2),unit)) = ld(X,unit),
inference(transitivity,[status(thm)],[c192,c196]) ).
cnf(c198,plain,
mult(X2,ld(mult(rd(X,X2),X2),unit)) = ld(rd(X,X2),unit),
inference(substitution,[status(thm)],[c197]) ).
cnf(c199,plain,
rd(X,mult(rd(X2,X),X)) = ld(rd(X2,X),unit),
inference(substitution,[status(thm)],[c133]) ).
cnf(c200,plain,
ld(rd(X2,X),unit) = rd(X,mult(rd(X2,X),X)),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c202,plain,
rd(X,mult(rd(X2,X),X)) = rd(X,X2),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
ld(rd(X2,X),unit) = rd(X,X2),
inference(transitivity,[status(thm)],[c200,c202]) ).
cnf(c204,plain,
ld(rd(X,X2),unit) = rd(X2,X),
inference(substitution,[status(thm)],[c203]) ).
cnf(c205,plain,
mult(X2,ld(mult(rd(X,X2),X2),unit)) = rd(X2,X),
inference(transitivity,[status(thm)],[c198,c204]) ).
cnf(c206,plain,
mult(X2,ld(X,unit)) = rd(X2,X),
inference(transitivity,[status(thm)],[c174,c205]) ).
cnf(c207,plain,
mult(X2,rd(X2,mult(X,X2))) = rd(X2,X),
inference(transitivity,[status(thm)],[c170,c206]) ).
cnf(c208,plain,
rd(mult(rd(X2,mult(X,X2)),mult(mult(X,X2),X2)),mult(X,X2)) = rd(X2,X),
inference(transitivity,[status(thm)],[c169,c207]) ).
cnf(c209,plain,
rd(mult(rd(X2,mult(X,X2)),mult(X,mult(X2,X2))),mult(X,X2)) = rd(X2,X),
inference(transitivity,[status(thm)],[c156,c208]) ).
cnf(c210,plain,
rd(mult(ld(X,unit),mult(X,mult(X2,X2))),mult(X,X2)) = rd(X2,X),
inference(transitivity,[status(thm)],[c136,c209]) ).
cnf(c211,plain,
rd(mult(X2,X2),mult(X,X2)) = rd(X2,X),
inference(transitivity,[status(thm)],[c128,c210]) ).
cnf(c212,plain,
rd(X2,X) = rd(mult(X2,X2),mult(X,X2)),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
mult(rd(X2,X),mult(X,X2)) = mult(rd(mult(X2,X2),mult(X,X2)),mult(X,X2)),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
mult(rd(mult(X2,X2),mult(X,X2)),mult(X,X2)) = mult(X2,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c215,plain,
mult(rd(X2,X),mult(X,X2)) = mult(X2,X2),
inference(transitivity,[status(thm)],[c213,c214]) ).
cnf(c216,plain,
mult(rd(X,X2),mult(X2,X)) = mult(X,X),
inference(substitution,[status(thm)],[c215]) ).
cnf(c217,plain,
mult(X2,mult(rd(X,X2),mult(X2,X))) = mult(X2,mult(X,X)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
mult(X2,mult(rd(X,X2),mult(X2,mult(rd(X,X2),X2)))) = mult(X2,mult(X,X)),
inference(transitivity,[status(thm)],[c125,c217]) ).
cnf(c219,plain,
mult(mult(X2,rd(X,X2)),mult(X2,mult(rd(X,X2),X2))) = mult(X2,mult(X,X)),
inference(transitivity,[status(thm)],[c121,c218]) ).
cnf(c220,plain,
mult(mult(X2,rd(X,X2)),mult(X2,X)) = mult(X2,mult(X,X)),
inference(transitivity,[status(thm)],[c105,c219]) ).
cnf(c221,plain,
mult(mult(X,rd(ld(X,X2),X)),mult(X,ld(X,X2))) = mult(X,mult(ld(X,X2),ld(X,X2))),
inference(substitution,[status(thm)],[c220]) ).
cnf(c222,plain,
mult(mult(X2,ld(X2,X)),ld(X2,X)) = mult(X2,mult(ld(X2,X),ld(X2,X))),
inference(substitution,[status(thm)],[c152]) ).
cnf(c223,plain,
mult(X2,mult(ld(X2,X),ld(X2,X))) = mult(mult(X2,ld(X2,X)),ld(X2,X)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c225,plain,
mult(mult(X2,ld(X2,X)),ld(X2,X)) = mult(X,ld(X2,X)),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
mult(X2,mult(ld(X2,X),ld(X2,X))) = mult(X,ld(X2,X)),
inference(transitivity,[status(thm)],[c223,c225]) ).
cnf(c227,plain,
mult(X,mult(ld(X,X2),ld(X,X2))) = mult(X2,ld(X,X2)),
inference(substitution,[status(thm)],[c226]) ).
cnf(c228,plain,
mult(mult(X,rd(ld(X,X2),X)),mult(X,ld(X,X2))) = mult(X2,ld(X,X2)),
inference(transitivity,[status(thm)],[c221,c227]) ).
cnf(c229,plain,
mult(mult(X,rd(ld(X,X2),X)),X2) = mult(X2,ld(X,X2)),
inference(transitivity,[status(thm)],[c101,c228]) ).
cnf(c230,plain,
mult(rd(X2,X),X2) = mult(X2,ld(X,X2)),
inference(transitivity,[status(thm)],[c98,c229]) ).
cnf(c231,plain,
mult(rd(X2,mult(mult(X2,X),X2)),X2) = mult(X2,ld(mult(mult(X2,X),X2),X2)),
inference(substitution,[status(thm)],[c230]) ).
cnf(c232,plain,
mult(X2,ld(mult(mult(X2,X),X2),X2)) = mult(rd(X2,mult(mult(X2,X),X2)),X2),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
mult(mult(X2,ld(mult(mult(X2,X),X2),X2)),mult(X,mult(X2,X))) = mult(mult(rd(X2,mult(mult(X2,X),X2)),X2),mult(X,mult(X2,X))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c235,plain,
rd(X3,mult(mult(X2,X),X2)) = rd(X3,mult(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
mult(rd(X3,mult(mult(X2,X),X2)),X2) = mult(rd(X3,mult(X2,mult(X,X2))),X2),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
mult(mult(rd(X3,mult(mult(X2,X),X2)),X2),mult(X,mult(X2,X))) = mult(mult(rd(X3,mult(X2,mult(X,X2))),X2),mult(X,mult(X2,X))),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
mult(mult(rd(X3,mult(X2,mult(X,X2))),mult(X2,mult(X,X2))),X) = mult(mult(rd(X3,mult(X2,mult(X,X2))),X2),mult(X,mult(X2,X))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c239,plain,
mult(mult(rd(X3,mult(X2,mult(X,X2))),X2),mult(X,mult(X2,X))) = mult(mult(rd(X3,mult(X2,mult(X,X2))),mult(X2,mult(X,X2))),X),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
mult(rd(X3,mult(X2,mult(X,X2))),mult(X2,mult(X,X2))) = X3,
inference(substitution,[status(thm)],[c11]) ).
cnf(c241,plain,
mult(mult(rd(X3,mult(X2,mult(X,X2))),mult(X2,mult(X,X2))),X) = mult(X3,X),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
mult(mult(rd(X3,mult(X2,mult(X,X2))),X2),mult(X,mult(X2,X))) = mult(X3,X),
inference(transitivity,[status(thm)],[c239,c241]) ).
cnf(c243,plain,
mult(mult(rd(X3,mult(mult(X2,X),X2)),X2),mult(X,mult(X2,X))) = mult(X3,X),
inference(transitivity,[status(thm)],[c237,c242]) ).
cnf(c244,plain,
mult(mult(rd(X2,mult(mult(X2,X),X2)),X2),mult(X,mult(X2,X))) = mult(X2,X),
inference(substitution,[status(thm)],[c243]) ).
cnf(c245,plain,
mult(mult(X2,ld(mult(mult(X2,X),X2),X2)),mult(X,mult(X2,X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c233,c244]) ).
cnf(c246,plain,
rd(mult(mult(X2,ld(mult(mult(X2,X),X2),X2)),mult(X,mult(X2,X))),mult(X,mult(X2,X))) = rd(mult(X2,X),mult(X,mult(X2,X))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
rd(mult(X2,X),mult(X,mult(X2,X))) = ld(X,unit),
inference(substitution,[status(thm)],[c133]) ).
cnf(c248,plain,
rd(mult(mult(X2,ld(mult(mult(X2,X),X2),X2)),mult(X,mult(X2,X))),mult(X,mult(X2,X))) = ld(X,unit),
inference(transitivity,[status(thm)],[c246,c247]) ).
cnf(c249,plain,
mult(X2,ld(mult(mult(X2,X),X2),X2)) = ld(X,unit),
inference(transitivity,[status(thm)],[c79,c248]) ).
cnf(c250,plain,
mult(X,ld(mult(mult(X,X2),X),X)) = ld(X2,unit),
inference(substitution,[status(thm)],[c249]) ).
cnf(c251,plain,
ld(X2,unit) = mult(X,ld(mult(mult(X,X2),X),X)),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
rd(ld(X2,unit),X) = rd(mult(X,ld(mult(mult(X,X2),X),X)),X),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
rd(mult(X,ld(mult(mult(X,X2),X),X)),X) = mult(X,rd(ld(mult(mult(X,X2),X),X),X)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c254,plain,
ld(X2,X) = mult(ld(X2,unit),X),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c255,plain,
rd(ld(X2,X),X) = rd(mult(ld(X2,unit),X),X),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
rd(mult(ld(X2,unit),X),X) = ld(X2,unit),
inference(substitution,[status(thm)],[c32]) ).
cnf(c257,plain,
rd(ld(X2,X),X) = ld(X2,unit),
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
rd(ld(mult(mult(X,X2),X),X),X) = ld(mult(mult(X,X2),X),unit),
inference(substitution,[status(thm)],[c257]) ).
cnf(c259,plain,
mult(X,rd(ld(mult(mult(X,X2),X),X),X)) = mult(X,ld(mult(mult(X,X2),X),unit)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
mult(X,ld(mult(mult(X,X2),X),unit)) = ld(mult(X,X2),unit),
inference(substitution,[status(thm)],[c197]) ).
cnf(c261,plain,
mult(X,rd(ld(mult(mult(X,X2),X),X),X)) = ld(mult(X,X2),unit),
inference(transitivity,[status(thm)],[c259,c260]) ).
cnf(c262,plain,
rd(mult(X,ld(mult(mult(X,X2),X),X)),X) = ld(mult(X,X2),unit),
inference(transitivity,[status(thm)],[c253,c261]) ).
cnf(c263,plain,
rd(ld(X2,unit),X) = ld(mult(X,X2),unit),
inference(transitivity,[status(thm)],[c252,c262]) ).
cnf(c264,plain,
rd(ld(X,unit),X2) = ld(mult(X2,X),unit),
inference(substitution,[status(thm)],[c263]) ).
cnf(c265,plain,
ld(mult(X2,X),unit) = rd(ld(X,unit),X2),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
mult(ld(mult(X3,X2),unit),mult(mult(X3,mult(X2,X)),X3)) = mult(rd(ld(X2,unit),X3),mult(mult(X3,mult(X2,X)),X3)),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c268,plain,
mult(X3,mult(mult(X2,X),X2)) = mult(X3,mult(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
mult(mult(X3,mult(mult(X2,X),X2)),X) = mult(mult(X3,mult(X2,mult(X,X2))),X),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
mult(mult(X3,mult(mult(X2,X),X2)),X) = mult(mult(X3,X2),mult(X,mult(X2,X))),
inference(transitivity,[status(thm)],[c269,c29]) ).
cnf(c271,plain,
mult(mult(rd(X3,X2),mult(mult(X2,X),X2)),X) = mult(mult(rd(X3,X2),X2),mult(X,mult(X2,X))),
inference(substitution,[status(thm)],[c270]) ).
cnf(c272,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c273,plain,
mult(mult(rd(X3,X2),X2),mult(X,mult(X2,X))) = mult(X3,mult(X,mult(X2,X))),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
mult(mult(rd(X3,X2),mult(mult(X2,X),X2)),X) = mult(X3,mult(X,mult(X2,X))),
inference(transitivity,[status(thm)],[c271,c273]) ).
cnf(c275,plain,
mult(mult(rd(X3,X),mult(mult(X,X2),X)),X2) = mult(X3,mult(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c274]) ).
cnf(c276,plain,
mult(X3,mult(X2,mult(X,X2))) = mult(mult(rd(X3,X),mult(mult(X,X2),X)),X2),
inference(symmetry,[status(thm)],[c275]) ).
cnf(c277,plain,
rd(mult(X3,mult(X2,mult(X,X2))),X2) = rd(mult(mult(rd(X3,X),mult(mult(X,X2),X)),X2),X2),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
rd(mult(mult(rd(X3,X),mult(mult(X,X2),X)),X2),X2) = mult(rd(X3,X),mult(mult(X,X2),X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c279,plain,
rd(mult(X3,mult(X2,mult(X,X2))),X2) = mult(rd(X3,X),mult(mult(X,X2),X)),
inference(transitivity,[status(thm)],[c277,c278]) ).
cnf(c280,plain,
rd(mult(X3,mult(X,mult(X2,X))),X) = mult(rd(X3,X2),mult(mult(X2,X),X2)),
inference(substitution,[status(thm)],[c279]) ).
cnf(c281,plain,
mult(rd(X3,X2),mult(mult(X2,X),X2)) = rd(mult(X3,mult(X,mult(X2,X))),X),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,axiom,
mult(f(A2),f(A2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
cnf(c283,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c282]) ).
cnf(c284,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
mult(X2,X) = mult(X2,mult(f(X),f(X))),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
mult(X3,mult(X2,X)) = mult(X3,mult(X2,mult(f(X),f(X)))),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
rd(mult(X3,mult(X2,X)),X2) = rd(mult(X3,mult(X2,mult(f(X),f(X)))),X2),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
mult(mult(X3,mult(X2,mult(X,X))),ld(X2,unit)) = rd(mult(X3,mult(X2,mult(X,X))),X2),
inference(substitution,[status(thm)],[c206]) ).
cnf(c289,plain,
rd(mult(X3,mult(X2,mult(X,X))),X2) = mult(mult(X3,mult(X2,mult(X,X))),ld(X2,unit)),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
rd(X,mult(X2,X)) = ld(X2,unit),
inference(substitution,[status(thm)],[c133]) ).
cnf(c291,plain,
ld(X2,unit) = rd(X,mult(X2,X)),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
mult(mult(X3,mult(X2,mult(X,X))),ld(X2,unit)) = mult(mult(X3,mult(X2,mult(X,X))),rd(X,mult(X2,X))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
mult(X2,mult(X,X)) = mult(mult(X2,X),X),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c294,plain,
mult(X3,mult(X2,mult(X,X))) = mult(X3,mult(mult(X2,X),X)),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
mult(mult(X3,mult(X2,mult(X,X))),rd(X,mult(X2,X))) = mult(mult(X3,mult(mult(X2,X),X)),rd(X,mult(X2,X))),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c297,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
mult(X2,X) = mult(X2,mult(rd(X,X2),X2)),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
mult(X3,mult(X2,X)) = mult(X3,mult(X2,mult(rd(X,X2),X2))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
mult(mult(X3,mult(X2,X)),rd(X,X2)) = mult(mult(X3,mult(X2,mult(rd(X,X2),X2))),rd(X,X2)),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
mult(mult(X3,mult(X2,mult(rd(X,X2),X2))),rd(X,X2)) = mult(mult(X3,X2),mult(rd(X,X2),mult(X2,rd(X,X2)))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c302,plain,
mult(rd(X,X2),mult(X2,rd(X,X2))) = mult(X,rd(X,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c303,plain,
mult(mult(X3,X2),mult(rd(X,X2),mult(X2,rd(X,X2)))) = mult(mult(X3,X2),mult(X,rd(X,X2))),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
mult(mult(X3,mult(X2,mult(rd(X,X2),X2))),rd(X,X2)) = mult(mult(X3,X2),mult(X,rd(X,X2))),
inference(transitivity,[status(thm)],[c301,c303]) ).
cnf(c305,plain,
mult(mult(X3,mult(X2,X)),rd(X,X2)) = mult(mult(X3,X2),mult(X,rd(X,X2))),
inference(transitivity,[status(thm)],[c300,c304]) ).
cnf(c306,plain,
mult(mult(X3,mult(mult(X2,X),X)),rd(X,mult(X2,X))) = mult(mult(X3,mult(X2,X)),mult(X,rd(X,mult(X2,X)))),
inference(substitution,[status(thm)],[c305]) ).
cnf(c307,plain,
rd(X,mult(X2,X)) = ld(X2,unit),
inference(substitution,[status(thm)],[c133]) ).
cnf(c308,plain,
mult(X,rd(X,mult(X2,X))) = mult(X,ld(X2,unit)),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
mult(mult(X3,mult(X2,X)),mult(X,rd(X,mult(X2,X)))) = mult(mult(X3,mult(X2,X)),mult(X,ld(X2,unit))),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
mult(X,ld(X2,unit)) = rd(X,X2),
inference(substitution,[status(thm)],[c206]) ).
cnf(c311,plain,
mult(mult(X3,mult(X2,X)),mult(X,ld(X2,unit))) = mult(mult(X3,mult(X2,X)),rd(X,X2)),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
mult(mult(X3,mult(X2,X)),mult(X,ld(X2,unit))) = mult(mult(X3,X2),mult(X,rd(X,X2))),
inference(transitivity,[status(thm)],[c311,c305]) ).
cnf(c313,plain,
mult(mult(X3,mult(X2,X)),mult(X,rd(X,mult(X2,X)))) = mult(mult(X3,X2),mult(X,rd(X,X2))),
inference(transitivity,[status(thm)],[c309,c312]) ).
cnf(c314,plain,
mult(mult(X3,mult(mult(X2,X),X)),rd(X,mult(X2,X))) = mult(mult(X3,X2),mult(X,rd(X,X2))),
inference(transitivity,[status(thm)],[c306,c313]) ).
cnf(c315,plain,
mult(mult(X3,mult(X2,mult(X,X))),rd(X,mult(X2,X))) = mult(mult(X3,X2),mult(X,rd(X,X2))),
inference(transitivity,[status(thm)],[c295,c314]) ).
cnf(c316,plain,
mult(mult(X3,mult(X2,mult(X,X))),ld(X2,unit)) = mult(mult(X3,X2),mult(X,rd(X,X2))),
inference(transitivity,[status(thm)],[c292,c315]) ).
cnf(c317,plain,
rd(mult(X3,mult(X2,mult(X,X))),X2) = mult(mult(X3,X2),mult(X,rd(X,X2))),
inference(transitivity,[status(thm)],[c289,c316]) ).
cnf(c318,plain,
rd(mult(X3,mult(X2,mult(f(X),f(X)))),X2) = mult(mult(X3,X2),mult(f(X),rd(f(X),X2))),
inference(substitution,[status(thm)],[c317]) ).
cnf(c319,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c320,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c319]) ).
cnf(c321,plain,
rd(X2,ld(X,X2)) = rd(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
rd(mult(X,ld(X,X2)),ld(X,X2)) = X,
inference(substitution,[status(thm)],[c32]) ).
cnf(c323,plain,
rd(X2,ld(X,X2)) = X,
inference(transitivity,[status(thm)],[c321,c322]) ).
cnf(c324,plain,
rd(X2,ld(mult(f(X2),rd(f(X2),X)),X2)) = mult(f(X2),rd(f(X2),X)),
inference(substitution,[status(thm)],[c323]) ).
cnf(c325,plain,
mult(f(X2),rd(f(X2),X)) = rd(X2,ld(mult(f(X2),rd(f(X2),X)),X2)),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c326,plain,
ld(X,mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c50]) ).
cnf(c327,plain,
X2 = ld(X,mult(X,X2)),
inference(symmetry,[status(thm)],[c326]) ).
cnf(c328,plain,
ld(mult(f(X2),rd(f(X2),X)),X2) = ld(mult(f(X2),rd(f(X2),X)),ld(X,mult(X,X2))),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
mult(f(X),f(X)) = X,
inference(substitution,[status(thm)],[c282]) ).
cnf(c330,plain,
X = mult(f(X),f(X)),
inference(symmetry,[status(thm)],[c329]) ).
cnf(c331,plain,
mult(X2,X) = mult(X2,mult(f(X),f(X))),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
ld(mult(X2,mult(f(X),rd(f(X),X2))),mult(X2,X)) = ld(mult(X2,mult(f(X),rd(f(X),X2))),mult(X2,mult(f(X),f(X)))),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
mult(rd(X,X2),mult(X2,X)) = mult(X,X),
inference(substitution,[status(thm)],[c215]) ).
cnf(c334,plain,
mult(X,X) = mult(rd(X,X2),mult(X2,X)),
inference(symmetry,[status(thm)],[c333]) ).
cnf(c335,plain,
mult(X2,mult(X,X)) = mult(X2,mult(rd(X,X2),mult(X2,X))),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
ld(mult(X2,mult(X,rd(X,X2))),mult(X2,mult(X,X))) = ld(mult(X2,mult(X,rd(X,X2))),mult(X2,mult(rd(X,X2),mult(X2,X)))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
mult(rd(X,X2),mult(X2,rd(X,X2))) = mult(X,rd(X,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c338,plain,
mult(X,rd(X,X2)) = mult(rd(X,X2),mult(X2,rd(X,X2))),
inference(symmetry,[status(thm)],[c337]) ).
cnf(c339,plain,
mult(X2,mult(X,rd(X,X2))) = mult(X2,mult(rd(X,X2),mult(X2,rd(X,X2)))),
inference(congruence,[status(thm)],[c338]) ).
cnf(c340,plain,
ld(mult(X2,mult(X,rd(X,X2))),mult(X2,mult(rd(X,X2),mult(X2,X)))) = ld(mult(X2,mult(rd(X,X2),mult(X2,rd(X,X2)))),mult(X2,mult(rd(X,X2),mult(X2,X)))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c342,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
mult(X2,X) = mult(X2,mult(rd(X,X2),X2)),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,plain,
mult(rd(X,X2),mult(X2,X)) = mult(rd(X,X2),mult(X2,mult(rd(X,X2),X2))),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
mult(X2,mult(rd(X,X2),mult(X2,X))) = mult(X2,mult(rd(X,X2),mult(X2,mult(rd(X,X2),X2)))),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
ld(mult(X2,mult(rd(X,X2),mult(X2,rd(X,X2)))),mult(X2,mult(rd(X,X2),mult(X2,X)))) = ld(mult(X2,mult(rd(X,X2),mult(X2,rd(X,X2)))),mult(X2,mult(rd(X,X2),mult(X2,mult(rd(X,X2),X2))))),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
mult(mult(X,mult(X2,X)),X2) = mult(X,mult(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c116]) ).
cnf(c348,plain,
mult(X,mult(X2,mult(X,X2))) = mult(mult(X,mult(X2,X)),X2),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c349,plain,
mult(X2,mult(X,mult(X2,mult(X,X2)))) = mult(X2,mult(mult(X,mult(X2,X)),X2)),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
ld(mult(X2,mult(X,mult(X2,X))),mult(X2,mult(X,mult(X2,mult(X,X2))))) = ld(mult(X2,mult(X,mult(X2,X))),mult(X2,mult(mult(X,mult(X2,X)),X2))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
mult(mult(X2,X),X2) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c352,plain,
mult(X2,mult(X,X2)) = mult(mult(X2,X),X2),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
ld(mult(X2,X),mult(X2,mult(X,X2))) = ld(mult(X2,X),mult(mult(X2,X),X2)),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
ld(mult(X2,X),mult(mult(X2,X),X2)) = X2,
inference(substitution,[status(thm)],[c50]) ).
cnf(c355,plain,
ld(mult(X2,X),mult(X2,mult(X,X2))) = X2,
inference(transitivity,[status(thm)],[c353,c354]) ).
cnf(c356,plain,
ld(mult(X2,mult(X,mult(X2,X))),mult(X2,mult(mult(X,mult(X2,X)),X2))) = X2,
inference(substitution,[status(thm)],[c355]) ).
cnf(c357,plain,
ld(mult(X2,mult(X,mult(X2,X))),mult(X2,mult(X,mult(X2,mult(X,X2))))) = X2,
inference(transitivity,[status(thm)],[c350,c356]) ).
cnf(c358,plain,
ld(mult(X2,mult(rd(X,X2),mult(X2,rd(X,X2)))),mult(X2,mult(rd(X,X2),mult(X2,mult(rd(X,X2),X2))))) = X2,
inference(substitution,[status(thm)],[c357]) ).
cnf(c359,plain,
ld(mult(X2,mult(rd(X,X2),mult(X2,rd(X,X2)))),mult(X2,mult(rd(X,X2),mult(X2,X)))) = X2,
inference(transitivity,[status(thm)],[c346,c358]) ).
cnf(c360,plain,
ld(mult(X2,mult(X,rd(X,X2))),mult(X2,mult(rd(X,X2),mult(X2,X)))) = X2,
inference(transitivity,[status(thm)],[c340,c359]) ).
cnf(c361,plain,
ld(mult(X2,mult(X,rd(X,X2))),mult(X2,mult(X,X))) = X2,
inference(transitivity,[status(thm)],[c336,c360]) ).
cnf(c362,plain,
ld(mult(X2,mult(f(X),rd(f(X),X2))),mult(X2,mult(f(X),f(X)))) = X2,
inference(substitution,[status(thm)],[c361]) ).
cnf(c363,plain,
ld(mult(X2,mult(f(X),rd(f(X),X2))),mult(X2,X)) = X2,
inference(transitivity,[status(thm)],[c332,c362]) ).
cnf(c364,plain,
ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)) = X,
inference(substitution,[status(thm)],[c363]) ).
cnf(c365,plain,
X = ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
ld(X,mult(X,X2)) = ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,X2)),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
ld(mult(f(X2),rd(f(X2),X)),ld(X,mult(X,X2))) = ld(mult(f(X2),rd(f(X2),X)),ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,X2))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
ld(X,mult(X,mult(f(X2),rd(f(X2),X)))) = mult(f(X2),rd(f(X2),X)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c369,plain,
mult(f(X2),rd(f(X2),X)) = ld(X,mult(X,mult(f(X2),rd(f(X2),X)))),
inference(symmetry,[status(thm)],[c368]) ).
cnf(c370,plain,
ld(mult(f(X2),rd(f(X2),X)),ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,X2))) = ld(ld(X,mult(X,mult(f(X2),rd(f(X2),X)))),ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,X2))),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)) = X,
inference(substitution,[status(thm)],[c363]) ).
cnf(c372,plain,
X = ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),
inference(symmetry,[status(thm)],[c371]) ).
cnf(c373,plain,
ld(X,mult(X,mult(f(X2),rd(f(X2),X)))) = ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,mult(f(X2),rd(f(X2),X)))),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
ld(ld(X,mult(X,mult(f(X2),rd(f(X2),X)))),ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,X2))) = ld(ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,mult(f(X2),rd(f(X2),X)))),ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,X2))),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
ld(ld(X2,X),mult(X2,ld(X2,X))) = mult(ld(ld(X2,X),X2),ld(X2,X)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c376,plain,
mult(ld(ld(X2,X),X2),ld(X2,X)) = ld(ld(X2,X),mult(X2,ld(X2,X))),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c378,plain,
ld(ld(X2,X),mult(X2,ld(X2,X))) = ld(ld(X2,X),X),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
mult(ld(ld(X2,X),X2),ld(X2,X)) = ld(ld(X2,X),X),
inference(transitivity,[status(thm)],[c376,c378]) ).
cnf(c380,plain,
ld(ld(X2,X),X) = mult(ld(ld(X2,X),X2),ld(X2,X)),
inference(symmetry,[status(thm)],[c379]) ).
cnf(c381,plain,
ld(ld(ld(X2,X),X2),ld(ld(X2,X),X)) = ld(ld(ld(X2,X),X2),mult(ld(ld(X2,X),X2),ld(X2,X))),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
ld(ld(ld(X2,X),X2),mult(ld(ld(X2,X),X2),ld(X2,X))) = ld(X2,X),
inference(substitution,[status(thm)],[c50]) ).
cnf(c383,plain,
ld(ld(ld(X2,X),X2),ld(ld(X2,X),X)) = ld(X2,X),
inference(transitivity,[status(thm)],[c381,c382]) ).
cnf(c384,plain,
ld(ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,mult(f(X2),rd(f(X2),X)))),ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,X2))) = ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),
inference(substitution,[status(thm)],[c383]) ).
cnf(c385,plain,
ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)) = X,
inference(substitution,[status(thm)],[c363]) ).
cnf(c386,plain,
ld(ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,mult(f(X2),rd(f(X2),X)))),ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,X2))) = X,
inference(transitivity,[status(thm)],[c384,c385]) ).
cnf(c387,plain,
ld(ld(X,mult(X,mult(f(X2),rd(f(X2),X)))),ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,X2))) = X,
inference(transitivity,[status(thm)],[c374,c386]) ).
cnf(c388,plain,
ld(mult(f(X2),rd(f(X2),X)),ld(ld(mult(X,mult(f(X2),rd(f(X2),X))),mult(X,X2)),mult(X,X2))) = X,
inference(transitivity,[status(thm)],[c370,c387]) ).
cnf(c389,plain,
ld(mult(f(X2),rd(f(X2),X)),ld(X,mult(X,X2))) = X,
inference(transitivity,[status(thm)],[c367,c388]) ).
cnf(c390,plain,
ld(mult(f(X2),rd(f(X2),X)),X2) = X,
inference(transitivity,[status(thm)],[c328,c389]) ).
cnf(c391,plain,
rd(X2,ld(mult(f(X2),rd(f(X2),X)),X2)) = rd(X2,X),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
mult(f(X2),rd(f(X2),X)) = rd(X2,X),
inference(transitivity,[status(thm)],[c325,c391]) ).
cnf(c393,plain,
mult(f(X),rd(f(X),X2)) = rd(X,X2),
inference(substitution,[status(thm)],[c392]) ).
cnf(c394,plain,
mult(mult(X3,X2),mult(f(X),rd(f(X),X2))) = mult(mult(X3,X2),rd(X,X2)),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
rd(mult(X3,mult(X2,mult(f(X),f(X)))),X2) = mult(mult(X3,X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c318,c394]) ).
cnf(c396,plain,
rd(mult(X3,mult(X2,X)),X2) = mult(mult(X3,X2),rd(X,X2)),
inference(transitivity,[status(thm)],[c287,c395]) ).
cnf(c397,plain,
rd(mult(X3,mult(X,mult(X2,X))),X) = mult(mult(X3,X),rd(mult(X2,X),X)),
inference(substitution,[status(thm)],[c396]) ).
cnf(c398,plain,
rd(mult(X2,X),X) = X2,
inference(substitution,[status(thm)],[c32]) ).
cnf(c399,plain,
mult(mult(X3,X),rd(mult(X2,X),X)) = mult(mult(X3,X),X2),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
rd(mult(X3,mult(X,mult(X2,X))),X) = mult(mult(X3,X),X2),
inference(transitivity,[status(thm)],[c397,c399]) ).
cnf(c401,plain,
mult(rd(X3,X2),mult(mult(X2,X),X2)) = mult(mult(X3,X),X2),
inference(transitivity,[status(thm)],[c281,c400]) ).
cnf(c402,plain,
mult(rd(ld(X2,unit),X3),mult(mult(X3,mult(X2,X)),X3)) = mult(mult(ld(X2,unit),mult(X2,X)),X3),
inference(substitution,[status(thm)],[c401]) ).
cnf(c403,plain,
mult(mult(ld(X2,unit),mult(X2,X)),X3) = mult(X,X3),
inference(congruence,[status(thm)],[c73]) ).
cnf(c404,plain,
mult(rd(ld(X2,unit),X3),mult(mult(X3,mult(X2,X)),X3)) = mult(X,X3),
inference(transitivity,[status(thm)],[c402,c403]) ).
cnf(c405,plain,
mult(ld(mult(X3,X2),unit),mult(mult(X3,mult(X2,X)),X3)) = mult(X,X3),
inference(transitivity,[status(thm)],[c266,c404]) ).
cnf(c406,plain,
ld(mult(X3,X2),mult(mult(X3,mult(X2,X)),X3)) = mult(X,X3),
inference(transitivity,[status(thm)],[c77,c405]) ).
cnf(c407,plain,
mult(mult(X3,X2),ld(mult(X3,X2),mult(mult(X3,mult(X2,X)),X3))) = mult(mult(X3,X2),mult(X,X3)),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
mult(mult(X3,mult(X2,X)),X3) = mult(mult(X3,X2),mult(X,X3)),
inference(transitivity,[status(thm)],[c4,c407]) ).
cnf(c409,plain,
mult(mult(a,mult(b,c)),a) = mult(mult(a,b),mult(c,a)),
inference(substitution,[status(thm)],[c408]) ).
cnf(c410,plain,
mult(mult(a,b),mult(c,a)) = mult(mult(a,mult(b,c)),a),
inference(symmetry,[status(thm)],[c409]) ).
cnf(c411,plain,
$false,
inference(resolution,[status(thm)],[c1,c410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP667-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n005.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sun Sep 27 10:34:16 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 159.68/20.65 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 159.68/20.65
% 159.68/20.65 % SZS status Unsatisfiable
% 159.68/20.65
% 159.68/20.68 % SZS output start CNFRefutation
% See solution above
% 161.25/20.88
% 161.25/20.88 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------