%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP765-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 10:11:56 AM UTC 2026
% Result : Unsatisfiable 194.98s 25.06s
% Output : CNFRefutation 213.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 210
% Number of leaves : 13
% Syntax : Number of clauses : 3158 (3158 unt; 0 nHn; 19 RR)
% Number of literals : 3158 (3157 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 5811 ( 36 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
product(i(i(x0)),x1) != product(eta(x0),product(x0,x1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
j(A) = quotient(one,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
cnf(c3,plain,
j(i(X)) = quotient(one,i(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
i(A2) = difference(A2,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
cnf(c5,plain,
i(X) = difference(X,one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
product(X,i(X)) = product(X,difference(X,one)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
product(A2,difference(A2,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
cnf(c8,plain,
product(X,difference(X,one)) = one,
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
product(X,i(X)) = one,
inference(transitivity,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
one = product(X,i(X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
quotient(one,i(X)) = quotient(product(X,i(X)),i(X)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
quotient(product(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
cnf(c13,plain,
quotient(product(X,i(X)),i(X)) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
quotient(one,i(X)) = X,
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
j(i(X)) = X,
inference(transitivity,[status(thm)],[c3,c14]) ).
cnf(c16,plain,
j(i(x1)) = x1,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
x1 = j(i(x1)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
product(i(i(x0)),x1) = product(i(i(x0)),j(i(x1))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
product(i(A2),A2) = product(A2,j(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
cnf(c20,plain,
product(i(X),X) = product(X,j(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
product(X,j(X)) = product(i(X),X),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
eta(A2) = product(i(A2),A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
cnf(c23,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
product(X,j(X)) = eta(X),
inference(transitivity,[status(thm)],[c21,c24]) ).
cnf(c26,plain,
product(i(X),j(i(X))) = eta(i(X)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
eta(i(X)) = product(i(X),j(i(X))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
product(i(X),j(i(X))) = product(i(X),X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c29,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c30,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
product(i(X),j(i(X))) = eta(X),
inference(transitivity,[status(thm)],[c28,c30]) ).
cnf(c32,plain,
eta(i(X)) = eta(X),
inference(transitivity,[status(thm)],[c27,c31]) ).
cnf(c33,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
quotient(eta(X),quotient(X2,i(i(X)))) = quotient(eta(i(X)),quotient(X2,i(i(X)))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
i(j(X)) = difference(j(X),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c36,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
product(j(X),X) = product(quotient(one,X),X),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
product(quotient(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
cnf(c39,plain,
product(quotient(one,X),X) = one,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
product(j(X),X) = one,
inference(transitivity,[status(thm)],[c37,c39]) ).
cnf(c41,plain,
one = product(j(X),X),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
difference(j(X),one) = difference(j(X),product(j(X),X)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,axiom,
difference(A2,product(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
cnf(c44,plain,
difference(j(X),product(j(X),X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
difference(j(X),one) = X,
inference(transitivity,[status(thm)],[c42,c44]) ).
cnf(c46,plain,
i(j(X)) = X,
inference(transitivity,[status(thm)],[c35,c45]) ).
cnf(c47,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
quotient(X,i(X2)) = quotient(i(j(X)),i(X2)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
quotient(eta(X2),quotient(X,i(X2))) = quotient(eta(X2),quotient(i(j(X)),i(X2))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c51,plain,
difference(product(i(X2),X),eta(X2)) = difference(product(i(X2),X),product(i(X2),X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c53,plain,
X = product(X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
product(X,X3) = product(product(X2,difference(X2,X)),X3),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
difference(X3,product(X2,X)) = difference(X3,product(product(X3,difference(X3,X2)),X)),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
quotient(difference(X3,product(X2,X)),X) = quotient(difference(X3,product(product(X3,difference(X3,X2)),X)),X),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,axiom,
difference(A2,product(product(A2,B2),C)) = quotient(product(B2,product(C,A2)),A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
cnf(c58,plain,
difference(X3,product(product(X3,X2),X)) = quotient(product(X2,product(X,X3)),X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
quotient(difference(X3,product(product(X3,X2),X)),X) = quotient(quotient(product(X2,product(X,X3)),X3),X),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,axiom,
difference(product(A2,B2),product(A2,product(B2,C2))) = quotient(quotient(product(C2,product(A2,B2)),B2),A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
cnf(c61,plain,
difference(product(X,X3),product(X,product(X3,X2))) = quotient(quotient(product(X2,product(X,X3)),X3),X),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
quotient(quotient(product(X2,product(X,X3)),X3),X) = difference(product(X,X3),product(X,product(X3,X2))),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
quotient(difference(X3,product(product(X3,X2),X)),X) = difference(product(X,X3),product(X,product(X3,X2))),
inference(transitivity,[status(thm)],[c59,c62]) ).
cnf(c64,plain,
quotient(difference(X3,product(product(X3,difference(X3,X2)),X)),X) = difference(product(X,X3),product(X,product(X3,difference(X3,X2)))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c66,plain,
product(X,product(X3,difference(X3,X2))) = product(X,X2),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
difference(product(X,X3),product(X,product(X3,difference(X3,X2)))) = difference(product(X,X3),product(X,X2)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
quotient(difference(X3,product(product(X3,difference(X3,X2)),X)),X) = difference(product(X,X3),product(X,X2)),
inference(transitivity,[status(thm)],[c64,c67]) ).
cnf(c69,plain,
quotient(difference(X3,product(X2,X)),X) = difference(product(X,X3),product(X,X2)),
inference(transitivity,[status(thm)],[c56,c68]) ).
cnf(c70,plain,
quotient(difference(X,product(X2,i(X2))),i(X2)) = difference(product(i(X2),X),product(i(X2),X2)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
difference(product(i(X2),X),product(i(X2),X2)) = quotient(difference(X,product(X2,i(X2))),i(X2)),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
difference(X,product(X2,i(X2))) = difference(X,one),
inference(congruence,[status(thm)],[c9]) ).
cnf(c73,plain,
quotient(difference(X,product(X2,i(X2))),i(X2)) = quotient(difference(X,one),i(X2)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
i(X) = difference(X,one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c75,plain,
difference(X,one) = i(X),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
quotient(difference(X,one),i(X2)) = quotient(i(X),i(X2)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
quotient(difference(X,product(X2,i(X2))),i(X2)) = quotient(i(X),i(X2)),
inference(transitivity,[status(thm)],[c73,c76]) ).
cnf(c78,plain,
difference(product(i(X2),X),product(i(X2),X2)) = quotient(i(X),i(X2)),
inference(transitivity,[status(thm)],[c71,c77]) ).
cnf(c79,plain,
difference(product(i(X2),X),eta(X2)) = quotient(i(X),i(X2)),
inference(transitivity,[status(thm)],[c51,c78]) ).
cnf(c80,plain,
quotient(i(X),i(X2)) = difference(product(i(X2),X),eta(X2)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
quotient(eta(X2),quotient(i(X),i(X2))) = quotient(eta(X2),difference(product(i(X2),X),eta(X2))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
product(X,difference(X,X2)) = X2,
inference(substitution,[status(thm)],[c7]) ).
cnf(c83,plain,
X2 = product(X,difference(X,X2)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
quotient(X2,difference(X,X2)) = quotient(product(X,difference(X,X2)),difference(X,X2)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
quotient(product(X,difference(X,X2)),difference(X,X2)) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c86,plain,
quotient(X2,difference(X,X2)) = X,
inference(transitivity,[status(thm)],[c84,c85]) ).
cnf(c87,plain,
quotient(eta(X2),difference(product(i(X2),X),eta(X2))) = product(i(X2),X),
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
quotient(eta(X2),quotient(i(X),i(X2))) = product(i(X2),X),
inference(transitivity,[status(thm)],[c81,c87]) ).
cnf(c89,plain,
quotient(eta(X2),quotient(i(j(X)),i(X2))) = product(i(X2),j(X)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
quotient(eta(X2),quotient(X,i(X2))) = product(i(X2),j(X)),
inference(transitivity,[status(thm)],[c49,c89]) ).
cnf(c91,plain,
quotient(eta(i(X2)),quotient(X,i(i(X2)))) = product(i(i(X2)),j(X)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
quotient(eta(X2),quotient(X,i(i(X2)))) = product(i(i(X2)),j(X)),
inference(transitivity,[status(thm)],[c34,c91]) ).
cnf(c93,plain,
quotient(eta(x0),quotient(i(x1),i(i(x0)))) = product(i(i(x0)),j(i(x1))),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
product(i(i(x0)),j(i(x1))) = quotient(eta(x0),quotient(i(x1),i(i(x0)))),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c96,plain,
product(X2,X) = product(X2,j(i(X))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
i(product(X2,X)) = i(product(X2,j(i(X)))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c99,plain,
product(X2,j(X)) = product(j(i(X2)),j(X)),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
i(product(X2,j(X))) = i(product(j(i(X2)),j(X))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
difference(X,product(X,X2)) = X2,
inference(substitution,[status(thm)],[c43]) ).
cnf(c102,plain,
X2 = difference(X,product(X,X2)),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
i(X2) = i(difference(X,product(X,X2))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
product(i(X2),eta(X)) = product(i(difference(X,product(X,X2))),eta(X)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c106,plain,
difference(i(X),X) = difference(i(X),j(i(X))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
i(difference(i(X),X)) = i(difference(i(X),j(i(X)))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
eta(j(X)) = product(i(j(X)),j(X)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c109,plain,
product(i(j(X)),j(X)) = product(X,j(X)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c110,plain,
product(i(j(X)),j(X)) = eta(X),
inference(transitivity,[status(thm)],[c109,c25]) ).
cnf(c111,plain,
eta(j(X)) = eta(X),
inference(transitivity,[status(thm)],[c108,c110]) ).
cnf(c112,plain,
eta(X) = eta(j(X)),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
difference(j(X),eta(X)) = difference(j(X),eta(j(X))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
eta(X) = product(X,j(X)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c115,plain,
difference(X,eta(X)) = difference(X,product(X,j(X))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
difference(X,product(X,j(X))) = j(X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c117,plain,
difference(X,eta(X)) = j(X),
inference(transitivity,[status(thm)],[c115,c116]) ).
cnf(c118,plain,
difference(j(X),eta(j(X))) = j(j(X)),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
difference(j(X),eta(X)) = j(j(X)),
inference(transitivity,[status(thm)],[c113,c118]) ).
cnf(c120,plain,
j(j(X)) = difference(j(X),eta(X)),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
product(j(j(X)),X) = product(difference(j(X),eta(X)),X),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
eta(X) = product(X,j(X)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c123,plain,
difference(product(X2,X),eta(X2)) = difference(product(X2,X),product(X2,j(X2))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
quotient(difference(X,product(j(X2),X2)),X2) = difference(product(X2,X),product(X2,j(X2))),
inference(substitution,[status(thm)],[c69]) ).
cnf(c125,plain,
difference(product(X2,X),product(X2,j(X2))) = quotient(difference(X,product(j(X2),X2)),X2),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
difference(X,product(j(X2),X2)) = difference(X,one),
inference(congruence,[status(thm)],[c40]) ).
cnf(c127,plain,
quotient(difference(X,product(j(X2),X2)),X2) = quotient(difference(X,one),X2),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
i(X) = difference(X,one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c129,plain,
difference(X,one) = i(X),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
quotient(difference(X,one),X2) = quotient(i(X),X2),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
quotient(difference(X,product(j(X2),X2)),X2) = quotient(i(X),X2),
inference(transitivity,[status(thm)],[c127,c130]) ).
cnf(c132,plain,
difference(product(X2,X),product(X2,j(X2))) = quotient(i(X),X2),
inference(transitivity,[status(thm)],[c125,c131]) ).
cnf(c133,plain,
difference(product(X2,X),eta(X2)) = quotient(i(X),X2),
inference(transitivity,[status(thm)],[c123,c132]) ).
cnf(c134,plain,
difference(product(X2,difference(X2,X)),eta(X2)) = quotient(i(difference(X2,X)),X2),
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
quotient(i(difference(X2,X)),X2) = difference(product(X2,difference(X2,X)),eta(X2)),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c137,plain,
difference(product(X2,difference(X2,X)),eta(X2)) = difference(X,eta(X2)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
quotient(i(difference(X2,X)),X2) = difference(X,eta(X2)),
inference(transitivity,[status(thm)],[c135,c137]) ).
cnf(c139,plain,
quotient(i(difference(X,X2)),X) = difference(X2,eta(X)),
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
difference(X2,eta(X)) = quotient(i(difference(X,X2)),X),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
product(difference(X2,eta(X)),X) = product(quotient(i(difference(X,X2)),X),X),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
product(quotient(i(difference(X,X2)),X),X) = i(difference(X,X2)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c143,plain,
product(difference(X2,eta(X)),X) = i(difference(X,X2)),
inference(transitivity,[status(thm)],[c141,c142]) ).
cnf(c144,plain,
product(difference(j(X),eta(X)),X) = i(difference(X,j(X))),
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
product(j(j(X)),X) = i(difference(X,j(X))),
inference(transitivity,[status(thm)],[c121,c144]) ).
cnf(c146,plain,
i(difference(X,j(X))) = product(j(j(X)),X),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
j(i(product(X,eta(X)))) = product(X,eta(X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c148,plain,
product(X,eta(X)) = j(i(product(X,eta(X)))),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c150,plain,
difference(X2,eta(X)) = difference(X2,product(i(X),X)),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
quotient(difference(X2,eta(X)),X) = quotient(difference(X2,product(i(X),X)),X),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
quotient(difference(X2,product(i(X),X)),X) = difference(product(X,X2),product(X,i(X))),
inference(substitution,[status(thm)],[c69]) ).
cnf(c153,plain,
difference(product(X,X2),product(X,i(X))) = difference(product(X,X2),one),
inference(congruence,[status(thm)],[c9]) ).
cnf(c154,plain,
i(product(X,X2)) = difference(product(X,X2),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c155,plain,
difference(product(X,X2),one) = i(product(X,X2)),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
difference(product(X,X2),product(X,i(X))) = i(product(X,X2)),
inference(transitivity,[status(thm)],[c153,c155]) ).
cnf(c157,plain,
quotient(difference(X2,product(i(X),X)),X) = i(product(X,X2)),
inference(transitivity,[status(thm)],[c152,c156]) ).
cnf(c158,plain,
quotient(difference(X2,eta(X)),X) = i(product(X,X2)),
inference(transitivity,[status(thm)],[c151,c157]) ).
cnf(c159,plain,
quotient(difference(eta(X),eta(X)),X) = i(product(X,eta(X))),
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
i(product(X,eta(X))) = quotient(difference(eta(X),eta(X)),X),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,axiom,
product(A2,one) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
cnf(c162,plain,
product(X,one) = X,
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
X = product(X,one),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
difference(X,X) = difference(X,product(X,one)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
difference(X,product(X,one)) = one,
inference(substitution,[status(thm)],[c43]) ).
cnf(c166,plain,
difference(X,X) = one,
inference(transitivity,[status(thm)],[c164,c165]) ).
cnf(c167,plain,
difference(eta(X),eta(X)) = one,
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
quotient(difference(eta(X),eta(X)),X) = quotient(one,X),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c170,plain,
quotient(one,X) = j(X),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
quotient(difference(eta(X),eta(X)),X) = j(X),
inference(transitivity,[status(thm)],[c168,c170]) ).
cnf(c172,plain,
i(product(X,eta(X))) = j(X),
inference(transitivity,[status(thm)],[c160,c171]) ).
cnf(c173,plain,
j(i(product(X,eta(X)))) = j(j(X)),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
product(X,eta(X)) = j(j(X)),
inference(transitivity,[status(thm)],[c148,c173]) ).
cnf(c175,plain,
j(j(X)) = product(X,eta(X)),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
quotient(X,j(j(X))) = quotient(X,product(X,eta(X))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c178,plain,
quotient(X,product(X,eta(X))) = quotient(i(j(X)),product(X,eta(X))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
j(X) = i(product(X,eta(X))),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c180,plain,
i(j(X)) = i(i(product(X,eta(X)))),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
quotient(i(j(X)),product(X,eta(X))) = quotient(i(i(product(X,eta(X)))),product(X,eta(X))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
difference(product(X,i(X)),eta(X)) = quotient(i(i(X)),X),
inference(substitution,[status(thm)],[c133]) ).
cnf(c183,plain,
quotient(i(i(X)),X) = difference(product(X,i(X)),eta(X)),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
difference(product(X,i(X)),eta(X)) = difference(one,eta(X)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c185,axiom,
product(one,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
cnf(c186,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
X = product(one,X),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
difference(one,X) = difference(one,product(one,X)),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
difference(one,product(one,X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c190,plain,
difference(one,X) = X,
inference(transitivity,[status(thm)],[c188,c189]) ).
cnf(c191,plain,
difference(one,eta(X)) = eta(X),
inference(substitution,[status(thm)],[c190]) ).
cnf(c192,plain,
difference(product(X,i(X)),eta(X)) = eta(X),
inference(transitivity,[status(thm)],[c184,c191]) ).
cnf(c193,plain,
quotient(i(i(X)),X) = eta(X),
inference(transitivity,[status(thm)],[c183,c192]) ).
cnf(c194,plain,
quotient(i(i(product(X,eta(X)))),product(X,eta(X))) = eta(product(X,eta(X))),
inference(substitution,[status(thm)],[c193]) ).
cnf(c195,plain,
eta(product(X,eta(X))) = eta(j(j(X))),
inference(congruence,[status(thm)],[c174]) ).
cnf(c196,plain,
eta(j(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c197,plain,
eta(j(j(X))) = eta(X),
inference(transitivity,[status(thm)],[c196,c111]) ).
cnf(c198,plain,
eta(product(X,eta(X))) = eta(X),
inference(transitivity,[status(thm)],[c195,c197]) ).
cnf(c199,plain,
quotient(i(i(product(X,eta(X)))),product(X,eta(X))) = eta(X),
inference(transitivity,[status(thm)],[c194,c198]) ).
cnf(c200,plain,
quotient(i(j(X)),product(X,eta(X))) = eta(X),
inference(transitivity,[status(thm)],[c181,c199]) ).
cnf(c201,plain,
quotient(X,product(X,eta(X))) = eta(X),
inference(transitivity,[status(thm)],[c178,c200]) ).
cnf(c202,plain,
quotient(X,j(j(X))) = eta(X),
inference(transitivity,[status(thm)],[c176,c201]) ).
cnf(c203,plain,
eta(X) = quotient(X,j(j(X))),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
difference(eta(X),X) = difference(quotient(X,j(j(X))),X),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
product(quotient(X2,X),X) = X2,
inference(substitution,[status(thm)],[c38]) ).
cnf(c206,plain,
X2 = product(quotient(X2,X),X),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
difference(quotient(X2,X),X2) = difference(quotient(X2,X),product(quotient(X2,X),X)),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
difference(quotient(X2,X),product(quotient(X2,X),X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c209,plain,
difference(quotient(X2,X),X2) = X,
inference(transitivity,[status(thm)],[c207,c208]) ).
cnf(c210,plain,
difference(quotient(X,j(j(X))),X) = j(j(X)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
difference(eta(X),X) = j(j(X)),
inference(transitivity,[status(thm)],[c204,c210]) ).
cnf(c212,plain,
j(j(X)) = difference(eta(X),X),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
product(j(j(X)),X) = product(difference(eta(X),X),X),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
eta(X) = product(X,j(X)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c215,plain,
difference(eta(X),X) = difference(product(X,j(X)),X),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
product(difference(eta(X),X),X) = product(difference(product(X,j(X)),X),X),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c185]) ).
cnf(c218,plain,
X = product(one,X),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
difference(X2,X) = difference(X2,product(one,X)),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
quotient(difference(X2,X),X) = quotient(difference(X2,product(one,X)),X),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
one = product(X,i(X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c222,plain,
product(one,X) = product(product(X2,i(X2)),X),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
difference(X2,product(one,X)) = difference(X2,product(product(X2,i(X2)),X)),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
quotient(difference(X2,product(one,X)),X) = quotient(difference(X2,product(product(X2,i(X2)),X)),X),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
quotient(difference(X2,product(product(X2,i(X2)),X)),X) = difference(product(X,X2),product(X,product(X2,i(X2)))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c226,plain,
product(X,product(X2,i(X2))) = product(X,one),
inference(congruence,[status(thm)],[c9]) ).
cnf(c227,plain,
difference(product(X,X2),product(X,product(X2,i(X2)))) = difference(product(X,X2),product(X,one)),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
product(X,one) = X,
inference(substitution,[status(thm)],[c161]) ).
cnf(c229,plain,
difference(product(X,X2),product(X,one)) = difference(product(X,X2),X),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
difference(product(X,X2),product(X,product(X2,i(X2)))) = difference(product(X,X2),X),
inference(transitivity,[status(thm)],[c227,c229]) ).
cnf(c231,plain,
quotient(difference(X2,product(product(X2,i(X2)),X)),X) = difference(product(X,X2),X),
inference(transitivity,[status(thm)],[c225,c230]) ).
cnf(c232,plain,
quotient(difference(X2,product(one,X)),X) = difference(product(X,X2),X),
inference(transitivity,[status(thm)],[c224,c231]) ).
cnf(c233,plain,
quotient(difference(X2,X),X) = difference(product(X,X2),X),
inference(transitivity,[status(thm)],[c220,c232]) ).
cnf(c234,plain,
quotient(difference(X,X2),X2) = difference(product(X2,X),X2),
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
difference(product(X2,X),X2) = quotient(difference(X,X2),X2),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
product(difference(product(X2,X),X2),X2) = product(quotient(difference(X,X2),X2),X2),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
product(quotient(difference(X,X2),X2),X2) = difference(X,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c238,plain,
product(difference(product(X2,X),X2),X2) = difference(X,X2),
inference(transitivity,[status(thm)],[c236,c237]) ).
cnf(c239,plain,
product(difference(product(X,j(X)),X),X) = difference(j(X),X),
inference(substitution,[status(thm)],[c238]) ).
cnf(c240,plain,
product(difference(eta(X),X),X) = difference(j(X),X),
inference(transitivity,[status(thm)],[c216,c239]) ).
cnf(c241,plain,
product(j(j(X)),X) = difference(j(X),X),
inference(transitivity,[status(thm)],[c213,c240]) ).
cnf(c242,plain,
i(difference(X,j(X))) = difference(j(X),X),
inference(transitivity,[status(thm)],[c146,c241]) ).
cnf(c243,plain,
i(difference(i(X),j(i(X)))) = difference(j(i(X)),i(X)),
inference(substitution,[status(thm)],[c242]) ).
cnf(c244,plain,
difference(j(i(X)),i(X)) = difference(X,i(X)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c245,plain,
i(difference(i(X),j(i(X)))) = difference(X,i(X)),
inference(transitivity,[status(thm)],[c243,c244]) ).
cnf(c246,plain,
i(difference(i(X),X)) = difference(X,i(X)),
inference(transitivity,[status(thm)],[c107,c245]) ).
cnf(c247,plain,
difference(X,i(X)) = i(difference(i(X),X)),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
difference(difference(X,i(X)),j(X)) = difference(i(difference(i(X),X)),j(X)),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
X = difference(one,X),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c250,plain,
product(X,X) = product(difference(one,X),X),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
one = product(X,i(X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c252,plain,
difference(one,X) = difference(product(X,i(X)),X),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
product(difference(one,X),X) = product(difference(product(X,i(X)),X),X),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
product(difference(product(X,i(X)),X),X) = difference(i(X),X),
inference(substitution,[status(thm)],[c238]) ).
cnf(c255,plain,
product(difference(one,X),X) = difference(i(X),X),
inference(transitivity,[status(thm)],[c253,c254]) ).
cnf(c256,plain,
product(X,X) = difference(i(X),X),
inference(transitivity,[status(thm)],[c250,c255]) ).
cnf(c257,plain,
difference(i(X),X) = product(X,X),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
i(difference(i(X),X)) = i(product(X,X)),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
difference(i(difference(i(X),X)),j(X)) = difference(i(product(X,X)),j(X)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
j(X) = difference(X,eta(X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c261,plain,
quotient(j(X),X) = quotient(difference(X,eta(X)),X),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
quotient(difference(X,eta(X)),X) = i(product(X,X)),
inference(substitution,[status(thm)],[c158]) ).
cnf(c263,plain,
quotient(j(X),X) = i(product(X,X)),
inference(transitivity,[status(thm)],[c261,c262]) ).
cnf(c264,plain,
i(product(X,X)) = quotient(j(X),X),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
difference(i(product(X,X)),j(X)) = difference(quotient(j(X),X),j(X)),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
difference(quotient(j(X),X),j(X)) = X,
inference(substitution,[status(thm)],[c209]) ).
cnf(c267,plain,
difference(i(product(X,X)),j(X)) = X,
inference(transitivity,[status(thm)],[c265,c266]) ).
cnf(c268,plain,
difference(i(difference(i(X),X)),j(X)) = X,
inference(transitivity,[status(thm)],[c259,c267]) ).
cnf(c269,plain,
difference(difference(X,i(X)),j(X)) = X,
inference(transitivity,[status(thm)],[c248,c268]) ).
cnf(c270,plain,
X = difference(difference(X,i(X)),j(X)),
inference(symmetry,[status(thm)],[c269]) ).
cnf(c271,plain,
product(difference(X,i(X)),X) = product(difference(X,i(X)),difference(difference(X,i(X)),j(X))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
product(difference(X,i(X)),difference(difference(X,i(X)),j(X))) = j(X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c273,plain,
product(difference(X,i(X)),X) = j(X),
inference(transitivity,[status(thm)],[c271,c272]) ).
cnf(c274,plain,
j(X) = product(difference(X,i(X)),X),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
difference(X2,j(X)) = difference(X2,product(difference(X,i(X)),X)),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
quotient(difference(X2,j(X)),X) = quotient(difference(X2,product(difference(X,i(X)),X)),X),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
quotient(difference(X2,product(difference(X,i(X)),X)),X) = difference(product(X,X2),product(X,difference(X,i(X)))),
inference(substitution,[status(thm)],[c69]) ).
cnf(c278,plain,
product(X,difference(X,i(X))) = i(X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c279,plain,
difference(product(X,X2),product(X,difference(X,i(X)))) = difference(product(X,X2),i(X)),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
quotient(difference(X2,product(difference(X,i(X)),X)),X) = difference(product(X,X2),i(X)),
inference(transitivity,[status(thm)],[c277,c279]) ).
cnf(c281,plain,
quotient(difference(X2,j(X)),X) = difference(product(X,X2),i(X)),
inference(transitivity,[status(thm)],[c276,c280]) ).
cnf(c282,plain,
quotient(difference(X,j(X2)),X2) = difference(product(X2,X),i(X2)),
inference(substitution,[status(thm)],[c281]) ).
cnf(c283,plain,
difference(product(X2,X),i(X2)) = quotient(difference(X,j(X2)),X2),
inference(symmetry,[status(thm)],[c282]) ).
cnf(c284,plain,
eta(difference(product(X2,X),i(X2))) = eta(quotient(difference(X,j(X2)),X2)),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
product(quotient(X,X2),X2) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c286,plain,
X = product(quotient(X,X2),X2),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
difference(X,eta(quotient(X,X2))) = difference(product(quotient(X,X2),X2),eta(quotient(X,X2))),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
difference(product(quotient(X,X2),X2),eta(quotient(X,X2))) = quotient(i(X2),quotient(X,X2)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c289,plain,
difference(X,eta(quotient(X,X2))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c287,c288]) ).
cnf(c290,plain,
difference(X2,eta(quotient(X2,X))) = quotient(i(X),quotient(X2,X)),
inference(substitution,[status(thm)],[c289]) ).
cnf(c291,plain,
quotient(i(X),quotient(X2,X)) = difference(X2,eta(quotient(X2,X))),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
product(X2,quotient(i(X),quotient(X2,X))) = product(X2,difference(X2,eta(quotient(X2,X)))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
product(X2,difference(X2,eta(quotient(X2,X)))) = eta(quotient(X2,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c294,plain,
product(X2,quotient(i(X),quotient(X2,X))) = eta(quotient(X2,X)),
inference(transitivity,[status(thm)],[c292,c293]) ).
cnf(c295,plain,
product(difference(X,j(X2)),quotient(i(X2),quotient(difference(X,j(X2)),X2))) = eta(quotient(difference(X,j(X2)),X2)),
inference(substitution,[status(thm)],[c294]) ).
cnf(c296,plain,
eta(quotient(difference(X,j(X2)),X2)) = product(difference(X,j(X2)),quotient(i(X2),quotient(difference(X,j(X2)),X2))),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
quotient(difference(X,j(X2)),X2) = difference(product(X2,X),i(X2)),
inference(substitution,[status(thm)],[c281]) ).
cnf(c298,plain,
quotient(i(X2),quotient(difference(X,j(X2)),X2)) = quotient(i(X2),difference(product(X2,X),i(X2))),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
product(difference(X,j(X2)),quotient(i(X2),quotient(difference(X,j(X2)),X2))) = product(difference(X,j(X2)),quotient(i(X2),difference(product(X2,X),i(X2)))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
quotient(i(X2),difference(product(X2,X),i(X2))) = product(X2,X),
inference(substitution,[status(thm)],[c86]) ).
cnf(c301,plain,
product(difference(X,j(X2)),quotient(i(X2),difference(product(X2,X),i(X2)))) = product(difference(X,j(X2)),product(X2,X)),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
difference(X3,product(product(X3,X2),X)) = quotient(product(X2,product(X,X3)),X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c303,plain,
product(difference(X3,product(product(X3,X2),X)),X3) = product(quotient(product(X2,product(X,X3)),X3),X3),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
product(quotient(product(X2,product(X,X3)),X3),X3) = product(X2,product(X,X3)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c305,plain,
product(difference(X3,product(product(X3,X2),X)),X3) = product(X2,product(X,X3)),
inference(transitivity,[status(thm)],[c303,c304]) ).
cnf(c306,plain,
product(difference(X3,product(product(X3,difference(X3,X2)),X)),X3) = product(difference(X3,X2),product(X,X3)),
inference(substitution,[status(thm)],[c305]) ).
cnf(c307,plain,
product(difference(X3,X2),product(X,X3)) = product(difference(X3,product(product(X3,difference(X3,X2)),X)),X3),
inference(symmetry,[status(thm)],[c306]) ).
cnf(c308,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c309,plain,
product(product(X3,difference(X3,X2)),X) = product(X2,X),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
difference(X3,product(product(X3,difference(X3,X2)),X)) = difference(X3,product(X2,X)),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
product(difference(X3,product(product(X3,difference(X3,X2)),X)),X3) = product(difference(X3,product(X2,X)),X3),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c185]) ).
cnf(c313,plain,
X = product(one,X),
inference(symmetry,[status(thm)],[c312]) ).
cnf(c314,plain,
difference(X2,X) = difference(X2,product(one,X)),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
product(difference(X2,X),X2) = product(difference(X2,product(one,X)),X2),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
one = product(X,i(X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c317,plain,
product(one,X) = product(product(X2,i(X2)),X),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
difference(X2,product(one,X)) = difference(X2,product(product(X2,i(X2)),X)),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
product(difference(X2,product(one,X)),X2) = product(difference(X2,product(product(X2,i(X2)),X)),X2),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
product(difference(X2,product(product(X2,i(X2)),X)),X2) = product(i(X2),product(X,X2)),
inference(substitution,[status(thm)],[c305]) ).
cnf(c321,plain,
product(difference(X2,product(one,X)),X2) = product(i(X2),product(X,X2)),
inference(transitivity,[status(thm)],[c319,c320]) ).
cnf(c322,plain,
product(difference(X2,X),X2) = product(i(X2),product(X,X2)),
inference(transitivity,[status(thm)],[c315,c321]) ).
cnf(c323,plain,
product(difference(X3,product(X2,X)),X3) = product(i(X3),product(product(X2,X),X3)),
inference(substitution,[status(thm)],[c322]) ).
cnf(c324,plain,
product(difference(X3,product(product(X3,difference(X3,X2)),X)),X3) = product(i(X3),product(product(X2,X),X3)),
inference(transitivity,[status(thm)],[c311,c323]) ).
cnf(c325,plain,
product(difference(X3,X2),product(X,X3)) = product(i(X3),product(product(X2,X),X3)),
inference(transitivity,[status(thm)],[c307,c324]) ).
cnf(c326,plain,
product(difference(X,j(X2)),product(X2,X)) = product(i(X),product(product(j(X2),X2),X)),
inference(substitution,[status(thm)],[c325]) ).
cnf(c327,plain,
product(product(j(X2),X2),X) = product(one,X),
inference(congruence,[status(thm)],[c40]) ).
cnf(c328,plain,
product(i(X),product(product(j(X2),X2),X)) = product(i(X),product(one,X)),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c185]) ).
cnf(c330,plain,
product(i(X),product(one,X)) = product(i(X),X),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c332,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c331]) ).
cnf(c333,plain,
product(i(X),product(one,X)) = eta(X),
inference(transitivity,[status(thm)],[c330,c332]) ).
cnf(c334,plain,
product(i(X),product(product(j(X2),X2),X)) = eta(X),
inference(transitivity,[status(thm)],[c328,c333]) ).
cnf(c335,plain,
product(difference(X,j(X2)),product(X2,X)) = eta(X),
inference(transitivity,[status(thm)],[c326,c334]) ).
cnf(c336,plain,
product(difference(X,j(X2)),quotient(i(X2),difference(product(X2,X),i(X2)))) = eta(X),
inference(transitivity,[status(thm)],[c301,c335]) ).
cnf(c337,plain,
product(difference(X,j(X2)),quotient(i(X2),quotient(difference(X,j(X2)),X2))) = eta(X),
inference(transitivity,[status(thm)],[c299,c336]) ).
cnf(c338,plain,
eta(quotient(difference(X,j(X2)),X2)) = eta(X),
inference(transitivity,[status(thm)],[c296,c337]) ).
cnf(c339,plain,
eta(difference(product(X2,X),i(X2))) = eta(X),
inference(transitivity,[status(thm)],[c284,c338]) ).
cnf(c340,plain,
eta(difference(product(i(X),X2),i(i(X)))) = eta(X2),
inference(substitution,[status(thm)],[c339]) ).
cnf(c341,plain,
eta(X2) = eta(difference(product(i(X),X2),i(i(X)))),
inference(symmetry,[status(thm)],[c340]) ).
cnf(c342,plain,
product(i(difference(X2,X)),eta(X2)) = product(i(difference(X2,X)),eta(difference(product(i(X),X2),i(i(X))))),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c344,plain,
difference(X2,X) = difference(X2,j(i(X))),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
i(difference(X2,X)) = i(difference(X2,j(i(X)))),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
product(i(difference(X2,X)),eta(difference(product(i(X),X2),i(i(X))))) = product(i(difference(X2,j(i(X)))),eta(difference(product(i(X),X2),i(i(X))))),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
quotient(difference(X2,j(i(X))),i(X)) = difference(product(i(X),X2),i(i(X))),
inference(substitution,[status(thm)],[c281]) ).
cnf(c348,plain,
difference(product(i(X),X2),i(i(X))) = quotient(difference(X2,j(i(X))),i(X)),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c349,plain,
eta(difference(product(i(X),X2),i(i(X)))) = eta(quotient(difference(X2,j(i(X))),i(X))),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
product(i(difference(X2,j(i(X)))),eta(difference(product(i(X),X2),i(i(X))))) = product(i(difference(X2,j(i(X)))),eta(quotient(difference(X2,j(i(X))),i(X)))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
product(quotient(X2,i(X)),i(X)) = X2,
inference(substitution,[status(thm)],[c38]) ).
cnf(c352,plain,
X2 = product(quotient(X2,i(X)),i(X)),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
quotient(X,X2) = quotient(X,product(quotient(X2,i(X)),i(X))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
eta(quotient(X,X2)) = eta(quotient(X,product(quotient(X2,i(X)),i(X)))),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
quotient(difference(X,eta(X2)),X2) = i(product(X2,X)),
inference(substitution,[status(thm)],[c158]) ).
cnf(c356,plain,
i(product(X2,X)) = quotient(difference(X,eta(X2)),X2),
inference(symmetry,[status(thm)],[c355]) ).
cnf(c357,plain,
product(i(product(X2,X)),X2) = product(quotient(difference(X,eta(X2)),X2),X2),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
product(quotient(difference(X,eta(X2)),X2),X2) = difference(X,eta(X2)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c359,plain,
product(i(product(X2,X)),X2) = difference(X,eta(X2)),
inference(transitivity,[status(thm)],[c357,c358]) ).
cnf(c360,plain,
product(i(product(quotient(X,X2),X2)),quotient(X,X2)) = difference(X2,eta(quotient(X,X2))),
inference(substitution,[status(thm)],[c359]) ).
cnf(c361,plain,
difference(X2,eta(quotient(X,X2))) = product(i(product(quotient(X,X2),X2)),quotient(X,X2)),
inference(symmetry,[status(thm)],[c360]) ).
cnf(c362,plain,
product(quotient(X,X2),X2) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c363,plain,
i(product(quotient(X,X2),X2)) = i(X),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
product(i(product(quotient(X,X2),X2)),quotient(X,X2)) = product(i(X),quotient(X,X2)),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
difference(X2,eta(quotient(X,X2))) = product(i(X),quotient(X,X2)),
inference(transitivity,[status(thm)],[c361,c364]) ).
cnf(c366,plain,
product(i(X),quotient(X,X2)) = difference(X2,eta(quotient(X,X2))),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c367,plain,
product(X2,product(i(X),quotient(X,X2))) = product(X2,difference(X2,eta(quotient(X,X2)))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
product(X2,difference(X2,eta(quotient(X,X2)))) = eta(quotient(X,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c369,plain,
product(X2,product(i(X),quotient(X,X2))) = eta(quotient(X,X2)),
inference(transitivity,[status(thm)],[c367,c368]) ).
cnf(c370,plain,
product(product(X,i(X2)),product(i(X2),quotient(X2,product(X,i(X2))))) = eta(quotient(X2,product(X,i(X2)))),
inference(substitution,[status(thm)],[c369]) ).
cnf(c371,plain,
eta(quotient(X2,product(X,i(X2)))) = product(product(X,i(X2)),product(i(X2),quotient(X2,product(X,i(X2))))),
inference(symmetry,[status(thm)],[c370]) ).
cnf(c372,plain,
quotient(product(product(X3,quotient(X2,product(X,X3))),X),X) = product(X3,quotient(X2,product(X,X3))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c373,plain,
product(X3,quotient(X2,product(X,X3))) = quotient(product(product(X3,quotient(X2,product(X,X3))),X),X),
inference(symmetry,[status(thm)],[c372]) ).
cnf(c374,plain,
product(X3,difference(X3,product(product(X3,quotient(X2,product(X,X3))),X))) = product(product(X3,quotient(X2,product(X,X3))),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c375,plain,
product(product(X3,quotient(X2,product(X,X3))),X) = product(X3,difference(X3,product(product(X3,quotient(X2,product(X,X3))),X))),
inference(symmetry,[status(thm)],[c374]) ).
cnf(c376,plain,
difference(X3,product(product(X3,quotient(X2,product(X,X3))),X)) = quotient(product(quotient(X2,product(X,X3)),product(X,X3)),X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c377,plain,
product(quotient(X2,product(X,X3)),product(X,X3)) = X2,
inference(substitution,[status(thm)],[c38]) ).
cnf(c378,plain,
quotient(product(quotient(X2,product(X,X3)),product(X,X3)),X3) = quotient(X2,X3),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
difference(X3,product(product(X3,quotient(X2,product(X,X3))),X)) = quotient(X2,X3),
inference(transitivity,[status(thm)],[c376,c378]) ).
cnf(c380,plain,
product(X3,difference(X3,product(product(X3,quotient(X2,product(X,X3))),X))) = product(X3,quotient(X2,X3)),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c382,plain,
quotient(X,X2) = quotient(X,j(i(X2))),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
product(X2,quotient(X,X2)) = product(X2,quotient(X,j(i(X2)))),
inference(congruence,[status(thm)],[c382]) ).
cnf(c384,plain,
quotient(difference(product(X,X2),product(X,X2)),X2) = difference(product(X2,product(X,X2)),product(X2,X)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c385,plain,
difference(product(X2,product(X,X2)),product(X2,X)) = quotient(difference(product(X,X2),product(X,X2)),X2),
inference(symmetry,[status(thm)],[c384]) ).
cnf(c386,plain,
difference(product(X,X2),product(X,X2)) = one,
inference(substitution,[status(thm)],[c166]) ).
cnf(c387,plain,
quotient(difference(product(X,X2),product(X,X2)),X2) = quotient(one,X2),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c389,plain,
quotient(one,X) = j(X),
inference(symmetry,[status(thm)],[c388]) ).
cnf(c390,plain,
quotient(difference(product(X,X2),product(X,X2)),X2) = j(X2),
inference(transitivity,[status(thm)],[c387,c389]) ).
cnf(c391,plain,
difference(product(X2,product(X,X2)),product(X2,X)) = j(X2),
inference(transitivity,[status(thm)],[c385,c390]) ).
cnf(c392,plain,
j(X2) = difference(product(X2,product(X,X2)),product(X2,X)),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
quotient(product(X2,X),j(X2)) = quotient(product(X2,X),difference(product(X2,product(X,X2)),product(X2,X))),
inference(congruence,[status(thm)],[c392]) ).
cnf(c394,plain,
quotient(product(X2,X),difference(product(X2,product(X,X2)),product(X2,X))) = product(X2,product(X,X2)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c395,plain,
quotient(product(X2,X),j(X2)) = product(X2,product(X,X2)),
inference(transitivity,[status(thm)],[c393,c394]) ).
cnf(c396,plain,
quotient(product(X2,difference(X2,X)),j(X2)) = product(X2,product(difference(X2,X),X2)),
inference(substitution,[status(thm)],[c395]) ).
cnf(c397,plain,
product(X2,product(difference(X2,X),X2)) = quotient(product(X2,difference(X2,X)),j(X2)),
inference(symmetry,[status(thm)],[c396]) ).
cnf(c398,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c399,plain,
quotient(product(X2,difference(X2,X)),j(X2)) = quotient(X,j(X2)),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
product(X2,product(difference(X2,X),X2)) = quotient(X,j(X2)),
inference(transitivity,[status(thm)],[c397,c399]) ).
cnf(c401,plain,
product(i(X2),product(difference(i(X2),X),i(X2))) = quotient(X,j(i(X2))),
inference(substitution,[status(thm)],[c400]) ).
cnf(c402,plain,
quotient(X,j(i(X2))) = product(i(X2),product(difference(i(X2),X),i(X2))),
inference(symmetry,[status(thm)],[c401]) ).
cnf(c403,plain,
product(X2,quotient(X,j(i(X2)))) = product(X2,product(i(X2),product(difference(i(X2),X),i(X2)))),
inference(congruence,[status(thm)],[c402]) ).
cnf(c404,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c405,plain,
product(X2,product(i(X2),X)) = product(j(i(X2)),product(i(X2),X)),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
difference(one,product(j(X2),product(X2,X))) = product(j(X2),product(X2,X)),
inference(substitution,[status(thm)],[c190]) ).
cnf(c407,plain,
product(j(X2),product(X2,X)) = difference(one,product(j(X2),product(X2,X))),
inference(symmetry,[status(thm)],[c406]) ).
cnf(c408,plain,
one = product(j(X),X),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c409,plain,
difference(one,product(j(X2),product(X2,X))) = difference(product(j(X2),X2),product(j(X2),product(X2,X))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
quotient(difference(X2,product(product(X2,X),j(X2))),j(X2)) = difference(product(j(X2),X2),product(j(X2),product(X2,X))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c411,plain,
difference(product(j(X2),X2),product(j(X2),product(X2,X))) = quotient(difference(X2,product(product(X2,X),j(X2))),j(X2)),
inference(symmetry,[status(thm)],[c410]) ).
cnf(c412,plain,
difference(X2,product(product(X2,X),j(X2))) = quotient(product(X,product(j(X2),X2)),X2),
inference(substitution,[status(thm)],[c57]) ).
cnf(c413,plain,
product(X,product(j(X2),X2)) = product(X,one),
inference(congruence,[status(thm)],[c40]) ).
cnf(c414,plain,
quotient(product(X,product(j(X2),X2)),X2) = quotient(product(X,one),X2),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
product(X,one) = X,
inference(substitution,[status(thm)],[c161]) ).
cnf(c416,plain,
quotient(product(X,one),X2) = quotient(X,X2),
inference(congruence,[status(thm)],[c415]) ).
cnf(c417,plain,
quotient(product(X,product(j(X2),X2)),X2) = quotient(X,X2),
inference(transitivity,[status(thm)],[c414,c416]) ).
cnf(c418,plain,
difference(X2,product(product(X2,X),j(X2))) = quotient(X,X2),
inference(transitivity,[status(thm)],[c412,c417]) ).
cnf(c419,plain,
quotient(difference(X2,product(product(X2,X),j(X2))),j(X2)) = quotient(quotient(X,X2),j(X2)),
inference(congruence,[status(thm)],[c418]) ).
cnf(c420,plain,
difference(product(j(X2),X2),product(j(X2),product(X2,X))) = quotient(quotient(X,X2),j(X2)),
inference(transitivity,[status(thm)],[c411,c419]) ).
cnf(c421,plain,
difference(one,product(j(X2),product(X2,X))) = quotient(quotient(X,X2),j(X2)),
inference(transitivity,[status(thm)],[c409,c420]) ).
cnf(c422,plain,
product(j(X2),product(X2,X)) = quotient(quotient(X,X2),j(X2)),
inference(transitivity,[status(thm)],[c407,c421]) ).
cnf(c423,plain,
product(j(i(X2)),product(i(X2),X)) = quotient(quotient(X,i(X2)),j(i(X2))),
inference(substitution,[status(thm)],[c422]) ).
cnf(c424,plain,
quotient(quotient(X,i(X2)),j(i(X2))) = quotient(quotient(X,i(X2)),X2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c425,plain,
product(j(i(X2)),product(i(X2),X)) = quotient(quotient(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c423,c424]) ).
cnf(c426,plain,
product(X2,product(i(X2),X)) = quotient(quotient(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c405,c425]) ).
cnf(c427,plain,
product(X2,product(i(X2),product(difference(i(X2),X),i(X2)))) = quotient(quotient(product(difference(i(X2),X),i(X2)),i(X2)),X2),
inference(substitution,[status(thm)],[c426]) ).
cnf(c428,plain,
quotient(product(difference(i(X2),X),i(X2)),i(X2)) = difference(i(X2),X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c429,plain,
quotient(quotient(product(difference(i(X2),X),i(X2)),i(X2)),X2) = quotient(difference(i(X2),X),X2),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
product(X2,product(i(X2),product(difference(i(X2),X),i(X2)))) = quotient(difference(i(X2),X),X2),
inference(transitivity,[status(thm)],[c427,c429]) ).
cnf(c431,plain,
product(X2,quotient(X,j(i(X2)))) = quotient(difference(i(X2),X),X2),
inference(transitivity,[status(thm)],[c403,c430]) ).
cnf(c432,plain,
product(X2,quotient(X,X2)) = quotient(difference(i(X2),X),X2),
inference(transitivity,[status(thm)],[c383,c431]) ).
cnf(c433,plain,
product(X3,difference(X3,product(product(X3,quotient(X2,product(X,X3))),X))) = quotient(difference(i(X3),X2),X3),
inference(transitivity,[status(thm)],[c380,c432]) ).
cnf(c434,plain,
product(product(X3,quotient(X2,product(X,X3))),X) = quotient(difference(i(X3),X2),X3),
inference(transitivity,[status(thm)],[c375,c433]) ).
cnf(c435,plain,
quotient(product(product(X3,quotient(X2,product(X,X3))),X),X) = quotient(quotient(difference(i(X3),X2),X3),X),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
product(X3,quotient(X2,product(X,X3))) = quotient(quotient(difference(i(X3),X2),X3),X),
inference(transitivity,[status(thm)],[c373,c435]) ).
cnf(c437,plain,
product(i(X2),quotient(X2,product(X,i(X2)))) = quotient(quotient(difference(i(i(X2)),X2),i(X2)),X),
inference(substitution,[status(thm)],[c436]) ).
cnf(c438,plain,
product(product(X,i(X2)),product(i(X2),quotient(X2,product(X,i(X2))))) = product(product(X,i(X2)),quotient(quotient(difference(i(i(X2)),X2),i(X2)),X)),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
product(X3,difference(X3,product(product(X3,X2),quotient(X,X3)))) = product(product(X3,X2),quotient(X,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c440,plain,
product(product(X3,X2),quotient(X,X3)) = product(X3,difference(X3,product(product(X3,X2),quotient(X,X3)))),
inference(symmetry,[status(thm)],[c439]) ).
cnf(c441,plain,
difference(X3,product(product(X3,X2),quotient(X,X3))) = quotient(product(X2,product(quotient(X,X3),X3)),X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c442,plain,
product(quotient(X,X2),X2) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c443,plain,
product(X2,product(quotient(X,X3),X3)) = product(X2,X),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
quotient(product(X2,product(quotient(X,X3),X3)),X3) = quotient(product(X2,X),X3),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
difference(X3,product(product(X3,X2),quotient(X,X3))) = quotient(product(X2,X),X3),
inference(transitivity,[status(thm)],[c441,c444]) ).
cnf(c446,plain,
product(X3,difference(X3,product(product(X3,X2),quotient(X,X3)))) = product(X3,quotient(product(X2,X),X3)),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
product(X3,quotient(product(X2,X),X3)) = quotient(difference(i(X3),product(X2,X)),X3),
inference(substitution,[status(thm)],[c432]) ).
cnf(c448,plain,
product(X3,difference(X3,product(product(X3,X2),quotient(X,X3)))) = quotient(difference(i(X3),product(X2,X)),X3),
inference(transitivity,[status(thm)],[c446,c447]) ).
cnf(c449,plain,
product(product(X3,X2),quotient(X,X3)) = quotient(difference(i(X3),product(X2,X)),X3),
inference(transitivity,[status(thm)],[c440,c448]) ).
cnf(c450,plain,
product(product(X,i(X2)),quotient(quotient(difference(i(i(X2)),X2),i(X2)),X)) = quotient(difference(i(X),product(i(X2),quotient(difference(i(i(X2)),X2),i(X2)))),X),
inference(substitution,[status(thm)],[c449]) ).
cnf(c451,plain,
product(i(X),quotient(difference(i(i(X)),X),i(X))) = quotient(difference(i(i(X)),difference(i(i(X)),X)),i(X)),
inference(substitution,[status(thm)],[c432]) ).
cnf(c452,plain,
difference(i(X),product(i(X2),quotient(difference(i(i(X2)),X2),i(X2)))) = difference(i(X),quotient(difference(i(i(X2)),difference(i(i(X2)),X2)),i(X2))),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
quotient(difference(i(X),product(i(X2),quotient(difference(i(i(X2)),X2),i(X2)))),X) = quotient(difference(i(X),quotient(difference(i(i(X2)),difference(i(i(X2)),X2)),i(X2))),X),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
product(i(product(X2,difference(X2,X))),X2) = difference(difference(X2,X),eta(X2)),
inference(substitution,[status(thm)],[c359]) ).
cnf(c455,plain,
difference(difference(X2,X),eta(X2)) = product(i(product(X2,difference(X2,X))),X2),
inference(symmetry,[status(thm)],[c454]) ).
cnf(c456,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c457,plain,
i(product(X2,difference(X2,X))) = i(X),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
product(i(product(X2,difference(X2,X))),X2) = product(i(X),X2),
inference(congruence,[status(thm)],[c457]) ).
cnf(c459,plain,
difference(difference(X2,X),eta(X2)) = product(i(X),X2),
inference(transitivity,[status(thm)],[c455,c458]) ).
cnf(c460,plain,
difference(difference(eta(X),i(X)),eta(eta(X))) = product(i(i(X)),eta(X)),
inference(substitution,[status(thm)],[c459]) ).
cnf(c461,plain,
product(i(i(X)),eta(X)) = difference(difference(eta(X),i(X)),eta(eta(X))),
inference(symmetry,[status(thm)],[c460]) ).
cnf(c462,plain,
difference(product(j(X),X),eta(j(X))) = quotient(i(X),j(X)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c463,plain,
quotient(i(X),j(X)) = difference(product(j(X),X),eta(j(X))),
inference(symmetry,[status(thm)],[c462]) ).
cnf(c464,plain,
difference(product(j(X),X),eta(j(X))) = difference(one,eta(j(X))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c465,plain,
difference(one,eta(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c190]) ).
cnf(c466,plain,
difference(one,eta(j(X))) = eta(X),
inference(transitivity,[status(thm)],[c465,c111]) ).
cnf(c467,plain,
difference(product(j(X),X),eta(j(X))) = eta(X),
inference(transitivity,[status(thm)],[c464,c466]) ).
cnf(c468,plain,
quotient(i(X),j(X)) = eta(X),
inference(transitivity,[status(thm)],[c463,c467]) ).
cnf(c469,plain,
eta(X) = quotient(i(X),j(X)),
inference(symmetry,[status(thm)],[c468]) ).
cnf(c470,plain,
difference(eta(X),i(X)) = difference(quotient(i(X),j(X)),i(X)),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,plain,
difference(quotient(i(X),j(X)),i(X)) = j(X),
inference(substitution,[status(thm)],[c209]) ).
cnf(c472,plain,
difference(eta(X),i(X)) = j(X),
inference(transitivity,[status(thm)],[c470,c471]) ).
cnf(c473,plain,
difference(difference(eta(X),i(X)),eta(eta(X))) = difference(j(X),eta(eta(X))),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
product(X,difference(X,eta(eta(X)))) = eta(eta(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c475,plain,
eta(eta(X)) = product(X,difference(X,eta(eta(X)))),
inference(symmetry,[status(thm)],[c474]) ).
cnf(c476,plain,
quotient(i(difference(eta(X),X)),eta(X)) = difference(X,eta(eta(X))),
inference(substitution,[status(thm)],[c138]) ).
cnf(c477,plain,
difference(X,eta(eta(X))) = quotient(i(difference(eta(X),X)),eta(X)),
inference(symmetry,[status(thm)],[c476]) ).
cnf(c478,plain,
i(difference(eta(X),X)) = i(j(j(X))),
inference(congruence,[status(thm)],[c211]) ).
cnf(c479,plain,
quotient(i(difference(eta(X),X)),eta(X)) = quotient(i(j(j(X))),eta(X)),
inference(congruence,[status(thm)],[c478]) ).
cnf(c480,plain,
i(j(j(X))) = j(X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c481,plain,
quotient(i(j(j(X))),eta(X)) = quotient(j(X),eta(X)),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
quotient(difference(X,eta(X)),eta(X)) = difference(product(eta(X),X),eta(X)),
inference(substitution,[status(thm)],[c233]) ).
cnf(c483,plain,
difference(product(eta(X),X),eta(X)) = quotient(difference(X,eta(X)),eta(X)),
inference(symmetry,[status(thm)],[c482]) ).
cnf(c484,plain,
quotient(difference(X,eta(X)),eta(X)) = quotient(j(X),eta(X)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c485,plain,
difference(product(eta(X),X),eta(X)) = quotient(j(X),eta(X)),
inference(transitivity,[status(thm)],[c483,c484]) ).
cnf(c486,plain,
quotient(j(X),eta(X)) = difference(product(eta(X),X),eta(X)),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
eta(X) = quotient(i(i(X)),X),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c488,plain,
product(eta(X),X) = product(quotient(i(i(X)),X),X),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
product(quotient(i(i(X)),X),X) = i(i(X)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c490,plain,
product(eta(X),X) = i(i(X)),
inference(transitivity,[status(thm)],[c488,c489]) ).
cnf(c491,plain,
difference(product(eta(X),X),eta(X)) = difference(i(i(X)),eta(X)),
inference(congruence,[status(thm)],[c490]) ).
cnf(c492,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c493,plain,
difference(i(i(X)),eta(X)) = difference(i(i(X)),eta(i(X))),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c495,plain,
difference(i(X),eta(X)) = difference(i(X),product(i(X),X)),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
difference(i(X),product(i(X),X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c497,plain,
difference(i(X),eta(X)) = X,
inference(transitivity,[status(thm)],[c495,c496]) ).
cnf(c498,plain,
difference(i(i(X)),eta(i(X))) = i(X),
inference(substitution,[status(thm)],[c497]) ).
cnf(c499,plain,
difference(i(i(X)),eta(X)) = i(X),
inference(transitivity,[status(thm)],[c493,c498]) ).
cnf(c500,plain,
difference(product(eta(X),X),eta(X)) = i(X),
inference(transitivity,[status(thm)],[c491,c499]) ).
cnf(c501,plain,
quotient(j(X),eta(X)) = i(X),
inference(transitivity,[status(thm)],[c486,c500]) ).
cnf(c502,plain,
quotient(i(j(j(X))),eta(X)) = i(X),
inference(transitivity,[status(thm)],[c481,c501]) ).
cnf(c503,plain,
quotient(i(difference(eta(X),X)),eta(X)) = i(X),
inference(transitivity,[status(thm)],[c479,c502]) ).
cnf(c504,plain,
difference(X,eta(eta(X))) = i(X),
inference(transitivity,[status(thm)],[c477,c503]) ).
cnf(c505,plain,
product(X,difference(X,eta(eta(X)))) = product(X,i(X)),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
product(X,difference(X,eta(eta(X)))) = one,
inference(transitivity,[status(thm)],[c505,c9]) ).
cnf(c507,plain,
eta(eta(X)) = one,
inference(transitivity,[status(thm)],[c475,c506]) ).
cnf(c508,plain,
difference(j(X),eta(eta(X))) = difference(j(X),one),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
i(j(X)) = difference(j(X),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c510,plain,
difference(j(X),one) = i(j(X)),
inference(symmetry,[status(thm)],[c509]) ).
cnf(c511,plain,
difference(j(X),one) = X,
inference(transitivity,[status(thm)],[c510,c46]) ).
cnf(c512,plain,
difference(j(X),eta(eta(X))) = X,
inference(transitivity,[status(thm)],[c508,c511]) ).
cnf(c513,plain,
difference(difference(eta(X),i(X)),eta(eta(X))) = X,
inference(transitivity,[status(thm)],[c473,c512]) ).
cnf(c514,plain,
product(i(i(X)),eta(X)) = X,
inference(transitivity,[status(thm)],[c461,c513]) ).
cnf(c515,plain,
X = product(i(i(X)),eta(X)),
inference(symmetry,[status(thm)],[c514]) ).
cnf(c516,plain,
difference(i(i(X)),X) = difference(i(i(X)),product(i(i(X)),eta(X))),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
difference(i(i(X)),product(i(i(X)),eta(X))) = eta(X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c518,plain,
difference(i(i(X)),X) = eta(X),
inference(transitivity,[status(thm)],[c516,c517]) ).
cnf(c519,plain,
difference(i(i(X)),difference(i(i(X)),X)) = difference(i(i(X)),eta(X)),
inference(congruence,[status(thm)],[c518]) ).
cnf(c520,plain,
quotient(difference(i(i(X)),difference(i(i(X)),X)),i(X)) = quotient(difference(i(i(X)),eta(X)),i(X)),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
difference(i(X),quotient(difference(i(i(X2)),difference(i(i(X2)),X2)),i(X2))) = difference(i(X),quotient(difference(i(i(X2)),eta(X2)),i(X2))),
inference(congruence,[status(thm)],[c520]) ).
cnf(c522,plain,
quotient(difference(i(X),quotient(difference(i(i(X2)),difference(i(i(X2)),X2)),i(X2))),X) = quotient(difference(i(X),quotient(difference(i(i(X2)),eta(X2)),i(X2))),X),
inference(congruence,[status(thm)],[c521]) ).
cnf(c523,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c524,plain,
difference(X2,eta(X)) = difference(X2,eta(i(X))),
inference(congruence,[status(thm)],[c523]) ).
cnf(c525,plain,
quotient(difference(X2,eta(X)),i(X)) = quotient(difference(X2,eta(i(X))),i(X)),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
quotient(difference(X2,eta(i(X))),i(X)) = i(product(i(X),X2)),
inference(substitution,[status(thm)],[c158]) ).
cnf(c527,plain,
quotient(difference(X2,eta(X)),i(X)) = i(product(i(X),X2)),
inference(transitivity,[status(thm)],[c525,c526]) ).
cnf(c528,plain,
quotient(difference(i(i(X)),eta(X)),i(X)) = i(product(i(X),i(i(X)))),
inference(substitution,[status(thm)],[c527]) ).
cnf(c529,plain,
difference(i(X),quotient(difference(i(i(X2)),eta(X2)),i(X2))) = difference(i(X),i(product(i(X2),i(i(X2))))),
inference(congruence,[status(thm)],[c528]) ).
cnf(c530,plain,
quotient(difference(i(X),quotient(difference(i(i(X2)),eta(X2)),i(X2))),X) = quotient(difference(i(X),i(product(i(X2),i(i(X2))))),X),
inference(congruence,[status(thm)],[c529]) ).
cnf(c531,plain,
product(i(X),i(i(X))) = one,
inference(substitution,[status(thm)],[c9]) ).
cnf(c532,plain,
i(product(i(X),i(i(X)))) = i(one),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
difference(i(X),i(product(i(X2),i(i(X2))))) = difference(i(X),i(one)),
inference(congruence,[status(thm)],[c532]) ).
cnf(c534,plain,
quotient(difference(i(X),i(product(i(X2),i(i(X2))))),X) = quotient(difference(i(X),i(one)),X),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
i(one) = difference(one,one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c536,plain,
difference(one,one) = one,
inference(substitution,[status(thm)],[c166]) ).
cnf(c537,plain,
i(one) = one,
inference(transitivity,[status(thm)],[c535,c536]) ).
cnf(c538,plain,
difference(i(X),i(one)) = difference(i(X),one),
inference(congruence,[status(thm)],[c537]) ).
cnf(c539,plain,
quotient(difference(i(X),i(one)),X) = quotient(difference(i(X),one),X),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
i(i(X)) = difference(i(X),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c541,plain,
difference(i(X),one) = i(i(X)),
inference(symmetry,[status(thm)],[c540]) ).
cnf(c542,plain,
quotient(difference(i(X),one),X) = quotient(i(i(X)),X),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
quotient(difference(i(X),one),X) = eta(X),
inference(transitivity,[status(thm)],[c542,c193]) ).
cnf(c544,plain,
quotient(difference(i(X),i(one)),X) = eta(X),
inference(transitivity,[status(thm)],[c539,c543]) ).
cnf(c545,plain,
quotient(difference(i(X),i(product(i(X2),i(i(X2))))),X) = eta(X),
inference(transitivity,[status(thm)],[c534,c544]) ).
cnf(c546,plain,
quotient(difference(i(X),quotient(difference(i(i(X2)),eta(X2)),i(X2))),X) = eta(X),
inference(transitivity,[status(thm)],[c530,c545]) ).
cnf(c547,plain,
quotient(difference(i(X),quotient(difference(i(i(X2)),difference(i(i(X2)),X2)),i(X2))),X) = eta(X),
inference(transitivity,[status(thm)],[c522,c546]) ).
cnf(c548,plain,
quotient(difference(i(X),product(i(X2),quotient(difference(i(i(X2)),X2),i(X2)))),X) = eta(X),
inference(transitivity,[status(thm)],[c453,c547]) ).
cnf(c549,plain,
product(product(X,i(X2)),quotient(quotient(difference(i(i(X2)),X2),i(X2)),X)) = eta(X),
inference(transitivity,[status(thm)],[c450,c548]) ).
cnf(c550,plain,
product(product(X,i(X2)),product(i(X2),quotient(X2,product(X,i(X2))))) = eta(X),
inference(transitivity,[status(thm)],[c438,c549]) ).
cnf(c551,plain,
eta(quotient(X2,product(X,i(X2)))) = eta(X),
inference(transitivity,[status(thm)],[c371,c550]) ).
cnf(c552,plain,
eta(quotient(X,product(quotient(X2,i(X)),i(X)))) = eta(quotient(X2,i(X))),
inference(substitution,[status(thm)],[c551]) ).
cnf(c553,plain,
eta(quotient(X,X2)) = eta(quotient(X2,i(X))),
inference(transitivity,[status(thm)],[c354,c552]) ).
cnf(c554,plain,
eta(quotient(X,i(X2))) = eta(quotient(i(X2),i(X))),
inference(substitution,[status(thm)],[c553]) ).
cnf(c555,plain,
eta(quotient(i(X2),i(X))) = eta(quotient(X,i(X2))),
inference(symmetry,[status(thm)],[c554]) ).
cnf(c556,plain,
eta(quotient(X2,X)) = eta(quotient(X,i(X2))),
inference(substitution,[status(thm)],[c553]) ).
cnf(c557,plain,
eta(quotient(X,i(X2))) = eta(quotient(X2,X)),
inference(symmetry,[status(thm)],[c556]) ).
cnf(c558,plain,
eta(quotient(i(X2),i(X))) = eta(quotient(X2,X)),
inference(transitivity,[status(thm)],[c555,c557]) ).
cnf(c559,plain,
eta(quotient(i(X2),i(i(X)))) = eta(quotient(X2,i(X))),
inference(substitution,[status(thm)],[c558]) ).
cnf(c560,plain,
eta(quotient(X2,i(X))) = eta(quotient(i(X2),i(i(X)))),
inference(symmetry,[status(thm)],[c559]) ).
cnf(c561,plain,
product(i(X2),eta(quotient(X2,i(X)))) = product(i(X2),eta(quotient(i(X2),i(i(X))))),
inference(congruence,[status(thm)],[c560]) ).
cnf(c562,plain,
product(i(X2),product(X,X2)) = product(difference(X2,X),X2),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c563,plain,
eta(product(i(X2),product(X,X2))) = eta(product(difference(X2,X),X2)),
inference(congruence,[status(thm)],[c562]) ).
cnf(c564,plain,
quotient(X,j(X2)) = product(X2,product(difference(X2,X),X2)),
inference(symmetry,[status(thm)],[c400]) ).
cnf(c565,plain,
difference(X2,quotient(X,j(X2))) = difference(X2,product(X2,product(difference(X2,X),X2))),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
difference(X2,product(X2,product(difference(X2,X),X2))) = product(difference(X2,X),X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c567,plain,
difference(X2,quotient(X,j(X2))) = product(difference(X2,X),X2),
inference(transitivity,[status(thm)],[c565,c566]) ).
cnf(c568,plain,
product(difference(X2,X),X2) = difference(X2,quotient(X,j(X2))),
inference(symmetry,[status(thm)],[c567]) ).
cnf(c569,plain,
eta(product(difference(X2,X),X2)) = eta(difference(X2,quotient(X,j(X2)))),
inference(congruence,[status(thm)],[c568]) ).
cnf(c570,plain,
i(j(quotient(X,j(X2)))) = quotient(X,j(X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c571,plain,
quotient(X,j(X2)) = i(j(quotient(X,j(X2)))),
inference(symmetry,[status(thm)],[c570]) ).
cnf(c572,plain,
difference(X2,quotient(X,j(X2))) = difference(X2,i(j(quotient(X,j(X2))))),
inference(congruence,[status(thm)],[c571]) ).
cnf(c573,plain,
eta(difference(X2,quotient(X,j(X2)))) = eta(difference(X2,i(j(quotient(X,j(X2)))))),
inference(congruence,[status(thm)],[c572]) ).
cnf(c574,plain,
j(i(product(X2,quotient(eta(X2),X)))) = product(X2,quotient(eta(X2),X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c575,plain,
product(X2,quotient(eta(X2),X)) = j(i(product(X2,quotient(eta(X2),X)))),
inference(symmetry,[status(thm)],[c574]) ).
cnf(c576,plain,
quotient(difference(quotient(eta(X2),X),eta(X2)),X2) = i(product(X2,quotient(eta(X2),X))),
inference(substitution,[status(thm)],[c158]) ).
cnf(c577,plain,
i(product(X2,quotient(eta(X2),X))) = quotient(difference(quotient(eta(X2),X),eta(X2)),X2),
inference(symmetry,[status(thm)],[c576]) ).
cnf(c578,plain,
difference(quotient(eta(X2),X),eta(X2)) = X,
inference(substitution,[status(thm)],[c209]) ).
cnf(c579,plain,
quotient(difference(quotient(eta(X2),X),eta(X2)),X2) = quotient(X,X2),
inference(congruence,[status(thm)],[c578]) ).
cnf(c580,plain,
i(product(X2,quotient(eta(X2),X))) = quotient(X,X2),
inference(transitivity,[status(thm)],[c577,c579]) ).
cnf(c581,plain,
j(i(product(X2,quotient(eta(X2),X)))) = j(quotient(X,X2)),
inference(congruence,[status(thm)],[c580]) ).
cnf(c582,plain,
product(X2,quotient(eta(X2),X)) = j(quotient(X,X2)),
inference(transitivity,[status(thm)],[c575,c581]) ).
cnf(c583,plain,
product(j(X2),quotient(eta(j(X2)),X)) = j(quotient(X,j(X2))),
inference(substitution,[status(thm)],[c582]) ).
cnf(c584,plain,
j(quotient(X,j(X2))) = product(j(X2),quotient(eta(j(X2)),X)),
inference(symmetry,[status(thm)],[c583]) ).
cnf(c585,plain,
i(j(quotient(X,j(X2)))) = i(product(j(X2),quotient(eta(j(X2)),X))),
inference(congruence,[status(thm)],[c584]) ).
cnf(c586,plain,
difference(X2,i(j(quotient(X,j(X2))))) = difference(X2,i(product(j(X2),quotient(eta(j(X2)),X)))),
inference(congruence,[status(thm)],[c585]) ).
cnf(c587,plain,
eta(difference(X2,i(j(quotient(X,j(X2)))))) = eta(difference(X2,i(product(j(X2),quotient(eta(j(X2)),X))))),
inference(congruence,[status(thm)],[c586]) ).
cnf(c588,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c589,plain,
X = product(X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c588]) ).
cnf(c590,plain,
difference(X,i(X2)) = difference(product(X2,difference(X2,X)),i(X2)),
inference(congruence,[status(thm)],[c589]) ).
cnf(c591,plain,
eta(difference(X,i(X2))) = eta(difference(product(X2,difference(X2,X)),i(X2))),
inference(congruence,[status(thm)],[c590]) ).
cnf(c592,plain,
eta(difference(product(X2,difference(X2,X)),i(X2))) = eta(difference(X2,X)),
inference(substitution,[status(thm)],[c339]) ).
cnf(c593,plain,
eta(difference(X,i(X2))) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c591,c592]) ).
cnf(c594,plain,
eta(difference(X2,i(product(j(X2),X)))) = eta(difference(product(j(X2),X),X2)),
inference(substitution,[status(thm)],[c593]) ).
cnf(c595,plain,
quotient(X,difference(X2,X)) = X2,
inference(substitution,[status(thm)],[c86]) ).
cnf(c596,plain,
X2 = quotient(X,difference(X2,X)),
inference(symmetry,[status(thm)],[c595]) ).
cnf(c597,plain,
product(product(difference(X2,X),j(X)),X2) = product(product(difference(X2,X),j(X)),quotient(X,difference(X2,X))),
inference(congruence,[status(thm)],[c596]) ).
cnf(c598,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c599,plain,
quotient(X,X2) = quotient(i(j(X)),X2),
inference(congruence,[status(thm)],[c598]) ).
cnf(c600,plain,
product(product(X2,j(X)),quotient(X,X2)) = product(product(X2,j(X)),quotient(i(j(X)),X2)),
inference(congruence,[status(thm)],[c599]) ).
cnf(c601,plain,
quotient(i(X),X2) = difference(product(X2,X),eta(X2)),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c602,plain,
product(product(X2,X),quotient(i(X),X2)) = product(product(X2,X),difference(product(X2,X),eta(X2))),
inference(congruence,[status(thm)],[c601]) ).
cnf(c603,plain,
product(product(X2,X),difference(product(X2,X),eta(X2))) = eta(X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c604,plain,
product(product(X2,X),quotient(i(X),X2)) = eta(X2),
inference(transitivity,[status(thm)],[c602,c603]) ).
cnf(c605,plain,
product(product(X2,j(X)),quotient(i(j(X)),X2)) = eta(X2),
inference(substitution,[status(thm)],[c604]) ).
cnf(c606,plain,
product(product(X2,j(X)),quotient(X,X2)) = eta(X2),
inference(transitivity,[status(thm)],[c600,c605]) ).
cnf(c607,plain,
product(product(difference(X2,X),j(X)),quotient(X,difference(X2,X))) = eta(difference(X2,X)),
inference(substitution,[status(thm)],[c606]) ).
cnf(c608,plain,
product(product(difference(X2,X),j(X)),X2) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c597,c607]) ).
cnf(c609,plain,
product(product(difference(product(j(X2),X),X2),j(X2)),product(j(X2),X)) = eta(difference(product(j(X2),X),X2)),
inference(substitution,[status(thm)],[c608]) ).
cnf(c610,plain,
eta(difference(product(j(X2),X),X2)) = product(product(difference(product(j(X2),X),X2),j(X2)),product(j(X2),X)),
inference(symmetry,[status(thm)],[c609]) ).
cnf(c611,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c612,plain,
X = product(X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c611]) ).
cnf(c613,plain,
difference(product(X3,X2),X) = difference(product(X3,X2),product(X3,difference(X3,X))),
inference(congruence,[status(thm)],[c612]) ).
cnf(c614,plain,
product(difference(product(X3,X2),X),X3) = product(difference(product(X3,X2),product(X3,difference(X3,X))),X3),
inference(congruence,[status(thm)],[c613]) ).
cnf(c615,plain,
quotient(difference(X2,product(X,X3)),X3) = difference(product(X3,X2),product(X3,X)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c616,plain,
difference(product(X3,X2),product(X3,X)) = quotient(difference(X2,product(X,X3)),X3),
inference(symmetry,[status(thm)],[c615]) ).
cnf(c617,plain,
product(difference(product(X3,X2),product(X3,X)),X3) = product(quotient(difference(X2,product(X,X3)),X3),X3),
inference(congruence,[status(thm)],[c616]) ).
cnf(c618,plain,
product(quotient(difference(X2,product(X,X3)),X3),X3) = difference(X2,product(X,X3)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c619,plain,
product(difference(product(X3,X2),product(X3,X)),X3) = difference(X2,product(X,X3)),
inference(transitivity,[status(thm)],[c617,c618]) ).
cnf(c620,plain,
product(difference(product(X3,X2),product(X3,difference(X3,X))),X3) = difference(X2,product(difference(X3,X),X3)),
inference(substitution,[status(thm)],[c619]) ).
cnf(c621,plain,
difference(X2,product(difference(X3,X),X3)) = difference(X2,product(i(X3),product(X,X3))),
inference(congruence,[status(thm)],[c322]) ).
cnf(c622,plain,
product(difference(product(X3,X2),product(X3,difference(X3,X))),X3) = difference(X2,product(i(X3),product(X,X3))),
inference(transitivity,[status(thm)],[c620,c621]) ).
cnf(c623,plain,
product(difference(product(X3,X2),X),X3) = difference(X2,product(i(X3),product(X,X3))),
inference(transitivity,[status(thm)],[c614,c622]) ).
cnf(c624,plain,
product(difference(product(j(X2),X),X2),j(X2)) = difference(X,product(i(j(X2)),product(X2,j(X2)))),
inference(substitution,[status(thm)],[c623]) ).
cnf(c625,plain,
product(product(difference(product(j(X2),X),X2),j(X2)),product(j(X2),X)) = product(difference(X,product(i(j(X2)),product(X2,j(X2)))),product(j(X2),X)),
inference(congruence,[status(thm)],[c624]) ).
cnf(c626,plain,
product(difference(X,product(i(j(X2)),product(X2,j(X2)))),product(j(X2),X)) = product(i(X),product(product(product(i(j(X2)),product(X2,j(X2))),j(X2)),X)),
inference(substitution,[status(thm)],[c325]) ).
cnf(c627,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c628,plain,
product(product(i(X2),X),X2) = product(product(i(X2),X),j(i(X2))),
inference(congruence,[status(thm)],[c627]) ).
cnf(c629,plain,
product(X2,difference(X2,product(product(X2,X),j(X2)))) = product(product(X2,X),j(X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c630,plain,
product(product(X2,X),j(X2)) = product(X2,difference(X2,product(product(X2,X),j(X2)))),
inference(symmetry,[status(thm)],[c629]) ).
cnf(c631,plain,
product(X2,difference(X2,product(product(X2,X),j(X2)))) = product(X2,quotient(X,X2)),
inference(congruence,[status(thm)],[c418]) ).
cnf(c632,plain,
product(product(X2,X),j(X2)) = product(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c630,c631]) ).
cnf(c633,plain,
product(product(i(X2),X),j(i(X2))) = product(i(X2),quotient(X,i(X2))),
inference(substitution,[status(thm)],[c632]) ).
cnf(c634,plain,
product(product(i(X2),X),X2) = product(i(X2),quotient(X,i(X2))),
inference(transitivity,[status(thm)],[c628,c633]) ).
cnf(c635,plain,
product(product(i(j(X)),product(X,j(X))),j(X)) = product(i(j(X)),quotient(product(X,j(X)),i(j(X)))),
inference(substitution,[status(thm)],[c634]) ).
cnf(c636,plain,
product(product(product(i(j(X2)),product(X2,j(X2))),j(X2)),X) = product(product(i(j(X2)),quotient(product(X2,j(X2)),i(j(X2)))),X),
inference(congruence,[status(thm)],[c635]) ).
cnf(c637,plain,
product(i(X),product(product(product(i(j(X2)),product(X2,j(X2))),j(X2)),X)) = product(i(X),product(product(i(j(X2)),quotient(product(X2,j(X2)),i(j(X2)))),X)),
inference(congruence,[status(thm)],[c636]) ).
cnf(c638,plain,
product(i(j(X)),quotient(product(X,j(X)),i(j(X)))) = quotient(difference(i(i(j(X))),product(X,j(X))),i(j(X))),
inference(substitution,[status(thm)],[c432]) ).
cnf(c639,plain,
product(product(i(j(X2)),quotient(product(X2,j(X2)),i(j(X2)))),X) = product(quotient(difference(i(i(j(X2))),product(X2,j(X2))),i(j(X2))),X),
inference(congruence,[status(thm)],[c638]) ).
cnf(c640,plain,
product(i(X),product(product(i(j(X2)),quotient(product(X2,j(X2)),i(j(X2)))),X)) = product(i(X),product(quotient(difference(i(i(j(X2))),product(X2,j(X2))),i(j(X2))),X)),
inference(congruence,[status(thm)],[c639]) ).
cnf(c641,plain,
i(i(j(X))) = i(X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c642,plain,
difference(i(i(j(X))),product(X,j(X))) = difference(i(X),product(X,j(X))),
inference(congruence,[status(thm)],[c641]) ).
cnf(c643,plain,
quotient(difference(i(i(j(X))),product(X,j(X))),i(j(X))) = quotient(difference(i(X),product(X,j(X))),i(j(X))),
inference(congruence,[status(thm)],[c642]) ).
cnf(c644,plain,
product(quotient(difference(i(i(j(X2))),product(X2,j(X2))),i(j(X2))),X) = product(quotient(difference(i(X2),product(X2,j(X2))),i(j(X2))),X),
inference(congruence,[status(thm)],[c643]) ).
cnf(c645,plain,
product(i(X),product(quotient(difference(i(i(j(X2))),product(X2,j(X2))),i(j(X2))),X)) = product(i(X),product(quotient(difference(i(X2),product(X2,j(X2))),i(j(X2))),X)),
inference(congruence,[status(thm)],[c644]) ).
cnf(c646,plain,
quotient(difference(i(X),product(X,j(X))),i(j(X))) = quotient(difference(i(X),product(X,j(X))),X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c647,plain,
product(quotient(difference(i(X2),product(X2,j(X2))),i(j(X2))),X) = product(quotient(difference(i(X2),product(X2,j(X2))),X2),X),
inference(congruence,[status(thm)],[c646]) ).
cnf(c648,plain,
product(i(X),product(quotient(difference(i(X2),product(X2,j(X2))),i(j(X2))),X)) = product(i(X),product(quotient(difference(i(X2),product(X2,j(X2))),X2),X)),
inference(congruence,[status(thm)],[c647]) ).
cnf(c649,plain,
difference(i(X),product(X,j(X))) = difference(i(X),eta(X)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c650,plain,
quotient(difference(i(X),product(X,j(X))),X) = quotient(difference(i(X),eta(X)),X),
inference(congruence,[status(thm)],[c649]) ).
cnf(c651,plain,
product(quotient(difference(i(X2),product(X2,j(X2))),X2),X) = product(quotient(difference(i(X2),eta(X2)),X2),X),
inference(congruence,[status(thm)],[c650]) ).
cnf(c652,plain,
product(i(X),product(quotient(difference(i(X2),product(X2,j(X2))),X2),X)) = product(i(X),product(quotient(difference(i(X2),eta(X2)),X2),X)),
inference(congruence,[status(thm)],[c651]) ).
cnf(c653,plain,
quotient(difference(i(X),eta(X)),X) = i(product(X,i(X))),
inference(substitution,[status(thm)],[c158]) ).
cnf(c654,plain,
product(quotient(difference(i(X2),eta(X2)),X2),X) = product(i(product(X2,i(X2))),X),
inference(congruence,[status(thm)],[c653]) ).
cnf(c655,plain,
product(i(X),product(quotient(difference(i(X2),eta(X2)),X2),X)) = product(i(X),product(i(product(X2,i(X2))),X)),
inference(congruence,[status(thm)],[c654]) ).
cnf(c656,plain,
i(product(X,i(X))) = i(one),
inference(congruence,[status(thm)],[c9]) ).
cnf(c657,plain,
product(i(product(X2,i(X2))),X) = product(i(one),X),
inference(congruence,[status(thm)],[c656]) ).
cnf(c658,plain,
product(i(X),product(i(product(X2,i(X2))),X)) = product(i(X),product(i(one),X)),
inference(congruence,[status(thm)],[c657]) ).
cnf(c659,plain,
product(i(one),X) = product(one,X),
inference(congruence,[status(thm)],[c537]) ).
cnf(c660,plain,
product(i(X),product(i(one),X)) = product(i(X),product(one,X)),
inference(congruence,[status(thm)],[c659]) ).
cnf(c661,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c185]) ).
cnf(c662,plain,
product(i(X),product(one,X)) = product(i(X),X),
inference(congruence,[status(thm)],[c661]) ).
cnf(c663,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c664,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c663]) ).
cnf(c665,plain,
product(i(X),product(one,X)) = eta(X),
inference(transitivity,[status(thm)],[c662,c664]) ).
cnf(c666,plain,
product(i(X),product(i(one),X)) = eta(X),
inference(transitivity,[status(thm)],[c660,c665]) ).
cnf(c667,plain,
product(i(X),product(i(product(X2,i(X2))),X)) = eta(X),
inference(transitivity,[status(thm)],[c658,c666]) ).
cnf(c668,plain,
product(i(X),product(quotient(difference(i(X2),eta(X2)),X2),X)) = eta(X),
inference(transitivity,[status(thm)],[c655,c667]) ).
cnf(c669,plain,
product(i(X),product(quotient(difference(i(X2),product(X2,j(X2))),X2),X)) = eta(X),
inference(transitivity,[status(thm)],[c652,c668]) ).
cnf(c670,plain,
product(i(X),product(quotient(difference(i(X2),product(X2,j(X2))),i(j(X2))),X)) = eta(X),
inference(transitivity,[status(thm)],[c648,c669]) ).
cnf(c671,plain,
product(i(X),product(quotient(difference(i(i(j(X2))),product(X2,j(X2))),i(j(X2))),X)) = eta(X),
inference(transitivity,[status(thm)],[c645,c670]) ).
cnf(c672,plain,
product(i(X),product(product(i(j(X2)),quotient(product(X2,j(X2)),i(j(X2)))),X)) = eta(X),
inference(transitivity,[status(thm)],[c640,c671]) ).
cnf(c673,plain,
product(i(X),product(product(product(i(j(X2)),product(X2,j(X2))),j(X2)),X)) = eta(X),
inference(transitivity,[status(thm)],[c637,c672]) ).
cnf(c674,plain,
product(difference(X,product(i(j(X2)),product(X2,j(X2)))),product(j(X2),X)) = eta(X),
inference(transitivity,[status(thm)],[c626,c673]) ).
cnf(c675,plain,
product(product(difference(product(j(X2),X),X2),j(X2)),product(j(X2),X)) = eta(X),
inference(transitivity,[status(thm)],[c625,c674]) ).
cnf(c676,plain,
eta(difference(product(j(X2),X),X2)) = eta(X),
inference(transitivity,[status(thm)],[c610,c675]) ).
cnf(c677,plain,
eta(difference(X2,i(product(j(X2),X)))) = eta(X),
inference(transitivity,[status(thm)],[c594,c676]) ).
cnf(c678,plain,
eta(difference(X2,i(product(j(X2),quotient(eta(j(X2)),X))))) = eta(quotient(eta(j(X2)),X)),
inference(substitution,[status(thm)],[c677]) ).
cnf(c679,plain,
quotient(eta(j(X2)),X) = quotient(eta(X2),X),
inference(congruence,[status(thm)],[c111]) ).
cnf(c680,plain,
eta(quotient(eta(j(X2)),X)) = eta(quotient(eta(X2),X)),
inference(congruence,[status(thm)],[c679]) ).
cnf(c681,plain,
eta(difference(X2,i(product(j(X2),quotient(eta(j(X2)),X))))) = eta(quotient(eta(X2),X)),
inference(transitivity,[status(thm)],[c678,c680]) ).
cnf(c682,plain,
eta(difference(X2,i(j(quotient(X,j(X2)))))) = eta(quotient(eta(X2),X)),
inference(transitivity,[status(thm)],[c587,c681]) ).
cnf(c683,plain,
eta(difference(X2,quotient(X,j(X2)))) = eta(quotient(eta(X2),X)),
inference(transitivity,[status(thm)],[c573,c682]) ).
cnf(c684,plain,
eta(product(difference(X2,X),X2)) = eta(quotient(eta(X2),X)),
inference(transitivity,[status(thm)],[c569,c683]) ).
cnf(c685,plain,
eta(product(i(X2),product(X,X2))) = eta(quotient(eta(X2),X)),
inference(transitivity,[status(thm)],[c563,c684]) ).
cnf(c686,plain,
eta(product(i(X2),product(product(X2,X),X2))) = eta(quotient(eta(X2),product(X2,X))),
inference(substitution,[status(thm)],[c685]) ).
cnf(c687,plain,
eta(quotient(eta(X2),product(X2,X))) = eta(product(i(X2),product(product(X2,X),X2))),
inference(symmetry,[status(thm)],[c686]) ).
cnf(c688,plain,
difference(i(X2),product(i(X2),product(product(X2,X),X2))) = product(product(X2,X),X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c689,plain,
product(product(X2,X),X2) = difference(i(X2),product(i(X2),product(product(X2,X),X2))),
inference(symmetry,[status(thm)],[c688]) ).
cnf(c690,plain,
product(difference(X2,product(X2,X)),X2) = product(i(X2),product(product(X2,X),X2)),
inference(substitution,[status(thm)],[c322]) ).
cnf(c691,plain,
product(i(X2),product(product(X2,X),X2)) = product(difference(X2,product(X2,X)),X2),
inference(symmetry,[status(thm)],[c690]) ).
cnf(c692,plain,
difference(X2,product(X2,X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c693,plain,
product(difference(X2,product(X2,X)),X2) = product(X,X2),
inference(congruence,[status(thm)],[c692]) ).
cnf(c694,plain,
product(i(X2),product(product(X2,X),X2)) = product(X,X2),
inference(transitivity,[status(thm)],[c691,c693]) ).
cnf(c695,plain,
difference(i(X2),product(i(X2),product(product(X2,X),X2))) = difference(i(X2),product(X,X2)),
inference(congruence,[status(thm)],[c694]) ).
cnf(c696,plain,
product(product(X2,X),X2) = difference(i(X2),product(X,X2)),
inference(transitivity,[status(thm)],[c689,c695]) ).
cnf(c697,plain,
product(i(X2),product(product(X2,X),X2)) = product(i(X2),difference(i(X2),product(X,X2))),
inference(congruence,[status(thm)],[c696]) ).
cnf(c698,plain,
eta(product(i(X2),product(product(X2,X),X2))) = eta(product(i(X2),difference(i(X2),product(X,X2)))),
inference(congruence,[status(thm)],[c697]) ).
cnf(c699,plain,
product(i(X2),difference(i(X2),product(X,X2))) = product(X,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c700,plain,
eta(product(i(X2),difference(i(X2),product(X,X2)))) = eta(product(X,X2)),
inference(congruence,[status(thm)],[c699]) ).
cnf(c701,plain,
eta(product(i(X2),product(product(X2,X),X2))) = eta(product(X,X2)),
inference(transitivity,[status(thm)],[c698,c700]) ).
cnf(c702,plain,
eta(quotient(eta(X2),product(X2,X))) = eta(product(X,X2)),
inference(transitivity,[status(thm)],[c687,c701]) ).
cnf(c703,plain,
eta(quotient(eta(X),product(X,X2))) = eta(product(X2,X)),
inference(substitution,[status(thm)],[c702]) ).
cnf(c704,plain,
eta(product(X2,X)) = eta(quotient(eta(X),product(X,X2))),
inference(symmetry,[status(thm)],[c703]) ).
cnf(c705,plain,
eta(quotient(eta(X2),X)) = eta(quotient(X,i(eta(X2)))),
inference(substitution,[status(thm)],[c553]) ).
cnf(c706,plain,
eta(i(product(eta(X2),X))) = eta(product(eta(X2),X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c707,plain,
eta(product(eta(X2),X)) = eta(i(product(eta(X2),X))),
inference(symmetry,[status(thm)],[c706]) ).
cnf(c708,plain,
quotient(difference(X,eta(eta(X2))),eta(X2)) = i(product(eta(X2),X)),
inference(substitution,[status(thm)],[c158]) ).
cnf(c709,plain,
i(product(eta(X2),X)) = quotient(difference(X,eta(eta(X2))),eta(X2)),
inference(symmetry,[status(thm)],[c708]) ).
cnf(c710,plain,
difference(X,eta(eta(X2))) = difference(X,one),
inference(congruence,[status(thm)],[c507]) ).
cnf(c711,plain,
quotient(difference(X,eta(eta(X2))),eta(X2)) = quotient(difference(X,one),eta(X2)),
inference(congruence,[status(thm)],[c710]) ).
cnf(c712,plain,
i(X) = difference(X,one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c713,plain,
difference(X,one) = i(X),
inference(symmetry,[status(thm)],[c712]) ).
cnf(c714,plain,
quotient(difference(X,one),eta(X2)) = quotient(i(X),eta(X2)),
inference(congruence,[status(thm)],[c713]) ).
cnf(c715,plain,
quotient(difference(X,eta(eta(X2))),eta(X2)) = quotient(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c711,c714]) ).
cnf(c716,plain,
i(product(eta(X2),X)) = quotient(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c709,c715]) ).
cnf(c717,plain,
eta(i(product(eta(X2),X))) = eta(quotient(i(X),eta(X2))),
inference(congruence,[status(thm)],[c716]) ).
cnf(c718,plain,
eta(product(eta(X2),X)) = eta(quotient(i(X),eta(X2))),
inference(transitivity,[status(thm)],[c707,c717]) ).
cnf(c719,plain,
eta(product(eta(X),X2)) = eta(quotient(i(X2),eta(X))),
inference(substitution,[status(thm)],[c718]) ).
cnf(c720,plain,
eta(quotient(i(X2),eta(X))) = eta(product(eta(X),X2)),
inference(symmetry,[status(thm)],[c719]) ).
cnf(c721,plain,
i(i(eta(X))) = difference(i(eta(X)),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c722,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c723,plain,
difference(i(eta(X)),one) = difference(i(eta(X)),eta(eta(X))),
inference(congruence,[status(thm)],[c722]) ).
cnf(c724,plain,
difference(i(eta(X)),eta(eta(X))) = eta(X),
inference(substitution,[status(thm)],[c497]) ).
cnf(c725,plain,
difference(i(eta(X)),one) = eta(X),
inference(transitivity,[status(thm)],[c723,c724]) ).
cnf(c726,plain,
i(i(eta(X))) = eta(X),
inference(transitivity,[status(thm)],[c721,c725]) ).
cnf(c727,plain,
eta(X) = i(i(eta(X))),
inference(symmetry,[status(thm)],[c726]) ).
cnf(c728,plain,
product(eta(X),X2) = product(i(i(eta(X))),X2),
inference(congruence,[status(thm)],[c727]) ).
cnf(c729,plain,
eta(product(eta(X),X2)) = eta(product(i(i(eta(X))),X2)),
inference(congruence,[status(thm)],[c728]) ).
cnf(c730,plain,
product(quotient(i(X),X2),X2) = i(X),
inference(substitution,[status(thm)],[c38]) ).
cnf(c731,plain,
i(X) = product(quotient(i(X),X2),X2),
inference(symmetry,[status(thm)],[c730]) ).
cnf(c732,plain,
product(i(X2),i(X)) = product(i(X2),product(quotient(i(X),X2),X2)),
inference(congruence,[status(thm)],[c731]) ).
cnf(c733,plain,
eta(product(i(X2),i(X))) = eta(product(i(X2),product(quotient(i(X),X2),X2))),
inference(congruence,[status(thm)],[c732]) ).
cnf(c734,plain,
product(difference(X2,quotient(i(X),X2)),X2) = product(i(X2),product(quotient(i(X),X2),X2)),
inference(substitution,[status(thm)],[c322]) ).
cnf(c735,plain,
product(i(X2),product(quotient(i(X),X2),X2)) = product(difference(X2,quotient(i(X),X2)),X2),
inference(symmetry,[status(thm)],[c734]) ).
cnf(c736,plain,
eta(product(i(X2),product(quotient(i(X),X2),X2))) = eta(product(difference(X2,quotient(i(X),X2)),X2)),
inference(congruence,[status(thm)],[c735]) ).
cnf(c737,plain,
difference(X2,quotient(quotient(i(X),X2),j(X2))) = product(difference(X2,quotient(i(X),X2)),X2),
inference(substitution,[status(thm)],[c567]) ).
cnf(c738,plain,
product(difference(X2,quotient(i(X),X2)),X2) = difference(X2,quotient(quotient(i(X),X2),j(X2))),
inference(symmetry,[status(thm)],[c737]) ).
cnf(c739,plain,
eta(product(difference(X2,quotient(i(X),X2)),X2)) = eta(difference(X2,quotient(quotient(i(X),X2),j(X2)))),
inference(congruence,[status(thm)],[c738]) ).
cnf(c740,plain,
product(j(X),product(X,X2)) = quotient(quotient(X2,X),j(X)),
inference(substitution,[status(thm)],[c422]) ).
cnf(c741,plain,
quotient(quotient(X2,X),j(X)) = product(j(X),product(X,X2)),
inference(symmetry,[status(thm)],[c740]) ).
cnf(c742,plain,
i(quotient(quotient(X2,X),j(X))) = i(product(j(X),product(X,X2))),
inference(congruence,[status(thm)],[c741]) ).
cnf(c743,plain,
eta(X) = product(X,j(X)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c744,plain,
difference(X2,eta(X)) = difference(X2,product(X,j(X))),
inference(congruence,[status(thm)],[c743]) ).
cnf(c745,plain,
quotient(difference(X2,eta(X)),j(X)) = quotient(difference(X2,product(X,j(X))),j(X)),
inference(congruence,[status(thm)],[c744]) ).
cnf(c746,plain,
quotient(difference(X2,product(X,j(X))),j(X)) = difference(product(j(X),X2),product(j(X),X)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c747,plain,
difference(product(j(X),X2),product(j(X),X)) = difference(product(j(X),X2),one),
inference(congruence,[status(thm)],[c40]) ).
cnf(c748,plain,
i(product(j(X),X2)) = difference(product(j(X),X2),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c749,plain,
difference(product(j(X),X2),one) = i(product(j(X),X2)),
inference(symmetry,[status(thm)],[c748]) ).
cnf(c750,plain,
difference(product(j(X),X2),product(j(X),X)) = i(product(j(X),X2)),
inference(transitivity,[status(thm)],[c747,c749]) ).
cnf(c751,plain,
quotient(difference(X2,product(X,j(X))),j(X)) = i(product(j(X),X2)),
inference(transitivity,[status(thm)],[c746,c750]) ).
cnf(c752,plain,
quotient(difference(X2,eta(X)),j(X)) = i(product(j(X),X2)),
inference(transitivity,[status(thm)],[c745,c751]) ).
cnf(c753,plain,
quotient(difference(product(X,X2),eta(X)),j(X)) = i(product(j(X),product(X,X2))),
inference(substitution,[status(thm)],[c752]) ).
cnf(c754,plain,
i(product(j(X),product(X,X2))) = quotient(difference(product(X,X2),eta(X)),j(X)),
inference(symmetry,[status(thm)],[c753]) ).
cnf(c755,plain,
difference(product(X,X2),eta(X)) = quotient(i(X2),X),
inference(substitution,[status(thm)],[c133]) ).
cnf(c756,plain,
quotient(difference(product(X,X2),eta(X)),j(X)) = quotient(quotient(i(X2),X),j(X)),
inference(congruence,[status(thm)],[c755]) ).
cnf(c757,plain,
i(product(j(X),product(X,X2))) = quotient(quotient(i(X2),X),j(X)),
inference(transitivity,[status(thm)],[c754,c756]) ).
cnf(c758,plain,
i(quotient(quotient(X2,X),j(X))) = quotient(quotient(i(X2),X),j(X)),
inference(transitivity,[status(thm)],[c742,c757]) ).
cnf(c759,plain,
i(quotient(quotient(X,X2),j(X2))) = quotient(quotient(i(X),X2),j(X2)),
inference(substitution,[status(thm)],[c758]) ).
cnf(c760,plain,
quotient(quotient(i(X),X2),j(X2)) = i(quotient(quotient(X,X2),j(X2))),
inference(symmetry,[status(thm)],[c759]) ).
cnf(c761,plain,
difference(X2,quotient(quotient(i(X),X2),j(X2))) = difference(X2,i(quotient(quotient(X,X2),j(X2)))),
inference(congruence,[status(thm)],[c760]) ).
cnf(c762,plain,
eta(difference(X2,quotient(quotient(i(X),X2),j(X2)))) = eta(difference(X2,i(quotient(quotient(X,X2),j(X2))))),
inference(congruence,[status(thm)],[c761]) ).
cnf(c763,plain,
quotient(quotient(X,X2),j(X2)) = product(j(X2),product(X2,X)),
inference(symmetry,[status(thm)],[c422]) ).
cnf(c764,plain,
i(quotient(quotient(X,X2),j(X2))) = i(product(j(X2),product(X2,X))),
inference(congruence,[status(thm)],[c763]) ).
cnf(c765,plain,
difference(X2,i(quotient(quotient(X,X2),j(X2)))) = difference(X2,i(product(j(X2),product(X2,X)))),
inference(congruence,[status(thm)],[c764]) ).
cnf(c766,plain,
eta(difference(X2,i(quotient(quotient(X,X2),j(X2))))) = eta(difference(X2,i(product(j(X2),product(X2,X))))),
inference(congruence,[status(thm)],[c765]) ).
cnf(c767,plain,
eta(difference(X2,i(product(j(X2),product(X2,X))))) = eta(product(X2,X)),
inference(substitution,[status(thm)],[c677]) ).
cnf(c768,plain,
eta(difference(X2,i(quotient(quotient(X,X2),j(X2))))) = eta(product(X2,X)),
inference(transitivity,[status(thm)],[c766,c767]) ).
cnf(c769,plain,
eta(difference(X2,quotient(quotient(i(X),X2),j(X2)))) = eta(product(X2,X)),
inference(transitivity,[status(thm)],[c762,c768]) ).
cnf(c770,plain,
eta(product(difference(X2,quotient(i(X),X2)),X2)) = eta(product(X2,X)),
inference(transitivity,[status(thm)],[c739,c769]) ).
cnf(c771,plain,
eta(product(i(X2),product(quotient(i(X),X2),X2))) = eta(product(X2,X)),
inference(transitivity,[status(thm)],[c736,c770]) ).
cnf(c772,plain,
eta(product(i(X2),i(X))) = eta(product(X2,X)),
inference(transitivity,[status(thm)],[c733,c771]) ).
cnf(c773,plain,
eta(product(i(X2),i(j(X)))) = eta(product(X2,j(X))),
inference(substitution,[status(thm)],[c772]) ).
cnf(c774,plain,
eta(product(X2,j(X))) = eta(product(i(X2),i(j(X)))),
inference(symmetry,[status(thm)],[c773]) ).
cnf(c775,plain,
product(i(X2),i(j(X))) = product(i(X2),X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c776,plain,
eta(product(i(X2),i(j(X)))) = eta(product(i(X2),X)),
inference(congruence,[status(thm)],[c775]) ).
cnf(c777,plain,
eta(product(X2,j(X))) = eta(product(i(X2),X)),
inference(transitivity,[status(thm)],[c774,c776]) ).
cnf(c778,plain,
eta(product(i(eta(X)),j(X2))) = eta(product(i(i(eta(X))),X2)),
inference(substitution,[status(thm)],[c777]) ).
cnf(c779,plain,
eta(product(i(i(eta(X))),X2)) = eta(product(i(eta(X)),j(X2))),
inference(symmetry,[status(thm)],[c778]) ).
cnf(c780,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c781,plain,
product(i(eta(X2)),j(X)) = product(i(eta(X2)),quotient(one,X)),
inference(congruence,[status(thm)],[c780]) ).
cnf(c782,plain,
difference(eta(X),eta(eta(X))) = j(eta(X)),
inference(substitution,[status(thm)],[c117]) ).
cnf(c783,plain,
j(eta(X)) = difference(eta(X),eta(eta(X))),
inference(symmetry,[status(thm)],[c782]) ).
cnf(c784,plain,
difference(eta(X),eta(eta(X))) = difference(eta(X),one),
inference(congruence,[status(thm)],[c507]) ).
cnf(c785,plain,
i(eta(X)) = difference(eta(X),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c786,plain,
difference(eta(X),one) = i(eta(X)),
inference(symmetry,[status(thm)],[c785]) ).
cnf(c787,plain,
difference(eta(X),eta(eta(X))) = i(eta(X)),
inference(transitivity,[status(thm)],[c784,c786]) ).
cnf(c788,plain,
j(eta(X)) = i(eta(X)),
inference(transitivity,[status(thm)],[c783,c787]) ).
cnf(c789,plain,
i(eta(X)) = j(eta(X)),
inference(symmetry,[status(thm)],[c788]) ).
cnf(c790,plain,
product(i(eta(X2)),quotient(one,X)) = product(j(eta(X2)),quotient(one,X)),
inference(congruence,[status(thm)],[c789]) ).
cnf(c791,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c792,plain,
quotient(one,X) = quotient(eta(eta(X2)),X),
inference(congruence,[status(thm)],[c791]) ).
cnf(c793,plain,
product(j(eta(X2)),quotient(one,X)) = product(j(eta(X2)),quotient(eta(eta(X2)),X)),
inference(congruence,[status(thm)],[c792]) ).
cnf(c794,plain,
j(i(product(j(X2),quotient(eta(X2),X)))) = product(j(X2),quotient(eta(X2),X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c795,plain,
product(j(X2),quotient(eta(X2),X)) = j(i(product(j(X2),quotient(eta(X2),X)))),
inference(symmetry,[status(thm)],[c794]) ).
cnf(c796,plain,
quotient(difference(quotient(eta(X2),X),eta(X2)),j(X2)) = i(product(j(X2),quotient(eta(X2),X))),
inference(substitution,[status(thm)],[c752]) ).
cnf(c797,plain,
i(product(j(X2),quotient(eta(X2),X))) = quotient(difference(quotient(eta(X2),X),eta(X2)),j(X2)),
inference(symmetry,[status(thm)],[c796]) ).
cnf(c798,plain,
difference(quotient(eta(X2),X),eta(X2)) = X,
inference(substitution,[status(thm)],[c209]) ).
cnf(c799,plain,
quotient(difference(quotient(eta(X2),X),eta(X2)),j(X2)) = quotient(X,j(X2)),
inference(congruence,[status(thm)],[c798]) ).
cnf(c800,plain,
i(product(j(X2),quotient(eta(X2),X))) = quotient(X,j(X2)),
inference(transitivity,[status(thm)],[c797,c799]) ).
cnf(c801,plain,
j(i(product(j(X2),quotient(eta(X2),X)))) = j(quotient(X,j(X2))),
inference(congruence,[status(thm)],[c800]) ).
cnf(c802,plain,
product(j(X2),quotient(eta(X2),X)) = j(quotient(X,j(X2))),
inference(transitivity,[status(thm)],[c795,c801]) ).
cnf(c803,plain,
product(j(eta(X2)),quotient(eta(eta(X2)),X)) = j(quotient(X,j(eta(X2)))),
inference(substitution,[status(thm)],[c802]) ).
cnf(c804,plain,
quotient(X,j(eta(X2))) = quotient(X,i(eta(X2))),
inference(congruence,[status(thm)],[c788]) ).
cnf(c805,plain,
j(quotient(X,j(eta(X2)))) = j(quotient(X,i(eta(X2)))),
inference(congruence,[status(thm)],[c804]) ).
cnf(c806,plain,
product(j(eta(X2)),quotient(eta(eta(X2)),X)) = j(quotient(X,i(eta(X2)))),
inference(transitivity,[status(thm)],[c803,c805]) ).
cnf(c807,plain,
product(j(eta(X2)),quotient(one,X)) = j(quotient(X,i(eta(X2)))),
inference(transitivity,[status(thm)],[c793,c806]) ).
cnf(c808,plain,
product(i(eta(X2)),quotient(one,X)) = j(quotient(X,i(eta(X2)))),
inference(transitivity,[status(thm)],[c790,c807]) ).
cnf(c809,plain,
product(i(eta(X2)),j(X)) = j(quotient(X,i(eta(X2)))),
inference(transitivity,[status(thm)],[c781,c808]) ).
cnf(c810,plain,
product(i(eta(X)),j(X2)) = j(quotient(X2,i(eta(X)))),
inference(substitution,[status(thm)],[c809]) ).
cnf(c811,plain,
eta(product(i(eta(X)),j(X2))) = eta(j(quotient(X2,i(eta(X))))),
inference(congruence,[status(thm)],[c810]) ).
cnf(c812,plain,
eta(j(quotient(X2,i(eta(X))))) = eta(quotient(X2,i(eta(X)))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c813,plain,
eta(product(i(eta(X)),j(X2))) = eta(quotient(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c811,c812]) ).
cnf(c814,plain,
eta(product(i(i(eta(X))),X2)) = eta(quotient(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c779,c813]) ).
cnf(c815,plain,
eta(product(eta(X),X2)) = eta(quotient(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c729,c814]) ).
cnf(c816,plain,
eta(quotient(i(X2),eta(X))) = eta(quotient(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c720,c815]) ).
cnf(c817,plain,
eta(quotient(X2,i(eta(X)))) = eta(quotient(i(X2),eta(X))),
inference(symmetry,[status(thm)],[c816]) ).
cnf(c818,plain,
eta(product(eta(X),X2)) = eta(quotient(i(X2),eta(X))),
inference(substitution,[status(thm)],[c718]) ).
cnf(c819,plain,
eta(quotient(i(X2),eta(X))) = eta(product(eta(X),X2)),
inference(symmetry,[status(thm)],[c818]) ).
cnf(c820,plain,
eta(j(product(eta(X),X2))) = eta(product(eta(X),X2)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c821,plain,
eta(product(eta(X),X2)) = eta(j(product(eta(X),X2))),
inference(symmetry,[status(thm)],[c820]) ).
cnf(c822,plain,
j(product(eta(X),X2)) = quotient(one,product(eta(X),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c823,plain,
eta(j(product(eta(X),X2))) = eta(quotient(one,product(eta(X),X2))),
inference(congruence,[status(thm)],[c822]) ).
cnf(c824,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c825,plain,
quotient(one,product(eta(X),X2)) = quotient(eta(eta(X)),product(eta(X),X2)),
inference(congruence,[status(thm)],[c824]) ).
cnf(c826,plain,
eta(quotient(one,product(eta(X),X2))) = eta(quotient(eta(eta(X)),product(eta(X),X2))),
inference(congruence,[status(thm)],[c825]) ).
cnf(c827,plain,
eta(quotient(eta(eta(X)),product(eta(X),X2))) = eta(product(X2,eta(X))),
inference(substitution,[status(thm)],[c702]) ).
cnf(c828,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c829,plain,
product(X2,eta(X)) = product(i(j(X2)),eta(X)),
inference(congruence,[status(thm)],[c828]) ).
cnf(c830,plain,
eta(product(X2,eta(X))) = eta(product(i(j(X2)),eta(X))),
inference(congruence,[status(thm)],[c829]) ).
cnf(c831,plain,
i(difference(eta(X2),X)) = difference(difference(eta(X2),X),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c832,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c833,plain,
difference(difference(eta(X2),X),one) = difference(difference(eta(X2),X),eta(eta(X2))),
inference(congruence,[status(thm)],[c832]) ).
cnf(c834,plain,
difference(difference(eta(X2),X),eta(eta(X2))) = product(i(X),eta(X2)),
inference(substitution,[status(thm)],[c459]) ).
cnf(c835,plain,
difference(difference(eta(X2),X),one) = product(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c833,c834]) ).
cnf(c836,plain,
i(difference(eta(X2),X)) = product(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c831,c835]) ).
cnf(c837,plain,
i(difference(eta(X),X2)) = product(i(X2),eta(X)),
inference(substitution,[status(thm)],[c836]) ).
cnf(c838,plain,
product(i(X2),eta(X)) = i(difference(eta(X),X2)),
inference(symmetry,[status(thm)],[c837]) ).
cnf(c839,plain,
eta(product(i(X2),eta(X))) = eta(i(difference(eta(X),X2))),
inference(congruence,[status(thm)],[c838]) ).
cnf(c840,plain,
eta(i(difference(eta(X),X2))) = eta(difference(eta(X),X2)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c841,plain,
eta(difference(X2,i(eta(X)))) = eta(difference(eta(X),X2)),
inference(substitution,[status(thm)],[c593]) ).
cnf(c842,plain,
eta(difference(eta(X),X2)) = eta(difference(X2,i(eta(X)))),
inference(symmetry,[status(thm)],[c841]) ).
cnf(c843,plain,
eta(i(difference(eta(X),X2))) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c840,c842]) ).
cnf(c844,plain,
eta(product(i(X2),eta(X))) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c839,c843]) ).
cnf(c845,plain,
eta(product(i(j(X2)),eta(X))) = eta(difference(j(X2),i(eta(X)))),
inference(substitution,[status(thm)],[c844]) ).
cnf(c846,plain,
eta(difference(X,i(j(X2)))) = eta(difference(j(X2),X)),
inference(substitution,[status(thm)],[c593]) ).
cnf(c847,plain,
eta(difference(j(X2),X)) = eta(difference(X,i(j(X2)))),
inference(symmetry,[status(thm)],[c846]) ).
cnf(c848,plain,
difference(X,i(j(X2))) = difference(X,X2),
inference(congruence,[status(thm)],[c46]) ).
cnf(c849,plain,
eta(difference(X,i(j(X2)))) = eta(difference(X,X2)),
inference(congruence,[status(thm)],[c848]) ).
cnf(c850,plain,
eta(difference(X2,i(X))) = eta(difference(X,X2)),
inference(substitution,[status(thm)],[c593]) ).
cnf(c851,plain,
eta(difference(X,X2)) = eta(difference(X2,i(X))),
inference(symmetry,[status(thm)],[c850]) ).
cnf(c852,plain,
eta(difference(X,i(j(X2)))) = eta(difference(X2,i(X))),
inference(transitivity,[status(thm)],[c849,c851]) ).
cnf(c853,plain,
eta(difference(j(X2),X)) = eta(difference(X2,i(X))),
inference(transitivity,[status(thm)],[c847,c852]) ).
cnf(c854,plain,
eta(difference(j(X2),i(eta(X)))) = eta(difference(X2,i(i(eta(X))))),
inference(substitution,[status(thm)],[c853]) ).
cnf(c855,plain,
difference(X2,i(i(eta(X)))) = difference(X2,eta(X)),
inference(congruence,[status(thm)],[c726]) ).
cnf(c856,plain,
eta(difference(X2,i(i(eta(X))))) = eta(difference(X2,eta(X))),
inference(congruence,[status(thm)],[c855]) ).
cnf(c857,plain,
eta(difference(j(X2),i(eta(X)))) = eta(difference(X2,eta(X))),
inference(transitivity,[status(thm)],[c854,c856]) ).
cnf(c858,plain,
eta(product(i(j(X2)),eta(X))) = eta(difference(X2,eta(X))),
inference(transitivity,[status(thm)],[c845,c857]) ).
cnf(c859,plain,
eta(product(X2,eta(X))) = eta(difference(X2,eta(X))),
inference(transitivity,[status(thm)],[c830,c858]) ).
cnf(c860,plain,
eta(quotient(eta(eta(X)),product(eta(X),X2))) = eta(difference(X2,eta(X))),
inference(transitivity,[status(thm)],[c827,c859]) ).
cnf(c861,plain,
eta(quotient(one,product(eta(X),X2))) = eta(difference(X2,eta(X))),
inference(transitivity,[status(thm)],[c826,c860]) ).
cnf(c862,plain,
eta(j(product(eta(X),X2))) = eta(difference(X2,eta(X))),
inference(transitivity,[status(thm)],[c823,c861]) ).
cnf(c863,plain,
eta(product(eta(X),X2)) = eta(difference(X2,eta(X))),
inference(transitivity,[status(thm)],[c821,c862]) ).
cnf(c864,plain,
eta(quotient(i(X2),eta(X))) = eta(difference(X2,eta(X))),
inference(transitivity,[status(thm)],[c819,c863]) ).
cnf(c865,plain,
eta(quotient(X2,i(eta(X)))) = eta(difference(X2,eta(X))),
inference(transitivity,[status(thm)],[c817,c864]) ).
cnf(c866,plain,
eta(quotient(X,i(eta(X2)))) = eta(difference(X,eta(X2))),
inference(substitution,[status(thm)],[c865]) ).
cnf(c867,plain,
eta(quotient(eta(X2),X)) = eta(difference(X,eta(X2))),
inference(transitivity,[status(thm)],[c705,c866]) ).
cnf(c868,plain,
eta(quotient(eta(X),product(X,X2))) = eta(difference(product(X,X2),eta(X))),
inference(substitution,[status(thm)],[c867]) ).
cnf(c869,plain,
difference(product(X,X2),eta(X)) = quotient(i(X2),X),
inference(substitution,[status(thm)],[c133]) ).
cnf(c870,plain,
eta(difference(product(X,X2),eta(X))) = eta(quotient(i(X2),X)),
inference(congruence,[status(thm)],[c869]) ).
cnf(c871,plain,
eta(quotient(i(X2),X)) = eta(quotient(X,i(i(X2)))),
inference(substitution,[status(thm)],[c553]) ).
cnf(c872,plain,
eta(difference(product(X,X2),eta(X))) = eta(quotient(X,i(i(X2)))),
inference(transitivity,[status(thm)],[c870,c871]) ).
cnf(c873,plain,
eta(quotient(eta(X),product(X,X2))) = eta(quotient(X,i(i(X2)))),
inference(transitivity,[status(thm)],[c868,c872]) ).
cnf(c874,plain,
eta(product(X2,X)) = eta(quotient(X,i(i(X2)))),
inference(transitivity,[status(thm)],[c704,c873]) ).
cnf(c875,plain,
eta(product(X,i(X2))) = eta(quotient(i(X2),i(i(X)))),
inference(substitution,[status(thm)],[c874]) ).
cnf(c876,plain,
eta(quotient(i(X2),i(i(X)))) = eta(product(X,i(X2))),
inference(symmetry,[status(thm)],[c875]) ).
cnf(c877,plain,
product(i(X2),eta(quotient(i(X2),i(i(X))))) = product(i(X2),eta(product(X,i(X2)))),
inference(congruence,[status(thm)],[c876]) ).
cnf(c878,plain,
quotient(quotient(X,i(X2)),X2) = product(X2,product(i(X2),X)),
inference(symmetry,[status(thm)],[c426]) ).
cnf(c879,plain,
difference(X2,quotient(quotient(X,i(X2)),X2)) = difference(X2,product(X2,product(i(X2),X))),
inference(congruence,[status(thm)],[c878]) ).
cnf(c880,plain,
difference(X2,product(X2,product(i(X2),X))) = product(i(X2),X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c881,plain,
difference(X2,quotient(quotient(X,i(X2)),X2)) = product(i(X2),X),
inference(transitivity,[status(thm)],[c879,c880]) ).
cnf(c882,plain,
difference(X,quotient(quotient(eta(product(X2,i(X))),i(X)),X)) = product(i(X),eta(product(X2,i(X)))),
inference(substitution,[status(thm)],[c881]) ).
cnf(c883,plain,
product(i(X),eta(product(X2,i(X)))) = difference(X,quotient(quotient(eta(product(X2,i(X))),i(X)),X)),
inference(symmetry,[status(thm)],[c882]) ).
cnf(c884,plain,
difference(X2,product(product(X2,i(product(X,X2))),X)) = quotient(product(i(product(X,X2)),product(X,X2)),X2),
inference(substitution,[status(thm)],[c57]) ).
cnf(c885,plain,
eta(product(X,X2)) = product(i(product(X,X2)),product(X,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c886,plain,
product(i(product(X,X2)),product(X,X2)) = eta(product(X,X2)),
inference(symmetry,[status(thm)],[c885]) ).
cnf(c887,plain,
quotient(product(i(product(X,X2)),product(X,X2)),X2) = quotient(eta(product(X,X2)),X2),
inference(congruence,[status(thm)],[c886]) ).
cnf(c888,plain,
difference(X2,product(product(X2,i(product(X,X2))),X)) = quotient(eta(product(X,X2)),X2),
inference(transitivity,[status(thm)],[c884,c887]) ).
cnf(c889,plain,
difference(i(X),product(product(i(X),i(product(X2,i(X)))),X2)) = quotient(eta(product(X2,i(X))),i(X)),
inference(substitution,[status(thm)],[c888]) ).
cnf(c890,plain,
quotient(eta(product(X2,i(X))),i(X)) = difference(i(X),product(product(i(X),i(product(X2,i(X)))),X2)),
inference(symmetry,[status(thm)],[c889]) ).
cnf(c891,plain,
quotient(quotient(eta(product(X2,i(X))),i(X)),X) = quotient(difference(i(X),product(product(i(X),i(product(X2,i(X)))),X2)),X),
inference(congruence,[status(thm)],[c890]) ).
cnf(c892,plain,
difference(X,quotient(quotient(eta(product(X2,i(X))),i(X)),X)) = difference(X,quotient(difference(i(X),product(product(i(X),i(product(X2,i(X)))),X2)),X)),
inference(congruence,[status(thm)],[c891]) ).
cnf(c893,plain,
difference(X2,product(product(X2,i(X2)),quotient(X,X2))) = quotient(product(i(X2),X),X2),
inference(substitution,[status(thm)],[c445]) ).
cnf(c894,plain,
quotient(product(i(X2),X),X2) = difference(X2,product(product(X2,i(X2)),quotient(X,X2))),
inference(symmetry,[status(thm)],[c893]) ).
cnf(c895,plain,
product(product(X2,i(X2)),quotient(X,X2)) = product(one,quotient(X,X2)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c896,plain,
difference(X2,product(product(X2,i(X2)),quotient(X,X2))) = difference(X2,product(one,quotient(X,X2))),
inference(congruence,[status(thm)],[c895]) ).
cnf(c897,plain,
product(one,quotient(X,X2)) = quotient(X,X2),
inference(substitution,[status(thm)],[c185]) ).
cnf(c898,plain,
difference(X2,product(one,quotient(X,X2))) = difference(X2,quotient(X,X2)),
inference(congruence,[status(thm)],[c897]) ).
cnf(c899,plain,
difference(X2,product(product(X2,i(X2)),quotient(X,X2))) = difference(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c896,c898]) ).
cnf(c900,plain,
quotient(product(i(X2),X),X2) = difference(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c894,c899]) ).
cnf(c901,plain,
quotient(product(i(X2),difference(i(X2),X)),X2) = difference(X2,quotient(difference(i(X2),X),X2)),
inference(substitution,[status(thm)],[c900]) ).
cnf(c902,plain,
difference(X2,quotient(difference(i(X2),X),X2)) = quotient(product(i(X2),difference(i(X2),X)),X2),
inference(symmetry,[status(thm)],[c901]) ).
cnf(c903,plain,
product(i(X2),difference(i(X2),X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c904,plain,
quotient(product(i(X2),difference(i(X2),X)),X2) = quotient(X,X2),
inference(congruence,[status(thm)],[c903]) ).
cnf(c905,plain,
difference(X2,quotient(difference(i(X2),X),X2)) = quotient(X,X2),
inference(transitivity,[status(thm)],[c902,c904]) ).
cnf(c906,plain,
difference(X,quotient(difference(i(X),product(product(i(X),i(product(X2,i(X)))),X2)),X)) = quotient(product(product(i(X),i(product(X2,i(X)))),X2),X),
inference(substitution,[status(thm)],[c905]) ).
cnf(c907,plain,
quotient(product(i(X2),X),j(i(X2))) = product(i(X2),product(X,i(X2))),
inference(substitution,[status(thm)],[c395]) ).
cnf(c908,plain,
product(i(X2),product(X,i(X2))) = quotient(product(i(X2),X),j(i(X2))),
inference(symmetry,[status(thm)],[c907]) ).
cnf(c909,plain,
quotient(product(i(X2),X),j(i(X2))) = quotient(product(i(X2),X),X2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c910,plain,
quotient(product(i(X2),X),j(i(X2))) = difference(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c909,c900]) ).
cnf(c911,plain,
product(i(X2),product(X,i(X2))) = difference(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c908,c910]) ).
cnf(c912,plain,
difference(X2,quotient(X,X2)) = product(i(X2),product(X,i(X2))),
inference(symmetry,[status(thm)],[c911]) ).
cnf(c913,plain,
difference(i(X2),difference(X2,quotient(X,X2))) = difference(i(X2),product(i(X2),product(X,i(X2)))),
inference(congruence,[status(thm)],[c912]) ).
cnf(c914,plain,
difference(i(X2),product(i(X2),product(X,i(X2)))) = product(X,i(X2)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c915,plain,
difference(i(X2),difference(X2,quotient(X,X2))) = product(X,i(X2)),
inference(transitivity,[status(thm)],[c913,c914]) ).
cnf(c916,plain,
product(X,i(X2)) = difference(i(X2),difference(X2,quotient(X,X2))),
inference(symmetry,[status(thm)],[c915]) ).
cnf(c917,plain,
i(product(X,i(X2))) = i(difference(i(X2),difference(X2,quotient(X,X2)))),
inference(congruence,[status(thm)],[c916]) ).
cnf(c918,plain,
product(i(X2),i(product(X,i(X2)))) = product(i(X2),i(difference(i(X2),difference(X2,quotient(X,X2))))),
inference(congruence,[status(thm)],[c917]) ).
cnf(c919,plain,
quotient(difference(X,eta(j(X2))),j(X2)) = i(product(j(X2),X)),
inference(substitution,[status(thm)],[c158]) ).
cnf(c920,plain,
i(product(j(X2),X)) = quotient(difference(X,eta(j(X2))),j(X2)),
inference(symmetry,[status(thm)],[c919]) ).
cnf(c921,plain,
difference(j(X2),i(product(j(X2),X))) = difference(j(X2),quotient(difference(X,eta(j(X2))),j(X2))),
inference(congruence,[status(thm)],[c920]) ).
cnf(c922,plain,
product(one,quotient(X,j(X2))) = quotient(X,j(X2)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c923,plain,
quotient(X,j(X2)) = product(one,quotient(X,j(X2))),
inference(symmetry,[status(thm)],[c922]) ).
cnf(c924,plain,
difference(j(X2),quotient(X,j(X2))) = difference(j(X2),product(one,quotient(X,j(X2)))),
inference(congruence,[status(thm)],[c923]) ).
cnf(c925,plain,
one = product(j(X),X),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c926,plain,
product(one,quotient(X,j(X2))) = product(product(j(X2),X2),quotient(X,j(X2))),
inference(congruence,[status(thm)],[c925]) ).
cnf(c927,plain,
difference(j(X2),product(one,quotient(X,j(X2)))) = difference(j(X2),product(product(j(X2),X2),quotient(X,j(X2)))),
inference(congruence,[status(thm)],[c926]) ).
cnf(c928,plain,
difference(j(X2),product(product(j(X2),X2),quotient(X,j(X2)))) = quotient(product(X2,X),j(X2)),
inference(substitution,[status(thm)],[c445]) ).
cnf(c929,plain,
difference(j(X2),product(product(j(X2),X2),quotient(X,j(X2)))) = product(X2,product(X,X2)),
inference(transitivity,[status(thm)],[c928,c395]) ).
cnf(c930,plain,
difference(j(X2),product(one,quotient(X,j(X2)))) = product(X2,product(X,X2)),
inference(transitivity,[status(thm)],[c927,c929]) ).
cnf(c931,plain,
difference(j(X2),quotient(X,j(X2))) = product(X2,product(X,X2)),
inference(transitivity,[status(thm)],[c924,c930]) ).
cnf(c932,plain,
difference(j(X2),quotient(difference(X,eta(j(X2))),j(X2))) = product(X2,product(difference(X,eta(j(X2))),X2)),
inference(substitution,[status(thm)],[c931]) ).
cnf(c933,plain,
difference(X,eta(j(X2))) = difference(X,eta(X2)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c934,plain,
product(difference(X,eta(j(X2))),X2) = product(difference(X,eta(X2)),X2),
inference(congruence,[status(thm)],[c933]) ).
cnf(c935,plain,
product(X2,product(difference(X,eta(j(X2))),X2)) = product(X2,product(difference(X,eta(X2)),X2)),
inference(congruence,[status(thm)],[c934]) ).
cnf(c936,plain,
product(difference(X,eta(X2)),X2) = i(difference(X2,X)),
inference(substitution,[status(thm)],[c143]) ).
cnf(c937,plain,
product(X2,product(difference(X,eta(X2)),X2)) = product(X2,i(difference(X2,X))),
inference(congruence,[status(thm)],[c936]) ).
cnf(c938,plain,
product(X2,product(difference(X,eta(j(X2))),X2)) = product(X2,i(difference(X2,X))),
inference(transitivity,[status(thm)],[c935,c937]) ).
cnf(c939,plain,
difference(j(X2),quotient(difference(X,eta(j(X2))),j(X2))) = product(X2,i(difference(X2,X))),
inference(transitivity,[status(thm)],[c932,c938]) ).
cnf(c940,plain,
difference(j(X2),i(product(j(X2),X))) = product(X2,i(difference(X2,X))),
inference(transitivity,[status(thm)],[c921,c939]) ).
cnf(c941,plain,
difference(j(i(X2)),i(product(j(i(X2)),X))) = product(i(X2),i(difference(i(X2),X))),
inference(substitution,[status(thm)],[c940]) ).
cnf(c942,plain,
product(i(X2),i(difference(i(X2),X))) = difference(j(i(X2)),i(product(j(i(X2)),X))),
inference(symmetry,[status(thm)],[c941]) ).
cnf(c943,plain,
difference(j(i(X2)),i(product(j(i(X2)),X))) = difference(X2,i(product(j(i(X2)),X))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c944,plain,
product(j(i(X2)),X) = product(X2,X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c945,plain,
i(product(j(i(X2)),X)) = i(product(X2,X)),
inference(congruence,[status(thm)],[c944]) ).
cnf(c946,plain,
difference(X2,i(product(j(i(X2)),X))) = difference(X2,i(product(X2,X))),
inference(congruence,[status(thm)],[c945]) ).
cnf(c947,plain,
difference(j(i(X2)),i(product(j(i(X2)),X))) = difference(X2,i(product(X2,X))),
inference(transitivity,[status(thm)],[c943,c946]) ).
cnf(c948,plain,
product(i(X2),i(difference(i(X2),X))) = difference(X2,i(product(X2,X))),
inference(transitivity,[status(thm)],[c942,c947]) ).
cnf(c949,plain,
product(i(X2),i(difference(i(X2),difference(X2,quotient(X,X2))))) = difference(X2,i(product(X2,difference(X2,quotient(X,X2))))),
inference(substitution,[status(thm)],[c948]) ).
cnf(c950,plain,
product(X2,difference(X2,quotient(X,X2))) = quotient(X,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c951,plain,
i(product(X2,difference(X2,quotient(X,X2)))) = i(quotient(X,X2)),
inference(congruence,[status(thm)],[c950]) ).
cnf(c952,plain,
difference(X2,i(product(X2,difference(X2,quotient(X,X2))))) = difference(X2,i(quotient(X,X2))),
inference(congruence,[status(thm)],[c951]) ).
cnf(c953,plain,
product(i(X2),i(difference(i(X2),difference(X2,quotient(X,X2))))) = difference(X2,i(quotient(X,X2))),
inference(transitivity,[status(thm)],[c949,c952]) ).
cnf(c954,plain,
product(i(X2),i(product(X,i(X2)))) = difference(X2,i(quotient(X,X2))),
inference(transitivity,[status(thm)],[c918,c953]) ).
cnf(c955,plain,
product(i(X),i(product(X2,i(X)))) = difference(X,i(quotient(X2,X))),
inference(substitution,[status(thm)],[c954]) ).
cnf(c956,plain,
product(product(i(X),i(product(X2,i(X)))),X2) = product(difference(X,i(quotient(X2,X))),X2),
inference(congruence,[status(thm)],[c955]) ).
cnf(c957,plain,
quotient(product(product(i(X),i(product(X2,i(X)))),X2),X) = quotient(product(difference(X,i(quotient(X2,X))),X2),X),
inference(congruence,[status(thm)],[c956]) ).
cnf(c958,plain,
difference(X3,product(product(X3,difference(X3,X2)),quotient(X,X3))) = quotient(product(difference(X3,X2),X),X3),
inference(substitution,[status(thm)],[c445]) ).
cnf(c959,plain,
quotient(product(difference(X3,X2),X),X3) = difference(X3,product(product(X3,difference(X3,X2)),quotient(X,X3))),
inference(symmetry,[status(thm)],[c958]) ).
cnf(c960,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c961,plain,
product(product(X3,difference(X3,X2)),quotient(X,X3)) = product(X2,quotient(X,X3)),
inference(congruence,[status(thm)],[c960]) ).
cnf(c962,plain,
difference(X3,product(product(X3,difference(X3,X2)),quotient(X,X3))) = difference(X3,product(X2,quotient(X,X3))),
inference(congruence,[status(thm)],[c961]) ).
cnf(c963,plain,
quotient(product(difference(X3,X2),X),X3) = difference(X3,product(X2,quotient(X,X3))),
inference(transitivity,[status(thm)],[c959,c962]) ).
cnf(c964,plain,
quotient(product(difference(X,i(quotient(X2,X))),X2),X) = difference(X,product(i(quotient(X2,X)),quotient(X2,X))),
inference(substitution,[status(thm)],[c963]) ).
cnf(c965,plain,
eta(quotient(X2,X)) = product(i(quotient(X2,X)),quotient(X2,X)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c966,plain,
product(i(quotient(X2,X)),quotient(X2,X)) = eta(quotient(X2,X)),
inference(symmetry,[status(thm)],[c965]) ).
cnf(c967,plain,
difference(X,product(i(quotient(X2,X)),quotient(X2,X))) = difference(X,eta(quotient(X2,X))),
inference(congruence,[status(thm)],[c966]) ).
cnf(c968,plain,
difference(X,eta(quotient(X2,X))) = product(i(X2),quotient(X2,X)),
inference(substitution,[status(thm)],[c365]) ).
cnf(c969,plain,
difference(X,product(i(quotient(X2,X)),quotient(X2,X))) = product(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c967,c968]) ).
cnf(c970,plain,
quotient(product(difference(X,i(quotient(X2,X))),X2),X) = product(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c964,c969]) ).
cnf(c971,plain,
quotient(product(product(i(X),i(product(X2,i(X)))),X2),X) = product(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c957,c970]) ).
cnf(c972,plain,
difference(X,quotient(difference(i(X),product(product(i(X),i(product(X2,i(X)))),X2)),X)) = product(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c906,c971]) ).
cnf(c973,plain,
difference(X,quotient(quotient(eta(product(X2,i(X))),i(X)),X)) = product(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c892,c972]) ).
cnf(c974,plain,
product(i(X),eta(product(X2,i(X)))) = product(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c883,c973]) ).
cnf(c975,plain,
product(i(X2),eta(product(X,i(X2)))) = product(i(X),quotient(X,X2)),
inference(substitution,[status(thm)],[c974]) ).
cnf(c976,plain,
product(quotient(quotient(X2,X),X2),X2) = quotient(X2,X),
inference(substitution,[status(thm)],[c38]) ).
cnf(c977,plain,
quotient(X2,X) = product(quotient(quotient(X2,X),X2),X2),
inference(symmetry,[status(thm)],[c976]) ).
cnf(c978,plain,
product(i(X2),quotient(X2,X)) = product(i(X2),product(quotient(quotient(X2,X),X2),X2)),
inference(congruence,[status(thm)],[c977]) ).
cnf(c979,plain,
product(difference(X2,quotient(quotient(X2,X),X2)),X2) = product(i(X2),product(quotient(quotient(X2,X),X2),X2)),
inference(substitution,[status(thm)],[c322]) ).
cnf(c980,plain,
product(i(X2),product(quotient(quotient(X2,X),X2),X2)) = product(difference(X2,quotient(quotient(X2,X),X2)),X2),
inference(symmetry,[status(thm)],[c979]) ).
cnf(c981,plain,
eta(quotient(X2,X)) = eta(quotient(X,i(X2))),
inference(substitution,[status(thm)],[c553]) ).
cnf(c982,plain,
difference(X,eta(quotient(X2,X))) = difference(X,eta(quotient(X,i(X2)))),
inference(congruence,[status(thm)],[c981]) ).
cnf(c983,plain,
difference(X2,eta(quotient(j(X),X2))) = product(i(j(X)),quotient(j(X),X2)),
inference(substitution,[status(thm)],[c365]) ).
cnf(c984,plain,
product(i(j(X)),quotient(j(X),X2)) = product(X,quotient(j(X),X2)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c985,plain,
difference(X2,eta(quotient(j(X),X2))) = product(X,quotient(j(X),X2)),
inference(transitivity,[status(thm)],[c983,c984]) ).
cnf(c986,plain,
difference(X,eta(quotient(j(X2),X))) = product(X2,quotient(j(X2),X)),
inference(substitution,[status(thm)],[c985]) ).
cnf(c987,plain,
product(X2,quotient(j(X2),X)) = difference(X,eta(quotient(j(X2),X))),
inference(symmetry,[status(thm)],[c986]) ).
cnf(c988,plain,
eta(quotient(j(X2),X)) = eta(quotient(X,i(j(X2)))),
inference(substitution,[status(thm)],[c553]) ).
cnf(c989,plain,
difference(X,eta(quotient(j(X2),X))) = difference(X,eta(quotient(X,i(j(X2))))),
inference(congruence,[status(thm)],[c988]) ).
cnf(c990,plain,
quotient(X,i(j(X2))) = quotient(X,X2),
inference(congruence,[status(thm)],[c46]) ).
cnf(c991,plain,
eta(quotient(X,i(j(X2)))) = eta(quotient(X,X2)),
inference(congruence,[status(thm)],[c990]) ).
cnf(c992,plain,
difference(X,eta(quotient(X,i(j(X2))))) = difference(X,eta(quotient(X,X2))),
inference(congruence,[status(thm)],[c991]) ).
cnf(c993,plain,
difference(X,eta(quotient(j(X2),X))) = difference(X,eta(quotient(X,X2))),
inference(transitivity,[status(thm)],[c989,c992]) ).
cnf(c994,plain,
product(X2,quotient(j(X2),X)) = difference(X,eta(quotient(X,X2))),
inference(transitivity,[status(thm)],[c987,c993]) ).
cnf(c995,plain,
product(i(X2),quotient(j(i(X2)),X)) = difference(X,eta(quotient(X,i(X2)))),
inference(substitution,[status(thm)],[c994]) ).
cnf(c996,plain,
difference(X,eta(quotient(X,i(X2)))) = product(i(X2),quotient(j(i(X2)),X)),
inference(symmetry,[status(thm)],[c995]) ).
cnf(c997,plain,
product(X2,quotient(j(X2),X)) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c994,c289]) ).
cnf(c998,plain,
product(i(X2),quotient(j(i(X2)),X)) = quotient(i(i(X2)),quotient(X,i(X2))),
inference(substitution,[status(thm)],[c997]) ).
cnf(c999,plain,
difference(X,eta(quotient(X,i(X2)))) = quotient(i(i(X2)),quotient(X,i(X2))),
inference(transitivity,[status(thm)],[c996,c998]) ).
cnf(c1000,plain,
difference(X,eta(quotient(X2,X))) = quotient(i(i(X2)),quotient(X,i(X2))),
inference(transitivity,[status(thm)],[c982,c999]) ).
cnf(c1001,plain,
quotient(i(i(X2)),quotient(X,i(X2))) = difference(X,eta(quotient(X2,X))),
inference(symmetry,[status(thm)],[c1000]) ).
cnf(c1002,plain,
quotient(quotient(i(i(X2)),quotient(X,i(X2))),X2) = quotient(difference(X,eta(quotient(X2,X))),X2),
inference(congruence,[status(thm)],[c1001]) ).
cnf(c1003,plain,
difference(X,eta(quotient(X2,X))) = product(i(X2),quotient(X2,X)),
inference(substitution,[status(thm)],[c365]) ).
cnf(c1004,plain,
quotient(difference(X,eta(quotient(X2,X))),X2) = quotient(product(i(X2),quotient(X2,X)),X2),
inference(congruence,[status(thm)],[c1003]) ).
cnf(c1005,plain,
quotient(product(i(X2),quotient(X2,X)),X2) = difference(X2,quotient(quotient(X2,X),X2)),
inference(substitution,[status(thm)],[c900]) ).
cnf(c1006,plain,
quotient(difference(X,eta(quotient(X2,X))),X2) = difference(X2,quotient(quotient(X2,X),X2)),
inference(transitivity,[status(thm)],[c1004,c1005]) ).
cnf(c1007,plain,
quotient(quotient(i(i(X2)),quotient(X,i(X2))),X2) = difference(X2,quotient(quotient(X2,X),X2)),
inference(transitivity,[status(thm)],[c1002,c1006]) ).
cnf(c1008,plain,
difference(X2,quotient(quotient(X2,X),X2)) = quotient(quotient(i(i(X2)),quotient(X,i(X2))),X2),
inference(symmetry,[status(thm)],[c1007]) ).
cnf(c1009,plain,
product(difference(X2,quotient(quotient(X2,X),X2)),X2) = product(quotient(quotient(i(i(X2)),quotient(X,i(X2))),X2),X2),
inference(congruence,[status(thm)],[c1008]) ).
cnf(c1010,plain,
product(quotient(quotient(i(i(X2)),quotient(X,i(X2))),X2),X2) = quotient(i(i(X2)),quotient(X,i(X2))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c1011,plain,
product(difference(X2,quotient(quotient(X2,X),X2)),X2) = quotient(i(i(X2)),quotient(X,i(X2))),
inference(transitivity,[status(thm)],[c1009,c1010]) ).
cnf(c1012,plain,
product(i(X2),product(quotient(quotient(X2,X),X2),X2)) = quotient(i(i(X2)),quotient(X,i(X2))),
inference(transitivity,[status(thm)],[c980,c1011]) ).
cnf(c1013,plain,
product(i(X2),quotient(X2,X)) = quotient(i(i(X2)),quotient(X,i(X2))),
inference(transitivity,[status(thm)],[c978,c1012]) ).
cnf(c1014,plain,
product(i(X),quotient(X,X2)) = quotient(i(i(X)),quotient(X2,i(X))),
inference(substitution,[status(thm)],[c1013]) ).
cnf(c1015,plain,
product(i(X2),eta(product(X,i(X2)))) = quotient(i(i(X)),quotient(X2,i(X))),
inference(transitivity,[status(thm)],[c975,c1014]) ).
cnf(c1016,plain,
product(i(X2),eta(quotient(i(X2),i(i(X))))) = quotient(i(i(X)),quotient(X2,i(X))),
inference(transitivity,[status(thm)],[c877,c1015]) ).
cnf(c1017,plain,
product(i(X2),eta(quotient(X2,i(X)))) = quotient(i(i(X)),quotient(X2,i(X))),
inference(transitivity,[status(thm)],[c561,c1016]) ).
cnf(c1018,plain,
product(i(difference(X2,j(i(X)))),eta(quotient(difference(X2,j(i(X))),i(X)))) = quotient(i(i(X)),quotient(difference(X2,j(i(X))),i(X))),
inference(substitution,[status(thm)],[c1017]) ).
cnf(c1019,plain,
quotient(difference(X2,j(i(X))),i(X)) = difference(product(i(X),X2),i(i(X))),
inference(substitution,[status(thm)],[c281]) ).
cnf(c1020,plain,
quotient(i(i(X)),quotient(difference(X2,j(i(X))),i(X))) = quotient(i(i(X)),difference(product(i(X),X2),i(i(X)))),
inference(congruence,[status(thm)],[c1019]) ).
cnf(c1021,plain,
quotient(i(i(X)),difference(product(i(X),X2),i(i(X)))) = product(i(X),X2),
inference(substitution,[status(thm)],[c86]) ).
cnf(c1022,plain,
quotient(i(i(X)),quotient(difference(X2,j(i(X))),i(X))) = product(i(X),X2),
inference(transitivity,[status(thm)],[c1020,c1021]) ).
cnf(c1023,plain,
product(i(difference(X2,j(i(X)))),eta(quotient(difference(X2,j(i(X))),i(X)))) = product(i(X),X2),
inference(transitivity,[status(thm)],[c1018,c1022]) ).
cnf(c1024,plain,
product(i(difference(X2,j(i(X)))),eta(difference(product(i(X),X2),i(i(X))))) = product(i(X),X2),
inference(transitivity,[status(thm)],[c350,c1023]) ).
cnf(c1025,plain,
product(i(difference(X2,X)),eta(difference(product(i(X),X2),i(i(X))))) = product(i(X),X2),
inference(transitivity,[status(thm)],[c346,c1024]) ).
cnf(c1026,plain,
product(i(difference(X2,X)),eta(X2)) = product(i(X),X2),
inference(transitivity,[status(thm)],[c342,c1025]) ).
cnf(c1027,plain,
product(i(difference(X,product(X,X2))),eta(X)) = product(i(product(X,X2)),X),
inference(substitution,[status(thm)],[c1026]) ).
cnf(c1028,plain,
product(i(product(X,X2)),X) = difference(X2,eta(X)),
inference(substitution,[status(thm)],[c359]) ).
cnf(c1029,plain,
product(i(difference(X,product(X,X2))),eta(X)) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c1027,c1028]) ).
cnf(c1030,plain,
product(i(X2),eta(X)) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c104,c1029]) ).
cnf(c1031,plain,
product(i(j(X2)),eta(X)) = difference(j(X2),eta(X)),
inference(substitution,[status(thm)],[c1030]) ).
cnf(c1032,plain,
difference(j(X2),eta(X)) = product(i(j(X2)),eta(X)),
inference(symmetry,[status(thm)],[c1031]) ).
cnf(c1033,plain,
product(i(j(X2)),eta(X)) = product(X2,eta(X)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1034,plain,
difference(j(X2),eta(X)) = product(X2,eta(X)),
inference(transitivity,[status(thm)],[c1032,c1033]) ).
cnf(c1035,plain,
product(X2,eta(X)) = difference(j(X2),eta(X)),
inference(symmetry,[status(thm)],[c1034]) ).
cnf(c1036,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1037,plain,
difference(j(X2),eta(X)) = difference(quotient(one,X2),eta(X)),
inference(congruence,[status(thm)],[c1036]) ).
cnf(c1038,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c1039,plain,
quotient(one,X2) = quotient(eta(eta(X)),X2),
inference(congruence,[status(thm)],[c1038]) ).
cnf(c1040,plain,
difference(quotient(one,X2),eta(X)) = difference(quotient(eta(eta(X)),X2),eta(X)),
inference(congruence,[status(thm)],[c1039]) ).
cnf(c1041,plain,
eta(i(eta(X))) = eta(eta(X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c1042,plain,
eta(eta(X)) = eta(i(eta(X))),
inference(symmetry,[status(thm)],[c1041]) ).
cnf(c1043,plain,
quotient(eta(eta(X)),X2) = quotient(eta(i(eta(X))),X2),
inference(congruence,[status(thm)],[c1042]) ).
cnf(c1044,plain,
difference(quotient(eta(eta(X)),X2),eta(X)) = difference(quotient(eta(i(eta(X))),X2),eta(X)),
inference(congruence,[status(thm)],[c1043]) ).
cnf(c1045,plain,
j(quotient(X,X2)) = product(X2,quotient(eta(X2),X)),
inference(symmetry,[status(thm)],[c582]) ).
cnf(c1046,plain,
difference(X2,j(quotient(X,X2))) = difference(X2,product(X2,quotient(eta(X2),X))),
inference(congruence,[status(thm)],[c1045]) ).
cnf(c1047,plain,
difference(X2,product(X2,quotient(eta(X2),X))) = quotient(eta(X2),X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c1048,plain,
difference(X2,j(quotient(X,X2))) = quotient(eta(X2),X),
inference(transitivity,[status(thm)],[c1046,c1047]) ).
cnf(c1049,plain,
difference(i(eta(X)),j(quotient(X2,i(eta(X))))) = quotient(eta(i(eta(X))),X2),
inference(substitution,[status(thm)],[c1048]) ).
cnf(c1050,plain,
quotient(eta(i(eta(X))),X2) = difference(i(eta(X)),j(quotient(X2,i(eta(X))))),
inference(symmetry,[status(thm)],[c1049]) ).
cnf(c1051,plain,
difference(quotient(eta(i(eta(X))),X2),eta(X)) = difference(difference(i(eta(X)),j(quotient(X2,i(eta(X))))),eta(X)),
inference(congruence,[status(thm)],[c1050]) ).
cnf(c1052,plain,
eta(X) = i(i(eta(X))),
inference(symmetry,[status(thm)],[c726]) ).
cnf(c1053,plain,
difference(difference(i(eta(X2)),X),eta(X2)) = difference(difference(i(eta(X2)),X),i(i(eta(X2)))),
inference(congruence,[status(thm)],[c1052]) ).
cnf(c1054,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c1055,plain,
difference(X2,X) = difference(X2,j(i(X))),
inference(congruence,[status(thm)],[c1054]) ).
cnf(c1056,plain,
product(difference(X2,X),i(X)) = product(difference(X2,j(i(X))),i(X)),
inference(congruence,[status(thm)],[c1055]) ).
cnf(c1057,plain,
product(one,j(X)) = j(X),
inference(substitution,[status(thm)],[c185]) ).
cnf(c1058,plain,
j(X) = product(one,j(X)),
inference(symmetry,[status(thm)],[c1057]) ).
cnf(c1059,plain,
difference(X,j(X)) = difference(X,product(one,j(X))),
inference(congruence,[status(thm)],[c1058]) ).
cnf(c1060,plain,
one = product(X,i(X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c1061,plain,
product(one,j(X)) = product(product(X,i(X)),j(X)),
inference(congruence,[status(thm)],[c1060]) ).
cnf(c1062,plain,
difference(X,product(one,j(X))) = difference(X,product(product(X,i(X)),j(X))),
inference(congruence,[status(thm)],[c1061]) ).
cnf(c1063,plain,
difference(X,product(product(X,i(X)),j(X))) = quotient(i(X),X),
inference(substitution,[status(thm)],[c418]) ).
cnf(c1064,plain,
quotient(difference(X,X),X) = difference(product(X,X),X),
inference(substitution,[status(thm)],[c233]) ).
cnf(c1065,plain,
difference(product(X,X),X) = quotient(difference(X,X),X),
inference(symmetry,[status(thm)],[c1064]) ).
cnf(c1066,plain,
quotient(difference(X,X),X) = quotient(one,X),
inference(congruence,[status(thm)],[c166]) ).
cnf(c1067,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1068,plain,
quotient(one,X) = j(X),
inference(symmetry,[status(thm)],[c1067]) ).
cnf(c1069,plain,
quotient(difference(X,X),X) = j(X),
inference(transitivity,[status(thm)],[c1066,c1068]) ).
cnf(c1070,plain,
difference(product(X,X),X) = j(X),
inference(transitivity,[status(thm)],[c1065,c1069]) ).
cnf(c1071,plain,
j(X) = difference(product(X,X),X),
inference(symmetry,[status(thm)],[c1070]) ).
cnf(c1072,plain,
quotient(X,j(X)) = quotient(X,difference(product(X,X),X)),
inference(congruence,[status(thm)],[c1071]) ).
cnf(c1073,plain,
quotient(X,difference(product(X,X),X)) = product(X,X),
inference(substitution,[status(thm)],[c86]) ).
cnf(c1074,plain,
quotient(X,j(X)) = product(X,X),
inference(transitivity,[status(thm)],[c1072,c1073]) ).
cnf(c1075,plain,
quotient(i(X),j(i(X))) = product(i(X),i(X)),
inference(substitution,[status(thm)],[c1074]) ).
cnf(c1076,plain,
product(i(X),i(X)) = quotient(i(X),j(i(X))),
inference(symmetry,[status(thm)],[c1075]) ).
cnf(c1077,plain,
quotient(i(X),j(i(X))) = quotient(i(X),X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c1078,plain,
product(i(X),i(X)) = quotient(i(X),X),
inference(transitivity,[status(thm)],[c1076,c1077]) ).
cnf(c1079,plain,
quotient(i(X),X) = product(i(X),i(X)),
inference(symmetry,[status(thm)],[c1078]) ).
cnf(c1080,plain,
product(i(X),i(X)) = difference(i(i(X)),i(X)),
inference(substitution,[status(thm)],[c256]) ).
cnf(c1081,plain,
quotient(i(X),X) = difference(i(i(X)),i(X)),
inference(transitivity,[status(thm)],[c1079,c1080]) ).
cnf(c1082,plain,
difference(X,product(product(X,i(X)),j(X))) = difference(i(i(X)),i(X)),
inference(transitivity,[status(thm)],[c1063,c1081]) ).
cnf(c1083,plain,
difference(X,product(one,j(X))) = difference(i(i(X)),i(X)),
inference(transitivity,[status(thm)],[c1062,c1082]) ).
cnf(c1084,plain,
difference(X,j(X)) = difference(i(i(X)),i(X)),
inference(transitivity,[status(thm)],[c1059,c1083]) ).
cnf(c1085,plain,
difference(i(i(X)),i(X)) = difference(X,j(X)),
inference(symmetry,[status(thm)],[c1084]) ).
cnf(c1086,plain,
product(X,difference(i(i(X)),i(X))) = product(X,difference(X,j(X))),
inference(congruence,[status(thm)],[c1085]) ).
cnf(c1087,plain,
product(X,difference(X,j(X))) = j(X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1088,plain,
product(X,difference(i(i(X)),i(X))) = j(X),
inference(transitivity,[status(thm)],[c1086,c1087]) ).
cnf(c1089,plain,
j(X) = product(X,difference(i(i(X)),i(X))),
inference(symmetry,[status(thm)],[c1088]) ).
cnf(c1090,plain,
difference(X2,j(X)) = difference(X2,product(X,difference(i(i(X)),i(X)))),
inference(congruence,[status(thm)],[c1089]) ).
cnf(c1091,plain,
product(difference(X2,j(X)),X) = product(difference(X2,product(X,difference(i(i(X)),i(X)))),X),
inference(congruence,[status(thm)],[c1090]) ).
cnf(c1092,plain,
product(X,difference(X,X2)) = X2,
inference(substitution,[status(thm)],[c7]) ).
cnf(c1093,plain,
X2 = product(X,difference(X,X2)),
inference(symmetry,[status(thm)],[c1092]) ).
cnf(c1094,plain,
difference(X3,product(X2,X)) = difference(product(X2,difference(X2,X3)),product(X2,X)),
inference(congruence,[status(thm)],[c1093]) ).
cnf(c1095,plain,
product(difference(X3,product(X2,X)),X2) = product(difference(product(X2,difference(X2,X3)),product(X2,X)),X2),
inference(congruence,[status(thm)],[c1094]) ).
cnf(c1096,plain,
product(difference(product(X2,difference(X2,X3)),product(X2,X)),X2) = difference(difference(X2,X3),product(X,X2)),
inference(substitution,[status(thm)],[c619]) ).
cnf(c1097,plain,
product(difference(X3,product(X2,X)),X2) = difference(difference(X2,X3),product(X,X2)),
inference(transitivity,[status(thm)],[c1095,c1096]) ).
cnf(c1098,plain,
product(difference(X2,product(X,difference(i(i(X)),i(X)))),X) = difference(difference(X,X2),product(difference(i(i(X)),i(X)),X)),
inference(substitution,[status(thm)],[c1097]) ).
cnf(c1099,plain,
product(i(X),i(X)) = difference(i(i(X)),i(X)),
inference(substitution,[status(thm)],[c256]) ).
cnf(c1100,plain,
difference(i(i(X)),i(X)) = product(i(X),i(X)),
inference(symmetry,[status(thm)],[c1099]) ).
cnf(c1101,plain,
product(difference(i(i(X)),i(X)),X) = product(product(i(X),i(X)),X),
inference(congruence,[status(thm)],[c1100]) ).
cnf(c1102,plain,
product(product(i(X),i(X)),X) = product(i(X),quotient(i(X),i(X))),
inference(substitution,[status(thm)],[c634]) ).
cnf(c1103,plain,
quotient(X2,difference(product(X2,quotient(X2,X)),X2)) = product(X2,quotient(X2,X)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c1104,plain,
product(X2,quotient(X2,X)) = quotient(X2,difference(product(X2,quotient(X2,X)),X2)),
inference(symmetry,[status(thm)],[c1103]) ).
cnf(c1105,plain,
quotient(difference(quotient(X2,X),X2),X2) = difference(product(X2,quotient(X2,X)),X2),
inference(substitution,[status(thm)],[c233]) ).
cnf(c1106,plain,
difference(product(X2,quotient(X2,X)),X2) = quotient(difference(quotient(X2,X),X2),X2),
inference(symmetry,[status(thm)],[c1105]) ).
cnf(c1107,plain,
quotient(difference(quotient(X2,X),X2),X2) = quotient(X,X2),
inference(congruence,[status(thm)],[c209]) ).
cnf(c1108,plain,
difference(product(X2,quotient(X2,X)),X2) = quotient(X,X2),
inference(transitivity,[status(thm)],[c1106,c1107]) ).
cnf(c1109,plain,
quotient(X2,difference(product(X2,quotient(X2,X)),X2)) = quotient(X2,quotient(X,X2)),
inference(congruence,[status(thm)],[c1108]) ).
cnf(c1110,plain,
product(X2,quotient(X2,X)) = quotient(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c1104,c1109]) ).
cnf(c1111,plain,
product(i(X),quotient(i(X),i(X))) = quotient(i(X),quotient(i(X),i(X))),
inference(substitution,[status(thm)],[c1110]) ).
cnf(c1112,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c185]) ).
cnf(c1113,plain,
X = product(one,X),
inference(symmetry,[status(thm)],[c1112]) ).
cnf(c1114,plain,
quotient(X,X) = quotient(product(one,X),X),
inference(congruence,[status(thm)],[c1113]) ).
cnf(c1115,plain,
quotient(product(one,X),X) = one,
inference(substitution,[status(thm)],[c12]) ).
cnf(c1116,plain,
quotient(X,X) = one,
inference(transitivity,[status(thm)],[c1114,c1115]) ).
cnf(c1117,plain,
quotient(i(X),i(X)) = one,
inference(substitution,[status(thm)],[c1116]) ).
cnf(c1118,plain,
quotient(i(X),quotient(i(X),i(X))) = quotient(i(X),one),
inference(congruence,[status(thm)],[c1117]) ).
cnf(c1119,plain,
product(X,one) = X,
inference(substitution,[status(thm)],[c161]) ).
cnf(c1120,plain,
X = product(X,one),
inference(symmetry,[status(thm)],[c1119]) ).
cnf(c1121,plain,
quotient(X,one) = quotient(product(X,one),one),
inference(congruence,[status(thm)],[c1120]) ).
cnf(c1122,plain,
quotient(product(X,one),one) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c1123,plain,
quotient(X,one) = X,
inference(transitivity,[status(thm)],[c1121,c1122]) ).
cnf(c1124,plain,
quotient(i(X),one) = i(X),
inference(substitution,[status(thm)],[c1123]) ).
cnf(c1125,plain,
quotient(i(X),quotient(i(X),i(X))) = i(X),
inference(transitivity,[status(thm)],[c1118,c1124]) ).
cnf(c1126,plain,
product(i(X),quotient(i(X),i(X))) = i(X),
inference(transitivity,[status(thm)],[c1111,c1125]) ).
cnf(c1127,plain,
product(product(i(X),i(X)),X) = i(X),
inference(transitivity,[status(thm)],[c1102,c1126]) ).
cnf(c1128,plain,
product(difference(i(i(X)),i(X)),X) = i(X),
inference(transitivity,[status(thm)],[c1101,c1127]) ).
cnf(c1129,plain,
difference(difference(X,X2),product(difference(i(i(X)),i(X)),X)) = difference(difference(X,X2),i(X)),
inference(congruence,[status(thm)],[c1128]) ).
cnf(c1130,plain,
product(difference(X2,product(X,difference(i(i(X)),i(X)))),X) = difference(difference(X,X2),i(X)),
inference(transitivity,[status(thm)],[c1098,c1129]) ).
cnf(c1131,plain,
product(difference(X2,j(X)),X) = difference(difference(X,X2),i(X)),
inference(transitivity,[status(thm)],[c1091,c1130]) ).
cnf(c1132,plain,
product(difference(X2,j(i(X))),i(X)) = difference(difference(i(X),X2),i(i(X))),
inference(substitution,[status(thm)],[c1131]) ).
cnf(c1133,plain,
product(difference(X2,X),i(X)) = difference(difference(i(X),X2),i(i(X))),
inference(transitivity,[status(thm)],[c1056,c1132]) ).
cnf(c1134,plain,
product(difference(X,eta(X2)),i(eta(X2))) = difference(difference(i(eta(X2)),X),i(i(eta(X2)))),
inference(substitution,[status(thm)],[c1133]) ).
cnf(c1135,plain,
difference(difference(i(eta(X2)),X),i(i(eta(X2)))) = product(difference(X,eta(X2)),i(eta(X2))),
inference(symmetry,[status(thm)],[c1134]) ).
cnf(c1136,plain,
eta(difference(i(X2),i(X))) = eta(difference(X,i(X2))),
inference(substitution,[status(thm)],[c593]) ).
cnf(c1137,plain,
eta(difference(i(X2),i(X))) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1136,c593]) ).
cnf(c1138,plain,
eta(difference(i(X),i(X2))) = eta(difference(X,X2)),
inference(substitution,[status(thm)],[c1137]) ).
cnf(c1139,plain,
eta(difference(X,X2)) = eta(difference(i(X),i(X2))),
inference(symmetry,[status(thm)],[c1138]) ).
cnf(c1140,plain,
eta(difference(i(X),i(X2))) = eta(difference(X2,i(X))),
inference(substitution,[status(thm)],[c593]) ).
cnf(c1141,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1142,plain,
i(X) = i(i(j(X))),
inference(congruence,[status(thm)],[c1141]) ).
cnf(c1143,plain,
difference(X2,i(X)) = difference(X2,i(i(j(X)))),
inference(congruence,[status(thm)],[c1142]) ).
cnf(c1144,plain,
eta(difference(X2,i(X))) = eta(difference(X2,i(i(j(X))))),
inference(congruence,[status(thm)],[c1143]) ).
cnf(c1145,plain,
eta(product(X,X2)) = eta(quotient(X2,i(i(X)))),
inference(substitution,[status(thm)],[c874]) ).
cnf(c1146,plain,
eta(quotient(X2,i(i(X)))) = eta(product(X,X2)),
inference(symmetry,[status(thm)],[c1145]) ).
cnf(c1147,plain,
quotient(X,difference(eta(product(X,X2)),X)) = eta(product(X,X2)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c1148,plain,
eta(product(X,X2)) = quotient(X,difference(eta(product(X,X2)),X)),
inference(symmetry,[status(thm)],[c1147]) ).
cnf(c1149,plain,
j(difference(X2,eta(X))) = quotient(one,difference(X2,eta(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1150,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c1151,plain,
quotient(one,difference(X2,eta(X))) = quotient(eta(eta(X)),difference(X2,eta(X))),
inference(congruence,[status(thm)],[c1150]) ).
cnf(c1152,plain,
difference(X2,eta(X)) = product(i(X2),eta(X)),
inference(symmetry,[status(thm)],[c1030]) ).
cnf(c1153,plain,
quotient(eta(eta(X)),difference(X2,eta(X))) = quotient(eta(eta(X)),product(i(X2),eta(X))),
inference(congruence,[status(thm)],[c1152]) ).
cnf(c1154,plain,
difference(X2,j(quotient(product(X,X2),X2))) = quotient(eta(X2),product(X,X2)),
inference(substitution,[status(thm)],[c1048]) ).
cnf(c1155,plain,
quotient(eta(X2),product(X,X2)) = difference(X2,j(quotient(product(X,X2),X2))),
inference(symmetry,[status(thm)],[c1154]) ).
cnf(c1156,plain,
quotient(product(X,X2),X2) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c1157,plain,
j(quotient(product(X,X2),X2)) = j(X),
inference(congruence,[status(thm)],[c1156]) ).
cnf(c1158,plain,
difference(X2,j(quotient(product(X,X2),X2))) = difference(X2,j(X)),
inference(congruence,[status(thm)],[c1157]) ).
cnf(c1159,plain,
quotient(eta(X2),product(X,X2)) = difference(X2,j(X)),
inference(transitivity,[status(thm)],[c1155,c1158]) ).
cnf(c1160,plain,
quotient(eta(eta(X)),product(i(X2),eta(X))) = difference(eta(X),j(i(X2))),
inference(substitution,[status(thm)],[c1159]) ).
cnf(c1161,plain,
quotient(eta(eta(X2)),product(X,eta(X2))) = difference(eta(X2),j(X)),
inference(substitution,[status(thm)],[c1159]) ).
cnf(c1162,plain,
difference(eta(X2),j(X)) = quotient(eta(eta(X2)),product(X,eta(X2))),
inference(symmetry,[status(thm)],[c1161]) ).
cnf(c1163,plain,
quotient(eta(eta(X2)),product(X,eta(X2))) = quotient(one,product(X,eta(X2))),
inference(congruence,[status(thm)],[c507]) ).
cnf(c1164,plain,
j(product(X,eta(X2))) = quotient(one,product(X,eta(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1165,plain,
quotient(one,product(X,eta(X2))) = j(product(X,eta(X2))),
inference(symmetry,[status(thm)],[c1164]) ).
cnf(c1166,plain,
quotient(eta(eta(X2)),product(X,eta(X2))) = j(product(X,eta(X2))),
inference(transitivity,[status(thm)],[c1163,c1165]) ).
cnf(c1167,plain,
difference(eta(X2),j(X)) = j(product(X,eta(X2))),
inference(transitivity,[status(thm)],[c1162,c1166]) ).
cnf(c1168,plain,
difference(eta(X),j(i(X2))) = j(product(i(X2),eta(X))),
inference(substitution,[status(thm)],[c1167]) ).
cnf(c1169,plain,
i(difference(eta(X),X2)) = product(i(X2),eta(X)),
inference(substitution,[status(thm)],[c836]) ).
cnf(c1170,plain,
product(i(X2),eta(X)) = i(difference(eta(X),X2)),
inference(symmetry,[status(thm)],[c1169]) ).
cnf(c1171,plain,
j(product(i(X2),eta(X))) = j(i(difference(eta(X),X2))),
inference(congruence,[status(thm)],[c1170]) ).
cnf(c1172,plain,
j(i(difference(eta(X),X2))) = difference(eta(X),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c1173,plain,
j(product(i(X2),eta(X))) = difference(eta(X),X2),
inference(transitivity,[status(thm)],[c1171,c1172]) ).
cnf(c1174,plain,
difference(eta(X),j(i(X2))) = difference(eta(X),X2),
inference(transitivity,[status(thm)],[c1168,c1173]) ).
cnf(c1175,plain,
quotient(eta(eta(X)),product(i(X2),eta(X))) = difference(eta(X),X2),
inference(transitivity,[status(thm)],[c1160,c1174]) ).
cnf(c1176,plain,
quotient(eta(eta(X)),difference(X2,eta(X))) = difference(eta(X),X2),
inference(transitivity,[status(thm)],[c1153,c1175]) ).
cnf(c1177,plain,
quotient(one,difference(X2,eta(X))) = difference(eta(X),X2),
inference(transitivity,[status(thm)],[c1151,c1176]) ).
cnf(c1178,plain,
j(difference(X2,eta(X))) = difference(eta(X),X2),
inference(transitivity,[status(thm)],[c1149,c1177]) ).
cnf(c1179,plain,
j(difference(X,eta(product(X,X2)))) = difference(eta(product(X,X2)),X),
inference(substitution,[status(thm)],[c1178]) ).
cnf(c1180,plain,
difference(eta(product(X,X2)),X) = j(difference(X,eta(product(X,X2)))),
inference(symmetry,[status(thm)],[c1179]) ).
cnf(c1181,plain,
quotient(X,difference(eta(product(X,X2)),X)) = quotient(X,j(difference(X,eta(product(X,X2))))),
inference(congruence,[status(thm)],[c1180]) ).
cnf(c1182,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c1183,plain,
quotient(X,j(difference(X,eta(product(X,X2))))) = quotient(j(i(X)),j(difference(X,eta(product(X,X2))))),
inference(congruence,[status(thm)],[c1182]) ).
cnf(c1184,plain,
j(i(X)) = quotient(one,i(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1185,plain,
quotient(j(i(X)),j(difference(X,eta(product(X,X2))))) = quotient(quotient(one,i(X)),j(difference(X,eta(product(X,X2))))),
inference(congruence,[status(thm)],[c1184]) ).
cnf(c1186,plain,
eta(eta(difference(X2,i(i(X))))) = one,
inference(substitution,[status(thm)],[c507]) ).
cnf(c1187,plain,
one = eta(eta(difference(X2,i(i(X))))),
inference(symmetry,[status(thm)],[c1186]) ).
cnf(c1188,plain,
quotient(one,i(X)) = quotient(eta(eta(difference(X2,i(i(X))))),i(X)),
inference(congruence,[status(thm)],[c1187]) ).
cnf(c1189,plain,
quotient(quotient(one,i(X)),j(difference(X,eta(product(X,X2))))) = quotient(quotient(eta(eta(difference(X2,i(i(X))))),i(X)),j(difference(X,eta(product(X,X2))))),
inference(congruence,[status(thm)],[c1188]) ).
cnf(c1190,plain,
eta(difference(X,i(i(X2)))) = eta(difference(i(X2),X)),
inference(substitution,[status(thm)],[c593]) ).
cnf(c1191,plain,
product(i(X2),eta(difference(X,i(i(X2))))) = product(i(X2),eta(difference(i(X2),X))),
inference(congruence,[status(thm)],[c1190]) ).
cnf(c1192,plain,
eta(i(difference(i(X2),X))) = eta(difference(i(X2),X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c1193,plain,
eta(difference(i(X2),X)) = eta(i(difference(i(X2),X))),
inference(symmetry,[status(thm)],[c1192]) ).
cnf(c1194,plain,
product(i(X2),eta(difference(i(X2),X))) = product(i(X2),eta(i(difference(i(X2),X)))),
inference(congruence,[status(thm)],[c1193]) ).
cnf(c1195,plain,
product(difference(X,eta(i(X2))),i(X2)) = i(difference(i(X2),X)),
inference(substitution,[status(thm)],[c143]) ).
cnf(c1196,plain,
i(difference(i(X2),X)) = product(difference(X,eta(i(X2))),i(X2)),
inference(symmetry,[status(thm)],[c1195]) ).
cnf(c1197,plain,
eta(i(difference(i(X2),X))) = eta(product(difference(X,eta(i(X2))),i(X2))),
inference(congruence,[status(thm)],[c1196]) ).
cnf(c1198,plain,
product(i(X2),eta(i(difference(i(X2),X)))) = product(i(X2),eta(product(difference(X,eta(i(X2))),i(X2)))),
inference(congruence,[status(thm)],[c1197]) ).
cnf(c1199,plain,
product(i(X2),eta(product(X,i(X2)))) = product(i(X),quotient(X,X2)),
inference(substitution,[status(thm)],[c974]) ).
cnf(c1200,plain,
product(i(X),quotient(X,X2)) = difference(X2,eta(quotient(X,X2))),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c1201,plain,
product(i(X2),eta(product(X,i(X2)))) = difference(X2,eta(quotient(X,X2))),
inference(transitivity,[status(thm)],[c1199,c1200]) ).
cnf(c1202,plain,
product(i(X2),eta(product(difference(X,eta(i(X2))),i(X2)))) = difference(X2,eta(quotient(difference(X,eta(i(X2))),X2))),
inference(substitution,[status(thm)],[c1201]) ).
cnf(c1203,plain,
difference(X,eta(i(X2))) = difference(X,eta(X2)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c1204,plain,
quotient(difference(X,eta(i(X2))),X2) = quotient(difference(X,eta(X2)),X2),
inference(congruence,[status(thm)],[c1203]) ).
cnf(c1205,plain,
eta(quotient(difference(X,eta(i(X2))),X2)) = eta(quotient(difference(X,eta(X2)),X2)),
inference(congruence,[status(thm)],[c1204]) ).
cnf(c1206,plain,
difference(X2,eta(quotient(difference(X,eta(i(X2))),X2))) = difference(X2,eta(quotient(difference(X,eta(X2)),X2))),
inference(congruence,[status(thm)],[c1205]) ).
cnf(c1207,plain,
quotient(difference(X,eta(X2)),X2) = i(product(X2,X)),
inference(substitution,[status(thm)],[c158]) ).
cnf(c1208,plain,
eta(quotient(difference(X,eta(X2)),X2)) = eta(i(product(X2,X))),
inference(congruence,[status(thm)],[c1207]) ).
cnf(c1209,plain,
difference(X2,eta(quotient(difference(X,eta(X2)),X2))) = difference(X2,eta(i(product(X2,X)))),
inference(congruence,[status(thm)],[c1208]) ).
cnf(c1210,plain,
eta(i(product(X2,X))) = eta(product(X2,X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c1211,plain,
difference(X2,eta(i(product(X2,X)))) = difference(X2,eta(product(X2,X))),
inference(congruence,[status(thm)],[c1210]) ).
cnf(c1212,plain,
difference(X2,eta(quotient(difference(X,eta(X2)),X2))) = difference(X2,eta(product(X2,X))),
inference(transitivity,[status(thm)],[c1209,c1211]) ).
cnf(c1213,plain,
difference(X2,eta(quotient(difference(X,eta(i(X2))),X2))) = difference(X2,eta(product(X2,X))),
inference(transitivity,[status(thm)],[c1206,c1212]) ).
cnf(c1214,plain,
product(i(X2),eta(product(difference(X,eta(i(X2))),i(X2)))) = difference(X2,eta(product(X2,X))),
inference(transitivity,[status(thm)],[c1202,c1213]) ).
cnf(c1215,plain,
product(i(X2),eta(i(difference(i(X2),X)))) = difference(X2,eta(product(X2,X))),
inference(transitivity,[status(thm)],[c1198,c1214]) ).
cnf(c1216,plain,
product(i(X2),eta(difference(i(X2),X))) = difference(X2,eta(product(X2,X))),
inference(transitivity,[status(thm)],[c1194,c1215]) ).
cnf(c1217,plain,
product(i(X2),eta(difference(X,i(i(X2))))) = difference(X2,eta(product(X2,X))),
inference(transitivity,[status(thm)],[c1191,c1216]) ).
cnf(c1218,plain,
product(i(X),eta(difference(X2,i(i(X))))) = difference(X,eta(product(X,X2))),
inference(substitution,[status(thm)],[c1217]) ).
cnf(c1219,plain,
difference(X,eta(product(X,X2))) = product(i(X),eta(difference(X2,i(i(X))))),
inference(symmetry,[status(thm)],[c1218]) ).
cnf(c1220,plain,
j(difference(X,eta(product(X,X2)))) = j(product(i(X),eta(difference(X2,i(i(X)))))),
inference(congruence,[status(thm)],[c1219]) ).
cnf(c1221,plain,
quotient(quotient(eta(eta(difference(X2,i(i(X))))),i(X)),j(difference(X,eta(product(X,X2))))) = quotient(quotient(eta(eta(difference(X2,i(i(X))))),i(X)),j(product(i(X),eta(difference(X2,i(i(X))))))),
inference(congruence,[status(thm)],[c1220]) ).
cnf(c1222,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1223,plain,
quotient(X,X2) = quotient(i(j(X)),X2),
inference(congruence,[status(thm)],[c1222]) ).
cnf(c1224,plain,
quotient(eta(X2),quotient(X,X2)) = quotient(eta(X2),quotient(i(j(X)),X2)),
inference(congruence,[status(thm)],[c1223]) ).
cnf(c1225,plain,
quotient(i(X),X2) = difference(product(X2,X),eta(X2)),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c1226,plain,
quotient(eta(X2),quotient(i(X),X2)) = quotient(eta(X2),difference(product(X2,X),eta(X2))),
inference(congruence,[status(thm)],[c1225]) ).
cnf(c1227,plain,
quotient(eta(X2),difference(product(X2,X),eta(X2))) = product(X2,X),
inference(substitution,[status(thm)],[c86]) ).
cnf(c1228,plain,
quotient(eta(X2),quotient(i(X),X2)) = product(X2,X),
inference(transitivity,[status(thm)],[c1226,c1227]) ).
cnf(c1229,plain,
quotient(eta(X2),quotient(i(j(X)),X2)) = product(X2,j(X)),
inference(substitution,[status(thm)],[c1228]) ).
cnf(c1230,plain,
quotient(eta(X2),quotient(X,X2)) = product(X2,j(X)),
inference(transitivity,[status(thm)],[c1224,c1229]) ).
cnf(c1231,plain,
quotient(eta(X2),quotient(product(X,X2),X2)) = product(X2,j(product(X,X2))),
inference(substitution,[status(thm)],[c1230]) ).
cnf(c1232,plain,
product(X2,j(product(X,X2))) = quotient(eta(X2),quotient(product(X,X2),X2)),
inference(symmetry,[status(thm)],[c1231]) ).
cnf(c1233,plain,
quotient(product(X,X2),X2) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c1234,plain,
quotient(eta(X2),quotient(product(X,X2),X2)) = quotient(eta(X2),X),
inference(congruence,[status(thm)],[c1233]) ).
cnf(c1235,plain,
product(X2,j(product(X,X2))) = quotient(eta(X2),X),
inference(transitivity,[status(thm)],[c1232,c1234]) ).
cnf(c1236,plain,
quotient(eta(X2),X) = product(X2,j(product(X,X2))),
inference(symmetry,[status(thm)],[c1235]) ).
cnf(c1237,plain,
quotient(quotient(eta(X2),X),j(product(X,X2))) = quotient(product(X2,j(product(X,X2))),j(product(X,X2))),
inference(congruence,[status(thm)],[c1236]) ).
cnf(c1238,plain,
quotient(product(X2,j(product(X,X2))),j(product(X,X2))) = X2,
inference(substitution,[status(thm)],[c12]) ).
cnf(c1239,plain,
quotient(quotient(eta(X2),X),j(product(X,X2))) = X2,
inference(transitivity,[status(thm)],[c1237,c1238]) ).
cnf(c1240,plain,
quotient(quotient(eta(eta(difference(X2,i(i(X))))),i(X)),j(product(i(X),eta(difference(X2,i(i(X))))))) = eta(difference(X2,i(i(X)))),
inference(substitution,[status(thm)],[c1239]) ).
cnf(c1241,plain,
quotient(quotient(eta(eta(difference(X2,i(i(X))))),i(X)),j(difference(X,eta(product(X,X2))))) = eta(difference(X2,i(i(X)))),
inference(transitivity,[status(thm)],[c1221,c1240]) ).
cnf(c1242,plain,
quotient(quotient(one,i(X)),j(difference(X,eta(product(X,X2))))) = eta(difference(X2,i(i(X)))),
inference(transitivity,[status(thm)],[c1189,c1241]) ).
cnf(c1243,plain,
quotient(j(i(X)),j(difference(X,eta(product(X,X2))))) = eta(difference(X2,i(i(X)))),
inference(transitivity,[status(thm)],[c1185,c1242]) ).
cnf(c1244,plain,
quotient(X,j(difference(X,eta(product(X,X2))))) = eta(difference(X2,i(i(X)))),
inference(transitivity,[status(thm)],[c1183,c1243]) ).
cnf(c1245,plain,
quotient(X,difference(eta(product(X,X2)),X)) = eta(difference(X2,i(i(X)))),
inference(transitivity,[status(thm)],[c1181,c1244]) ).
cnf(c1246,plain,
eta(product(X,X2)) = eta(difference(X2,i(i(X)))),
inference(transitivity,[status(thm)],[c1148,c1245]) ).
cnf(c1247,plain,
eta(quotient(X2,i(i(X)))) = eta(difference(X2,i(i(X)))),
inference(transitivity,[status(thm)],[c1146,c1246]) ).
cnf(c1248,plain,
eta(quotient(X2,i(i(j(X))))) = eta(difference(X2,i(i(j(X))))),
inference(substitution,[status(thm)],[c1247]) ).
cnf(c1249,plain,
eta(difference(X2,i(i(j(X))))) = eta(quotient(X2,i(i(j(X))))),
inference(symmetry,[status(thm)],[c1248]) ).
cnf(c1250,plain,
eta(product(j(X),X2)) = eta(quotient(X2,i(i(j(X))))),
inference(substitution,[status(thm)],[c874]) ).
cnf(c1251,plain,
eta(quotient(X2,i(i(j(X))))) = eta(product(j(X),X2)),
inference(symmetry,[status(thm)],[c1250]) ).
cnf(c1252,plain,
eta(difference(X2,i(difference(j(X2),X)))) = eta(difference(difference(j(X2),X),X2)),
inference(substitution,[status(thm)],[c593]) ).
cnf(c1253,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1254,plain,
quotient(X2,X) = quotient(X2,i(j(X))),
inference(congruence,[status(thm)],[c1253]) ).
cnf(c1255,plain,
eta(quotient(X2,X)) = eta(quotient(X2,i(j(X)))),
inference(congruence,[status(thm)],[c1254]) ).
cnf(c1256,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1257,plain,
i(X) = i(i(j(X))),
inference(congruence,[status(thm)],[c1256]) ).
cnf(c1258,plain,
quotient(X2,i(X)) = quotient(X2,i(i(j(X)))),
inference(congruence,[status(thm)],[c1257]) ).
cnf(c1259,plain,
eta(quotient(X2,i(X))) = eta(quotient(X2,i(i(j(X))))),
inference(congruence,[status(thm)],[c1258]) ).
cnf(c1260,plain,
eta(quotient(X2,i(i(j(X))))) = eta(difference(X2,i(i(j(X))))),
inference(substitution,[status(thm)],[c1247]) ).
cnf(c1261,plain,
i(i(j(X))) = i(X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1262,plain,
difference(X2,i(i(j(X)))) = difference(X2,i(X)),
inference(congruence,[status(thm)],[c1261]) ).
cnf(c1263,plain,
eta(difference(X2,i(i(j(X))))) = eta(difference(X2,i(X))),
inference(congruence,[status(thm)],[c1262]) ).
cnf(c1264,plain,
eta(quotient(X2,i(i(j(X))))) = eta(difference(X2,i(X))),
inference(transitivity,[status(thm)],[c1260,c1263]) ).
cnf(c1265,plain,
eta(quotient(X2,i(X))) = eta(difference(X2,i(X))),
inference(transitivity,[status(thm)],[c1259,c1264]) ).
cnf(c1266,plain,
eta(quotient(X2,i(j(X)))) = eta(difference(X2,i(j(X)))),
inference(substitution,[status(thm)],[c1265]) ).
cnf(c1267,plain,
difference(X2,i(j(X))) = difference(X2,X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1268,plain,
eta(difference(X2,i(j(X)))) = eta(difference(X2,X)),
inference(congruence,[status(thm)],[c1267]) ).
cnf(c1269,plain,
eta(quotient(X2,i(j(X)))) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1266,c1268]) ).
cnf(c1270,plain,
eta(quotient(X2,X)) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1255,c1269]) ).
cnf(c1271,plain,
eta(quotient(difference(j(X2),X),X2)) = eta(difference(difference(j(X2),X),X2)),
inference(substitution,[status(thm)],[c1270]) ).
cnf(c1272,plain,
eta(difference(difference(j(X2),X),X2)) = eta(quotient(difference(j(X2),X),X2)),
inference(symmetry,[status(thm)],[c1271]) ).
cnf(c1273,plain,
eta(quotient(i(difference(j(X2),X)),i(X2))) = eta(quotient(difference(j(X2),X),X2)),
inference(substitution,[status(thm)],[c558]) ).
cnf(c1274,plain,
eta(quotient(difference(j(X2),X),X2)) = eta(quotient(i(difference(j(X2),X)),i(X2))),
inference(symmetry,[status(thm)],[c1273]) ).
cnf(c1275,plain,
eta(quotient(i(i(difference(j(X2),X))),i(i(X2)))) = eta(quotient(i(difference(j(X2),X)),i(X2))),
inference(substitution,[status(thm)],[c558]) ).
cnf(c1276,plain,
eta(quotient(i(difference(j(X2),X)),i(X2))) = eta(quotient(i(i(difference(j(X2),X))),i(i(X2)))),
inference(symmetry,[status(thm)],[c1275]) ).
cnf(c1277,plain,
eta(product(X2,i(i(difference(j(X2),X))))) = eta(quotient(i(i(difference(j(X2),X))),i(i(X2)))),
inference(substitution,[status(thm)],[c874]) ).
cnf(c1278,plain,
eta(quotient(i(i(difference(j(X2),X))),i(i(X2)))) = eta(product(X2,i(i(difference(j(X2),X))))),
inference(symmetry,[status(thm)],[c1277]) ).
cnf(c1279,plain,
eta(product(i(j(X2)),i(X))) = eta(product(j(X2),X)),
inference(substitution,[status(thm)],[c772]) ).
cnf(c1280,plain,
eta(product(j(X2),X)) = eta(product(i(j(X2)),i(X))),
inference(symmetry,[status(thm)],[c1279]) ).
cnf(c1281,plain,
product(i(j(X2)),i(X)) = product(X2,i(X)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1282,plain,
eta(product(i(j(X2)),i(X))) = eta(product(X2,i(X))),
inference(congruence,[status(thm)],[c1281]) ).
cnf(c1283,plain,
eta(product(j(X2),X)) = eta(product(X2,i(X))),
inference(transitivity,[status(thm)],[c1280,c1282]) ).
cnf(c1284,plain,
eta(product(j(X2),i(difference(j(X2),X)))) = eta(product(X2,i(i(difference(j(X2),X))))),
inference(substitution,[status(thm)],[c1283]) ).
cnf(c1285,plain,
eta(product(X2,i(i(difference(j(X2),X))))) = eta(product(j(X2),i(difference(j(X2),X)))),
inference(symmetry,[status(thm)],[c1284]) ).
cnf(c1286,plain,
difference(difference(X,X2),eta(X)) = product(i(X2),X),
inference(substitution,[status(thm)],[c459]) ).
cnf(c1287,plain,
product(i(X2),X) = difference(difference(X,X2),eta(X)),
inference(symmetry,[status(thm)],[c1286]) ).
cnf(c1288,plain,
quotient(product(i(X2),X),eta(X)) = quotient(difference(difference(X,X2),eta(X)),eta(X)),
inference(congruence,[status(thm)],[c1287]) ).
cnf(c1289,plain,
quotient(difference(difference(X,X2),eta(X)),eta(X)) = difference(product(eta(X),difference(X,X2)),eta(X)),
inference(substitution,[status(thm)],[c233]) ).
cnf(c1290,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1291,plain,
product(eta(X2),X) = product(eta(X2),i(j(X))),
inference(congruence,[status(thm)],[c1290]) ).
cnf(c1292,plain,
product(X2,quotient(product(X,eta(X2)),X2)) = quotient(difference(i(X2),product(X,eta(X2))),X2),
inference(substitution,[status(thm)],[c432]) ).
cnf(c1293,plain,
quotient(difference(i(X2),product(X,eta(X2))),X2) = product(X2,quotient(product(X,eta(X2)),X2)),
inference(symmetry,[status(thm)],[c1292]) ).
cnf(c1294,plain,
difference(X2,product(product(X2,X),i(X2))) = quotient(product(X,product(i(X2),X2)),X2),
inference(substitution,[status(thm)],[c57]) ).
cnf(c1295,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c1296,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c1295]) ).
cnf(c1297,plain,
product(X,product(i(X2),X2)) = product(X,eta(X2)),
inference(congruence,[status(thm)],[c1296]) ).
cnf(c1298,plain,
quotient(product(X,product(i(X2),X2)),X2) = quotient(product(X,eta(X2)),X2),
inference(congruence,[status(thm)],[c1297]) ).
cnf(c1299,plain,
difference(X2,product(product(X2,X),i(X2))) = quotient(product(X,eta(X2)),X2),
inference(transitivity,[status(thm)],[c1294,c1298]) ).
cnf(c1300,plain,
quotient(product(X,eta(X2)),X2) = difference(X2,product(product(X2,X),i(X2))),
inference(symmetry,[status(thm)],[c1299]) ).
cnf(c1301,plain,
product(X2,quotient(product(X,eta(X2)),X2)) = product(X2,difference(X2,product(product(X2,X),i(X2)))),
inference(congruence,[status(thm)],[c1300]) ).
cnf(c1302,plain,
product(X2,difference(X2,product(product(X2,X),i(X2)))) = product(product(X2,X),i(X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1303,plain,
product(X2,quotient(product(X,eta(X2)),X2)) = product(product(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1301,c1302]) ).
cnf(c1304,plain,
quotient(difference(i(X2),product(X,eta(X2))),X2) = product(product(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1293,c1303]) ).
cnf(c1305,plain,
product(product(X2,X),i(X2)) = quotient(difference(i(X2),product(X,eta(X2))),X2),
inference(symmetry,[status(thm)],[c1304]) ).
cnf(c1306,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c1307,plain,
product(X,eta(X2)) = product(X,eta(i(X2))),
inference(congruence,[status(thm)],[c1306]) ).
cnf(c1308,plain,
difference(i(X2),product(X,eta(X2))) = difference(i(X2),product(X,eta(i(X2)))),
inference(congruence,[status(thm)],[c1307]) ).
cnf(c1309,plain,
quotient(difference(i(X2),product(X,eta(X2))),X2) = quotient(difference(i(X2),product(X,eta(i(X2)))),X2),
inference(congruence,[status(thm)],[c1308]) ).
cnf(c1310,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c1311,plain,
quotient(difference(i(X2),product(X,eta(i(X2)))),X2) = quotient(difference(i(X2),product(X,eta(i(X2)))),j(i(X2))),
inference(congruence,[status(thm)],[c1310]) ).
cnf(c1312,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1313,plain,
difference(X2,product(X,eta(X2))) = difference(i(j(X2)),product(X,eta(X2))),
inference(congruence,[status(thm)],[c1312]) ).
cnf(c1314,plain,
quotient(difference(X2,product(X,eta(X2))),j(X2)) = quotient(difference(i(j(X2)),product(X,eta(X2))),j(X2)),
inference(congruence,[status(thm)],[c1313]) ).
cnf(c1315,plain,
product(j(X2),quotient(product(X,eta(X2)),j(X2))) = quotient(difference(i(j(X2)),product(X,eta(X2))),j(X2)),
inference(substitution,[status(thm)],[c432]) ).
cnf(c1316,plain,
quotient(difference(i(j(X2)),product(X,eta(X2))),j(X2)) = product(j(X2),quotient(product(X,eta(X2)),j(X2))),
inference(symmetry,[status(thm)],[c1315]) ).
cnf(c1317,plain,
difference(j(X2),product(product(j(X2),X),X2)) = quotient(product(X,product(X2,j(X2))),j(X2)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c1318,plain,
product(X,product(X2,j(X2))) = product(X,eta(X2)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c1319,plain,
quotient(product(X,product(X2,j(X2))),j(X2)) = quotient(product(X,eta(X2)),j(X2)),
inference(congruence,[status(thm)],[c1318]) ).
cnf(c1320,plain,
difference(j(X2),product(product(j(X2),X),X2)) = quotient(product(X,eta(X2)),j(X2)),
inference(transitivity,[status(thm)],[c1317,c1319]) ).
cnf(c1321,plain,
quotient(product(X,eta(X2)),j(X2)) = difference(j(X2),product(product(j(X2),X),X2)),
inference(symmetry,[status(thm)],[c1320]) ).
cnf(c1322,plain,
product(j(X2),quotient(product(X,eta(X2)),j(X2))) = product(j(X2),difference(j(X2),product(product(j(X2),X),X2))),
inference(congruence,[status(thm)],[c1321]) ).
cnf(c1323,plain,
product(j(X2),difference(j(X2),product(product(j(X2),X),X2))) = product(product(j(X2),X),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1324,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c1325,plain,
X = product(X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c1324]) ).
cnf(c1326,plain,
product(X,j(X2)) = product(product(X2,difference(X2,X)),j(X2)),
inference(congruence,[status(thm)],[c1325]) ).
cnf(c1327,plain,
difference(X2,product(X,j(X2))) = difference(X2,product(product(X2,difference(X2,X)),j(X2))),
inference(congruence,[status(thm)],[c1326]) ).
cnf(c1328,plain,
difference(X2,product(product(X2,difference(X2,X)),j(X2))) = quotient(difference(X2,X),X2),
inference(substitution,[status(thm)],[c418]) ).
cnf(c1329,plain,
difference(X2,product(X,j(X2))) = quotient(difference(X2,X),X2),
inference(transitivity,[status(thm)],[c1327,c1328]) ).
cnf(c1330,plain,
quotient(difference(X2,X),X2) = difference(X2,product(X,j(X2))),
inference(symmetry,[status(thm)],[c1329]) ).
cnf(c1331,plain,
quotient(quotient(difference(X2,X),X2),j(X2)) = quotient(difference(X2,product(X,j(X2))),j(X2)),
inference(congruence,[status(thm)],[c1330]) ).
cnf(c1332,plain,
quotient(difference(X2,product(X,j(X2))),j(X2)) = difference(product(j(X2),X2),product(j(X2),X)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c1333,plain,
difference(product(j(X2),X2),product(j(X2),X)) = difference(one,product(j(X2),X)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c1334,plain,
difference(one,product(j(X2),X)) = product(j(X2),X),
inference(substitution,[status(thm)],[c190]) ).
cnf(c1335,plain,
difference(product(j(X2),X2),product(j(X2),X)) = product(j(X2),X),
inference(transitivity,[status(thm)],[c1333,c1334]) ).
cnf(c1336,plain,
quotient(difference(X2,product(X,j(X2))),j(X2)) = product(j(X2),X),
inference(transitivity,[status(thm)],[c1332,c1335]) ).
cnf(c1337,plain,
quotient(quotient(difference(X2,X),X2),j(X2)) = product(j(X2),X),
inference(transitivity,[status(thm)],[c1331,c1336]) ).
cnf(c1338,plain,
product(j(X2),X) = quotient(quotient(difference(X2,X),X2),j(X2)),
inference(symmetry,[status(thm)],[c1337]) ).
cnf(c1339,plain,
product(product(j(X2),X),X2) = product(quotient(quotient(difference(X2,X),X2),j(X2)),X2),
inference(congruence,[status(thm)],[c1338]) ).
cnf(c1340,plain,
product(X,product(difference(X,X2),X)) = quotient(X2,j(X)),
inference(substitution,[status(thm)],[c400]) ).
cnf(c1341,plain,
quotient(X2,j(X)) = product(X,product(difference(X,X2),X)),
inference(symmetry,[status(thm)],[c1340]) ).
cnf(c1342,plain,
product(quotient(X2,j(X)),X) = product(product(X,product(difference(X,X2),X)),X),
inference(congruence,[status(thm)],[c1341]) ).
cnf(c1343,plain,
product(product(X,product(difference(X,X2),X)),X) = difference(i(X),product(product(difference(X,X2),X),X)),
inference(substitution,[status(thm)],[c696]) ).
cnf(c1344,plain,
product(difference(X,X2),X) = product(i(X),product(X2,X)),
inference(substitution,[status(thm)],[c322]) ).
cnf(c1345,plain,
product(product(difference(X,X2),X),X) = product(product(i(X),product(X2,X)),X),
inference(congruence,[status(thm)],[c1344]) ).
cnf(c1346,plain,
difference(i(X),product(product(difference(X,X2),X),X)) = difference(i(X),product(product(i(X),product(X2,X)),X)),
inference(congruence,[status(thm)],[c1345]) ).
cnf(c1347,plain,
product(product(i(X),product(X2,X)),X) = product(i(X),quotient(product(X2,X),i(X))),
inference(substitution,[status(thm)],[c634]) ).
cnf(c1348,plain,
difference(i(X),product(product(i(X),product(X2,X)),X)) = difference(i(X),product(i(X),quotient(product(X2,X),i(X)))),
inference(congruence,[status(thm)],[c1347]) ).
cnf(c1349,plain,
difference(i(X),product(i(X),quotient(product(X2,X),i(X)))) = quotient(product(X2,X),i(X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c1350,plain,
difference(i(X),product(product(i(X),product(X2,X)),X)) = quotient(product(X2,X),i(X)),
inference(transitivity,[status(thm)],[c1348,c1349]) ).
cnf(c1351,plain,
difference(i(X),product(product(difference(X,X2),X),X)) = quotient(product(X2,X),i(X)),
inference(transitivity,[status(thm)],[c1346,c1350]) ).
cnf(c1352,plain,
product(product(X,product(difference(X,X2),X)),X) = quotient(product(X2,X),i(X)),
inference(transitivity,[status(thm)],[c1343,c1351]) ).
cnf(c1353,plain,
product(quotient(X2,j(X)),X) = quotient(product(X2,X),i(X)),
inference(transitivity,[status(thm)],[c1342,c1352]) ).
cnf(c1354,plain,
product(quotient(quotient(difference(X2,X),X2),j(X2)),X2) = quotient(product(quotient(difference(X2,X),X2),X2),i(X2)),
inference(substitution,[status(thm)],[c1353]) ).
cnf(c1355,plain,
product(quotient(difference(X2,X),X2),X2) = difference(X2,X),
inference(substitution,[status(thm)],[c38]) ).
cnf(c1356,plain,
quotient(product(quotient(difference(X2,X),X2),X2),i(X2)) = quotient(difference(X2,X),i(X2)),
inference(congruence,[status(thm)],[c1355]) ).
cnf(c1357,plain,
product(quotient(quotient(difference(X2,X),X2),j(X2)),X2) = quotient(difference(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1354,c1356]) ).
cnf(c1358,plain,
product(product(j(X2),X),X2) = quotient(difference(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1339,c1357]) ).
cnf(c1359,plain,
product(j(X2),difference(j(X2),product(product(j(X2),X),X2))) = quotient(difference(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1323,c1358]) ).
cnf(c1360,plain,
product(j(X2),quotient(product(X,eta(X2)),j(X2))) = quotient(difference(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1322,c1359]) ).
cnf(c1361,plain,
quotient(difference(i(j(X2)),product(X,eta(X2))),j(X2)) = quotient(difference(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1316,c1360]) ).
cnf(c1362,plain,
quotient(difference(X2,product(X,eta(X2))),j(X2)) = quotient(difference(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1314,c1361]) ).
cnf(c1363,plain,
quotient(difference(i(X2),product(X,eta(i(X2)))),j(i(X2))) = quotient(difference(i(X2),X),i(i(X2))),
inference(substitution,[status(thm)],[c1362]) ).
cnf(c1364,plain,
quotient(difference(i(X2),product(X,eta(i(X2)))),X2) = quotient(difference(i(X2),X),i(i(X2))),
inference(transitivity,[status(thm)],[c1311,c1363]) ).
cnf(c1365,plain,
quotient(difference(i(X2),product(X,eta(X2))),X2) = quotient(difference(i(X2),X),i(i(X2))),
inference(transitivity,[status(thm)],[c1309,c1364]) ).
cnf(c1366,plain,
product(product(X2,X),i(X2)) = quotient(difference(i(X2),X),i(i(X2))),
inference(transitivity,[status(thm)],[c1305,c1365]) ).
cnf(c1367,plain,
product(product(X2,difference(X2,X)),i(X2)) = quotient(difference(i(X2),difference(X2,X)),i(i(X2))),
inference(substitution,[status(thm)],[c1366]) ).
cnf(c1368,plain,
quotient(difference(i(X2),difference(X2,X)),i(i(X2))) = product(product(X2,difference(X2,X)),i(X2)),
inference(symmetry,[status(thm)],[c1367]) ).
cnf(c1369,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c1370,plain,
product(product(X2,difference(X2,X)),i(X2)) = product(X,i(X2)),
inference(congruence,[status(thm)],[c1369]) ).
cnf(c1371,plain,
quotient(difference(i(X2),difference(X2,X)),i(i(X2))) = product(X,i(X2)),
inference(transitivity,[status(thm)],[c1368,c1370]) ).
cnf(c1372,plain,
quotient(difference(i(j(X)),difference(j(X),eta(X2))),i(i(j(X)))) = product(eta(X2),i(j(X))),
inference(substitution,[status(thm)],[c1371]) ).
cnf(c1373,plain,
product(eta(X2),i(j(X))) = quotient(difference(i(j(X)),difference(j(X),eta(X2))),i(i(j(X)))),
inference(symmetry,[status(thm)],[c1372]) ).
cnf(c1374,plain,
difference(j(X),eta(X2)) = product(X,eta(X2)),
inference(substitution,[status(thm)],[c1034]) ).
cnf(c1375,plain,
difference(i(j(X)),difference(j(X),eta(X2))) = difference(i(j(X)),product(X,eta(X2))),
inference(congruence,[status(thm)],[c1374]) ).
cnf(c1376,plain,
quotient(difference(i(j(X)),difference(j(X),eta(X2))),i(i(j(X)))) = quotient(difference(i(j(X)),product(X,eta(X2))),i(i(j(X)))),
inference(congruence,[status(thm)],[c1375]) ).
cnf(c1377,plain,
difference(i(j(X)),product(X,eta(X2))) = difference(X,product(X,eta(X2))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1378,plain,
quotient(difference(i(j(X)),product(X,eta(X2))),i(i(j(X)))) = quotient(difference(X,product(X,eta(X2))),i(i(j(X)))),
inference(congruence,[status(thm)],[c1377]) ).
cnf(c1379,plain,
i(i(j(X))) = i(X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1380,plain,
quotient(difference(X,product(X,eta(X2))),i(i(j(X)))) = quotient(difference(X,product(X,eta(X2))),i(X)),
inference(congruence,[status(thm)],[c1379]) ).
cnf(c1381,plain,
difference(X,product(X,eta(X2))) = eta(X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c1382,plain,
quotient(difference(X,product(X,eta(X2))),i(X)) = quotient(eta(X2),i(X)),
inference(congruence,[status(thm)],[c1381]) ).
cnf(c1383,plain,
quotient(difference(X,product(X,eta(X2))),i(i(j(X)))) = quotient(eta(X2),i(X)),
inference(transitivity,[status(thm)],[c1380,c1382]) ).
cnf(c1384,plain,
quotient(difference(i(j(X)),product(X,eta(X2))),i(i(j(X)))) = quotient(eta(X2),i(X)),
inference(transitivity,[status(thm)],[c1378,c1383]) ).
cnf(c1385,plain,
quotient(difference(i(j(X)),difference(j(X),eta(X2))),i(i(j(X)))) = quotient(eta(X2),i(X)),
inference(transitivity,[status(thm)],[c1376,c1384]) ).
cnf(c1386,plain,
product(eta(X2),i(j(X))) = quotient(eta(X2),i(X)),
inference(transitivity,[status(thm)],[c1373,c1385]) ).
cnf(c1387,plain,
product(eta(X2),X) = quotient(eta(X2),i(X)),
inference(transitivity,[status(thm)],[c1291,c1386]) ).
cnf(c1388,plain,
product(eta(X),difference(X,X2)) = quotient(eta(X),i(difference(X,X2))),
inference(substitution,[status(thm)],[c1387]) ).
cnf(c1389,plain,
difference(product(eta(X),difference(X,X2)),eta(X)) = difference(quotient(eta(X),i(difference(X,X2))),eta(X)),
inference(congruence,[status(thm)],[c1388]) ).
cnf(c1390,plain,
difference(quotient(eta(X),i(difference(X,X2))),eta(X)) = i(difference(X,X2)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c1391,plain,
difference(product(eta(X),difference(X,X2)),eta(X)) = i(difference(X,X2)),
inference(transitivity,[status(thm)],[c1389,c1390]) ).
cnf(c1392,plain,
quotient(difference(difference(X,X2),eta(X)),eta(X)) = i(difference(X,X2)),
inference(transitivity,[status(thm)],[c1289,c1391]) ).
cnf(c1393,plain,
quotient(product(i(X2),X),eta(X)) = i(difference(X,X2)),
inference(transitivity,[status(thm)],[c1288,c1392]) ).
cnf(c1394,plain,
quotient(product(i(X),X2),eta(X2)) = i(difference(X2,X)),
inference(substitution,[status(thm)],[c1393]) ).
cnf(c1395,plain,
i(difference(X2,X)) = quotient(product(i(X),X2),eta(X2)),
inference(symmetry,[status(thm)],[c1394]) ).
cnf(c1396,plain,
product(X2,i(difference(X2,X))) = product(X2,quotient(product(i(X),X2),eta(X2))),
inference(congruence,[status(thm)],[c1395]) ).
cnf(c1397,plain,
product(X2,quotient(X,product(i(X2),X2))) = quotient(quotient(difference(i(X2),X),X2),i(X2)),
inference(substitution,[status(thm)],[c436]) ).
cnf(c1398,plain,
quotient(quotient(difference(i(X2),X),X2),i(X2)) = product(X2,quotient(X,product(i(X2),X2))),
inference(symmetry,[status(thm)],[c1397]) ).
cnf(c1399,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c1400,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c1399]) ).
cnf(c1401,plain,
quotient(X,product(i(X2),X2)) = quotient(X,eta(X2)),
inference(congruence,[status(thm)],[c1400]) ).
cnf(c1402,plain,
product(X2,quotient(X,product(i(X2),X2))) = product(X2,quotient(X,eta(X2))),
inference(congruence,[status(thm)],[c1401]) ).
cnf(c1403,plain,
quotient(quotient(difference(i(X2),X),X2),i(X2)) = product(X2,quotient(X,eta(X2))),
inference(transitivity,[status(thm)],[c1398,c1402]) ).
cnf(c1404,plain,
quotient(quotient(difference(i(X2),product(X,X2)),X2),i(X2)) = product(X2,quotient(product(X,X2),eta(X2))),
inference(substitution,[status(thm)],[c1403]) ).
cnf(c1405,plain,
product(X2,quotient(product(X,X2),eta(X2))) = quotient(quotient(difference(i(X2),product(X,X2)),X2),i(X2)),
inference(symmetry,[status(thm)],[c1404]) ).
cnf(c1406,plain,
quotient(difference(i(X2),product(X,X2)),X2) = difference(product(X2,i(X2)),product(X2,X)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c1407,plain,
quotient(quotient(difference(i(X2),product(X,X2)),X2),i(X2)) = quotient(difference(product(X2,i(X2)),product(X2,X)),i(X2)),
inference(congruence,[status(thm)],[c1406]) ).
cnf(c1408,plain,
difference(product(X2,i(X2)),product(X2,X)) = difference(one,product(X2,X)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c1409,plain,
quotient(difference(product(X2,i(X2)),product(X2,X)),i(X2)) = quotient(difference(one,product(X2,X)),i(X2)),
inference(congruence,[status(thm)],[c1408]) ).
cnf(c1410,plain,
difference(one,product(X2,X)) = product(X2,X),
inference(substitution,[status(thm)],[c190]) ).
cnf(c1411,plain,
quotient(difference(one,product(X2,X)),i(X2)) = quotient(product(X2,X),i(X2)),
inference(congruence,[status(thm)],[c1410]) ).
cnf(c1412,plain,
quotient(difference(product(X2,i(X2)),product(X2,X)),i(X2)) = quotient(product(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1409,c1411]) ).
cnf(c1413,plain,
quotient(quotient(difference(i(X2),product(X,X2)),X2),i(X2)) = quotient(product(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1407,c1412]) ).
cnf(c1414,plain,
product(X2,quotient(product(X,X2),eta(X2))) = quotient(product(X2,X),i(X2)),
inference(transitivity,[status(thm)],[c1405,c1413]) ).
cnf(c1415,plain,
product(X2,quotient(product(i(X),X2),eta(X2))) = quotient(product(X2,i(X)),i(X2)),
inference(substitution,[status(thm)],[c1414]) ).
cnf(c1416,plain,
product(X2,i(difference(X2,X))) = quotient(product(X2,i(X)),i(X2)),
inference(transitivity,[status(thm)],[c1396,c1415]) ).
cnf(c1417,plain,
product(j(X2),i(difference(j(X2),X))) = quotient(product(j(X2),i(X)),i(j(X2))),
inference(substitution,[status(thm)],[c1416]) ).
cnf(c1418,plain,
eta(product(j(X2),i(difference(j(X2),X)))) = eta(quotient(product(j(X2),i(X)),i(j(X2)))),
inference(congruence,[status(thm)],[c1417]) ).
cnf(c1419,plain,
eta(quotient(product(j(X2),i(X)),i(j(X2)))) = eta(difference(product(j(X2),i(X)),i(j(X2)))),
inference(substitution,[status(thm)],[c1265]) ).
cnf(c1420,plain,
eta(difference(product(j(X2),i(X)),i(j(X2)))) = eta(i(X)),
inference(substitution,[status(thm)],[c339]) ).
cnf(c1421,plain,
eta(difference(product(j(X2),i(X)),i(j(X2)))) = eta(X),
inference(transitivity,[status(thm)],[c1420,c32]) ).
cnf(c1422,plain,
eta(quotient(product(j(X2),i(X)),i(j(X2)))) = eta(X),
inference(transitivity,[status(thm)],[c1419,c1421]) ).
cnf(c1423,plain,
eta(product(j(X2),i(difference(j(X2),X)))) = eta(X),
inference(transitivity,[status(thm)],[c1418,c1422]) ).
cnf(c1424,plain,
eta(product(X2,i(i(difference(j(X2),X))))) = eta(X),
inference(transitivity,[status(thm)],[c1285,c1423]) ).
cnf(c1425,plain,
eta(quotient(i(i(difference(j(X2),X))),i(i(X2)))) = eta(X),
inference(transitivity,[status(thm)],[c1278,c1424]) ).
cnf(c1426,plain,
eta(quotient(i(difference(j(X2),X)),i(X2))) = eta(X),
inference(transitivity,[status(thm)],[c1276,c1425]) ).
cnf(c1427,plain,
eta(quotient(difference(j(X2),X),X2)) = eta(X),
inference(transitivity,[status(thm)],[c1274,c1426]) ).
cnf(c1428,plain,
eta(difference(difference(j(X2),X),X2)) = eta(X),
inference(transitivity,[status(thm)],[c1272,c1427]) ).
cnf(c1429,plain,
eta(difference(X2,i(difference(j(X2),X)))) = eta(X),
inference(transitivity,[status(thm)],[c1252,c1428]) ).
cnf(c1430,plain,
eta(difference(X,i(difference(j(X),product(j(X),X2))))) = eta(product(j(X),X2)),
inference(substitution,[status(thm)],[c1429]) ).
cnf(c1431,plain,
eta(product(j(X),X2)) = eta(difference(X,i(difference(j(X),product(j(X),X2))))),
inference(symmetry,[status(thm)],[c1430]) ).
cnf(c1432,plain,
difference(j(X),product(j(X),X2)) = X2,
inference(substitution,[status(thm)],[c43]) ).
cnf(c1433,plain,
i(difference(j(X),product(j(X),X2))) = i(X2),
inference(congruence,[status(thm)],[c1432]) ).
cnf(c1434,plain,
difference(X,i(difference(j(X),product(j(X),X2)))) = difference(X,i(X2)),
inference(congruence,[status(thm)],[c1433]) ).
cnf(c1435,plain,
eta(difference(X,i(difference(j(X),product(j(X),X2))))) = eta(difference(X,i(X2))),
inference(congruence,[status(thm)],[c1434]) ).
cnf(c1436,plain,
eta(difference(X,i(difference(j(X),product(j(X),X2))))) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1435,c593]) ).
cnf(c1437,plain,
eta(product(j(X),X2)) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1431,c1436]) ).
cnf(c1438,plain,
eta(quotient(X2,i(i(j(X))))) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1251,c1437]) ).
cnf(c1439,plain,
eta(difference(X2,i(i(j(X))))) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1249,c1438]) ).
cnf(c1440,plain,
eta(difference(X2,i(X))) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1144,c1439]) ).
cnf(c1441,plain,
eta(difference(i(X),i(X2))) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1140,c1440]) ).
cnf(c1442,plain,
eta(difference(X,X2)) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1139,c1441]) ).
cnf(c1443,plain,
eta(difference(X2,quotient(X,i(X2)))) = eta(difference(quotient(X,i(X2)),X2)),
inference(substitution,[status(thm)],[c1442]) ).
cnf(c1444,plain,
eta(difference(quotient(X,i(X2)),i(X2))) = eta(difference(quotient(X,i(X2)),X2)),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c1445,plain,
eta(difference(quotient(X,i(X2)),X2)) = eta(difference(quotient(X,i(X2)),i(X2))),
inference(symmetry,[status(thm)],[c1444]) ).
cnf(c1446,plain,
eta(difference(quotient(X,i(X2)),i(i(X2)))) = eta(difference(quotient(X,i(X2)),i(X2))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c1447,plain,
eta(difference(quotient(X,i(X2)),i(X2))) = eta(difference(quotient(X,i(X2)),i(i(X2)))),
inference(symmetry,[status(thm)],[c1446]) ).
cnf(c1448,plain,
eta(difference(quotient(X,i(X2)),i(i(i(X2))))) = eta(difference(quotient(X,i(X2)),i(i(X2)))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c1449,plain,
eta(difference(quotient(X,i(X2)),i(i(X2)))) = eta(difference(quotient(X,i(X2)),i(i(i(X2))))),
inference(symmetry,[status(thm)],[c1448]) ).
cnf(c1450,plain,
eta(quotient(quotient(X,i(X2)),i(i(i(X2))))) = eta(difference(quotient(X,i(X2)),i(i(i(X2))))),
inference(substitution,[status(thm)],[c1247]) ).
cnf(c1451,plain,
eta(difference(quotient(X,i(X2)),i(i(i(X2))))) = eta(quotient(quotient(X,i(X2)),i(i(i(X2))))),
inference(symmetry,[status(thm)],[c1450]) ).
cnf(c1452,plain,
eta(quotient(i(i(X2)),quotient(X,i(X2)))) = eta(quotient(quotient(X,i(X2)),i(i(i(X2))))),
inference(substitution,[status(thm)],[c553]) ).
cnf(c1453,plain,
eta(quotient(quotient(X,i(X2)),i(i(i(X2))))) = eta(quotient(i(i(X2)),quotient(X,i(X2)))),
inference(symmetry,[status(thm)],[c1452]) ).
cnf(c1454,plain,
quotient(quotient(i(i(X2)),quotient(X,i(X2))),one) = quotient(i(i(X2)),quotient(X,i(X2))),
inference(substitution,[status(thm)],[c1123]) ).
cnf(c1455,plain,
quotient(i(i(X2)),quotient(X,i(X2))) = quotient(quotient(i(i(X2)),quotient(X,i(X2))),one),
inference(symmetry,[status(thm)],[c1454]) ).
cnf(c1456,plain,
eta(eta(product(X2,i(X)))) = one,
inference(substitution,[status(thm)],[c507]) ).
cnf(c1457,plain,
one = eta(eta(product(X2,i(X)))),
inference(symmetry,[status(thm)],[c1456]) ).
cnf(c1458,plain,
quotient(quotient(i(i(X2)),quotient(X,i(X2))),one) = quotient(quotient(i(i(X2)),quotient(X,i(X2))),eta(eta(product(X2,i(X))))),
inference(congruence,[status(thm)],[c1457]) ).
cnf(c1459,plain,
quotient(i(i(X2)),quotient(X,i(X2))) = product(i(X2),quotient(X2,X)),
inference(symmetry,[status(thm)],[c1013]) ).
cnf(c1460,plain,
quotient(quotient(i(i(X2)),quotient(X,i(X2))),eta(eta(product(X2,i(X))))) = quotient(product(i(X2),quotient(X2,X)),eta(eta(product(X2,i(X))))),
inference(congruence,[status(thm)],[c1459]) ).
cnf(c1461,plain,
product(i(X2),quotient(X2,X)) = product(i(X),eta(product(X2,i(X)))),
inference(symmetry,[status(thm)],[c974]) ).
cnf(c1462,plain,
quotient(product(i(X2),quotient(X2,X)),eta(eta(product(X2,i(X))))) = quotient(product(i(X),eta(product(X2,i(X)))),eta(eta(product(X2,i(X))))),
inference(congruence,[status(thm)],[c1461]) ).
cnf(c1463,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1464,plain,
product(X2,X) = product(i(j(X2)),X),
inference(congruence,[status(thm)],[c1463]) ).
cnf(c1465,plain,
quotient(product(X2,X),eta(X)) = quotient(product(i(j(X2)),X),eta(X)),
inference(congruence,[status(thm)],[c1464]) ).
cnf(c1466,plain,
quotient(product(i(j(X2)),X),eta(X)) = i(difference(X,j(X2))),
inference(substitution,[status(thm)],[c1393]) ).
cnf(c1467,plain,
quotient(product(X2,X),eta(X)) = i(difference(X,j(X2))),
inference(transitivity,[status(thm)],[c1465,c1466]) ).
cnf(c1468,plain,
quotient(product(i(X),eta(product(X2,i(X)))),eta(eta(product(X2,i(X))))) = i(difference(eta(product(X2,i(X))),j(i(X)))),
inference(substitution,[status(thm)],[c1467]) ).
cnf(c1469,plain,
i(difference(eta(product(X2,i(X))),j(i(X)))) = product(i(j(i(X))),eta(product(X2,i(X)))),
inference(substitution,[status(thm)],[c836]) ).
cnf(c1470,plain,
product(i(j(i(X))),eta(product(X2,i(X)))) = difference(j(i(X)),eta(product(X2,i(X)))),
inference(substitution,[status(thm)],[c1030]) ).
cnf(c1471,plain,
difference(j(i(X)),eta(product(X2,i(X)))) = product(i(X),eta(product(X2,i(X)))),
inference(substitution,[status(thm)],[c1034]) ).
cnf(c1472,plain,
product(i(X),eta(product(X2,i(X)))) = difference(X,eta(quotient(X2,X))),
inference(substitution,[status(thm)],[c1201]) ).
cnf(c1473,plain,
difference(X,eta(quotient(X2,X))) = difference(X,eta(difference(X2,X))),
inference(congruence,[status(thm)],[c1270]) ).
cnf(c1474,plain,
eta(difference(X2,X)) = eta(difference(X,X2)),
inference(symmetry,[status(thm)],[c1442]) ).
cnf(c1475,plain,
difference(X,eta(difference(X2,X))) = difference(X,eta(difference(X,X2))),
inference(congruence,[status(thm)],[c1474]) ).
cnf(c1476,plain,
eta(difference(X2,X)) = eta(quotient(X2,X)),
inference(symmetry,[status(thm)],[c1270]) ).
cnf(c1477,plain,
difference(X2,eta(difference(X2,X))) = difference(X2,eta(quotient(X2,X))),
inference(congruence,[status(thm)],[c1476]) ).
cnf(c1478,plain,
eta(quotient(X2,X)) = eta(quotient(i(X2),i(X))),
inference(symmetry,[status(thm)],[c558]) ).
cnf(c1479,plain,
difference(X2,eta(quotient(X2,X))) = difference(X2,eta(quotient(i(X2),i(X)))),
inference(congruence,[status(thm)],[c1478]) ).
cnf(c1480,plain,
eta(quotient(i(i(X2)),i(i(X)))) = eta(quotient(i(X2),i(X))),
inference(substitution,[status(thm)],[c558]) ).
cnf(c1481,plain,
eta(quotient(i(X2),i(X))) = eta(quotient(i(i(X2)),i(i(X)))),
inference(symmetry,[status(thm)],[c1480]) ).
cnf(c1482,plain,
difference(X2,eta(quotient(i(X2),i(X)))) = difference(X2,eta(quotient(i(i(X2)),i(i(X))))),
inference(congruence,[status(thm)],[c1481]) ).
cnf(c1483,plain,
eta(product(X,i(i(X2)))) = eta(quotient(i(i(X2)),i(i(X)))),
inference(substitution,[status(thm)],[c874]) ).
cnf(c1484,plain,
eta(quotient(i(i(X2)),i(i(X)))) = eta(product(X,i(i(X2)))),
inference(symmetry,[status(thm)],[c1483]) ).
cnf(c1485,plain,
difference(X2,eta(quotient(i(i(X2)),i(i(X))))) = difference(X2,eta(product(X,i(i(X2))))),
inference(congruence,[status(thm)],[c1484]) ).
cnf(c1486,plain,
product(i(X2),eta(product(X,i(i(X2))))) = difference(X2,eta(product(X,i(i(X2))))),
inference(substitution,[status(thm)],[c1030]) ).
cnf(c1487,plain,
difference(X2,eta(product(X,i(i(X2))))) = product(i(X2),eta(product(X,i(i(X2))))),
inference(symmetry,[status(thm)],[c1486]) ).
cnf(c1488,plain,
i(difference(eta(product(X,i(i(X2)))),X2)) = product(i(X2),eta(product(X,i(i(X2))))),
inference(substitution,[status(thm)],[c836]) ).
cnf(c1489,plain,
product(i(X2),eta(product(X,i(i(X2))))) = i(difference(eta(product(X,i(i(X2)))),X2)),
inference(symmetry,[status(thm)],[c1488]) ).
cnf(c1490,plain,
quotient(product(i(X2),eta(product(X,i(i(X2))))),eta(eta(product(X,i(i(X2)))))) = i(difference(eta(product(X,i(i(X2)))),X2)),
inference(substitution,[status(thm)],[c1393]) ).
cnf(c1491,plain,
i(difference(eta(product(X,i(i(X2)))),X2)) = quotient(product(i(X2),eta(product(X,i(i(X2))))),eta(eta(product(X,i(i(X2)))))),
inference(symmetry,[status(thm)],[c1490]) ).
cnf(c1492,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1493,plain,
product(X,quotient(j(X),j(X2))) = product(i(j(X)),quotient(j(X),j(X2))),
inference(congruence,[status(thm)],[c1492]) ).
cnf(c1494,plain,
product(i(j(X)),eta(product(X2,i(j(X))))) = product(i(X2),quotient(X2,j(X))),
inference(substitution,[status(thm)],[c974]) ).
cnf(c1495,plain,
product(i(X2),quotient(X2,j(X))) = product(i(j(X)),eta(product(X2,i(j(X))))),
inference(symmetry,[status(thm)],[c1494]) ).
cnf(c1496,plain,
product(i(j(X)),eta(product(X2,i(j(X))))) = product(X,eta(product(X2,i(j(X))))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1497,plain,
product(X2,i(j(X))) = product(X2,X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1498,plain,
eta(product(X2,i(j(X)))) = eta(product(X2,X)),
inference(congruence,[status(thm)],[c1497]) ).
cnf(c1499,plain,
product(X,eta(product(X2,i(j(X))))) = product(X,eta(product(X2,X))),
inference(congruence,[status(thm)],[c1498]) ).
cnf(c1500,plain,
product(i(j(X)),eta(product(X2,i(j(X))))) = product(X,eta(product(X2,X))),
inference(transitivity,[status(thm)],[c1496,c1499]) ).
cnf(c1501,plain,
product(i(X2),quotient(X2,j(X))) = product(X,eta(product(X2,X))),
inference(transitivity,[status(thm)],[c1495,c1500]) ).
cnf(c1502,plain,
product(i(j(X)),quotient(j(X),j(X2))) = product(X2,eta(product(j(X),X2))),
inference(substitution,[status(thm)],[c1501]) ).
cnf(c1503,plain,
eta(product(j(X),X2)) = eta(product(X,i(X2))),
inference(substitution,[status(thm)],[c1283]) ).
cnf(c1504,plain,
product(X2,eta(product(j(X),X2))) = product(X2,eta(product(X,i(X2)))),
inference(congruence,[status(thm)],[c1503]) ).
cnf(c1505,plain,
product(i(j(X)),quotient(j(X),j(X2))) = product(X2,eta(product(X,i(X2)))),
inference(transitivity,[status(thm)],[c1502,c1504]) ).
cnf(c1506,plain,
product(X,quotient(j(X),j(X2))) = product(X2,eta(product(X,i(X2)))),
inference(transitivity,[status(thm)],[c1493,c1505]) ).
cnf(c1507,plain,
product(X,quotient(j(X),j(i(X2)))) = product(i(X2),eta(product(X,i(i(X2))))),
inference(substitution,[status(thm)],[c1506]) ).
cnf(c1508,plain,
product(i(X2),eta(product(X,i(i(X2))))) = product(X,quotient(j(X),j(i(X2)))),
inference(symmetry,[status(thm)],[c1507]) ).
cnf(c1509,plain,
quotient(product(i(X2),eta(product(X,i(i(X2))))),eta(eta(product(X,i(i(X2)))))) = quotient(product(X,quotient(j(X),j(i(X2)))),eta(eta(product(X,i(i(X2)))))),
inference(congruence,[status(thm)],[c1508]) ).
cnf(c1510,plain,
product(X,quotient(j(X),j(i(X2)))) = quotient(i(X),quotient(j(i(X2)),X)),
inference(substitution,[status(thm)],[c997]) ).
cnf(c1511,plain,
quotient(product(X,quotient(j(X),j(i(X2)))),eta(eta(product(X,i(i(X2)))))) = quotient(quotient(i(X),quotient(j(i(X2)),X)),eta(eta(product(X,i(i(X2)))))),
inference(congruence,[status(thm)],[c1510]) ).
cnf(c1512,plain,
quotient(j(i(X2)),X) = quotient(X2,X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c1513,plain,
quotient(i(X),quotient(j(i(X2)),X)) = quotient(i(X),quotient(X2,X)),
inference(congruence,[status(thm)],[c1512]) ).
cnf(c1514,plain,
quotient(quotient(i(X),quotient(j(i(X2)),X)),eta(eta(product(X,i(i(X2)))))) = quotient(quotient(i(X),quotient(X2,X)),eta(eta(product(X,i(i(X2)))))),
inference(congruence,[status(thm)],[c1513]) ).
cnf(c1515,plain,
eta(eta(product(X,i(i(X2))))) = one,
inference(substitution,[status(thm)],[c507]) ).
cnf(c1516,plain,
quotient(quotient(i(X),quotient(X2,X)),eta(eta(product(X,i(i(X2)))))) = quotient(quotient(i(X),quotient(X2,X)),one),
inference(congruence,[status(thm)],[c1515]) ).
cnf(c1517,plain,
quotient(quotient(i(X),quotient(X2,X)),one) = quotient(i(X),quotient(X2,X)),
inference(substitution,[status(thm)],[c1123]) ).
cnf(c1518,plain,
quotient(quotient(i(X),quotient(X2,X)),eta(eta(product(X,i(i(X2)))))) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1516,c1517]) ).
cnf(c1519,plain,
quotient(quotient(i(X),quotient(j(i(X2)),X)),eta(eta(product(X,i(i(X2)))))) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1514,c1518]) ).
cnf(c1520,plain,
quotient(product(X,quotient(j(X),j(i(X2)))),eta(eta(product(X,i(i(X2)))))) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1511,c1519]) ).
cnf(c1521,plain,
quotient(product(i(X2),eta(product(X,i(i(X2))))),eta(eta(product(X,i(i(X2)))))) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1509,c1520]) ).
cnf(c1522,plain,
i(difference(eta(product(X,i(i(X2)))),X2)) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1491,c1521]) ).
cnf(c1523,plain,
product(i(X2),eta(product(X,i(i(X2))))) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1489,c1522]) ).
cnf(c1524,plain,
difference(X2,eta(product(X,i(i(X2))))) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1487,c1523]) ).
cnf(c1525,plain,
difference(X2,eta(quotient(i(i(X2)),i(i(X))))) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1485,c1524]) ).
cnf(c1526,plain,
difference(X2,eta(quotient(i(X2),i(X)))) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1482,c1525]) ).
cnf(c1527,plain,
difference(X2,eta(quotient(X2,X))) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1479,c1526]) ).
cnf(c1528,plain,
difference(X2,eta(difference(X2,X))) = quotient(i(X),quotient(X2,X)),
inference(transitivity,[status(thm)],[c1477,c1527]) ).
cnf(c1529,plain,
difference(X,eta(difference(X,X2))) = quotient(i(X2),quotient(X,X2)),
inference(substitution,[status(thm)],[c1528]) ).
cnf(c1530,plain,
difference(X,eta(difference(X2,X))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1475,c1529]) ).
cnf(c1531,plain,
difference(X,eta(quotient(X2,X))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1473,c1530]) ).
cnf(c1532,plain,
product(i(X),eta(product(X2,i(X)))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1472,c1531]) ).
cnf(c1533,plain,
difference(j(i(X)),eta(product(X2,i(X)))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1471,c1532]) ).
cnf(c1534,plain,
product(i(j(i(X))),eta(product(X2,i(X)))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1470,c1533]) ).
cnf(c1535,plain,
i(difference(eta(product(X2,i(X))),j(i(X)))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1469,c1534]) ).
cnf(c1536,plain,
quotient(product(i(X),eta(product(X2,i(X)))),eta(eta(product(X2,i(X))))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1468,c1535]) ).
cnf(c1537,plain,
quotient(product(i(X2),quotient(X2,X)),eta(eta(product(X2,i(X))))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1462,c1536]) ).
cnf(c1538,plain,
quotient(quotient(i(i(X2)),quotient(X,i(X2))),eta(eta(product(X2,i(X))))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1460,c1537]) ).
cnf(c1539,plain,
quotient(quotient(i(i(X2)),quotient(X,i(X2))),one) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1458,c1538]) ).
cnf(c1540,plain,
quotient(i(i(X2)),quotient(X,i(X2))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1455,c1539]) ).
cnf(c1541,plain,
eta(quotient(i(i(X2)),quotient(X,i(X2)))) = eta(quotient(i(X2),quotient(X,X2))),
inference(congruence,[status(thm)],[c1540]) ).
cnf(c1542,plain,
eta(quotient(i(X2),quotient(X,X2))) = eta(difference(i(X2),quotient(X,X2))),
inference(substitution,[status(thm)],[c1270]) ).
cnf(c1543,plain,
eta(difference(i(X2),i(X))) = eta(difference(i(X2),X)),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c1544,plain,
eta(difference(i(X2),X)) = eta(difference(i(X2),i(X))),
inference(symmetry,[status(thm)],[c1543]) ).
cnf(c1545,plain,
eta(difference(i(X2),X)) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1544,c1137]) ).
cnf(c1546,plain,
eta(difference(i(X2),quotient(X,X2))) = eta(difference(X2,quotient(X,X2))),
inference(substitution,[status(thm)],[c1545]) ).
cnf(c1547,plain,
eta(difference(X2,quotient(X,X2))) = eta(difference(quotient(X,X2),X2)),
inference(substitution,[status(thm)],[c1442]) ).
cnf(c1548,plain,
difference(quotient(X,X2),X) = X2,
inference(substitution,[status(thm)],[c209]) ).
cnf(c1549,plain,
X2 = difference(quotient(X,X2),X),
inference(symmetry,[status(thm)],[c1548]) ).
cnf(c1550,plain,
difference(quotient(X,X2),X2) = difference(quotient(X,X2),difference(quotient(X,X2),X)),
inference(congruence,[status(thm)],[c1549]) ).
cnf(c1551,plain,
eta(difference(quotient(X,X2),X2)) = eta(difference(quotient(X,X2),difference(quotient(X,X2),X))),
inference(congruence,[status(thm)],[c1550]) ).
cnf(c1552,plain,
eta(difference(i(X2),i(difference(X2,X)))) = eta(difference(X2,difference(X2,X))),
inference(substitution,[status(thm)],[c1137]) ).
cnf(c1553,plain,
eta(difference(X2,difference(X2,X))) = eta(difference(i(X2),i(difference(X2,X)))),
inference(symmetry,[status(thm)],[c1552]) ).
cnf(c1554,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c1555,plain,
difference(X2,X) = difference(j(i(X2)),X),
inference(congruence,[status(thm)],[c1554]) ).
cnf(c1556,plain,
i(difference(X2,X)) = i(difference(j(i(X2)),X)),
inference(congruence,[status(thm)],[c1555]) ).
cnf(c1557,plain,
difference(i(X2),i(difference(X2,X))) = difference(i(X2),i(difference(j(i(X2)),X))),
inference(congruence,[status(thm)],[c1556]) ).
cnf(c1558,plain,
eta(difference(i(X2),i(difference(X2,X)))) = eta(difference(i(X2),i(difference(j(i(X2)),X)))),
inference(congruence,[status(thm)],[c1557]) ).
cnf(c1559,plain,
eta(difference(i(X2),i(difference(j(i(X2)),X)))) = eta(X),
inference(substitution,[status(thm)],[c1429]) ).
cnf(c1560,plain,
eta(difference(i(X2),i(difference(X2,X)))) = eta(X),
inference(transitivity,[status(thm)],[c1558,c1559]) ).
cnf(c1561,plain,
eta(difference(X2,difference(X2,X))) = eta(X),
inference(transitivity,[status(thm)],[c1553,c1560]) ).
cnf(c1562,plain,
eta(difference(quotient(X,X2),difference(quotient(X,X2),X))) = eta(X),
inference(substitution,[status(thm)],[c1561]) ).
cnf(c1563,plain,
eta(difference(quotient(X,X2),X2)) = eta(X),
inference(transitivity,[status(thm)],[c1551,c1562]) ).
cnf(c1564,plain,
eta(difference(X2,quotient(X,X2))) = eta(X),
inference(transitivity,[status(thm)],[c1547,c1563]) ).
cnf(c1565,plain,
eta(difference(i(X2),quotient(X,X2))) = eta(X),
inference(transitivity,[status(thm)],[c1546,c1564]) ).
cnf(c1566,plain,
eta(quotient(i(X2),quotient(X,X2))) = eta(X),
inference(transitivity,[status(thm)],[c1542,c1565]) ).
cnf(c1567,plain,
eta(quotient(i(i(X2)),quotient(X,i(X2)))) = eta(X),
inference(transitivity,[status(thm)],[c1541,c1566]) ).
cnf(c1568,plain,
eta(quotient(quotient(X,i(X2)),i(i(i(X2))))) = eta(X),
inference(transitivity,[status(thm)],[c1453,c1567]) ).
cnf(c1569,plain,
eta(difference(quotient(X,i(X2)),i(i(i(X2))))) = eta(X),
inference(transitivity,[status(thm)],[c1451,c1568]) ).
cnf(c1570,plain,
eta(difference(quotient(X,i(X2)),i(i(X2)))) = eta(X),
inference(transitivity,[status(thm)],[c1449,c1569]) ).
cnf(c1571,plain,
eta(difference(quotient(X,i(X2)),i(X2))) = eta(X),
inference(transitivity,[status(thm)],[c1447,c1570]) ).
cnf(c1572,plain,
eta(difference(quotient(X,i(X2)),X2)) = eta(X),
inference(transitivity,[status(thm)],[c1445,c1571]) ).
cnf(c1573,plain,
eta(difference(X2,quotient(X,i(X2)))) = eta(X),
inference(transitivity,[status(thm)],[c1443,c1572]) ).
cnf(c1574,plain,
eta(difference(X,quotient(X2,i(X)))) = eta(X2),
inference(substitution,[status(thm)],[c1573]) ).
cnf(c1575,plain,
eta(X2) = eta(difference(X,quotient(X2,i(X)))),
inference(symmetry,[status(thm)],[c1574]) ).
cnf(c1576,plain,
i(eta(X2)) = i(eta(difference(X,quotient(X2,i(X))))),
inference(congruence,[status(thm)],[c1575]) ).
cnf(c1577,plain,
product(difference(X2,eta(X3)),i(eta(X3))) = product(difference(X2,eta(X3)),i(eta(difference(X,quotient(X3,i(X)))))),
inference(congruence,[status(thm)],[c1576]) ).
cnf(c1578,plain,
eta(difference(X,quotient(X2,i(X)))) = eta(X2),
inference(substitution,[status(thm)],[c1573]) ).
cnf(c1579,plain,
eta(X2) = eta(difference(X,quotient(X2,i(X)))),
inference(symmetry,[status(thm)],[c1578]) ).
cnf(c1580,plain,
difference(X2,eta(X3)) = difference(X2,eta(difference(X,quotient(X3,i(X))))),
inference(congruence,[status(thm)],[c1579]) ).
cnf(c1581,plain,
product(difference(X2,eta(X3)),i(eta(difference(X,quotient(X3,i(X)))))) = product(difference(X2,eta(difference(X,quotient(X3,i(X))))),i(eta(difference(X,quotient(X3,i(X)))))),
inference(congruence,[status(thm)],[c1580]) ).
cnf(c1582,plain,
j(i(product(j(X),i(i(X))))) = product(j(X),i(i(X))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c1583,plain,
product(j(X),i(i(X))) = j(i(product(j(X),i(i(X))))),
inference(symmetry,[status(thm)],[c1582]) ).
cnf(c1584,plain,
i(i(X)) = product(eta(X),X),
inference(symmetry,[status(thm)],[c490]) ).
cnf(c1585,plain,
product(j(X),i(i(X))) = product(j(X),product(eta(X),X)),
inference(congruence,[status(thm)],[c1584]) ).
cnf(c1586,plain,
i(product(j(X),i(i(X)))) = i(product(j(X),product(eta(X),X))),
inference(congruence,[status(thm)],[c1585]) ).
cnf(c1587,plain,
quotient(difference(product(eta(X),X),eta(X)),j(X)) = i(product(j(X),product(eta(X),X))),
inference(substitution,[status(thm)],[c752]) ).
cnf(c1588,plain,
i(product(j(X),product(eta(X),X))) = quotient(difference(product(eta(X),X),eta(X)),j(X)),
inference(symmetry,[status(thm)],[c1587]) ).
cnf(c1589,plain,
quotient(difference(product(eta(X),X),eta(X)),j(X)) = quotient(quotient(j(X),eta(X)),j(X)),
inference(congruence,[status(thm)],[c485]) ).
cnf(c1590,plain,
quotient(quotient(j(X),eta(X)),j(X)) = quotient(i(X),j(X)),
inference(congruence,[status(thm)],[c501]) ).
cnf(c1591,plain,
quotient(quotient(j(X),eta(X)),j(X)) = eta(X),
inference(transitivity,[status(thm)],[c1590,c468]) ).
cnf(c1592,plain,
quotient(difference(product(eta(X),X),eta(X)),j(X)) = eta(X),
inference(transitivity,[status(thm)],[c1589,c1591]) ).
cnf(c1593,plain,
i(product(j(X),product(eta(X),X))) = eta(X),
inference(transitivity,[status(thm)],[c1588,c1592]) ).
cnf(c1594,plain,
i(product(j(X),i(i(X)))) = eta(X),
inference(transitivity,[status(thm)],[c1586,c1593]) ).
cnf(c1595,plain,
j(i(product(j(X),i(i(X))))) = j(eta(X)),
inference(congruence,[status(thm)],[c1594]) ).
cnf(c1596,plain,
j(i(product(j(X),i(i(X))))) = i(eta(X)),
inference(transitivity,[status(thm)],[c1595,c788]) ).
cnf(c1597,plain,
product(j(X),i(i(X))) = i(eta(X)),
inference(transitivity,[status(thm)],[c1583,c1596]) ).
cnf(c1598,plain,
i(eta(X)) = product(j(X),i(i(X))),
inference(symmetry,[status(thm)],[c1597]) ).
cnf(c1599,plain,
product(difference(X2,eta(X)),i(eta(X))) = product(difference(X2,eta(X)),product(j(X),i(i(X)))),
inference(congruence,[status(thm)],[c1598]) ).
cnf(c1600,plain,
eta(X) = i(product(j(X),i(i(X)))),
inference(symmetry,[status(thm)],[c1594]) ).
cnf(c1601,plain,
difference(X2,eta(X)) = difference(X2,i(product(j(X),i(i(X))))),
inference(congruence,[status(thm)],[c1600]) ).
cnf(c1602,plain,
product(difference(X2,eta(X)),product(j(X),i(i(X)))) = product(difference(X2,i(product(j(X),i(i(X))))),product(j(X),i(i(X)))),
inference(congruence,[status(thm)],[c1601]) ).
cnf(c1603,plain,
quotient(i(X),difference(X2,i(X))) = X2,
inference(substitution,[status(thm)],[c86]) ).
cnf(c1604,plain,
X2 = quotient(i(X),difference(X2,i(X))),
inference(symmetry,[status(thm)],[c1603]) ).
cnf(c1605,plain,
quotient(eta(difference(X2,i(X))),X2) = quotient(eta(difference(X2,i(X))),quotient(i(X),difference(X2,i(X)))),
inference(congruence,[status(thm)],[c1604]) ).
cnf(c1606,plain,
quotient(eta(difference(X2,i(X))),quotient(i(X),difference(X2,i(X)))) = product(difference(X2,i(X)),X),
inference(substitution,[status(thm)],[c1228]) ).
cnf(c1607,plain,
quotient(eta(difference(X2,i(X))),X2) = product(difference(X2,i(X)),X),
inference(transitivity,[status(thm)],[c1605,c1606]) ).
cnf(c1608,plain,
quotient(eta(difference(X2,i(product(j(X),i(i(X)))))),X2) = product(difference(X2,i(product(j(X),i(i(X))))),product(j(X),i(i(X)))),
inference(substitution,[status(thm)],[c1607]) ).
cnf(c1609,plain,
product(difference(X2,i(product(j(X),i(i(X))))),product(j(X),i(i(X)))) = quotient(eta(difference(X2,i(product(j(X),i(i(X)))))),X2),
inference(symmetry,[status(thm)],[c1608]) ).
cnf(c1610,plain,
difference(X2,i(product(j(X),i(i(X))))) = difference(X2,eta(X)),
inference(congruence,[status(thm)],[c1594]) ).
cnf(c1611,plain,
eta(difference(X2,i(product(j(X),i(i(X)))))) = eta(difference(X2,eta(X))),
inference(congruence,[status(thm)],[c1610]) ).
cnf(c1612,plain,
quotient(eta(difference(X2,i(product(j(X),i(i(X)))))),X2) = quotient(eta(difference(X2,eta(X))),X2),
inference(congruence,[status(thm)],[c1611]) ).
cnf(c1613,plain,
product(difference(X2,i(product(j(X),i(i(X))))),product(j(X),i(i(X)))) = quotient(eta(difference(X2,eta(X))),X2),
inference(transitivity,[status(thm)],[c1609,c1612]) ).
cnf(c1614,plain,
product(difference(X2,eta(X)),product(j(X),i(i(X)))) = quotient(eta(difference(X2,eta(X))),X2),
inference(transitivity,[status(thm)],[c1602,c1613]) ).
cnf(c1615,plain,
product(difference(X2,eta(X)),i(eta(X))) = quotient(eta(difference(X2,eta(X))),X2),
inference(transitivity,[status(thm)],[c1599,c1614]) ).
cnf(c1616,plain,
product(difference(X2,eta(difference(X,quotient(X3,i(X))))),i(eta(difference(X,quotient(X3,i(X)))))) = quotient(eta(difference(X2,eta(difference(X,quotient(X3,i(X)))))),X2),
inference(substitution,[status(thm)],[c1615]) ).
cnf(c1617,plain,
eta(j(difference(X2,eta(X)))) = eta(difference(X2,eta(X))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1618,plain,
eta(difference(X2,eta(X))) = eta(j(difference(X2,eta(X)))),
inference(symmetry,[status(thm)],[c1617]) ).
cnf(c1619,plain,
eta(difference(X,difference(X,j(difference(X2,eta(X)))))) = eta(j(difference(X2,eta(X)))),
inference(substitution,[status(thm)],[c1561]) ).
cnf(c1620,plain,
eta(j(difference(X2,eta(X)))) = eta(difference(X,difference(X,j(difference(X2,eta(X)))))),
inference(symmetry,[status(thm)],[c1619]) ).
cnf(c1621,plain,
difference(X,eta(X2)) = quotient(i(difference(X2,X)),X2),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c1622,plain,
j(difference(X,eta(X2))) = j(quotient(i(difference(X2,X)),X2)),
inference(congruence,[status(thm)],[c1621]) ).
cnf(c1623,plain,
difference(X2,j(difference(X,eta(X2)))) = difference(X2,j(quotient(i(difference(X2,X)),X2))),
inference(congruence,[status(thm)],[c1622]) ).
cnf(c1624,plain,
difference(X2,j(quotient(i(difference(X2,X)),X2))) = quotient(eta(X2),i(difference(X2,X))),
inference(substitution,[status(thm)],[c1048]) ).
cnf(c1625,plain,
difference(X2,j(difference(X,eta(X2)))) = quotient(eta(X2),i(difference(X2,X))),
inference(transitivity,[status(thm)],[c1623,c1624]) ).
cnf(c1626,plain,
difference(X,j(difference(X2,eta(X)))) = quotient(eta(X),i(difference(X,X2))),
inference(substitution,[status(thm)],[c1625]) ).
cnf(c1627,plain,
difference(X,difference(X,j(difference(X2,eta(X))))) = difference(X,quotient(eta(X),i(difference(X,X2)))),
inference(congruence,[status(thm)],[c1626]) ).
cnf(c1628,plain,
eta(difference(X,difference(X,j(difference(X2,eta(X)))))) = eta(difference(X,quotient(eta(X),i(difference(X,X2))))),
inference(congruence,[status(thm)],[c1627]) ).
cnf(c1629,plain,
quotient(eta(X2),X) = product(X2,j(product(X,X2))),
inference(symmetry,[status(thm)],[c1235]) ).
cnf(c1630,plain,
difference(X2,quotient(eta(X2),X)) = difference(X2,product(X2,j(product(X,X2)))),
inference(congruence,[status(thm)],[c1629]) ).
cnf(c1631,plain,
difference(X2,product(X2,j(product(X,X2)))) = j(product(X,X2)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c1632,plain,
difference(X2,quotient(eta(X2),X)) = j(product(X,X2)),
inference(transitivity,[status(thm)],[c1630,c1631]) ).
cnf(c1633,plain,
difference(X,quotient(eta(X),i(difference(X,X2)))) = j(product(i(difference(X,X2)),X)),
inference(substitution,[status(thm)],[c1632]) ).
cnf(c1634,plain,
eta(difference(X,quotient(eta(X),i(difference(X,X2))))) = eta(j(product(i(difference(X,X2)),X))),
inference(congruence,[status(thm)],[c1633]) ).
cnf(c1635,plain,
eta(j(product(i(difference(X,X2)),X))) = eta(product(i(difference(X,X2)),X)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c1636,plain,
eta(difference(X2,difference(X2,product(X2,X)))) = eta(product(X2,X)),
inference(substitution,[status(thm)],[c1561]) ).
cnf(c1637,plain,
eta(product(X2,X)) = eta(difference(X2,difference(X2,product(X2,X)))),
inference(symmetry,[status(thm)],[c1636]) ).
cnf(c1638,plain,
difference(X2,product(X2,X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c1639,plain,
difference(X2,difference(X2,product(X2,X))) = difference(X2,X),
inference(congruence,[status(thm)],[c1638]) ).
cnf(c1640,plain,
eta(difference(X2,difference(X2,product(X2,X)))) = eta(difference(X2,X)),
inference(congruence,[status(thm)],[c1639]) ).
cnf(c1641,plain,
eta(product(X2,X)) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1637,c1640]) ).
cnf(c1642,plain,
eta(product(i(difference(X,X2)),X)) = eta(difference(i(difference(X,X2)),X)),
inference(substitution,[status(thm)],[c1641]) ).
cnf(c1643,plain,
eta(difference(X,i(difference(X,X2)))) = eta(difference(i(difference(X,X2)),X)),
inference(substitution,[status(thm)],[c1442]) ).
cnf(c1644,plain,
eta(difference(i(difference(X,X2)),X)) = eta(difference(X,i(difference(X,X2)))),
inference(symmetry,[status(thm)],[c1643]) ).
cnf(c1645,plain,
eta(difference(X,i(difference(X,X2)))) = eta(difference(X,difference(X,X2))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c1646,plain,
eta(difference(X,difference(X,X2))) = eta(X2),
inference(substitution,[status(thm)],[c1561]) ).
cnf(c1647,plain,
eta(difference(X,i(difference(X,X2)))) = eta(X2),
inference(transitivity,[status(thm)],[c1645,c1646]) ).
cnf(c1648,plain,
eta(difference(i(difference(X,X2)),X)) = eta(X2),
inference(transitivity,[status(thm)],[c1644,c1647]) ).
cnf(c1649,plain,
eta(product(i(difference(X,X2)),X)) = eta(X2),
inference(transitivity,[status(thm)],[c1642,c1648]) ).
cnf(c1650,plain,
eta(j(product(i(difference(X,X2)),X))) = eta(X2),
inference(transitivity,[status(thm)],[c1635,c1649]) ).
cnf(c1651,plain,
eta(difference(X,quotient(eta(X),i(difference(X,X2))))) = eta(X2),
inference(transitivity,[status(thm)],[c1634,c1650]) ).
cnf(c1652,plain,
eta(difference(X,difference(X,j(difference(X2,eta(X)))))) = eta(X2),
inference(transitivity,[status(thm)],[c1628,c1651]) ).
cnf(c1653,plain,
eta(j(difference(X2,eta(X)))) = eta(X2),
inference(transitivity,[status(thm)],[c1620,c1652]) ).
cnf(c1654,plain,
eta(difference(X2,eta(X))) = eta(X2),
inference(transitivity,[status(thm)],[c1618,c1653]) ).
cnf(c1655,plain,
eta(difference(X2,eta(difference(X,quotient(X3,i(X)))))) = eta(X2),
inference(substitution,[status(thm)],[c1654]) ).
cnf(c1656,plain,
quotient(eta(difference(X2,eta(difference(X,quotient(X3,i(X)))))),X2) = quotient(eta(X2),X2),
inference(congruence,[status(thm)],[c1655]) ).
cnf(c1657,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c1658,plain,
quotient(eta(X),X) = quotient(product(i(X),X),X),
inference(congruence,[status(thm)],[c1657]) ).
cnf(c1659,plain,
quotient(product(i(X),X),X) = i(X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c1660,plain,
quotient(eta(X),X) = i(X),
inference(transitivity,[status(thm)],[c1658,c1659]) ).
cnf(c1661,plain,
quotient(eta(difference(X2,eta(difference(X,quotient(X3,i(X)))))),X2) = i(X2),
inference(transitivity,[status(thm)],[c1656,c1660]) ).
cnf(c1662,plain,
product(difference(X2,eta(difference(X,quotient(X3,i(X))))),i(eta(difference(X,quotient(X3,i(X)))))) = i(X2),
inference(transitivity,[status(thm)],[c1616,c1661]) ).
cnf(c1663,plain,
product(difference(X2,eta(X3)),i(eta(difference(X,quotient(X3,i(X)))))) = i(X2),
inference(transitivity,[status(thm)],[c1581,c1662]) ).
cnf(c1664,plain,
product(difference(X,eta(X2)),i(eta(X2))) = i(X),
inference(transitivity,[status(thm)],[c1577,c1663]) ).
cnf(c1665,plain,
difference(difference(i(eta(X2)),X),i(i(eta(X2)))) = i(X),
inference(transitivity,[status(thm)],[c1135,c1664]) ).
cnf(c1666,plain,
difference(difference(i(eta(X2)),X),eta(X2)) = i(X),
inference(transitivity,[status(thm)],[c1053,c1665]) ).
cnf(c1667,plain,
difference(difference(i(eta(X)),j(quotient(X2,i(eta(X))))),eta(X)) = i(j(quotient(X2,i(eta(X))))),
inference(substitution,[status(thm)],[c1666]) ).
cnf(c1668,plain,
i(j(quotient(X2,i(eta(X))))) = quotient(X2,i(eta(X))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1669,plain,
difference(difference(i(eta(X)),j(quotient(X2,i(eta(X))))),eta(X)) = quotient(X2,i(eta(X))),
inference(transitivity,[status(thm)],[c1667,c1668]) ).
cnf(c1670,plain,
difference(quotient(eta(i(eta(X))),X2),eta(X)) = quotient(X2,i(eta(X))),
inference(transitivity,[status(thm)],[c1051,c1669]) ).
cnf(c1671,plain,
difference(quotient(eta(eta(X)),X2),eta(X)) = quotient(X2,i(eta(X))),
inference(transitivity,[status(thm)],[c1044,c1670]) ).
cnf(c1672,plain,
difference(quotient(one,X2),eta(X)) = quotient(X2,i(eta(X))),
inference(transitivity,[status(thm)],[c1040,c1671]) ).
cnf(c1673,plain,
difference(j(X2),eta(X)) = quotient(X2,i(eta(X))),
inference(transitivity,[status(thm)],[c1037,c1672]) ).
cnf(c1674,plain,
product(X2,eta(X)) = quotient(X2,i(eta(X))),
inference(transitivity,[status(thm)],[c1035,c1673]) ).
cnf(c1675,plain,
quotient(X2,i(eta(X))) = product(X2,eta(X)),
inference(symmetry,[status(thm)],[c1674]) ).
cnf(c1676,plain,
quotient(quotient(X2,i(eta(X))),j(X)) = quotient(product(X2,eta(X)),j(X)),
inference(congruence,[status(thm)],[c1675]) ).
cnf(c1677,plain,
quotient(difference(X2,X),i(X2)) = product(product(j(X2),X),X2),
inference(symmetry,[status(thm)],[c1358]) ).
cnf(c1678,plain,
difference(j(X2),quotient(difference(X2,X),i(X2))) = difference(j(X2),product(product(j(X2),X),X2)),
inference(congruence,[status(thm)],[c1677]) ).
cnf(c1679,plain,
difference(j(X2),product(product(j(X2),X),X2)) = quotient(product(X,product(X2,j(X2))),j(X2)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c1680,plain,
product(X,product(X2,j(X2))) = product(X,eta(X2)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c1681,plain,
quotient(product(X,product(X2,j(X2))),j(X2)) = quotient(product(X,eta(X2)),j(X2)),
inference(congruence,[status(thm)],[c1680]) ).
cnf(c1682,plain,
difference(j(X2),product(product(j(X2),X),X2)) = quotient(product(X,eta(X2)),j(X2)),
inference(transitivity,[status(thm)],[c1679,c1681]) ).
cnf(c1683,plain,
difference(j(X2),quotient(difference(X2,X),i(X2))) = quotient(product(X,eta(X2)),j(X2)),
inference(transitivity,[status(thm)],[c1678,c1682]) ).
cnf(c1684,plain,
difference(j(X),quotient(difference(X,X2),i(X))) = quotient(product(X2,eta(X)),j(X)),
inference(substitution,[status(thm)],[c1683]) ).
cnf(c1685,plain,
quotient(product(X2,eta(X)),j(X)) = difference(j(X),quotient(difference(X,X2),i(X))),
inference(symmetry,[status(thm)],[c1684]) ).
cnf(c1686,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1687,plain,
i(X) = i(i(j(X))),
inference(congruence,[status(thm)],[c1686]) ).
cnf(c1688,plain,
quotient(difference(X,X2),i(X)) = quotient(difference(X,X2),i(i(j(X)))),
inference(congruence,[status(thm)],[c1687]) ).
cnf(c1689,plain,
difference(j(X),quotient(difference(X,X2),i(X))) = difference(j(X),quotient(difference(X,X2),i(i(j(X))))),
inference(congruence,[status(thm)],[c1688]) ).
cnf(c1690,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1691,plain,
difference(X,X2) = difference(i(j(X)),X2),
inference(congruence,[status(thm)],[c1690]) ).
cnf(c1692,plain,
quotient(difference(X,X2),i(i(j(X)))) = quotient(difference(i(j(X)),X2),i(i(j(X)))),
inference(congruence,[status(thm)],[c1691]) ).
cnf(c1693,plain,
difference(j(X),quotient(difference(X,X2),i(i(j(X))))) = difference(j(X),quotient(difference(i(j(X)),X2),i(i(j(X))))),
inference(congruence,[status(thm)],[c1692]) ).
cnf(c1694,plain,
quotient(difference(i(X2),X),i(i(X2))) = product(product(X2,X),i(X2)),
inference(symmetry,[status(thm)],[c1366]) ).
cnf(c1695,plain,
difference(X2,quotient(difference(i(X2),X),i(i(X2)))) = difference(X2,product(product(X2,X),i(X2))),
inference(congruence,[status(thm)],[c1694]) ).
cnf(c1696,plain,
difference(X2,product(product(X2,X),i(X2))) = quotient(product(X,product(i(X2),X2)),X2),
inference(substitution,[status(thm)],[c57]) ).
cnf(c1697,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c1698,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c1697]) ).
cnf(c1699,plain,
product(X,product(i(X2),X2)) = product(X,eta(X2)),
inference(congruence,[status(thm)],[c1698]) ).
cnf(c1700,plain,
quotient(product(X,product(i(X2),X2)),X2) = quotient(product(X,eta(X2)),X2),
inference(congruence,[status(thm)],[c1699]) ).
cnf(c1701,plain,
product(X,eta(X2)) = quotient(X,i(eta(X2))),
inference(substitution,[status(thm)],[c1674]) ).
cnf(c1702,plain,
quotient(product(X,eta(X2)),X2) = quotient(quotient(X,i(eta(X2))),X2),
inference(congruence,[status(thm)],[c1701]) ).
cnf(c1703,plain,
i(eta(X)) = j(eta(X)),
inference(symmetry,[status(thm)],[c788]) ).
cnf(c1704,plain,
quotient(X2,i(eta(X))) = quotient(X2,j(eta(X))),
inference(congruence,[status(thm)],[c1703]) ).
cnf(c1705,plain,
quotient(quotient(X2,i(eta(X))),X) = quotient(quotient(X2,j(eta(X))),X),
inference(congruence,[status(thm)],[c1704]) ).
cnf(c1706,plain,
eta(difference(X2,X)) = eta(difference(X2,i(X))),
inference(symmetry,[status(thm)],[c1440]) ).
cnf(c1707,plain,
difference(X,eta(difference(X2,X))) = difference(X,eta(difference(X2,i(X)))),
inference(congruence,[status(thm)],[c1706]) ).
cnf(c1708,plain,
eta(difference(X2,i(i(X)))) = eta(difference(X2,i(X))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c1709,plain,
eta(difference(X2,i(X))) = eta(difference(X2,i(i(X)))),
inference(symmetry,[status(thm)],[c1708]) ).
cnf(c1710,plain,
difference(X,eta(difference(X2,i(X)))) = difference(X,eta(difference(X2,i(i(X))))),
inference(congruence,[status(thm)],[c1709]) ).
cnf(c1711,plain,
eta(difference(X2,i(i(X)))) = eta(quotient(X2,i(i(X)))),
inference(symmetry,[status(thm)],[c1247]) ).
cnf(c1712,plain,
difference(X,eta(difference(X2,i(i(X))))) = difference(X,eta(quotient(X2,i(i(X))))),
inference(congruence,[status(thm)],[c1711]) ).
cnf(c1713,plain,
eta(quotient(i(X2),i(j(X)))) = eta(quotient(X2,j(X))),
inference(substitution,[status(thm)],[c558]) ).
cnf(c1714,plain,
eta(quotient(X2,j(X))) = eta(quotient(i(X2),i(j(X)))),
inference(symmetry,[status(thm)],[c1713]) ).
cnf(c1715,plain,
quotient(i(X2),i(j(X))) = quotient(i(X2),X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1716,plain,
eta(quotient(i(X2),i(j(X)))) = eta(quotient(i(X2),X)),
inference(congruence,[status(thm)],[c1715]) ).
cnf(c1717,plain,
eta(quotient(i(X2),X)) = eta(quotient(X,i(i(X2)))),
inference(substitution,[status(thm)],[c553]) ).
cnf(c1718,plain,
eta(quotient(i(X2),i(j(X)))) = eta(quotient(X,i(i(X2)))),
inference(transitivity,[status(thm)],[c1716,c1717]) ).
cnf(c1719,plain,
eta(quotient(X2,j(X))) = eta(quotient(X,i(i(X2)))),
inference(transitivity,[status(thm)],[c1714,c1718]) ).
cnf(c1720,plain,
eta(quotient(X,j(X2))) = eta(quotient(X2,i(i(X)))),
inference(substitution,[status(thm)],[c1719]) ).
cnf(c1721,plain,
eta(quotient(X2,i(i(X)))) = eta(quotient(X,j(X2))),
inference(symmetry,[status(thm)],[c1720]) ).
cnf(c1722,plain,
difference(X,eta(quotient(X2,i(i(X))))) = difference(X,eta(quotient(X,j(X2)))),
inference(congruence,[status(thm)],[c1721]) ).
cnf(c1723,plain,
difference(X2,eta(quotient(X2,j(X)))) = quotient(i(j(X)),quotient(X2,j(X))),
inference(substitution,[status(thm)],[c289]) ).
cnf(c1724,plain,
quotient(i(j(X)),quotient(X2,j(X))) = quotient(X,quotient(X2,j(X))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1725,plain,
difference(X2,eta(quotient(X2,j(X)))) = quotient(X,quotient(X2,j(X))),
inference(transitivity,[status(thm)],[c1723,c1724]) ).
cnf(c1726,plain,
difference(X,eta(quotient(X,j(X2)))) = quotient(X2,quotient(X,j(X2))),
inference(substitution,[status(thm)],[c1725]) ).
cnf(c1727,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c1728,plain,
quotient(X2,quotient(X,j(X2))) = quotient(i(j(X2)),quotient(X,j(X2))),
inference(congruence,[status(thm)],[c1727]) ).
cnf(c1729,plain,
quotient(i(i(j(X2))),quotient(X,i(j(X2)))) = quotient(i(j(X2)),quotient(X,j(X2))),
inference(substitution,[status(thm)],[c1540]) ).
cnf(c1730,plain,
quotient(i(j(X2)),quotient(X,j(X2))) = quotient(i(i(j(X2))),quotient(X,i(j(X2)))),
inference(symmetry,[status(thm)],[c1729]) ).
cnf(c1731,plain,
i(i(j(X))) = i(X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1732,plain,
quotient(i(i(j(X2))),quotient(X,i(j(X2)))) = quotient(i(X2),quotient(X,i(j(X2)))),
inference(congruence,[status(thm)],[c1731]) ).
cnf(c1733,plain,
quotient(X,i(j(X2))) = quotient(X,X2),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1734,plain,
quotient(i(X2),quotient(X,i(j(X2)))) = quotient(i(X2),quotient(X,X2)),
inference(congruence,[status(thm)],[c1733]) ).
cnf(c1735,plain,
quotient(i(i(j(X2))),quotient(X,i(j(X2)))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1732,c1734]) ).
cnf(c1736,plain,
quotient(i(j(X2)),quotient(X,j(X2))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1730,c1735]) ).
cnf(c1737,plain,
quotient(X2,quotient(X,j(X2))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1728,c1736]) ).
cnf(c1738,plain,
difference(X,eta(quotient(X,j(X2)))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1726,c1737]) ).
cnf(c1739,plain,
difference(X,eta(quotient(X2,i(i(X))))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1722,c1738]) ).
cnf(c1740,plain,
difference(X,eta(difference(X2,i(i(X))))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1712,c1739]) ).
cnf(c1741,plain,
difference(X,eta(difference(X2,i(X)))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1710,c1740]) ).
cnf(c1742,plain,
difference(X,eta(difference(X2,X))) = quotient(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c1707,c1741]) ).
cnf(c1743,plain,
quotient(i(X2),quotient(X,X2)) = difference(X,eta(difference(X2,X))),
inference(symmetry,[status(thm)],[c1742]) ).
cnf(c1744,plain,
difference(quotient(i(X2),quotient(X,X2)),X2) = difference(difference(X,eta(difference(X2,X))),X2),
inference(congruence,[status(thm)],[c1743]) ).
cnf(c1745,plain,
eta(difference(X2,X)) = eta(difference(X2,i(X))),
inference(symmetry,[status(thm)],[c1440]) ).
cnf(c1746,plain,
difference(X,eta(difference(X2,X))) = difference(X,eta(difference(X2,i(X)))),
inference(congruence,[status(thm)],[c1745]) ).
cnf(c1747,plain,
difference(difference(X,eta(difference(X2,X))),X2) = difference(difference(X,eta(difference(X2,i(X)))),X2),
inference(congruence,[status(thm)],[c1746]) ).
cnf(c1748,plain,
eta(difference(X2,i(i(X)))) = eta(difference(X2,i(X))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c1749,plain,
eta(difference(X2,i(X))) = eta(difference(X2,i(i(X)))),
inference(symmetry,[status(thm)],[c1748]) ).
cnf(c1750,plain,
difference(X,eta(difference(X2,i(X)))) = difference(X,eta(difference(X2,i(i(X))))),
inference(congruence,[status(thm)],[c1749]) ).
cnf(c1751,plain,
difference(difference(X,eta(difference(X2,i(X)))),X2) = difference(difference(X,eta(difference(X2,i(i(X))))),X2),
inference(congruence,[status(thm)],[c1750]) ).
cnf(c1752,plain,
eta(difference(X2,i(i(X)))) = eta(quotient(X2,i(i(X)))),
inference(symmetry,[status(thm)],[c1247]) ).
cnf(c1753,plain,
difference(X,eta(difference(X2,i(i(X))))) = difference(X,eta(quotient(X2,i(i(X))))),
inference(congruence,[status(thm)],[c1752]) ).
cnf(c1754,plain,
difference(difference(X,eta(difference(X2,i(i(X))))),X2) = difference(difference(X,eta(quotient(X2,i(i(X))))),X2),
inference(congruence,[status(thm)],[c1753]) ).
cnf(c1755,plain,
eta(quotient(X,j(X2))) = eta(quotient(X2,i(i(X)))),
inference(substitution,[status(thm)],[c1719]) ).
cnf(c1756,plain,
eta(quotient(X2,i(i(X)))) = eta(quotient(X,j(X2))),
inference(symmetry,[status(thm)],[c1755]) ).
cnf(c1757,plain,
difference(X,eta(quotient(X2,i(i(X))))) = difference(X,eta(quotient(X,j(X2)))),
inference(congruence,[status(thm)],[c1756]) ).
cnf(c1758,plain,
difference(difference(X,eta(quotient(X2,i(i(X))))),X2) = difference(difference(X,eta(quotient(X,j(X2)))),X2),
inference(congruence,[status(thm)],[c1757]) ).
cnf(c1759,plain,
difference(X,eta(quotient(X,j(X2)))) = quotient(X2,quotient(X,j(X2))),
inference(substitution,[status(thm)],[c1725]) ).
cnf(c1760,plain,
difference(difference(X,eta(quotient(X,j(X2)))),X2) = difference(quotient(X2,quotient(X,j(X2))),X2),
inference(congruence,[status(thm)],[c1759]) ).
cnf(c1761,plain,
difference(quotient(X2,quotient(X,j(X2))),X2) = quotient(X,j(X2)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c1762,plain,
difference(difference(X,eta(quotient(X,j(X2)))),X2) = quotient(X,j(X2)),
inference(transitivity,[status(thm)],[c1760,c1761]) ).
cnf(c1763,plain,
difference(difference(X,eta(quotient(X2,i(i(X))))),X2) = quotient(X,j(X2)),
inference(transitivity,[status(thm)],[c1758,c1762]) ).
cnf(c1764,plain,
difference(difference(X,eta(difference(X2,i(i(X))))),X2) = quotient(X,j(X2)),
inference(transitivity,[status(thm)],[c1754,c1763]) ).
cnf(c1765,plain,
difference(difference(X,eta(difference(X2,i(X)))),X2) = quotient(X,j(X2)),
inference(transitivity,[status(thm)],[c1751,c1764]) ).
cnf(c1766,plain,
difference(difference(X,eta(difference(X2,X))),X2) = quotient(X,j(X2)),
inference(transitivity,[status(thm)],[c1747,c1765]) ).
cnf(c1767,plain,
difference(quotient(i(X2),quotient(X,X2)),X2) = quotient(X,j(X2)),
inference(transitivity,[status(thm)],[c1744,c1766]) ).
cnf(c1768,plain,
difference(quotient(i(eta(X)),quotient(X2,eta(X))),eta(X)) = quotient(X2,j(eta(X))),
inference(substitution,[status(thm)],[c1767]) ).
cnf(c1769,plain,
quotient(X2,j(eta(X))) = difference(quotient(i(eta(X)),quotient(X2,eta(X))),eta(X)),
inference(symmetry,[status(thm)],[c1768]) ).
cnf(c1770,plain,
quotient(quotient(X2,j(eta(X))),X) = quotient(difference(quotient(i(eta(X)),quotient(X2,eta(X))),eta(X)),X),
inference(congruence,[status(thm)],[c1769]) ).
cnf(c1771,plain,
quotient(difference(quotient(i(eta(X)),quotient(X2,eta(X))),eta(X)),X) = i(product(X,quotient(i(eta(X)),quotient(X2,eta(X))))),
inference(substitution,[status(thm)],[c158]) ).
cnf(c1772,plain,
eta(X) = i(i(eta(X))),
inference(symmetry,[status(thm)],[c726]) ).
cnf(c1773,plain,
quotient(X,eta(X2)) = quotient(X,i(i(eta(X2)))),
inference(congruence,[status(thm)],[c1772]) ).
cnf(c1774,plain,
quotient(i(eta(X2)),quotient(X,eta(X2))) = quotient(i(eta(X2)),quotient(X,i(i(eta(X2))))),
inference(congruence,[status(thm)],[c1773]) ).
cnf(c1775,plain,
product(i(eta(X)),j(X2)) = j(quotient(X2,i(eta(X)))),
inference(substitution,[status(thm)],[c809]) ).
cnf(c1776,plain,
j(quotient(X2,i(eta(X)))) = product(i(eta(X)),j(X2)),
inference(symmetry,[status(thm)],[c1775]) ).
cnf(c1777,plain,
eta(difference(quotient(i(X2),X),i(X2))) = eta(difference(X2,quotient(i(X2),X))),
inference(substitution,[status(thm)],[c593]) ).
cnf(c1778,plain,
eta(difference(X2,quotient(i(X2),X))) = eta(difference(quotient(i(X2),X),i(X2))),
inference(symmetry,[status(thm)],[c1777]) ).
cnf(c1779,plain,
difference(quotient(i(X2),X),i(X2)) = X,
inference(substitution,[status(thm)],[c209]) ).
cnf(c1780,plain,
eta(difference(quotient(i(X2),X),i(X2))) = eta(X),
inference(congruence,[status(thm)],[c1779]) ).
cnf(c1781,plain,
eta(difference(X2,quotient(i(X2),X))) = eta(X),
inference(transitivity,[status(thm)],[c1778,c1780]) ).
cnf(c1782,plain,
eta(difference(X,quotient(i(X),X2))) = eta(X2),
inference(substitution,[status(thm)],[c1781]) ).
cnf(c1783,plain,
eta(X2) = eta(difference(X,quotient(i(X),X2))),
inference(symmetry,[status(thm)],[c1782]) ).
cnf(c1784,plain,
i(eta(X2)) = i(eta(difference(X,quotient(i(X),X2)))),
inference(congruence,[status(thm)],[c1783]) ).
cnf(c1785,plain,
quotient(X,i(eta(X2))) = quotient(X,i(eta(difference(X,quotient(i(X),X2))))),
inference(congruence,[status(thm)],[c1784]) ).
cnf(c1786,plain,
quotient(eta(X2),quotient(X,i(eta(X2)))) = quotient(eta(X2),quotient(X,i(eta(difference(X,quotient(i(X),X2)))))),
inference(congruence,[status(thm)],[c1785]) ).
cnf(c1787,plain,
eta(difference(i(X),i(quotient(i(X),X2)))) = eta(difference(X,quotient(i(X),X2))),
inference(substitution,[status(thm)],[c1137]) ).
cnf(c1788,plain,
eta(difference(X,quotient(i(X),X2))) = eta(difference(i(X),i(quotient(i(X),X2)))),
inference(symmetry,[status(thm)],[c1787]) ).
cnf(c1789,plain,
i(eta(difference(X,quotient(i(X),X2)))) = i(eta(difference(i(X),i(quotient(i(X),X2))))),
inference(congruence,[status(thm)],[c1788]) ).
cnf(c1790,plain,
quotient(X,i(eta(difference(X,quotient(i(X),X2))))) = quotient(X,i(eta(difference(i(X),i(quotient(i(X),X2)))))),
inference(congruence,[status(thm)],[c1789]) ).
cnf(c1791,plain,
quotient(eta(X2),quotient(X,i(eta(difference(X,quotient(i(X),X2)))))) = quotient(eta(X2),quotient(X,i(eta(difference(i(X),i(quotient(i(X),X2))))))),
inference(congruence,[status(thm)],[c1790]) ).
cnf(c1792,plain,
product(X,eta(difference(i(X),i(quotient(i(X),X2))))) = quotient(X,i(eta(difference(i(X),i(quotient(i(X),X2)))))),
inference(substitution,[status(thm)],[c1674]) ).
cnf(c1793,plain,
quotient(X,i(eta(difference(i(X),i(quotient(i(X),X2)))))) = product(X,eta(difference(i(X),i(quotient(i(X),X2))))),
inference(symmetry,[status(thm)],[c1792]) ).
cnf(c1794,plain,
quotient(eta(X2),quotient(X,i(eta(difference(i(X),i(quotient(i(X),X2))))))) = quotient(eta(X2),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))),
inference(congruence,[status(thm)],[c1793]) ).
cnf(c1795,plain,
difference(quotient(X,eta(X2)),X) = eta(X2),
inference(substitution,[status(thm)],[c209]) ).
cnf(c1796,plain,
eta(X2) = difference(quotient(X,eta(X2)),X),
inference(symmetry,[status(thm)],[c1795]) ).
cnf(c1797,plain,
quotient(eta(X2),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = quotient(difference(quotient(X,eta(X2)),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))),
inference(congruence,[status(thm)],[c1796]) ).
cnf(c1798,plain,
product(quotient(product(X2,i(eta(X))),eta(X)),eta(X)) = product(X2,i(eta(X))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c1799,plain,
product(X2,i(eta(X))) = product(quotient(product(X2,i(eta(X))),eta(X)),eta(X)),
inference(symmetry,[status(thm)],[c1798]) ).
cnf(c1800,plain,
difference(j(quotient(product(X2,i(eta(X))),eta(X))),eta(X)) = product(quotient(product(X2,i(eta(X))),eta(X)),eta(X)),
inference(substitution,[status(thm)],[c1034]) ).
cnf(c1801,plain,
product(quotient(product(X2,i(eta(X))),eta(X)),eta(X)) = difference(j(quotient(product(X2,i(eta(X))),eta(X))),eta(X)),
inference(symmetry,[status(thm)],[c1800]) ).
cnf(c1802,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c1803,plain,
product(eta(X2),j(X)) = product(eta(X2),quotient(one,X)),
inference(congruence,[status(thm)],[c1802]) ).
cnf(c1804,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c1805,plain,
quotient(one,X) = quotient(eta(eta(X2)),X),
inference(congruence,[status(thm)],[c1804]) ).
cnf(c1806,plain,
product(eta(X2),quotient(one,X)) = product(eta(X2),quotient(eta(eta(X2)),X)),
inference(congruence,[status(thm)],[c1805]) ).
cnf(c1807,plain,
product(eta(X2),quotient(eta(eta(X2)),X)) = j(quotient(X,eta(X2))),
inference(substitution,[status(thm)],[c582]) ).
cnf(c1808,plain,
product(eta(X2),quotient(one,X)) = j(quotient(X,eta(X2))),
inference(transitivity,[status(thm)],[c1806,c1807]) ).
cnf(c1809,plain,
product(eta(X2),j(X)) = j(quotient(X,eta(X2))),
inference(transitivity,[status(thm)],[c1803,c1808]) ).
cnf(c1810,plain,
product(eta(X),j(product(X2,i(eta(X))))) = j(quotient(product(X2,i(eta(X))),eta(X))),
inference(substitution,[status(thm)],[c1809]) ).
cnf(c1811,plain,
j(quotient(product(X2,i(eta(X))),eta(X))) = product(eta(X),j(product(X2,i(eta(X))))),
inference(symmetry,[status(thm)],[c1810]) ).
cnf(c1812,plain,
difference(j(quotient(product(X2,i(eta(X))),eta(X))),eta(X)) = difference(product(eta(X),j(product(X2,i(eta(X))))),eta(X)),
inference(congruence,[status(thm)],[c1811]) ).
cnf(c1813,plain,
eta(X) = i(i(eta(X))),
inference(symmetry,[status(thm)],[c726]) ).
cnf(c1814,plain,
product(eta(X),j(product(X2,i(eta(X))))) = product(i(i(eta(X))),j(product(X2,i(eta(X))))),
inference(congruence,[status(thm)],[c1813]) ).
cnf(c1815,plain,
difference(product(eta(X),j(product(X2,i(eta(X))))),eta(X)) = difference(product(i(i(eta(X))),j(product(X2,i(eta(X))))),eta(X)),
inference(congruence,[status(thm)],[c1814]) ).
cnf(c1816,plain,
product(X,product(i(X),product(X2,X))) = quotient(quotient(product(X2,X),i(X)),X),
inference(substitution,[status(thm)],[c426]) ).
cnf(c1817,plain,
quotient(quotient(product(X2,X),i(X)),X) = product(X,product(i(X),product(X2,X))),
inference(symmetry,[status(thm)],[c1816]) ).
cnf(c1818,plain,
product(difference(X,X2),X) = product(i(X),product(X2,X)),
inference(substitution,[status(thm)],[c322]) ).
cnf(c1819,plain,
product(i(X),product(X2,X)) = product(difference(X,X2),X),
inference(symmetry,[status(thm)],[c1818]) ).
cnf(c1820,plain,
product(X,product(i(X),product(X2,X))) = product(X,product(difference(X,X2),X)),
inference(congruence,[status(thm)],[c1819]) ).
cnf(c1821,plain,
product(X,product(difference(X,X2),X)) = quotient(X2,j(X)),
inference(substitution,[status(thm)],[c400]) ).
cnf(c1822,plain,
product(X,product(i(X),product(X2,X))) = quotient(X2,j(X)),
inference(transitivity,[status(thm)],[c1820,c1821]) ).
cnf(c1823,plain,
quotient(quotient(product(X2,X),i(X)),X) = quotient(X2,j(X)),
inference(transitivity,[status(thm)],[c1817,c1822]) ).
cnf(c1824,plain,
quotient(quotient(product(X,X2),i(X2)),X2) = quotient(X,j(X2)),
inference(substitution,[status(thm)],[c1823]) ).
cnf(c1825,plain,
quotient(X,j(X2)) = quotient(quotient(product(X,X2),i(X2)),X2),
inference(symmetry,[status(thm)],[c1824]) ).
cnf(c1826,plain,
j(quotient(X,j(X2))) = j(quotient(quotient(product(X,X2),i(X2)),X2)),
inference(congruence,[status(thm)],[c1825]) ).
cnf(c1827,plain,
difference(X2,j(quotient(X,j(X2)))) = difference(X2,j(quotient(quotient(product(X,X2),i(X2)),X2))),
inference(congruence,[status(thm)],[c1826]) ).
cnf(c1828,plain,
difference(X2,j(quotient(quotient(product(X,X2),i(X2)),X2))) = quotient(eta(X2),quotient(product(X,X2),i(X2))),
inference(substitution,[status(thm)],[c1048]) ).
cnf(c1829,plain,
quotient(eta(X2),quotient(product(X,X2),i(X2))) = product(i(X2),j(product(X,X2))),
inference(substitution,[status(thm)],[c90]) ).
cnf(c1830,plain,
difference(X2,j(quotient(quotient(product(X,X2),i(X2)),X2))) = product(i(X2),j(product(X,X2))),
inference(transitivity,[status(thm)],[c1828,c1829]) ).
cnf(c1831,plain,
difference(X2,j(quotient(X,j(X2)))) = product(i(X2),j(product(X,X2))),
inference(transitivity,[status(thm)],[c1827,c1830]) ).
cnf(c1832,plain,
difference(i(eta(X)),j(quotient(X2,j(i(eta(X)))))) = product(i(i(eta(X))),j(product(X2,i(eta(X))))),
inference(substitution,[status(thm)],[c1831]) ).
cnf(c1833,plain,
product(i(i(eta(X))),j(product(X2,i(eta(X))))) = difference(i(eta(X)),j(quotient(X2,j(i(eta(X)))))),
inference(symmetry,[status(thm)],[c1832]) ).
cnf(c1834,plain,
difference(product(i(i(eta(X))),j(product(X2,i(eta(X))))),eta(X)) = difference(difference(i(eta(X)),j(quotient(X2,j(i(eta(X)))))),eta(X)),
inference(congruence,[status(thm)],[c1833]) ).
cnf(c1835,plain,
difference(difference(i(eta(X)),j(quotient(X2,j(i(eta(X)))))),eta(X)) = i(j(quotient(X2,j(i(eta(X)))))),
inference(substitution,[status(thm)],[c1666]) ).
cnf(c1836,plain,
i(j(quotient(X2,j(i(eta(X)))))) = quotient(X2,j(i(eta(X)))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c1837,plain,
j(i(eta(X))) = eta(X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c1838,plain,
quotient(X2,j(i(eta(X)))) = quotient(X2,eta(X)),
inference(congruence,[status(thm)],[c1837]) ).
cnf(c1839,plain,
i(j(quotient(X2,j(i(eta(X)))))) = quotient(X2,eta(X)),
inference(transitivity,[status(thm)],[c1836,c1838]) ).
cnf(c1840,plain,
difference(difference(i(eta(X)),j(quotient(X2,j(i(eta(X)))))),eta(X)) = quotient(X2,eta(X)),
inference(transitivity,[status(thm)],[c1835,c1839]) ).
cnf(c1841,plain,
difference(product(i(i(eta(X))),j(product(X2,i(eta(X))))),eta(X)) = quotient(X2,eta(X)),
inference(transitivity,[status(thm)],[c1834,c1840]) ).
cnf(c1842,plain,
difference(product(eta(X),j(product(X2,i(eta(X))))),eta(X)) = quotient(X2,eta(X)),
inference(transitivity,[status(thm)],[c1815,c1841]) ).
cnf(c1843,plain,
difference(j(quotient(product(X2,i(eta(X))),eta(X))),eta(X)) = quotient(X2,eta(X)),
inference(transitivity,[status(thm)],[c1812,c1842]) ).
cnf(c1844,plain,
product(quotient(product(X2,i(eta(X))),eta(X)),eta(X)) = quotient(X2,eta(X)),
inference(transitivity,[status(thm)],[c1801,c1843]) ).
cnf(c1845,plain,
product(X2,i(eta(X))) = quotient(X2,eta(X)),
inference(transitivity,[status(thm)],[c1799,c1844]) ).
cnf(c1846,plain,
product(X,i(eta(X2))) = quotient(X,eta(X2)),
inference(substitution,[status(thm)],[c1845]) ).
cnf(c1847,plain,
quotient(X,eta(X2)) = product(X,i(eta(X2))),
inference(symmetry,[status(thm)],[c1846]) ).
cnf(c1848,plain,
difference(quotient(X,eta(X2)),X) = difference(product(X,i(eta(X2))),X),
inference(congruence,[status(thm)],[c1847]) ).
cnf(c1849,plain,
quotient(difference(quotient(X,eta(X2)),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = quotient(difference(product(X,i(eta(X2))),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))),
inference(congruence,[status(thm)],[c1848]) ).
cnf(c1850,plain,
quotient(difference(i(eta(X2)),X),X) = difference(product(X,i(eta(X2))),X),
inference(substitution,[status(thm)],[c233]) ).
cnf(c1851,plain,
difference(product(X,i(eta(X2))),X) = quotient(difference(i(eta(X2)),X),X),
inference(symmetry,[status(thm)],[c1850]) ).
cnf(c1852,plain,
quotient(difference(product(X,i(eta(X2))),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = quotient(quotient(difference(i(eta(X2)),X),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))),
inference(congruence,[status(thm)],[c1851]) ).
cnf(c1853,plain,
i(X) = difference(difference(i(eta(X2)),X),eta(X2)),
inference(symmetry,[status(thm)],[c1666]) ).
cnf(c1854,plain,
quotient(eta(X2),i(X)) = quotient(eta(X2),difference(difference(i(eta(X2)),X),eta(X2))),
inference(congruence,[status(thm)],[c1853]) ).
cnf(c1855,plain,
quotient(eta(X2),difference(difference(i(eta(X2)),X),eta(X2))) = difference(i(eta(X2)),X),
inference(substitution,[status(thm)],[c86]) ).
cnf(c1856,plain,
quotient(eta(X2),i(X)) = difference(i(eta(X2)),X),
inference(transitivity,[status(thm)],[c1854,c1855]) ).
cnf(c1857,plain,
difference(i(eta(X2)),X) = quotient(eta(X2),i(X)),
inference(symmetry,[status(thm)],[c1856]) ).
cnf(c1858,plain,
quotient(difference(i(eta(X2)),X),X) = quotient(quotient(eta(X2),i(X)),X),
inference(congruence,[status(thm)],[c1857]) ).
cnf(c1859,plain,
quotient(quotient(difference(i(eta(X2)),X),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = quotient(quotient(quotient(eta(X2),i(X)),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))),
inference(congruence,[status(thm)],[c1858]) ).
cnf(c1860,plain,
quotient(eta(difference(X2,i(quotient(X2,X)))),X2) = product(difference(X2,i(quotient(X2,X))),quotient(X2,X)),
inference(substitution,[status(thm)],[c1607]) ).
cnf(c1861,plain,
difference(difference(X2,X),j(quotient(X,difference(X2,X)))) = quotient(eta(difference(X2,X)),X),
inference(substitution,[status(thm)],[c1048]) ).
cnf(c1862,plain,
quotient(eta(difference(X2,X)),X) = difference(difference(X2,X),j(quotient(X,difference(X2,X)))),
inference(symmetry,[status(thm)],[c1861]) ).
cnf(c1863,plain,
quotient(X,difference(X2,X)) = X2,
inference(substitution,[status(thm)],[c86]) ).
cnf(c1864,plain,
j(quotient(X,difference(X2,X))) = j(X2),
inference(congruence,[status(thm)],[c1863]) ).
cnf(c1865,plain,
difference(difference(X2,X),j(quotient(X,difference(X2,X)))) = difference(difference(X2,X),j(X2)),
inference(congruence,[status(thm)],[c1864]) ).
cnf(c1866,plain,
quotient(eta(difference(X2,X)),X) = difference(difference(X2,X),j(X2)),
inference(transitivity,[status(thm)],[c1862,c1865]) ).
cnf(c1867,plain,
difference(difference(X2,X),j(X2)) = quotient(eta(difference(X2,X)),X),
inference(symmetry,[status(thm)],[c1866]) ).
cnf(c1868,plain,
eta(difference(X2,X)) = eta(difference(X,i(X2))),
inference(symmetry,[status(thm)],[c593]) ).
cnf(c1869,plain,
quotient(eta(difference(X2,X)),X) = quotient(eta(difference(X,i(X2))),X),
inference(congruence,[status(thm)],[c1868]) ).
cnf(c1870,plain,
quotient(i(X2),difference(X,i(X2))) = X,
inference(substitution,[status(thm)],[c86]) ).
cnf(c1871,plain,
X = quotient(i(X2),difference(X,i(X2))),
inference(symmetry,[status(thm)],[c1870]) ).
cnf(c1872,plain,
quotient(eta(difference(X,i(X2))),X) = quotient(eta(difference(X,i(X2))),quotient(i(X2),difference(X,i(X2)))),
inference(congruence,[status(thm)],[c1871]) ).
cnf(c1873,plain,
quotient(eta(difference(X,i(X2))),quotient(i(X2),difference(X,i(X2)))) = product(difference(X,i(X2)),X2),
inference(substitution,[status(thm)],[c1228]) ).
cnf(c1874,plain,
quotient(eta(difference(X,i(X2))),X) = product(difference(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c1872,c1873]) ).
cnf(c1875,plain,
quotient(eta(difference(X2,X)),X) = product(difference(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c1869,c1874]) ).
cnf(c1876,plain,
difference(difference(X2,X),j(X2)) = product(difference(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c1867,c1875]) ).
cnf(c1877,plain,
difference(difference(quotient(X2,X),X2),j(quotient(X2,X))) = product(difference(X2,i(quotient(X2,X))),quotient(X2,X)),
inference(substitution,[status(thm)],[c1876]) ).
cnf(c1878,plain,
product(difference(X2,i(quotient(X2,X))),quotient(X2,X)) = difference(difference(quotient(X2,X),X2),j(quotient(X2,X))),
inference(symmetry,[status(thm)],[c1877]) ).
cnf(c1879,plain,
difference(difference(quotient(X2,X),X2),j(quotient(X2,X))) = difference(X,j(quotient(X2,X))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c1880,plain,
difference(X,j(quotient(X2,X))) = quotient(eta(X),X2),
inference(substitution,[status(thm)],[c1048]) ).
cnf(c1881,plain,
difference(difference(quotient(X2,X),X2),j(quotient(X2,X))) = quotient(eta(X),X2),
inference(transitivity,[status(thm)],[c1879,c1880]) ).
cnf(c1882,plain,
product(difference(X2,i(quotient(X2,X))),quotient(X2,X)) = quotient(eta(X),X2),
inference(transitivity,[status(thm)],[c1878,c1881]) ).
cnf(c1883,plain,
quotient(eta(difference(X2,i(quotient(X2,X)))),X2) = quotient(eta(X),X2),
inference(transitivity,[status(thm)],[c1860,c1882]) ).
cnf(c1884,plain,
quotient(eta(difference(i(X),i(quotient(i(X),X2)))),i(X)) = quotient(eta(X2),i(X)),
inference(substitution,[status(thm)],[c1883]) ).
cnf(c1885,plain,
quotient(eta(X2),i(X)) = quotient(eta(difference(i(X),i(quotient(i(X),X2)))),i(X)),
inference(symmetry,[status(thm)],[c1884]) ).
cnf(c1886,plain,
quotient(quotient(eta(X2),i(X)),X) = quotient(quotient(eta(difference(i(X),i(quotient(i(X),X2)))),i(X)),X),
inference(congruence,[status(thm)],[c1885]) ).
cnf(c1887,plain,
quotient(quotient(quotient(eta(X2),i(X)),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = quotient(quotient(quotient(eta(difference(i(X),i(quotient(i(X),X2)))),i(X)),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))),
inference(congruence,[status(thm)],[c1886]) ).
cnf(c1888,plain,
difference(one,product(j(X2),product(X2,X))) = product(j(X2),product(X2,X)),
inference(substitution,[status(thm)],[c190]) ).
cnf(c1889,plain,
product(j(X2),product(X2,X)) = difference(one,product(j(X2),product(X2,X))),
inference(symmetry,[status(thm)],[c1888]) ).
cnf(c1890,plain,
one = product(j(X),X),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c1891,plain,
difference(one,product(j(X2),product(X2,X))) = difference(product(j(X2),X2),product(j(X2),product(X2,X))),
inference(congruence,[status(thm)],[c1890]) ).
cnf(c1892,plain,
quotient(difference(X2,product(product(X2,X),j(X2))),j(X2)) = difference(product(j(X2),X2),product(j(X2),product(X2,X))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c1893,plain,
difference(product(j(X2),X2),product(j(X2),product(X2,X))) = quotient(difference(X2,product(product(X2,X),j(X2))),j(X2)),
inference(symmetry,[status(thm)],[c1892]) ).
cnf(c1894,plain,
quotient(difference(X2,product(product(X2,X),j(X2))),j(X2)) = quotient(quotient(X,X2),j(X2)),
inference(congruence,[status(thm)],[c418]) ).
cnf(c1895,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c1896,plain,
j(X) = j(j(i(X))),
inference(congruence,[status(thm)],[c1895]) ).
cnf(c1897,plain,
quotient(quotient(X2,X),j(X)) = quotient(quotient(X2,X),j(j(i(X)))),
inference(congruence,[status(thm)],[c1896]) ).
cnf(c1898,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c1899,plain,
quotient(X2,X) = quotient(X2,j(i(X))),
inference(congruence,[status(thm)],[c1898]) ).
cnf(c1900,plain,
quotient(quotient(X2,X),j(j(i(X)))) = quotient(quotient(X2,j(i(X))),j(j(i(X)))),
inference(congruence,[status(thm)],[c1899]) ).
cnf(c1901,plain,
product(j(X),product(difference(j(X),quotient(X2,j(X))),j(X))) = quotient(quotient(X2,j(X)),j(j(X))),
inference(substitution,[status(thm)],[c400]) ).
cnf(c1902,plain,
quotient(quotient(X2,j(X)),j(j(X))) = product(j(X),product(difference(j(X),quotient(X2,j(X))),j(X))),
inference(symmetry,[status(thm)],[c1901]) ).
cnf(c1903,plain,
difference(j(X),quotient(X2,j(X))) = product(X,product(X2,X)),
inference(substitution,[status(thm)],[c931]) ).
cnf(c1904,plain,
product(difference(j(X),quotient(X2,j(X))),j(X)) = product(product(X,product(X2,X)),j(X)),
inference(congruence,[status(thm)],[c1903]) ).
cnf(c1905,plain,
product(j(X),product(difference(j(X),quotient(X2,j(X))),j(X))) = product(j(X),product(product(X,product(X2,X)),j(X))),
inference(congruence,[status(thm)],[c1904]) ).
cnf(c1906,plain,
product(product(X,product(X2,X)),j(X)) = product(X,quotient(product(X2,X),X)),
inference(substitution,[status(thm)],[c632]) ).
cnf(c1907,plain,
product(j(X),product(product(X,product(X2,X)),j(X))) = product(j(X),product(X,quotient(product(X2,X),X))),
inference(congruence,[status(thm)],[c1906]) ).
cnf(c1908,plain,
product(j(X),product(X,quotient(product(X2,X),X))) = quotient(quotient(quotient(product(X2,X),X),X),j(X)),
inference(substitution,[status(thm)],[c422]) ).
cnf(c1909,plain,
quotient(product(X2,X),X) = X2,
inference(substitution,[status(thm)],[c12]) ).
cnf(c1910,plain,
quotient(quotient(product(X2,X),X),X) = quotient(X2,X),
inference(congruence,[status(thm)],[c1909]) ).
cnf(c1911,plain,
quotient(quotient(quotient(product(X2,X),X),X),j(X)) = quotient(quotient(X2,X),j(X)),
inference(congruence,[status(thm)],[c1910]) ).
cnf(c1912,plain,
product(j(X),product(X,quotient(product(X2,X),X))) = quotient(quotient(X2,X),j(X)),
inference(transitivity,[status(thm)],[c1908,c1911]) ).
cnf(c1913,plain,
product(j(X),product(product(X,product(X2,X)),j(X))) = quotient(quotient(X2,X),j(X)),
inference(transitivity,[status(thm)],[c1907,c1912]) ).
cnf(c1914,plain,
product(j(X),product(difference(j(X),quotient(X2,j(X))),j(X))) = quotient(quotient(X2,X),j(X)),
inference(transitivity,[status(thm)],[c1905,c1913]) ).
cnf(c1915,plain,
quotient(quotient(X2,j(X)),j(j(X))) = quotient(quotient(X2,X),j(X)),
inference(transitivity,[status(thm)],[c1902,c1914]) ).
cnf(c1916,plain,
quotient(quotient(X2,j(i(X))),j(j(i(X)))) = quotient(quotient(X2,i(X)),j(i(X))),
inference(substitution,[status(thm)],[c1915]) ).
cnf(c1917,plain,
quotient(quotient(X2,i(X)),j(i(X))) = quotient(quotient(X2,i(X)),X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c1918,plain,
quotient(quotient(X2,j(i(X))),j(j(i(X)))) = quotient(quotient(X2,i(X)),X),
inference(transitivity,[status(thm)],[c1916,c1917]) ).
cnf(c1919,plain,
quotient(quotient(X2,X),j(j(i(X)))) = quotient(quotient(X2,i(X)),X),
inference(transitivity,[status(thm)],[c1900,c1918]) ).
cnf(c1920,plain,
quotient(quotient(X2,X),j(X)) = quotient(quotient(X2,i(X)),X),
inference(transitivity,[status(thm)],[c1897,c1919]) ).
cnf(c1921,plain,
quotient(quotient(X,X2),j(X2)) = quotient(quotient(X,i(X2)),X2),
inference(substitution,[status(thm)],[c1920]) ).
cnf(c1922,plain,
quotient(difference(X2,product(product(X2,X),j(X2))),j(X2)) = quotient(quotient(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c1894,c1921]) ).
cnf(c1923,plain,
difference(product(j(X2),X2),product(j(X2),product(X2,X))) = quotient(quotient(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c1893,c1922]) ).
cnf(c1924,plain,
difference(one,product(j(X2),product(X2,X))) = quotient(quotient(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c1891,c1923]) ).
cnf(c1925,plain,
product(j(X2),product(X2,X)) = quotient(quotient(X,i(X2)),X2),
inference(transitivity,[status(thm)],[c1889,c1924]) ).
cnf(c1926,plain,
product(j(X),product(X,X2)) = quotient(quotient(X2,i(X)),X),
inference(substitution,[status(thm)],[c1925]) ).
cnf(c1927,plain,
quotient(quotient(X2,i(X)),X) = product(j(X),product(X,X2)),
inference(symmetry,[status(thm)],[c1926]) ).
cnf(c1928,plain,
quotient(quotient(quotient(X2,i(X)),X),product(X,X2)) = quotient(product(j(X),product(X,X2)),product(X,X2)),
inference(congruence,[status(thm)],[c1927]) ).
cnf(c1929,plain,
quotient(product(j(X),product(X,X2)),product(X,X2)) = j(X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c1930,plain,
quotient(quotient(quotient(X2,i(X)),X),product(X,X2)) = j(X),
inference(transitivity,[status(thm)],[c1928,c1929]) ).
cnf(c1931,plain,
quotient(quotient(quotient(eta(difference(i(X),i(quotient(i(X),X2)))),i(X)),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = j(X),
inference(substitution,[status(thm)],[c1930]) ).
cnf(c1932,plain,
quotient(quotient(quotient(eta(X2),i(X)),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = j(X),
inference(transitivity,[status(thm)],[c1887,c1931]) ).
cnf(c1933,plain,
quotient(quotient(difference(i(eta(X2)),X),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = j(X),
inference(transitivity,[status(thm)],[c1859,c1932]) ).
cnf(c1934,plain,
quotient(difference(product(X,i(eta(X2))),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = j(X),
inference(transitivity,[status(thm)],[c1852,c1933]) ).
cnf(c1935,plain,
quotient(difference(quotient(X,eta(X2)),X),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = j(X),
inference(transitivity,[status(thm)],[c1849,c1934]) ).
cnf(c1936,plain,
quotient(eta(X2),product(X,eta(difference(i(X),i(quotient(i(X),X2)))))) = j(X),
inference(transitivity,[status(thm)],[c1797,c1935]) ).
cnf(c1937,plain,
quotient(eta(X2),quotient(X,i(eta(difference(i(X),i(quotient(i(X),X2))))))) = j(X),
inference(transitivity,[status(thm)],[c1794,c1936]) ).
cnf(c1938,plain,
quotient(eta(X2),quotient(X,i(eta(difference(X,quotient(i(X),X2)))))) = j(X),
inference(transitivity,[status(thm)],[c1791,c1937]) ).
cnf(c1939,plain,
quotient(eta(X2),quotient(X,i(eta(X2)))) = j(X),
inference(transitivity,[status(thm)],[c1786,c1938]) ).
cnf(c1940,plain,
quotient(eta(X),quotient(X2,i(eta(X)))) = j(X2),
inference(substitution,[status(thm)],[c1939]) ).
cnf(c1941,plain,
j(X2) = quotient(eta(X),quotient(X2,i(eta(X)))),
inference(symmetry,[status(thm)],[c1940]) ).
cnf(c1942,plain,
product(i(eta(X)),j(X2)) = product(i(eta(X)),quotient(eta(X),quotient(X2,i(eta(X))))),
inference(congruence,[status(thm)],[c1941]) ).
cnf(c1943,plain,
product(i(eta(X)),quotient(eta(X),quotient(X2,i(eta(X))))) = quotient(i(i(eta(X))),quotient(quotient(X2,i(eta(X))),i(eta(X)))),
inference(substitution,[status(thm)],[c1013]) ).
cnf(c1944,plain,
quotient(i(i(eta(X))),quotient(quotient(X2,i(eta(X))),i(eta(X)))) = quotient(i(eta(X)),quotient(quotient(X2,i(eta(X))),eta(X))),
inference(substitution,[status(thm)],[c1540]) ).
cnf(c1945,plain,
eta(difference(X2,difference(X,i(X2)))) = eta(difference(difference(X,i(X2)),X2)),
inference(substitution,[status(thm)],[c1442]) ).
cnf(c1946,plain,
eta(product(difference(X,i(X2)),X2)) = eta(difference(difference(X,i(X2)),X2)),
inference(substitution,[status(thm)],[c1641]) ).
cnf(c1947,plain,
eta(difference(difference(X,i(X2)),X2)) = eta(product(difference(X,i(X2)),X2)),
inference(symmetry,[status(thm)],[c1946]) ).
cnf(c1948,plain,
eta(i(product(difference(X,i(X2)),X2))) = eta(product(difference(X,i(X2)),X2)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c1949,plain,
eta(product(difference(X,i(X2)),X2)) = eta(i(product(difference(X,i(X2)),X2))),
inference(symmetry,[status(thm)],[c1948]) ).
cnf(c1950,plain,
eta(difference(X2,i(j(X)))) = eta(difference(X2,j(X))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c1951,plain,
eta(difference(X2,j(X))) = eta(difference(X2,i(j(X)))),
inference(symmetry,[status(thm)],[c1950]) ).
cnf(c1952,plain,
difference(X2,i(j(X))) = difference(X2,X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1953,plain,
eta(difference(X2,i(j(X)))) = eta(difference(X2,X)),
inference(congruence,[status(thm)],[c1952]) ).
cnf(c1954,plain,
eta(difference(X2,j(X))) = eta(difference(X2,X)),
inference(transitivity,[status(thm)],[c1951,c1953]) ).
cnf(c1955,plain,
eta(difference(X2,X)) = eta(difference(X2,j(X))),
inference(symmetry,[status(thm)],[c1954]) ).
cnf(c1956,plain,
quotient(X2,eta(difference(X2,X))) = quotient(X2,eta(difference(X2,j(X)))),
inference(congruence,[status(thm)],[c1955]) ).
cnf(c1957,plain,
eta(difference(X2,i(j(X)))) = eta(difference(X2,j(X))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c1958,plain,
eta(difference(X2,j(X))) = eta(difference(X2,i(j(X)))),
inference(symmetry,[status(thm)],[c1957]) ).
cnf(c1959,plain,
quotient(X2,eta(difference(X2,j(X)))) = quotient(X2,eta(difference(X2,i(j(X))))),
inference(congruence,[status(thm)],[c1958]) ).
cnf(c1960,plain,
eta(difference(X2,i(i(j(X))))) = eta(difference(X2,i(j(X)))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c1961,plain,
eta(difference(X2,i(j(X)))) = eta(difference(X2,i(i(j(X))))),
inference(symmetry,[status(thm)],[c1960]) ).
cnf(c1962,plain,
quotient(X2,eta(difference(X2,i(j(X))))) = quotient(X2,eta(difference(X2,i(i(j(X)))))),
inference(congruence,[status(thm)],[c1961]) ).
cnf(c1963,plain,
eta(difference(X,i(i(X2)))) = eta(difference(i(X2),X)),
inference(substitution,[status(thm)],[c593]) ).
cnf(c1964,plain,
quotient(X,eta(difference(X,i(i(X2))))) = quotient(X,eta(difference(i(X2),X))),
inference(congruence,[status(thm)],[c1963]) ).
cnf(c1965,plain,
product(i(X2),difference(i(X2),X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c1966,plain,
X = product(i(X2),difference(i(X2),X)),
inference(symmetry,[status(thm)],[c1965]) ).
cnf(c1967,plain,
quotient(X,eta(difference(i(X2),X))) = quotient(product(i(X2),difference(i(X2),X)),eta(difference(i(X2),X))),
inference(congruence,[status(thm)],[c1966]) ).
cnf(c1968,plain,
quotient(product(i(X2),difference(i(X2),X)),eta(difference(i(X2),X))) = i(difference(difference(i(X2),X),X2)),
inference(substitution,[status(thm)],[c1393]) ).
cnf(c1969,plain,
quotient(X,eta(difference(i(X2),X))) = i(difference(difference(i(X2),X),X2)),
inference(transitivity,[status(thm)],[c1967,c1968]) ).
cnf(c1970,plain,
quotient(X,eta(difference(X,i(i(X2))))) = i(difference(difference(i(X2),X),X2)),
inference(transitivity,[status(thm)],[c1964,c1969]) ).
cnf(c1971,plain,
quotient(X2,eta(difference(X2,i(i(j(X)))))) = i(difference(difference(i(j(X)),X2),j(X))),
inference(substitution,[status(thm)],[c1970]) ).
cnf(c1972,plain,
difference(i(j(X)),X2) = difference(X,X2),
inference(congruence,[status(thm)],[c46]) ).
cnf(c1973,plain,
difference(difference(i(j(X)),X2),j(X)) = difference(difference(X,X2),j(X)),
inference(congruence,[status(thm)],[c1972]) ).
cnf(c1974,plain,
i(difference(difference(i(j(X)),X2),j(X))) = i(difference(difference(X,X2),j(X))),
inference(congruence,[status(thm)],[c1973]) ).
cnf(c1975,plain,
difference(difference(X,X2),j(X)) = product(difference(X2,i(X)),X),
inference(substitution,[status(thm)],[c1876]) ).
cnf(c1976,plain,
i(difference(difference(X,X2),j(X))) = i(product(difference(X2,i(X)),X)),
inference(congruence,[status(thm)],[c1975]) ).
cnf(c1977,plain,
i(difference(difference(i(j(X)),X2),j(X))) = i(product(difference(X2,i(X)),X)),
inference(transitivity,[status(thm)],[c1974,c1976]) ).
cnf(c1978,plain,
quotient(X2,eta(difference(X2,i(i(j(X)))))) = i(product(difference(X2,i(X)),X)),
inference(transitivity,[status(thm)],[c1971,c1977]) ).
cnf(c1979,plain,
quotient(X2,eta(difference(X2,i(j(X))))) = i(product(difference(X2,i(X)),X)),
inference(transitivity,[status(thm)],[c1962,c1978]) ).
cnf(c1980,plain,
quotient(X2,eta(difference(X2,j(X)))) = i(product(difference(X2,i(X)),X)),
inference(transitivity,[status(thm)],[c1959,c1979]) ).
cnf(c1981,plain,
quotient(X2,eta(difference(X2,X))) = i(product(difference(X2,i(X)),X)),
inference(transitivity,[status(thm)],[c1956,c1980]) ).
cnf(c1982,plain,
quotient(X,eta(difference(X,X2))) = i(product(difference(X,i(X2)),X2)),
inference(substitution,[status(thm)],[c1981]) ).
cnf(c1983,plain,
i(product(difference(X,i(X2)),X2)) = quotient(X,eta(difference(X,X2))),
inference(symmetry,[status(thm)],[c1982]) ).
cnf(c1984,plain,
eta(i(product(difference(X,i(X2)),X2))) = eta(quotient(X,eta(difference(X,X2)))),
inference(congruence,[status(thm)],[c1983]) ).
cnf(c1985,plain,
eta(i(quotient(X2,eta(X)))) = eta(quotient(X2,eta(X))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c1986,plain,
eta(quotient(X2,eta(X))) = eta(i(quotient(X2,eta(X)))),
inference(symmetry,[status(thm)],[c1985]) ).
cnf(c1987,plain,
i(quotient(X2,eta(X))) = difference(quotient(X2,eta(X)),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c1988,plain,
eta(i(quotient(X2,eta(X)))) = eta(difference(quotient(X2,eta(X)),one)),
inference(congruence,[status(thm)],[c1987]) ).
cnf(c1989,plain,
one = i(one),
inference(symmetry,[status(thm)],[c537]) ).
cnf(c1990,plain,
difference(quotient(X2,eta(X)),one) = difference(quotient(X2,eta(X)),i(one)),
inference(congruence,[status(thm)],[c1989]) ).
cnf(c1991,plain,
eta(difference(quotient(X2,eta(X)),one)) = eta(difference(quotient(X2,eta(X)),i(one))),
inference(congruence,[status(thm)],[c1990]) ).
cnf(c1992,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c1993,plain,
i(one) = i(eta(eta(X))),
inference(congruence,[status(thm)],[c1992]) ).
cnf(c1994,plain,
difference(quotient(X2,eta(X)),i(one)) = difference(quotient(X2,eta(X)),i(eta(eta(X)))),
inference(congruence,[status(thm)],[c1993]) ).
cnf(c1995,plain,
eta(difference(quotient(X2,eta(X)),i(one))) = eta(difference(quotient(X2,eta(X)),i(eta(eta(X))))),
inference(congruence,[status(thm)],[c1994]) ).
cnf(c1996,plain,
eta(difference(j(quotient(X2,eta(X))),eta(eta(X)))) = eta(difference(quotient(X2,eta(X)),i(eta(eta(X))))),
inference(substitution,[status(thm)],[c853]) ).
cnf(c1997,plain,
eta(difference(quotient(X2,eta(X)),i(eta(eta(X))))) = eta(difference(j(quotient(X2,eta(X))),eta(eta(X)))),
inference(symmetry,[status(thm)],[c1996]) ).
cnf(c1998,plain,
eta(quotient(eta(eta(X)),j(quotient(X2,eta(X))))) = eta(difference(j(quotient(X2,eta(X))),eta(eta(X)))),
inference(substitution,[status(thm)],[c867]) ).
cnf(c1999,plain,
eta(difference(j(quotient(X2,eta(X))),eta(eta(X)))) = eta(quotient(eta(eta(X)),j(quotient(X2,eta(X))))),
inference(symmetry,[status(thm)],[c1998]) ).
cnf(c2000,plain,
product(eta(X),j(X2)) = j(quotient(X2,eta(X))),
inference(substitution,[status(thm)],[c1809]) ).
cnf(c2001,plain,
j(quotient(X2,eta(X))) = product(eta(X),j(X2)),
inference(symmetry,[status(thm)],[c2000]) ).
cnf(c2002,plain,
quotient(eta(eta(X)),j(quotient(X2,eta(X)))) = quotient(eta(eta(X)),product(eta(X),j(X2))),
inference(congruence,[status(thm)],[c2001]) ).
cnf(c2003,plain,
eta(quotient(eta(eta(X)),j(quotient(X2,eta(X))))) = eta(quotient(eta(eta(X)),product(eta(X),j(X2)))),
inference(congruence,[status(thm)],[c2002]) ).
cnf(c2004,plain,
eta(quotient(eta(eta(X)),product(eta(X),j(X2)))) = eta(product(j(X2),eta(X))),
inference(substitution,[status(thm)],[c702]) ).
cnf(c2005,plain,
eta(product(j(X2),eta(X))) = eta(product(X2,i(eta(X)))),
inference(substitution,[status(thm)],[c1283]) ).
cnf(c2006,plain,
eta(product(X2,i(eta(X)))) = eta(difference(X2,i(eta(X)))),
inference(substitution,[status(thm)],[c1641]) ).
cnf(c2007,plain,
eta(product(j(X2),eta(X))) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c2005,c2006]) ).
cnf(c2008,plain,
eta(quotient(eta(eta(X)),product(eta(X),j(X2)))) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c2004,c2007]) ).
cnf(c2009,plain,
eta(quotient(eta(eta(X)),j(quotient(X2,eta(X))))) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c2003,c2008]) ).
cnf(c2010,plain,
eta(difference(j(quotient(X2,eta(X))),eta(eta(X)))) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c1999,c2009]) ).
cnf(c2011,plain,
eta(difference(quotient(X2,eta(X)),i(eta(eta(X))))) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c1997,c2010]) ).
cnf(c2012,plain,
eta(difference(quotient(X2,eta(X)),i(one))) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c1995,c2011]) ).
cnf(c2013,plain,
eta(difference(quotient(X2,eta(X)),one)) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c1991,c2012]) ).
cnf(c2014,plain,
eta(i(quotient(X2,eta(X)))) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c1988,c2013]) ).
cnf(c2015,plain,
eta(quotient(X2,eta(X))) = eta(difference(X2,i(eta(X)))),
inference(transitivity,[status(thm)],[c1986,c2014]) ).
cnf(c2016,plain,
eta(quotient(X,eta(difference(X,X2)))) = eta(difference(X,i(eta(difference(X,X2))))),
inference(substitution,[status(thm)],[c2015]) ).
cnf(c2017,plain,
eta(difference(X,i(eta(difference(X,X2))))) = eta(difference(X,eta(difference(X,X2)))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c2018,plain,
eta(difference(X,eta(difference(X,X2)))) = eta(X),
inference(substitution,[status(thm)],[c1654]) ).
cnf(c2019,plain,
eta(difference(X,i(eta(difference(X,X2))))) = eta(X),
inference(transitivity,[status(thm)],[c2017,c2018]) ).
cnf(c2020,plain,
eta(quotient(X,eta(difference(X,X2)))) = eta(X),
inference(transitivity,[status(thm)],[c2016,c2019]) ).
cnf(c2021,plain,
eta(i(product(difference(X,i(X2)),X2))) = eta(X),
inference(transitivity,[status(thm)],[c1984,c2020]) ).
cnf(c2022,plain,
eta(product(difference(X,i(X2)),X2)) = eta(X),
inference(transitivity,[status(thm)],[c1949,c2021]) ).
cnf(c2023,plain,
eta(difference(difference(X,i(X2)),X2)) = eta(X),
inference(transitivity,[status(thm)],[c1947,c2022]) ).
cnf(c2024,plain,
eta(difference(X2,difference(X,i(X2)))) = eta(X),
inference(transitivity,[status(thm)],[c1945,c2023]) ).
cnf(c2025,plain,
eta(difference(X,difference(X2,i(X)))) = eta(X2),
inference(substitution,[status(thm)],[c2024]) ).
cnf(c2026,plain,
eta(X2) = eta(difference(X,difference(X2,i(X)))),
inference(symmetry,[status(thm)],[c2025]) ).
cnf(c2027,plain,
i(eta(X2)) = i(eta(difference(X,difference(X2,i(X))))),
inference(congruence,[status(thm)],[c2026]) ).
cnf(c2028,plain,
quotient(X3,i(eta(X2))) = quotient(X3,i(eta(difference(X,difference(X2,i(X)))))),
inference(congruence,[status(thm)],[c2027]) ).
cnf(c2029,plain,
quotient(quotient(X3,i(eta(X2))),eta(X2)) = quotient(quotient(X3,i(eta(difference(X,difference(X2,i(X)))))),eta(X2)),
inference(congruence,[status(thm)],[c2028]) ).
cnf(c2030,plain,
eta(difference(X,difference(X2,i(X)))) = eta(X2),
inference(substitution,[status(thm)],[c2024]) ).
cnf(c2031,plain,
eta(X2) = eta(difference(X,difference(X2,i(X)))),
inference(symmetry,[status(thm)],[c2030]) ).
cnf(c2032,plain,
quotient(quotient(X3,i(eta(difference(X,difference(X2,i(X)))))),eta(X2)) = quotient(quotient(X3,i(eta(difference(X,difference(X2,i(X)))))),eta(difference(X,difference(X2,i(X))))),
inference(congruence,[status(thm)],[c2031]) ).
cnf(c2033,plain,
difference(eta(X2),quotient(quotient(product(eta(X2),X),i(eta(X2))),eta(X2))) = product(i(eta(X2)),product(eta(X2),X)),
inference(substitution,[status(thm)],[c881]) ).
cnf(c2034,plain,
product(i(eta(X2)),product(eta(X2),X)) = difference(eta(X2),quotient(quotient(product(eta(X2),X),i(eta(X2))),eta(X2))),
inference(symmetry,[status(thm)],[c2033]) ).
cnf(c2035,plain,
i(eta(X)) = product(j(X),i(i(X))),
inference(symmetry,[status(thm)],[c1597]) ).
cnf(c2036,plain,
quotient(product(eta(X2),X),i(eta(X2))) = quotient(product(eta(X2),X),product(j(X2),i(i(X2)))),
inference(congruence,[status(thm)],[c2035]) ).
cnf(c2037,plain,
eta(X) = i(product(j(X),i(i(X)))),
inference(symmetry,[status(thm)],[c1594]) ).
cnf(c2038,plain,
product(eta(X2),X) = product(i(product(j(X2),i(i(X2)))),X),
inference(congruence,[status(thm)],[c2037]) ).
cnf(c2039,plain,
quotient(product(eta(X2),X),product(j(X2),i(i(X2)))) = quotient(product(i(product(j(X2),i(i(X2)))),X),product(j(X2),i(i(X2)))),
inference(congruence,[status(thm)],[c2038]) ).
cnf(c2040,plain,
quotient(product(i(product(j(X2),i(i(X2)))),X),product(j(X2),i(i(X2)))) = difference(product(j(X2),i(i(X2))),quotient(X,product(j(X2),i(i(X2))))),
inference(substitution,[status(thm)],[c900]) ).
cnf(c2041,plain,
difference(product(j(X2),i(i(X2))),quotient(X,product(j(X2),i(i(X2))))) = difference(i(eta(X2)),quotient(X,product(j(X2),i(i(X2))))),
inference(congruence,[status(thm)],[c1597]) ).
cnf(c2042,plain,
quotient(X,product(j(X2),i(i(X2)))) = quotient(X,i(eta(X2))),
inference(congruence,[status(thm)],[c1597]) ).
cnf(c2043,plain,
difference(i(eta(X2)),quotient(X,product(j(X2),i(i(X2))))) = difference(i(eta(X2)),quotient(X,i(eta(X2)))),
inference(congruence,[status(thm)],[c2042]) ).
cnf(c2044,plain,
difference(product(j(X2),i(i(X2))),quotient(X,product(j(X2),i(i(X2))))) = difference(i(eta(X2)),quotient(X,i(eta(X2)))),
inference(transitivity,[status(thm)],[c2041,c2043]) ).
cnf(c2045,plain,
quotient(product(i(product(j(X2),i(i(X2)))),X),product(j(X2),i(i(X2)))) = difference(i(eta(X2)),quotient(X,i(eta(X2)))),
inference(transitivity,[status(thm)],[c2040,c2044]) ).
cnf(c2046,plain,
quotient(product(eta(X2),X),product(j(X2),i(i(X2)))) = difference(i(eta(X2)),quotient(X,i(eta(X2)))),
inference(transitivity,[status(thm)],[c2039,c2045]) ).
cnf(c2047,plain,
quotient(product(eta(X2),X),i(eta(X2))) = difference(i(eta(X2)),quotient(X,i(eta(X2)))),
inference(transitivity,[status(thm)],[c2036,c2046]) ).
cnf(c2048,plain,
quotient(quotient(product(eta(X2),X),i(eta(X2))),eta(X2)) = quotient(difference(i(eta(X2)),quotient(X,i(eta(X2)))),eta(X2)),
inference(congruence,[status(thm)],[c2047]) ).
cnf(c2049,plain,
difference(eta(X2),quotient(quotient(product(eta(X2),X),i(eta(X2))),eta(X2))) = difference(eta(X2),quotient(difference(i(eta(X2)),quotient(X,i(eta(X2)))),eta(X2))),
inference(congruence,[status(thm)],[c2048]) ).
cnf(c2050,plain,
difference(eta(X2),quotient(difference(i(eta(X2)),quotient(X,i(eta(X2)))),eta(X2))) = quotient(quotient(X,i(eta(X2))),eta(X2)),
inference(substitution,[status(thm)],[c905]) ).
cnf(c2051,plain,
difference(eta(X2),quotient(quotient(product(eta(X2),X),i(eta(X2))),eta(X2))) = quotient(quotient(X,i(eta(X2))),eta(X2)),
inference(transitivity,[status(thm)],[c2049,c2050]) ).
cnf(c2052,plain,
product(i(eta(X2)),product(eta(X2),X)) = quotient(quotient(X,i(eta(X2))),eta(X2)),
inference(transitivity,[status(thm)],[c2034,c2051]) ).
cnf(c2053,plain,
product(i(eta(difference(X,difference(X2,i(X))))),product(eta(difference(X,difference(X2,i(X)))),X3)) = quotient(quotient(X3,i(eta(difference(X,difference(X2,i(X)))))),eta(difference(X,difference(X2,i(X))))),
inference(substitution,[status(thm)],[c2052]) ).
cnf(c2054,plain,
quotient(quotient(X3,i(eta(difference(X,difference(X2,i(X)))))),eta(difference(X,difference(X2,i(X))))) = product(i(eta(difference(X,difference(X2,i(X))))),product(eta(difference(X,difference(X2,i(X)))),X3)),
inference(symmetry,[status(thm)],[c2053]) ).
cnf(c2055,plain,
eta(difference(X,difference(X2,i(X)))) = eta(X2),
inference(substitution,[status(thm)],[c2024]) ).
cnf(c2056,plain,
i(eta(difference(X,difference(X2,i(X))))) = i(eta(X2)),
inference(congruence,[status(thm)],[c2055]) ).
cnf(c2057,plain,
product(i(eta(difference(X,difference(X2,i(X))))),product(eta(difference(X,difference(X2,i(X)))),X3)) = product(i(eta(X2)),product(eta(difference(X,difference(X2,i(X)))),X3)),
inference(congruence,[status(thm)],[c2056]) ).
cnf(c2058,plain,
difference(difference(X,eta(X2)),eta(X)) = product(i(eta(X2)),X),
inference(substitution,[status(thm)],[c459]) ).
cnf(c2059,plain,
product(i(eta(X2)),X) = difference(difference(X,eta(X2)),eta(X)),
inference(symmetry,[status(thm)],[c2058]) ).
cnf(c2060,plain,
eta(difference(X,eta(X2))) = eta(X),
inference(substitution,[status(thm)],[c1654]) ).
cnf(c2061,plain,
eta(X) = eta(difference(X,eta(X2))),
inference(symmetry,[status(thm)],[c2060]) ).
cnf(c2062,plain,
difference(difference(X,eta(X2)),eta(X)) = difference(difference(X,eta(X2)),eta(difference(X,eta(X2)))),
inference(congruence,[status(thm)],[c2061]) ).
cnf(c2063,plain,
difference(difference(X,eta(X2)),eta(difference(X,eta(X2)))) = j(difference(X,eta(X2))),
inference(substitution,[status(thm)],[c117]) ).
cnf(c2064,plain,
j(difference(X,eta(X2))) = difference(eta(X2),X),
inference(substitution,[status(thm)],[c1178]) ).
cnf(c2065,plain,
difference(difference(X,eta(X2)),eta(difference(X,eta(X2)))) = difference(eta(X2),X),
inference(transitivity,[status(thm)],[c2063,c2064]) ).
cnf(c2066,plain,
difference(difference(X,eta(X2)),eta(X)) = difference(eta(X2),X),
inference(transitivity,[status(thm)],[c2062,c2065]) ).
cnf(c2067,plain,
product(i(eta(X2)),X) = difference(eta(X2),X),
inference(transitivity,[status(thm)],[c2059,c2066]) ).
cnf(c2068,plain,
product(i(eta(X2)),product(eta(difference(X,difference(X2,i(X)))),X3)) = difference(eta(X2),product(eta(difference(X,difference(X2,i(X)))),X3)),
inference(substitution,[status(thm)],[c2067]) ).
cnf(c2069,plain,
product(eta(difference(X,difference(X2,i(X)))),X3) = quotient(eta(difference(X,difference(X2,i(X)))),i(X3)),
inference(substitution,[status(thm)],[c1387]) ).
cnf(c2070,plain,
difference(eta(X2),product(eta(difference(X,difference(X2,i(X)))),X3)) = difference(eta(X2),quotient(eta(difference(X,difference(X2,i(X)))),i(X3))),
inference(congruence,[status(thm)],[c2069]) ).
cnf(c2071,plain,
quotient(eta(difference(X,difference(X2,i(X)))),i(X3)) = difference(i(eta(difference(X,difference(X2,i(X))))),X3),
inference(substitution,[status(thm)],[c1856]) ).
cnf(c2072,plain,
difference(eta(X2),quotient(eta(difference(X,difference(X2,i(X)))),i(X3))) = difference(eta(X2),difference(i(eta(difference(X,difference(X2,i(X))))),X3)),
inference(congruence,[status(thm)],[c2071]) ).
cnf(c2073,plain,
eta(difference(X,difference(X2,i(X)))) = eta(X2),
inference(substitution,[status(thm)],[c2024]) ).
cnf(c2074,plain,
i(eta(difference(X,difference(X2,i(X))))) = i(eta(X2)),
inference(congruence,[status(thm)],[c2073]) ).
cnf(c2075,plain,
difference(i(eta(difference(X,difference(X2,i(X))))),X3) = difference(i(eta(X2)),X3),
inference(congruence,[status(thm)],[c2074]) ).
cnf(c2076,plain,
difference(eta(X2),difference(i(eta(difference(X,difference(X2,i(X))))),X3)) = difference(eta(X2),difference(i(eta(X2)),X3)),
inference(congruence,[status(thm)],[c2075]) ).
cnf(c2077,plain,
product(i(eta(X2)),difference(i(eta(X2)),X)) = difference(eta(X2),difference(i(eta(X2)),X)),
inference(substitution,[status(thm)],[c2067]) ).
cnf(c2078,plain,
difference(eta(X2),difference(i(eta(X2)),X)) = product(i(eta(X2)),difference(i(eta(X2)),X)),
inference(symmetry,[status(thm)],[c2077]) ).
cnf(c2079,plain,
i(eta(X)) = j(eta(X)),
inference(symmetry,[status(thm)],[c788]) ).
cnf(c2080,plain,
difference(i(eta(X2)),X) = difference(j(eta(X2)),X),
inference(congruence,[status(thm)],[c2079]) ).
cnf(c2081,plain,
product(i(eta(X2)),difference(i(eta(X2)),X)) = product(i(eta(X2)),difference(j(eta(X2)),X)),
inference(congruence,[status(thm)],[c2080]) ).
cnf(c2082,plain,
product(product(X2,difference(X2,X)),j(X2)) = product(X2,quotient(difference(X2,X),X2)),
inference(substitution,[status(thm)],[c632]) ).
cnf(c2083,plain,
product(X2,quotient(difference(X2,X),X2)) = product(product(X2,difference(X2,X)),j(X2)),
inference(symmetry,[status(thm)],[c2082]) ).
cnf(c2084,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c2085,plain,
product(product(X2,difference(X2,X)),j(X2)) = product(X,j(X2)),
inference(congruence,[status(thm)],[c2084]) ).
cnf(c2086,plain,
product(X2,quotient(difference(X2,X),X2)) = product(X,j(X2)),
inference(transitivity,[status(thm)],[c2083,c2085]) ).
cnf(c2087,plain,
product(X,quotient(difference(X,X2),X)) = product(X2,j(X)),
inference(substitution,[status(thm)],[c2086]) ).
cnf(c2088,plain,
product(X2,j(X)) = product(X,quotient(difference(X,X2),X)),
inference(symmetry,[status(thm)],[c2087]) ).
cnf(c2089,plain,
product(product(X2,j(X)),X) = product(product(X,quotient(difference(X,X2),X)),X),
inference(congruence,[status(thm)],[c2088]) ).
cnf(c2090,plain,
product(product(X,quotient(difference(X,X2),X)),X) = difference(i(X),product(quotient(difference(X,X2),X),X)),
inference(substitution,[status(thm)],[c696]) ).
cnf(c2091,plain,
product(quotient(difference(X,X2),X),X) = difference(X,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c2092,plain,
difference(i(X),product(quotient(difference(X,X2),X),X)) = difference(i(X),difference(X,X2)),
inference(congruence,[status(thm)],[c2091]) ).
cnf(c2093,plain,
product(product(X,quotient(difference(X,X2),X)),X) = difference(i(X),difference(X,X2)),
inference(transitivity,[status(thm)],[c2090,c2092]) ).
cnf(c2094,plain,
product(product(X2,j(X)),X) = difference(i(X),difference(X,X2)),
inference(transitivity,[status(thm)],[c2089,c2093]) ).
cnf(c2095,plain,
product(product(X,j(X2)),X2) = difference(i(X2),difference(X2,X)),
inference(substitution,[status(thm)],[c2094]) ).
cnf(c2096,plain,
difference(i(X2),difference(X2,X)) = product(product(X,j(X2)),X2),
inference(symmetry,[status(thm)],[c2095]) ).
cnf(c2097,plain,
product(X2,difference(i(X2),difference(X2,X))) = product(X2,product(product(X,j(X2)),X2)),
inference(congruence,[status(thm)],[c2096]) ).
cnf(c2098,plain,
difference(j(X2),quotient(product(X,j(X2)),j(X2))) = product(X2,product(product(X,j(X2)),X2)),
inference(substitution,[status(thm)],[c931]) ).
cnf(c2099,plain,
product(X2,product(product(X,j(X2)),X2)) = difference(j(X2),quotient(product(X,j(X2)),j(X2))),
inference(symmetry,[status(thm)],[c2098]) ).
cnf(c2100,plain,
quotient(product(X,j(X2)),j(X2)) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c2101,plain,
difference(j(X2),quotient(product(X,j(X2)),j(X2))) = difference(j(X2),X),
inference(congruence,[status(thm)],[c2100]) ).
cnf(c2102,plain,
product(X2,product(product(X,j(X2)),X2)) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2099,c2101]) ).
cnf(c2103,plain,
product(X2,difference(i(X2),difference(X2,X))) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2097,c2102]) ).
cnf(c2104,plain,
difference(j(X2),X) = product(X2,difference(i(X2),difference(X2,X))),
inference(symmetry,[status(thm)],[c2103]) ).
cnf(c2105,plain,
product(i(X2),difference(j(X2),X)) = product(i(X2),product(X2,difference(i(X2),difference(X2,X)))),
inference(congruence,[status(thm)],[c2104]) ).
cnf(c2106,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c2107,plain,
product(X2,difference(i(X2),difference(X2,X))) = product(j(i(X2)),difference(i(X2),difference(X2,X))),
inference(congruence,[status(thm)],[c2106]) ).
cnf(c2108,plain,
product(i(X2),product(X2,difference(i(X2),difference(X2,X)))) = product(i(X2),product(j(i(X2)),difference(i(X2),difference(X2,X)))),
inference(congruence,[status(thm)],[c2107]) ).
cnf(c2109,plain,
difference(i(X),difference(X,quotient(product(X2,X),X))) = product(product(X2,X),i(X)),
inference(substitution,[status(thm)],[c915]) ).
cnf(c2110,plain,
product(product(X2,X),i(X)) = difference(i(X),difference(X,quotient(product(X2,X),X))),
inference(symmetry,[status(thm)],[c2109]) ).
cnf(c2111,plain,
quotient(product(X2,X),X) = X2,
inference(substitution,[status(thm)],[c12]) ).
cnf(c2112,plain,
difference(X,quotient(product(X2,X),X)) = difference(X,X2),
inference(congruence,[status(thm)],[c2111]) ).
cnf(c2113,plain,
difference(i(X),difference(X,quotient(product(X2,X),X))) = difference(i(X),difference(X,X2)),
inference(congruence,[status(thm)],[c2112]) ).
cnf(c2114,plain,
product(product(X2,X),i(X)) = difference(i(X),difference(X,X2)),
inference(transitivity,[status(thm)],[c2110,c2113]) ).
cnf(c2115,plain,
product(product(X,X2),i(X2)) = difference(i(X2),difference(X2,X)),
inference(substitution,[status(thm)],[c2114]) ).
cnf(c2116,plain,
difference(i(X2),difference(X2,X)) = product(product(X,X2),i(X2)),
inference(symmetry,[status(thm)],[c2115]) ).
cnf(c2117,plain,
product(j(i(X2)),difference(i(X2),difference(X2,X))) = product(j(i(X2)),product(product(X,X2),i(X2))),
inference(congruence,[status(thm)],[c2116]) ).
cnf(c2118,plain,
product(i(X2),product(j(i(X2)),difference(i(X2),difference(X2,X)))) = product(i(X2),product(j(i(X2)),product(product(X,X2),i(X2)))),
inference(congruence,[status(thm)],[c2117]) ).
cnf(c2119,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c2120,plain,
product(X,X2) = product(X,i(j(X2))),
inference(congruence,[status(thm)],[c2119]) ).
cnf(c2121,plain,
product(j(X2),product(X,X2)) = product(j(X2),product(X,i(j(X2)))),
inference(congruence,[status(thm)],[c2120]) ).
cnf(c2122,plain,
product(X2,product(j(X2),product(X,X2))) = product(X2,product(j(X2),product(X,i(j(X2))))),
inference(congruence,[status(thm)],[c2121]) ).
cnf(c2123,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c2124,plain,
product(X2,product(j(X2),product(X,i(j(X2))))) = product(i(j(X2)),product(j(X2),product(X,i(j(X2))))),
inference(congruence,[status(thm)],[c2123]) ).
cnf(c2125,plain,
product(difference(i(X2),X),i(X2)) = product(i(i(X2)),product(X,i(X2))),
inference(substitution,[status(thm)],[c322]) ).
cnf(c2126,plain,
product(i(i(X2)),product(X,i(X2))) = product(difference(i(X2),X),i(X2)),
inference(symmetry,[status(thm)],[c2125]) ).
cnf(c2127,plain,
difference(i(X2),quotient(X,j(i(X2)))) = product(difference(i(X2),X),i(X2)),
inference(substitution,[status(thm)],[c567]) ).
cnf(c2128,plain,
product(difference(i(X2),X),i(X2)) = difference(i(X2),quotient(X,j(i(X2)))),
inference(symmetry,[status(thm)],[c2127]) ).
cnf(c2129,plain,
quotient(X,j(i(X2))) = quotient(X,X2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c2130,plain,
difference(i(X2),quotient(X,j(i(X2)))) = difference(i(X2),quotient(X,X2)),
inference(congruence,[status(thm)],[c2129]) ).
cnf(c2131,plain,
product(difference(i(X2),X),i(X2)) = difference(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c2128,c2130]) ).
cnf(c2132,plain,
product(i(i(X2)),product(X,i(X2))) = difference(i(X2),quotient(X,X2)),
inference(transitivity,[status(thm)],[c2126,c2131]) ).
cnf(c2133,plain,
product(i(i(X2)),product(product(eta(X2),X),i(X2))) = difference(i(X2),quotient(product(eta(X2),X),X2)),
inference(substitution,[status(thm)],[c2132]) ).
cnf(c2134,plain,
difference(i(X2),quotient(product(eta(X2),X),X2)) = product(i(i(X2)),product(product(eta(X2),X),i(X2))),
inference(symmetry,[status(thm)],[c2133]) ).
cnf(c2135,plain,
product(difference(i(X2),product(eta(X2),X)),i(X2)) = product(i(i(X2)),product(product(eta(X2),X),i(X2))),
inference(substitution,[status(thm)],[c322]) ).
cnf(c2136,plain,
product(i(i(X2)),product(product(eta(X2),X),i(X2))) = product(difference(i(X2),product(eta(X2),X)),i(X2)),
inference(symmetry,[status(thm)],[c2135]) ).
cnf(c2137,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c2138,plain,
product(eta(X2),X) = product(product(i(X2),X2),X),
inference(congruence,[status(thm)],[c2137]) ).
cnf(c2139,plain,
difference(i(X2),product(eta(X2),X)) = difference(i(X2),product(product(i(X2),X2),X)),
inference(congruence,[status(thm)],[c2138]) ).
cnf(c2140,plain,
product(difference(i(X2),product(eta(X2),X)),i(X2)) = product(difference(i(X2),product(product(i(X2),X2),X)),i(X2)),
inference(congruence,[status(thm)],[c2139]) ).
cnf(c2141,plain,
product(difference(i(X2),product(product(i(X2),X2),X)),i(X2)) = product(X2,product(X,i(X2))),
inference(substitution,[status(thm)],[c305]) ).
cnf(c2142,plain,
product(difference(i(X2),product(eta(X2),X)),i(X2)) = product(X2,product(X,i(X2))),
inference(transitivity,[status(thm)],[c2140,c2141]) ).
cnf(c2143,plain,
product(i(i(X2)),product(product(eta(X2),X),i(X2))) = product(X2,product(X,i(X2))),
inference(transitivity,[status(thm)],[c2136,c2142]) ).
cnf(c2144,plain,
difference(i(X2),quotient(product(eta(X2),X),X2)) = product(X2,product(X,i(X2))),
inference(transitivity,[status(thm)],[c2134,c2143]) ).
cnf(c2145,plain,
product(X2,product(X,i(X2))) = difference(i(X2),quotient(product(eta(X2),X),X2)),
inference(symmetry,[status(thm)],[c2144]) ).
cnf(c2146,plain,
product(i(X2),product(X2,product(X,i(X2)))) = product(i(X2),difference(i(X2),quotient(product(eta(X2),X),X2))),
inference(congruence,[status(thm)],[c2145]) ).
cnf(c2147,plain,
product(i(X2),difference(i(X2),quotient(product(eta(X2),X),X2))) = quotient(product(eta(X2),X),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c2148,plain,
product(i(X2),product(X2,product(X,i(X2)))) = quotient(product(eta(X2),X),X2),
inference(transitivity,[status(thm)],[c2146,c2147]) ).
cnf(c2149,plain,
product(i(j(X2)),product(j(X2),product(X,i(j(X2))))) = quotient(product(eta(j(X2)),X),j(X2)),
inference(substitution,[status(thm)],[c2148]) ).
cnf(c2150,plain,
product(eta(j(X2)),X) = product(eta(X2),X),
inference(congruence,[status(thm)],[c111]) ).
cnf(c2151,plain,
quotient(product(eta(j(X2)),X),j(X2)) = quotient(product(eta(X2),X),j(X2)),
inference(congruence,[status(thm)],[c2150]) ).
cnf(c2152,plain,
product(i(j(X2)),product(j(X2),product(X,i(j(X2))))) = quotient(product(eta(X2),X),j(X2)),
inference(transitivity,[status(thm)],[c2149,c2151]) ).
cnf(c2153,plain,
product(X2,product(j(X2),product(X,i(j(X2))))) = quotient(product(eta(X2),X),j(X2)),
inference(transitivity,[status(thm)],[c2124,c2152]) ).
cnf(c2154,plain,
product(X2,product(j(X2),product(X,X2))) = quotient(product(eta(X2),X),j(X2)),
inference(transitivity,[status(thm)],[c2122,c2153]) ).
cnf(c2155,plain,
product(i(X2),product(j(i(X2)),product(product(X,X2),i(X2)))) = quotient(product(eta(i(X2)),product(X,X2)),j(i(X2))),
inference(substitution,[status(thm)],[c2154]) ).
cnf(c2156,plain,
product(eta(i(X2)),product(X,X2)) = quotient(eta(i(X2)),i(product(X,X2))),
inference(substitution,[status(thm)],[c1387]) ).
cnf(c2157,plain,
quotient(product(eta(i(X2)),product(X,X2)),j(i(X2))) = quotient(quotient(eta(i(X2)),i(product(X,X2))),j(i(X2))),
inference(congruence,[status(thm)],[c2156]) ).
cnf(c2158,plain,
quotient(eta(i(X2)),i(product(X,X2))) = difference(i(eta(i(X2))),product(X,X2)),
inference(substitution,[status(thm)],[c1856]) ).
cnf(c2159,plain,
quotient(quotient(eta(i(X2)),i(product(X,X2))),j(i(X2))) = quotient(difference(i(eta(i(X2))),product(X,X2)),j(i(X2))),
inference(congruence,[status(thm)],[c2158]) ).
cnf(c2160,plain,
i(eta(i(X))) = i(eta(X)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c2161,plain,
difference(i(eta(i(X2))),product(X,X2)) = difference(i(eta(X2)),product(X,X2)),
inference(congruence,[status(thm)],[c2160]) ).
cnf(c2162,plain,
quotient(difference(i(eta(i(X2))),product(X,X2)),j(i(X2))) = quotient(difference(i(eta(X2)),product(X,X2)),j(i(X2))),
inference(congruence,[status(thm)],[c2161]) ).
cnf(c2163,plain,
quotient(difference(i(eta(X2)),product(X,X2)),j(i(X2))) = quotient(difference(i(eta(X2)),product(X,X2)),X2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c2164,plain,
quotient(difference(i(eta(X2)),product(X,X2)),X2) = difference(product(X2,i(eta(X2))),product(X2,X)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c2165,plain,
X = product(i(i(X)),eta(X)),
inference(symmetry,[status(thm)],[c514]) ).
cnf(c2166,plain,
difference(X,i(i(X))) = difference(product(i(i(X)),eta(X)),i(i(X))),
inference(congruence,[status(thm)],[c2165]) ).
cnf(c2167,plain,
eta(X) = quotient(i(i(X)),X),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c2168,plain,
product(i(i(X)),eta(X)) = product(i(i(X)),quotient(i(i(X)),X)),
inference(congruence,[status(thm)],[c2167]) ).
cnf(c2169,plain,
difference(product(i(i(X)),eta(X)),i(i(X))) = difference(product(i(i(X)),quotient(i(i(X)),X)),i(i(X))),
inference(congruence,[status(thm)],[c2168]) ).
cnf(c2170,plain,
difference(product(i(i(X)),quotient(i(i(X)),X)),i(i(X))) = quotient(X,i(i(X))),
inference(substitution,[status(thm)],[c1108]) ).
cnf(c2171,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c2172,plain,
quotient(X,i(i(X))) = quotient(j(i(X)),i(i(X))),
inference(congruence,[status(thm)],[c2171]) ).
cnf(c2173,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c2174,plain,
i(eta(X)) = i(product(i(X),X)),
inference(congruence,[status(thm)],[c2173]) ).
cnf(c2175,plain,
product(i(eta(X)),i(X)) = product(i(product(i(X),X)),i(X)),
inference(congruence,[status(thm)],[c2174]) ).
cnf(c2176,plain,
product(i(product(i(X),X)),i(X)) = difference(X,eta(i(X))),
inference(substitution,[status(thm)],[c359]) ).
cnf(c2177,plain,
difference(X,eta(i(X))) = difference(X,eta(X)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c2178,plain,
difference(X,eta(i(X))) = j(X),
inference(transitivity,[status(thm)],[c2177,c117]) ).
cnf(c2179,plain,
product(i(product(i(X),X)),i(X)) = j(X),
inference(transitivity,[status(thm)],[c2176,c2178]) ).
cnf(c2180,plain,
product(i(eta(X)),i(X)) = j(X),
inference(transitivity,[status(thm)],[c2175,c2179]) ).
cnf(c2181,plain,
j(X) = product(i(eta(X)),i(X)),
inference(symmetry,[status(thm)],[c2180]) ).
cnf(c2182,plain,
quotient(j(X),i(X)) = quotient(product(i(eta(X)),i(X)),i(X)),
inference(congruence,[status(thm)],[c2181]) ).
cnf(c2183,plain,
quotient(product(i(eta(X)),i(X)),i(X)) = i(eta(X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c2184,plain,
quotient(j(X),i(X)) = i(eta(X)),
inference(transitivity,[status(thm)],[c2182,c2183]) ).
cnf(c2185,plain,
quotient(j(i(X)),i(i(X))) = i(eta(i(X))),
inference(substitution,[status(thm)],[c2184]) ).
cnf(c2186,plain,
i(eta(i(X))) = i(eta(X)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c2187,plain,
quotient(j(i(X)),i(i(X))) = i(eta(X)),
inference(transitivity,[status(thm)],[c2185,c2186]) ).
cnf(c2188,plain,
quotient(X,i(i(X))) = i(eta(X)),
inference(transitivity,[status(thm)],[c2172,c2187]) ).
cnf(c2189,plain,
difference(product(i(i(X)),quotient(i(i(X)),X)),i(i(X))) = i(eta(X)),
inference(transitivity,[status(thm)],[c2170,c2188]) ).
cnf(c2190,plain,
difference(product(i(i(X)),eta(X)),i(i(X))) = i(eta(X)),
inference(transitivity,[status(thm)],[c2169,c2189]) ).
cnf(c2191,plain,
difference(X,i(i(X))) = i(eta(X)),
inference(transitivity,[status(thm)],[c2166,c2190]) ).
cnf(c2192,plain,
i(eta(X)) = difference(X,i(i(X))),
inference(symmetry,[status(thm)],[c2191]) ).
cnf(c2193,plain,
product(X,i(eta(X))) = product(X,difference(X,i(i(X)))),
inference(congruence,[status(thm)],[c2192]) ).
cnf(c2194,plain,
product(X,difference(X,i(i(X)))) = i(i(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c2195,plain,
product(X,i(eta(X))) = i(i(X)),
inference(transitivity,[status(thm)],[c2193,c2194]) ).
cnf(c2196,plain,
difference(product(X2,i(eta(X2))),product(X2,X)) = difference(i(i(X2)),product(X2,X)),
inference(congruence,[status(thm)],[c2195]) ).
cnf(c2197,plain,
quotient(difference(i(eta(X2)),product(X,X2)),X2) = difference(i(i(X2)),product(X2,X)),
inference(transitivity,[status(thm)],[c2164,c2196]) ).
cnf(c2198,plain,
quotient(difference(i(eta(X2)),product(X,X2)),j(i(X2))) = difference(i(i(X2)),product(X2,X)),
inference(transitivity,[status(thm)],[c2163,c2197]) ).
cnf(c2199,plain,
quotient(difference(i(eta(i(X2))),product(X,X2)),j(i(X2))) = difference(i(i(X2)),product(X2,X)),
inference(transitivity,[status(thm)],[c2162,c2198]) ).
cnf(c2200,plain,
quotient(quotient(eta(i(X2)),i(product(X,X2))),j(i(X2))) = difference(i(i(X2)),product(X2,X)),
inference(transitivity,[status(thm)],[c2159,c2199]) ).
cnf(c2201,plain,
quotient(product(eta(i(X2)),product(X,X2)),j(i(X2))) = difference(i(i(X2)),product(X2,X)),
inference(transitivity,[status(thm)],[c2157,c2200]) ).
cnf(c2202,plain,
product(i(X2),product(j(i(X2)),product(product(X,X2),i(X2)))) = difference(i(i(X2)),product(X2,X)),
inference(transitivity,[status(thm)],[c2155,c2201]) ).
cnf(c2203,plain,
product(i(X2),product(j(i(X2)),difference(i(X2),difference(X2,X)))) = difference(i(i(X2)),product(X2,X)),
inference(transitivity,[status(thm)],[c2118,c2202]) ).
cnf(c2204,plain,
product(i(X2),product(X2,difference(i(X2),difference(X2,X)))) = difference(i(i(X2)),product(X2,X)),
inference(transitivity,[status(thm)],[c2108,c2203]) ).
cnf(c2205,plain,
product(i(X2),difference(j(X2),X)) = difference(i(i(X2)),product(X2,X)),
inference(transitivity,[status(thm)],[c2105,c2204]) ).
cnf(c2206,plain,
product(i(eta(X2)),difference(j(eta(X2)),X)) = difference(i(i(eta(X2))),product(eta(X2),X)),
inference(substitution,[status(thm)],[c2205]) ).
cnf(c2207,plain,
difference(i(i(eta(X2))),product(eta(X2),X)) = difference(eta(X2),product(eta(X2),X)),
inference(congruence,[status(thm)],[c726]) ).
cnf(c2208,plain,
difference(eta(X2),product(eta(X2),X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c2209,plain,
difference(i(i(eta(X2))),product(eta(X2),X)) = X,
inference(transitivity,[status(thm)],[c2207,c2208]) ).
cnf(c2210,plain,
product(i(eta(X2)),difference(j(eta(X2)),X)) = X,
inference(transitivity,[status(thm)],[c2206,c2209]) ).
cnf(c2211,plain,
product(i(eta(X2)),difference(i(eta(X2)),X)) = X,
inference(transitivity,[status(thm)],[c2081,c2210]) ).
cnf(c2212,plain,
difference(eta(X2),difference(i(eta(X2)),X)) = X,
inference(transitivity,[status(thm)],[c2078,c2211]) ).
cnf(c2213,plain,
difference(eta(X),difference(i(eta(X)),X2)) = X2,
inference(substitution,[status(thm)],[c2212]) ).
cnf(c2214,plain,
difference(eta(X2),difference(i(eta(difference(X,difference(X2,i(X))))),X3)) = X3,
inference(transitivity,[status(thm)],[c2076,c2213]) ).
cnf(c2215,plain,
difference(eta(X2),quotient(eta(difference(X,difference(X2,i(X)))),i(X3))) = X3,
inference(transitivity,[status(thm)],[c2072,c2214]) ).
cnf(c2216,plain,
difference(eta(X2),product(eta(difference(X,difference(X2,i(X)))),X3)) = X3,
inference(transitivity,[status(thm)],[c2070,c2215]) ).
cnf(c2217,plain,
product(i(eta(X2)),product(eta(difference(X,difference(X2,i(X)))),X3)) = X3,
inference(transitivity,[status(thm)],[c2068,c2216]) ).
cnf(c2218,plain,
product(i(eta(difference(X,difference(X2,i(X))))),product(eta(difference(X,difference(X2,i(X)))),X3)) = X3,
inference(transitivity,[status(thm)],[c2057,c2217]) ).
cnf(c2219,plain,
quotient(quotient(X3,i(eta(difference(X,difference(X2,i(X)))))),eta(difference(X,difference(X2,i(X))))) = X3,
inference(transitivity,[status(thm)],[c2054,c2218]) ).
cnf(c2220,plain,
quotient(quotient(X3,i(eta(difference(X,difference(X2,i(X)))))),eta(X2)) = X3,
inference(transitivity,[status(thm)],[c2032,c2219]) ).
cnf(c2221,plain,
quotient(quotient(X2,i(eta(X))),eta(X)) = X2,
inference(transitivity,[status(thm)],[c2029,c2220]) ).
cnf(c2222,plain,
quotient(i(eta(X)),quotient(quotient(X2,i(eta(X))),eta(X))) = quotient(i(eta(X)),X2),
inference(congruence,[status(thm)],[c2221]) ).
cnf(c2223,plain,
quotient(i(i(eta(X))),quotient(quotient(X2,i(eta(X))),i(eta(X)))) = quotient(i(eta(X)),X2),
inference(transitivity,[status(thm)],[c1944,c2222]) ).
cnf(c2224,plain,
product(i(eta(X)),quotient(eta(X),quotient(X2,i(eta(X))))) = quotient(i(eta(X)),X2),
inference(transitivity,[status(thm)],[c1943,c2223]) ).
cnf(c2225,plain,
product(i(eta(X)),j(X2)) = quotient(i(eta(X)),X2),
inference(transitivity,[status(thm)],[c1942,c2224]) ).
cnf(c2226,plain,
j(quotient(X2,i(eta(X)))) = quotient(i(eta(X)),X2),
inference(transitivity,[status(thm)],[c1776,c2225]) ).
cnf(c2227,plain,
j(quotient(quotient(X,i(i(eta(X2)))),i(eta(X2)))) = quotient(i(eta(X2)),quotient(X,i(i(eta(X2))))),
inference(substitution,[status(thm)],[c2226]) ).
cnf(c2228,plain,
quotient(i(eta(X2)),quotient(X,i(i(eta(X2))))) = j(quotient(quotient(X,i(i(eta(X2)))),i(eta(X2)))),
inference(symmetry,[status(thm)],[c2227]) ).
cnf(c2229,plain,
product(j(i(X)),product(i(X),X2)) = quotient(quotient(X2,i(i(X))),i(X)),
inference(substitution,[status(thm)],[c1925]) ).
cnf(c2230,plain,
quotient(quotient(X2,i(i(X))),i(X)) = product(j(i(X)),product(i(X),X2)),
inference(symmetry,[status(thm)],[c2229]) ).
cnf(c2231,plain,
product(j(i(X)),product(i(X),X2)) = product(X,product(i(X),X2)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c2232,plain,
product(X,product(i(X),X2)) = quotient(quotient(X2,i(X)),X),
inference(substitution,[status(thm)],[c426]) ).
cnf(c2233,plain,
product(j(i(X)),product(i(X),X2)) = quotient(quotient(X2,i(X)),X),
inference(transitivity,[status(thm)],[c2231,c2232]) ).
cnf(c2234,plain,
quotient(quotient(X2,i(i(X))),i(X)) = quotient(quotient(X2,i(X)),X),
inference(transitivity,[status(thm)],[c2230,c2233]) ).
cnf(c2235,plain,
quotient(quotient(X,i(i(eta(X2)))),i(eta(X2))) = quotient(quotient(X,i(eta(X2))),eta(X2)),
inference(substitution,[status(thm)],[c2234]) ).
cnf(c2236,plain,
j(quotient(quotient(X,i(i(eta(X2)))),i(eta(X2)))) = j(quotient(quotient(X,i(eta(X2))),eta(X2))),
inference(congruence,[status(thm)],[c2235]) ).
cnf(c2237,plain,
i(quotient(eta(X2),X)) = difference(quotient(eta(X2),X),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c2238,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c2239,plain,
difference(quotient(eta(X2),X),one) = difference(quotient(eta(X2),X),eta(eta(X2))),
inference(congruence,[status(thm)],[c2238]) ).
cnf(c2240,plain,
quotient(X2,quotient(X,X2)) = product(X2,quotient(X2,X)),
inference(symmetry,[status(thm)],[c1110]) ).
cnf(c2241,plain,
i(quotient(X2,quotient(X,X2))) = i(product(X2,quotient(X2,X))),
inference(congruence,[status(thm)],[c2240]) ).
cnf(c2242,plain,
product(i(quotient(X2,quotient(X,X2))),X2) = product(i(product(X2,quotient(X2,X))),X2),
inference(congruence,[status(thm)],[c2241]) ).
cnf(c2243,plain,
product(i(product(X2,quotient(X2,X))),X2) = difference(quotient(X2,X),eta(X2)),
inference(substitution,[status(thm)],[c359]) ).
cnf(c2244,plain,
product(i(quotient(X2,quotient(X,X2))),X2) = difference(quotient(X2,X),eta(X2)),
inference(transitivity,[status(thm)],[c2242,c2243]) ).
cnf(c2245,plain,
product(i(quotient(eta(X2),quotient(X,eta(X2)))),eta(X2)) = difference(quotient(eta(X2),X),eta(eta(X2))),
inference(substitution,[status(thm)],[c2244]) ).
cnf(c2246,plain,
difference(quotient(eta(X2),X),eta(eta(X2))) = product(i(quotient(eta(X2),quotient(X,eta(X2)))),eta(X2)),
inference(symmetry,[status(thm)],[c2245]) ).
cnf(c2247,plain,
product(i(quotient(eta(X2),quotient(X,eta(X2)))),eta(X2)) = difference(quotient(eta(X2),quotient(X,eta(X2))),eta(X2)),
inference(substitution,[status(thm)],[c1030]) ).
cnf(c2248,plain,
difference(quotient(eta(X2),quotient(X,eta(X2))),eta(X2)) = quotient(X,eta(X2)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c2249,plain,
product(i(quotient(eta(X2),quotient(X,eta(X2)))),eta(X2)) = quotient(X,eta(X2)),
inference(transitivity,[status(thm)],[c2247,c2248]) ).
cnf(c2250,plain,
difference(quotient(eta(X2),X),eta(eta(X2))) = quotient(X,eta(X2)),
inference(transitivity,[status(thm)],[c2246,c2249]) ).
cnf(c2251,plain,
difference(quotient(eta(X2),X),one) = quotient(X,eta(X2)),
inference(transitivity,[status(thm)],[c2239,c2250]) ).
cnf(c2252,plain,
i(quotient(eta(X2),X)) = quotient(X,eta(X2)),
inference(transitivity,[status(thm)],[c2237,c2251]) ).
cnf(c2253,plain,
i(quotient(eta(X),X2)) = quotient(X2,eta(X)),
inference(substitution,[status(thm)],[c2252]) ).
cnf(c2254,plain,
quotient(X2,eta(X)) = i(quotient(eta(X),X2)),
inference(symmetry,[status(thm)],[c2253]) ).
cnf(c2255,plain,
j(quotient(X2,eta(X))) = j(i(quotient(eta(X),X2))),
inference(congruence,[status(thm)],[c2254]) ).
cnf(c2256,plain,
j(i(quotient(eta(X),X2))) = quotient(eta(X),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c2257,plain,
j(quotient(X2,eta(X))) = quotient(eta(X),X2),
inference(transitivity,[status(thm)],[c2255,c2256]) ).
cnf(c2258,plain,
j(quotient(quotient(X,i(eta(X2))),eta(X2))) = quotient(eta(X2),quotient(X,i(eta(X2)))),
inference(substitution,[status(thm)],[c2257]) ).
cnf(c2259,plain,
j(quotient(quotient(X,i(eta(X2))),eta(X2))) = j(X),
inference(transitivity,[status(thm)],[c2258,c1939]) ).
cnf(c2260,plain,
j(quotient(quotient(X,i(i(eta(X2)))),i(eta(X2)))) = j(X),
inference(transitivity,[status(thm)],[c2236,c2259]) ).
cnf(c2261,plain,
quotient(i(eta(X2)),quotient(X,i(i(eta(X2))))) = j(X),
inference(transitivity,[status(thm)],[c2228,c2260]) ).
cnf(c2262,plain,
quotient(i(eta(X2)),quotient(X,eta(X2))) = j(X),
inference(transitivity,[status(thm)],[c1774,c2261]) ).
cnf(c2263,plain,
quotient(i(eta(X)),quotient(X2,eta(X))) = j(X2),
inference(substitution,[status(thm)],[c2262]) ).
cnf(c2264,plain,
product(X,quotient(i(eta(X)),quotient(X2,eta(X)))) = product(X,j(X2)),
inference(congruence,[status(thm)],[c2263]) ).
cnf(c2265,plain,
i(product(X,quotient(i(eta(X)),quotient(X2,eta(X))))) = i(product(X,j(X2))),
inference(congruence,[status(thm)],[c2264]) ).
cnf(c2266,plain,
quotient(difference(quotient(i(eta(X)),quotient(X2,eta(X))),eta(X)),X) = i(product(X,j(X2))),
inference(transitivity,[status(thm)],[c1771,c2265]) ).
cnf(c2267,plain,
quotient(quotient(X2,j(eta(X))),X) = i(product(X,j(X2))),
inference(transitivity,[status(thm)],[c1770,c2266]) ).
cnf(c2268,plain,
quotient(quotient(X2,i(eta(X))),X) = i(product(X,j(X2))),
inference(transitivity,[status(thm)],[c1705,c2267]) ).
cnf(c2269,plain,
quotient(quotient(X,i(eta(X2))),X2) = i(product(X2,j(X))),
inference(substitution,[status(thm)],[c2268]) ).
cnf(c2270,plain,
quotient(product(X,eta(X2)),X2) = i(product(X2,j(X))),
inference(transitivity,[status(thm)],[c1702,c2269]) ).
cnf(c2271,plain,
quotient(product(X,product(i(X2),X2)),X2) = i(product(X2,j(X))),
inference(transitivity,[status(thm)],[c1700,c2270]) ).
cnf(c2272,plain,
difference(X2,product(product(X2,X),i(X2))) = i(product(X2,j(X))),
inference(transitivity,[status(thm)],[c1696,c2271]) ).
cnf(c2273,plain,
difference(X2,quotient(difference(i(X2),X),i(i(X2)))) = i(product(X2,j(X))),
inference(transitivity,[status(thm)],[c1695,c2272]) ).
cnf(c2274,plain,
difference(j(X),quotient(difference(i(j(X)),X2),i(i(j(X))))) = i(product(j(X),j(X2))),
inference(substitution,[status(thm)],[c2273]) ).
cnf(c2275,plain,
difference(j(X),quotient(difference(X,X2),i(i(j(X))))) = i(product(j(X),j(X2))),
inference(transitivity,[status(thm)],[c1693,c2274]) ).
cnf(c2276,plain,
difference(j(X),quotient(difference(X,X2),i(X))) = i(product(j(X),j(X2))),
inference(transitivity,[status(thm)],[c1689,c2275]) ).
cnf(c2277,plain,
quotient(product(X2,eta(X)),j(X)) = i(product(j(X),j(X2))),
inference(transitivity,[status(thm)],[c1685,c2276]) ).
cnf(c2278,plain,
quotient(quotient(X2,i(eta(X))),j(X)) = i(product(j(X),j(X2))),
inference(transitivity,[status(thm)],[c1676,c2277]) ).
cnf(c2279,plain,
quotient(quotient(X,i(eta(i(X2)))),j(i(X2))) = i(product(j(i(X2)),j(X))),
inference(substitution,[status(thm)],[c2278]) ).
cnf(c2280,plain,
i(product(j(i(X2)),j(X))) = quotient(quotient(X,i(eta(i(X2)))),j(i(X2))),
inference(symmetry,[status(thm)],[c2279]) ).
cnf(c2281,plain,
product(X,eta(i(X2))) = quotient(X,i(eta(i(X2)))),
inference(substitution,[status(thm)],[c1674]) ).
cnf(c2282,plain,
quotient(X,i(eta(i(X2)))) = product(X,eta(i(X2))),
inference(symmetry,[status(thm)],[c2281]) ).
cnf(c2283,plain,
quotient(quotient(X,i(eta(i(X2)))),j(i(X2))) = quotient(product(X,eta(i(X2))),j(i(X2))),
inference(congruence,[status(thm)],[c2282]) ).
cnf(c2284,plain,
difference(j(i(X2)),quotient(difference(i(X2),X),i(i(X2)))) = quotient(product(X,eta(i(X2))),j(i(X2))),
inference(substitution,[status(thm)],[c1683]) ).
cnf(c2285,plain,
quotient(product(X,eta(i(X2))),j(i(X2))) = difference(j(i(X2)),quotient(difference(i(X2),X),i(i(X2)))),
inference(symmetry,[status(thm)],[c2284]) ).
cnf(c2286,plain,
quotient(difference(i(X2),X),i(i(X2))) = product(product(X2,X),i(X2)),
inference(symmetry,[status(thm)],[c1366]) ).
cnf(c2287,plain,
difference(j(i(X2)),quotient(difference(i(X2),X),i(i(X2)))) = difference(j(i(X2)),product(product(X2,X),i(X2))),
inference(congruence,[status(thm)],[c2286]) ).
cnf(c2288,plain,
quotient(eta(difference(X,X2)),X) = quotient(eta(difference(X2,X)),X),
inference(congruence,[status(thm)],[c1442]) ).
cnf(c2289,plain,
eta(difference(X2,X)) = eta(difference(X,i(X2))),
inference(symmetry,[status(thm)],[c593]) ).
cnf(c2290,plain,
quotient(eta(difference(X2,X)),X) = quotient(eta(difference(X,i(X2))),X),
inference(congruence,[status(thm)],[c2289]) ).
cnf(c2291,plain,
j(quotient(X2,eta(difference(X2,X)))) = quotient(eta(difference(X2,X)),X2),
inference(substitution,[status(thm)],[c2257]) ).
cnf(c2292,plain,
quotient(eta(difference(X2,X)),X2) = j(quotient(X2,eta(difference(X2,X)))),
inference(symmetry,[status(thm)],[c2291]) ).
cnf(c2293,plain,
j(quotient(X2,eta(difference(X2,X)))) = j(i(product(difference(X2,i(X)),X))),
inference(congruence,[status(thm)],[c1981]) ).
cnf(c2294,plain,
j(i(product(difference(X2,i(X)),X))) = product(difference(X2,i(X)),X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c2295,plain,
j(quotient(X2,eta(difference(X2,X)))) = product(difference(X2,i(X)),X),
inference(transitivity,[status(thm)],[c2293,c2294]) ).
cnf(c2296,plain,
quotient(eta(difference(X2,X)),X2) = product(difference(X2,i(X)),X),
inference(transitivity,[status(thm)],[c2292,c2295]) ).
cnf(c2297,plain,
quotient(eta(difference(X,i(X2))),X) = product(difference(X,i(i(X2))),i(X2)),
inference(substitution,[status(thm)],[c2296]) ).
cnf(c2298,plain,
difference(difference(i(X),X2),j(i(X))) = product(difference(X2,i(i(X))),i(X)),
inference(substitution,[status(thm)],[c1876]) ).
cnf(c2299,plain,
product(difference(X2,i(i(X))),i(X)) = difference(difference(i(X),X2),j(i(X))),
inference(symmetry,[status(thm)],[c2298]) ).
cnf(c2300,plain,
difference(difference(i(X),X2),j(i(X))) = difference(difference(i(X),X2),X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c2301,plain,
product(difference(X2,i(i(X))),i(X)) = difference(difference(i(X),X2),X),
inference(transitivity,[status(thm)],[c2299,c2300]) ).
cnf(c2302,plain,
product(difference(X,i(i(X2))),i(X2)) = difference(difference(i(X2),X),X2),
inference(substitution,[status(thm)],[c2301]) ).
cnf(c2303,plain,
quotient(eta(difference(X,i(X2))),X) = difference(difference(i(X2),X),X2),
inference(transitivity,[status(thm)],[c2297,c2302]) ).
cnf(c2304,plain,
quotient(eta(difference(X2,X)),X) = difference(difference(i(X2),X),X2),
inference(transitivity,[status(thm)],[c2290,c2303]) ).
cnf(c2305,plain,
quotient(eta(difference(X,X2)),X) = difference(difference(i(X2),X),X2),
inference(transitivity,[status(thm)],[c2288,c2304]) ).
cnf(c2306,plain,
quotient(eta(difference(product(X2,X),X2)),product(X2,X)) = difference(difference(i(X2),product(X2,X)),X2),
inference(substitution,[status(thm)],[c2305]) ).
cnf(c2307,plain,
difference(difference(i(X2),product(X2,X)),X2) = quotient(eta(difference(product(X2,X),X2)),product(X2,X)),
inference(symmetry,[status(thm)],[c2306]) ).
cnf(c2308,plain,
eta(difference(product(X2,X),j(X2))) = eta(difference(product(X2,X),X2)),
inference(substitution,[status(thm)],[c1954]) ).
cnf(c2309,plain,
eta(difference(product(X2,X),X2)) = eta(difference(product(X2,X),j(X2))),
inference(symmetry,[status(thm)],[c2308]) ).
cnf(c2310,plain,
quotient(eta(difference(product(X2,X),X2)),product(X2,X)) = quotient(eta(difference(product(X2,X),j(X2))),product(X2,X)),
inference(congruence,[status(thm)],[c2309]) ).
cnf(c2311,plain,
eta(difference(product(X2,X),i(j(X2)))) = eta(difference(product(X2,X),j(X2))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c2312,plain,
eta(difference(product(X2,X),j(X2))) = eta(difference(product(X2,X),i(j(X2)))),
inference(symmetry,[status(thm)],[c2311]) ).
cnf(c2313,plain,
quotient(eta(difference(product(X2,X),j(X2))),product(X2,X)) = quotient(eta(difference(product(X2,X),i(j(X2)))),product(X2,X)),
inference(congruence,[status(thm)],[c2312]) ).
cnf(c2314,plain,
product(quotient(difference(i(X2),X),X2),X2) = difference(i(X2),X),
inference(substitution,[status(thm)],[c38]) ).
cnf(c2315,plain,
difference(i(X2),X) = product(quotient(difference(i(X2),X),X2),X2),
inference(symmetry,[status(thm)],[c2314]) ).
cnf(c2316,plain,
product(X2,difference(i(X2),X)) = product(X2,product(quotient(difference(i(X2),X),X2),X2)),
inference(congruence,[status(thm)],[c2315]) ).
cnf(c2317,plain,
quotient(product(X2,X),product(X2,difference(i(X2),X))) = quotient(product(X2,X),product(X2,product(quotient(difference(i(X2),X),X2),X2))),
inference(congruence,[status(thm)],[c2316]) ).
cnf(c2318,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c2319,plain,
product(X2,X) = product(i(j(X2)),X),
inference(congruence,[status(thm)],[c2318]) ).
cnf(c2320,plain,
quotient(product(X2,X),product(X2,product(quotient(difference(i(X2),X),X2),X2))) = quotient(product(i(j(X2)),X),product(X2,product(quotient(difference(i(X2),X),X2),X2))),
inference(congruence,[status(thm)],[c2319]) ).
cnf(c2321,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c2322,plain,
i(X) = i(i(j(X))),
inference(congruence,[status(thm)],[c2321]) ).
cnf(c2323,plain,
difference(i(X2),X) = difference(i(i(j(X2))),X),
inference(congruence,[status(thm)],[c2322]) ).
cnf(c2324,plain,
quotient(difference(i(X2),X),X2) = quotient(difference(i(i(j(X2))),X),X2),
inference(congruence,[status(thm)],[c2323]) ).
cnf(c2325,plain,
product(quotient(difference(i(X2),X),X2),X2) = product(quotient(difference(i(i(j(X2))),X),X2),X2),
inference(congruence,[status(thm)],[c2324]) ).
cnf(c2326,plain,
product(X2,product(quotient(difference(i(X2),X),X2),X2)) = product(X2,product(quotient(difference(i(i(j(X2))),X),X2),X2)),
inference(congruence,[status(thm)],[c2325]) ).
cnf(c2327,plain,
quotient(product(i(j(X2)),X),product(X2,product(quotient(difference(i(X2),X),X2),X2))) = quotient(product(i(j(X2)),X),product(X2,product(quotient(difference(i(i(j(X2))),X),X2),X2))),
inference(congruence,[status(thm)],[c2326]) ).
cnf(c2328,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c2329,plain,
quotient(difference(i(i(j(X2))),X),X2) = quotient(difference(i(i(j(X2))),X),i(j(X2))),
inference(congruence,[status(thm)],[c2328]) ).
cnf(c2330,plain,
product(quotient(difference(i(i(j(X2))),X),X2),X2) = product(quotient(difference(i(i(j(X2))),X),i(j(X2))),X2),
inference(congruence,[status(thm)],[c2329]) ).
cnf(c2331,plain,
product(X2,product(quotient(difference(i(i(j(X2))),X),X2),X2)) = product(X2,product(quotient(difference(i(i(j(X2))),X),i(j(X2))),X2)),
inference(congruence,[status(thm)],[c2330]) ).
cnf(c2332,plain,
quotient(product(i(j(X2)),X),product(X2,product(quotient(difference(i(i(j(X2))),X),X2),X2))) = quotient(product(i(j(X2)),X),product(X2,product(quotient(difference(i(i(j(X2))),X),i(j(X2))),X2))),
inference(congruence,[status(thm)],[c2331]) ).
cnf(c2333,plain,
product(product(i(X2),quotient(X,product(eta(X2),i(X2)))),eta(X2)) = quotient(difference(i(i(X2)),X),i(X2)),
inference(substitution,[status(thm)],[c434]) ).
cnf(c2334,plain,
quotient(difference(i(i(X2)),X),i(X2)) = product(product(i(X2),quotient(X,product(eta(X2),i(X2)))),eta(X2)),
inference(symmetry,[status(thm)],[c2333]) ).
cnf(c2335,plain,
quotient(quotient(difference(i(i(X2)),X),i(X2)),X2) = quotient(product(product(i(X2),quotient(X,product(eta(X2),i(X2)))),eta(X2)),X2),
inference(congruence,[status(thm)],[c2334]) ).
cnf(c2336,plain,
quotient(difference(i(X2),X),i(i(X2))) = product(product(X2,X),i(X2)),
inference(symmetry,[status(thm)],[c1366]) ).
cnf(c2337,plain,
difference(X2,quotient(difference(i(X2),X),i(i(X2)))) = difference(X2,product(product(X2,X),i(X2))),
inference(congruence,[status(thm)],[c2336]) ).
cnf(c2338,plain,
difference(X2,product(product(X2,X),i(X2))) = quotient(product(X,product(i(X2),X2)),X2),
inference(substitution,[status(thm)],[c57]) ).
cnf(c2339,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c2340,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c2339]) ).
cnf(c2341,plain,
product(X,product(i(X2),X2)) = product(X,eta(X2)),
inference(congruence,[status(thm)],[c2340]) ).
cnf(c2342,plain,
quotient(product(X,product(i(X2),X2)),X2) = quotient(product(X,eta(X2)),X2),
inference(congruence,[status(thm)],[c2341]) ).
cnf(c2343,plain,
difference(X2,product(product(X2,X),i(X2))) = quotient(product(X,eta(X2)),X2),
inference(transitivity,[status(thm)],[c2338,c2342]) ).
cnf(c2344,plain,
difference(X2,quotient(difference(i(X2),X),i(i(X2)))) = quotient(product(X,eta(X2)),X2),
inference(transitivity,[status(thm)],[c2337,c2343]) ).
cnf(c2345,plain,
difference(X2,quotient(difference(i(X2),product(i(X2),X)),i(i(X2)))) = quotient(product(product(i(X2),X),eta(X2)),X2),
inference(substitution,[status(thm)],[c2344]) ).
cnf(c2346,plain,
quotient(product(product(i(X2),X),eta(X2)),X2) = difference(X2,quotient(difference(i(X2),product(i(X2),X)),i(i(X2)))),
inference(symmetry,[status(thm)],[c2345]) ).
cnf(c2347,plain,
difference(i(X2),product(i(X2),X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c2348,plain,
quotient(difference(i(X2),product(i(X2),X)),i(i(X2))) = quotient(X,i(i(X2))),
inference(congruence,[status(thm)],[c2347]) ).
cnf(c2349,plain,
difference(X2,quotient(difference(i(X2),product(i(X2),X)),i(i(X2)))) = difference(X2,quotient(X,i(i(X2)))),
inference(congruence,[status(thm)],[c2348]) ).
cnf(c2350,plain,
quotient(product(product(i(X2),X),eta(X2)),X2) = difference(X2,quotient(X,i(i(X2)))),
inference(transitivity,[status(thm)],[c2346,c2349]) ).
cnf(c2351,plain,
quotient(product(product(i(X2),quotient(X,product(eta(X2),i(X2)))),eta(X2)),X2) = difference(X2,quotient(quotient(X,product(eta(X2),i(X2))),i(i(X2)))),
inference(substitution,[status(thm)],[c2350]) ).
cnf(c2352,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c2353,plain,
product(eta(X),i(X)) = product(eta(i(X)),i(X)),
inference(congruence,[status(thm)],[c2352]) ).
cnf(c2354,plain,
product(eta(i(X)),i(X)) = i(i(i(X))),
inference(substitution,[status(thm)],[c490]) ).
cnf(c2355,plain,
product(eta(X),i(X)) = i(i(i(X))),
inference(transitivity,[status(thm)],[c2353,c2354]) ).
cnf(c2356,plain,
quotient(X,product(eta(X2),i(X2))) = quotient(X,i(i(i(X2)))),
inference(congruence,[status(thm)],[c2355]) ).
cnf(c2357,plain,
quotient(quotient(X,product(eta(X2),i(X2))),i(i(X2))) = quotient(quotient(X,i(i(i(X2)))),i(i(X2))),
inference(congruence,[status(thm)],[c2356]) ).
cnf(c2358,plain,
difference(X2,quotient(quotient(X,product(eta(X2),i(X2))),i(i(X2)))) = difference(X2,quotient(quotient(X,i(i(i(X2)))),i(i(X2)))),
inference(congruence,[status(thm)],[c2357]) ).
cnf(c2359,plain,
quotient(quotient(X,i(i(i(X2)))),i(i(X2))) = quotient(quotient(X,i(i(X2))),i(X2)),
inference(substitution,[status(thm)],[c2234]) ).
cnf(c2360,plain,
difference(X2,quotient(quotient(X,i(i(i(X2)))),i(i(X2)))) = difference(X2,quotient(quotient(X,i(i(X2))),i(X2))),
inference(congruence,[status(thm)],[c2359]) ).
cnf(c2361,plain,
quotient(quotient(X,i(i(X2))),i(X2)) = quotient(quotient(X,i(X2)),X2),
inference(substitution,[status(thm)],[c2234]) ).
cnf(c2362,plain,
difference(X2,quotient(quotient(X,i(i(X2))),i(X2))) = difference(X2,quotient(quotient(X,i(X2)),X2)),
inference(congruence,[status(thm)],[c2361]) ).
cnf(c2363,plain,
difference(X2,quotient(quotient(X,i(i(X2))),i(X2))) = product(i(X2),X),
inference(transitivity,[status(thm)],[c2362,c881]) ).
cnf(c2364,plain,
difference(X2,quotient(quotient(X,i(i(i(X2)))),i(i(X2)))) = product(i(X2),X),
inference(transitivity,[status(thm)],[c2360,c2363]) ).
cnf(c2365,plain,
difference(X2,quotient(quotient(X,product(eta(X2),i(X2))),i(i(X2)))) = product(i(X2),X),
inference(transitivity,[status(thm)],[c2358,c2364]) ).
cnf(c2366,plain,
quotient(product(product(i(X2),quotient(X,product(eta(X2),i(X2)))),eta(X2)),X2) = product(i(X2),X),
inference(transitivity,[status(thm)],[c2351,c2365]) ).
cnf(c2367,plain,
quotient(quotient(difference(i(i(X2)),X),i(X2)),X2) = product(i(X2),X),
inference(transitivity,[status(thm)],[c2335,c2366]) ).
cnf(c2368,plain,
quotient(quotient(difference(i(i(j(X2))),X),i(j(X2))),j(X2)) = product(i(j(X2)),X),
inference(substitution,[status(thm)],[c2367]) ).
cnf(c2369,plain,
product(i(j(X2)),X) = quotient(quotient(difference(i(i(j(X2))),X),i(j(X2))),j(X2)),
inference(symmetry,[status(thm)],[c2368]) ).
cnf(c2370,plain,
quotient(product(i(j(X2)),X),product(X2,product(quotient(difference(i(i(j(X2))),X),i(j(X2))),X2))) = quotient(quotient(quotient(difference(i(i(j(X2))),X),i(j(X2))),j(X2)),product(X2,product(quotient(difference(i(i(j(X2))),X),i(j(X2))),X2))),
inference(congruence,[status(thm)],[c2369]) ).
cnf(c2371,plain,
difference(j(X),quotient(X2,j(X))) = product(X,product(X2,X)),
inference(substitution,[status(thm)],[c931]) ).
cnf(c2372,plain,
product(X,product(X2,X)) = difference(j(X),quotient(X2,j(X))),
inference(symmetry,[status(thm)],[c2371]) ).
cnf(c2373,plain,
quotient(quotient(X2,j(X)),product(X,product(X2,X))) = quotient(quotient(X2,j(X)),difference(j(X),quotient(X2,j(X)))),
inference(congruence,[status(thm)],[c2372]) ).
cnf(c2374,plain,
quotient(quotient(X2,j(X)),difference(j(X),quotient(X2,j(X)))) = j(X),
inference(substitution,[status(thm)],[c86]) ).
cnf(c2375,plain,
quotient(quotient(X2,j(X)),product(X,product(X2,X))) = j(X),
inference(transitivity,[status(thm)],[c2373,c2374]) ).
cnf(c2376,plain,
quotient(quotient(quotient(difference(i(i(j(X2))),X),i(j(X2))),j(X2)),product(X2,product(quotient(difference(i(i(j(X2))),X),i(j(X2))),X2))) = j(X2),
inference(substitution,[status(thm)],[c2375]) ).
cnf(c2377,plain,
quotient(product(i(j(X2)),X),product(X2,product(quotient(difference(i(i(j(X2))),X),i(j(X2))),X2))) = j(X2),
inference(transitivity,[status(thm)],[c2370,c2376]) ).
cnf(c2378,plain,
quotient(product(i(j(X2)),X),product(X2,product(quotient(difference(i(i(j(X2))),X),X2),X2))) = j(X2),
inference(transitivity,[status(thm)],[c2332,c2377]) ).
cnf(c2379,plain,
quotient(product(i(j(X2)),X),product(X2,product(quotient(difference(i(X2),X),X2),X2))) = j(X2),
inference(transitivity,[status(thm)],[c2327,c2378]) ).
cnf(c2380,plain,
quotient(product(X2,X),product(X2,product(quotient(difference(i(X2),X),X2),X2))) = j(X2),
inference(transitivity,[status(thm)],[c2320,c2379]) ).
cnf(c2381,plain,
quotient(product(X2,X),product(X2,difference(i(X2),X))) = j(X2),
inference(transitivity,[status(thm)],[c2317,c2380]) ).
cnf(c2382,plain,
j(X2) = quotient(product(X2,X),product(X2,difference(i(X2),X))),
inference(symmetry,[status(thm)],[c2381]) ).
cnf(c2383,plain,
i(j(X2)) = i(quotient(product(X2,X),product(X2,difference(i(X2),X)))),
inference(congruence,[status(thm)],[c2382]) ).
cnf(c2384,plain,
difference(product(X2,X),i(j(X2))) = difference(product(X2,X),i(quotient(product(X2,X),product(X2,difference(i(X2),X))))),
inference(congruence,[status(thm)],[c2383]) ).
cnf(c2385,plain,
eta(difference(product(X2,X),i(j(X2)))) = eta(difference(product(X2,X),i(quotient(product(X2,X),product(X2,difference(i(X2),X)))))),
inference(congruence,[status(thm)],[c2384]) ).
cnf(c2386,plain,
quotient(eta(difference(product(X2,X),i(j(X2)))),product(X2,X)) = quotient(eta(difference(product(X2,X),i(quotient(product(X2,X),product(X2,difference(i(X2),X)))))),product(X2,X)),
inference(congruence,[status(thm)],[c2385]) ).
cnf(c2387,plain,
quotient(eta(difference(product(X2,X),i(quotient(product(X2,X),product(X2,difference(i(X2),X)))))),product(X2,X)) = quotient(eta(product(X2,difference(i(X2),X))),product(X2,X)),
inference(substitution,[status(thm)],[c1883]) ).
cnf(c2388,plain,
eta(product(X2,difference(i(X2),X))) = eta(difference(X2,difference(i(X2),X))),
inference(substitution,[status(thm)],[c1641]) ).
cnf(c2389,plain,
quotient(eta(product(X2,difference(i(X2),X))),product(X2,X)) = quotient(eta(difference(X2,difference(i(X2),X))),product(X2,X)),
inference(congruence,[status(thm)],[c2388]) ).
cnf(c2390,plain,
eta(difference(i(X2),difference(i(X2),X))) = eta(difference(X2,difference(i(X2),X))),
inference(substitution,[status(thm)],[c1545]) ).
cnf(c2391,plain,
eta(difference(X2,difference(i(X2),X))) = eta(difference(i(X2),difference(i(X2),X))),
inference(symmetry,[status(thm)],[c2390]) ).
cnf(c2392,plain,
eta(difference(i(i(X2)),difference(i(X2),X))) = eta(difference(i(X2),difference(i(X2),X))),
inference(substitution,[status(thm)],[c1545]) ).
cnf(c2393,plain,
eta(difference(i(X2),difference(i(X2),X))) = eta(difference(i(i(X2)),difference(i(X2),X))),
inference(symmetry,[status(thm)],[c2392]) ).
cnf(c2394,plain,
eta(difference(X2,quotient(difference(i(i(X2)),difference(i(X2),X)),i(X2)))) = eta(difference(i(i(X2)),difference(i(X2),X))),
inference(substitution,[status(thm)],[c1573]) ).
cnf(c2395,plain,
eta(difference(i(i(X2)),difference(i(X2),X))) = eta(difference(X2,quotient(difference(i(i(X2)),difference(i(X2),X)),i(X2)))),
inference(symmetry,[status(thm)],[c2394]) ).
cnf(c2396,plain,
difference(j(X2),X) = product(X2,difference(i(X2),difference(X2,X))),
inference(symmetry,[status(thm)],[c2103]) ).
cnf(c2397,plain,
difference(X2,difference(j(X2),X)) = difference(X2,product(X2,difference(i(X2),difference(X2,X)))),
inference(congruence,[status(thm)],[c2396]) ).
cnf(c2398,plain,
difference(X2,product(X2,difference(i(X2),difference(X2,X)))) = difference(i(X2),difference(X2,X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c2399,plain,
difference(X2,difference(j(X2),X)) = difference(i(X2),difference(X2,X)),
inference(transitivity,[status(thm)],[c2397,c2398]) ).
cnf(c2400,plain,
difference(i(X2),difference(X2,X)) = difference(X2,difference(j(X2),X)),
inference(symmetry,[status(thm)],[c2399]) ).
cnf(c2401,plain,
quotient(difference(i(X2),difference(X2,X)),X2) = quotient(difference(X2,difference(j(X2),X)),X2),
inference(congruence,[status(thm)],[c2400]) ).
cnf(c2402,plain,
difference(X2,product(difference(j(X2),X),j(X2))) = quotient(difference(X2,difference(j(X2),X)),X2),
inference(substitution,[status(thm)],[c1329]) ).
cnf(c2403,plain,
quotient(difference(X2,difference(j(X2),X)),X2) = difference(X2,product(difference(j(X2),X),j(X2))),
inference(symmetry,[status(thm)],[c2402]) ).
cnf(c2404,plain,
product(difference(j(X2),X),j(X2)) = product(i(j(X2)),product(X,j(X2))),
inference(substitution,[status(thm)],[c322]) ).
cnf(c2405,plain,
difference(X2,product(difference(j(X2),X),j(X2))) = difference(X2,product(i(j(X2)),product(X,j(X2)))),
inference(congruence,[status(thm)],[c2404]) ).
cnf(c2406,plain,
product(i(j(X2)),product(X,j(X2))) = product(X2,product(X,j(X2))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c2407,plain,
difference(X2,product(i(j(X2)),product(X,j(X2)))) = difference(X2,product(X2,product(X,j(X2)))),
inference(congruence,[status(thm)],[c2406]) ).
cnf(c2408,plain,
difference(X2,product(X2,product(X,j(X2)))) = product(X,j(X2)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c2409,plain,
difference(X2,product(i(j(X2)),product(X,j(X2)))) = product(X,j(X2)),
inference(transitivity,[status(thm)],[c2407,c2408]) ).
cnf(c2410,plain,
difference(X2,product(difference(j(X2),X),j(X2))) = product(X,j(X2)),
inference(transitivity,[status(thm)],[c2405,c2409]) ).
cnf(c2411,plain,
quotient(difference(X2,difference(j(X2),X)),X2) = product(X,j(X2)),
inference(transitivity,[status(thm)],[c2403,c2410]) ).
cnf(c2412,plain,
quotient(difference(i(X2),difference(X2,X)),X2) = product(X,j(X2)),
inference(transitivity,[status(thm)],[c2401,c2411]) ).
cnf(c2413,plain,
quotient(difference(i(i(X2)),difference(i(X2),X)),i(X2)) = product(X,j(i(X2))),
inference(substitution,[status(thm)],[c2412]) ).
cnf(c2414,plain,
difference(X2,quotient(difference(i(i(X2)),difference(i(X2),X)),i(X2))) = difference(X2,product(X,j(i(X2)))),
inference(congruence,[status(thm)],[c2413]) ).
cnf(c2415,plain,
eta(difference(X2,quotient(difference(i(i(X2)),difference(i(X2),X)),i(X2)))) = eta(difference(X2,product(X,j(i(X2))))),
inference(congruence,[status(thm)],[c2414]) ).
cnf(c2416,plain,
product(X,j(i(X2))) = product(X,X2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c2417,plain,
difference(X2,product(X,j(i(X2)))) = difference(X2,product(X,X2)),
inference(congruence,[status(thm)],[c2416]) ).
cnf(c2418,plain,
eta(difference(X2,product(X,j(i(X2))))) = eta(difference(X2,product(X,X2))),
inference(congruence,[status(thm)],[c2417]) ).
cnf(c2419,plain,
eta(difference(X2,i(product(X,X2)))) = eta(difference(X2,product(X,X2))),
inference(substitution,[status(thm)],[c1440]) ).
cnf(c2420,plain,
eta(difference(X2,product(X,X2))) = eta(difference(X2,i(product(X,X2)))),
inference(symmetry,[status(thm)],[c2419]) ).
cnf(c2421,plain,
eta(difference(X2,i(product(X,X2)))) = eta(difference(product(X,X2),X2)),
inference(substitution,[status(thm)],[c593]) ).
cnf(c2422,plain,
eta(quotient(product(X,X2),X2)) = eta(difference(product(X,X2),X2)),
inference(substitution,[status(thm)],[c1270]) ).
cnf(c2423,plain,
eta(difference(product(X,X2),X2)) = eta(quotient(product(X,X2),X2)),
inference(symmetry,[status(thm)],[c2422]) ).
cnf(c2424,plain,
quotient(product(X,X2),X2) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c2425,plain,
eta(quotient(product(X,X2),X2)) = eta(X),
inference(congruence,[status(thm)],[c2424]) ).
cnf(c2426,plain,
eta(difference(product(X,X2),X2)) = eta(X),
inference(transitivity,[status(thm)],[c2423,c2425]) ).
cnf(c2427,plain,
eta(difference(X2,i(product(X,X2)))) = eta(X),
inference(transitivity,[status(thm)],[c2421,c2426]) ).
cnf(c2428,plain,
eta(difference(X2,product(X,X2))) = eta(X),
inference(transitivity,[status(thm)],[c2420,c2427]) ).
cnf(c2429,plain,
eta(difference(X2,product(X,j(i(X2))))) = eta(X),
inference(transitivity,[status(thm)],[c2418,c2428]) ).
cnf(c2430,plain,
eta(difference(X2,quotient(difference(i(i(X2)),difference(i(X2),X)),i(X2)))) = eta(X),
inference(transitivity,[status(thm)],[c2415,c2429]) ).
cnf(c2431,plain,
eta(difference(i(i(X2)),difference(i(X2),X))) = eta(X),
inference(transitivity,[status(thm)],[c2395,c2430]) ).
cnf(c2432,plain,
eta(difference(i(X2),difference(i(X2),X))) = eta(X),
inference(transitivity,[status(thm)],[c2393,c2431]) ).
cnf(c2433,plain,
eta(difference(X2,difference(i(X2),X))) = eta(X),
inference(transitivity,[status(thm)],[c2391,c2432]) ).
cnf(c2434,plain,
quotient(eta(difference(X2,difference(i(X2),X))),product(X2,X)) = quotient(eta(X),product(X2,X)),
inference(congruence,[status(thm)],[c2433]) ).
cnf(c2435,plain,
quotient(eta(X),product(X2,X)) = difference(X,j(X2)),
inference(substitution,[status(thm)],[c1159]) ).
cnf(c2436,plain,
quotient(eta(difference(X2,difference(i(X2),X))),product(X2,X)) = difference(X,j(X2)),
inference(transitivity,[status(thm)],[c2434,c2435]) ).
cnf(c2437,plain,
quotient(eta(product(X2,difference(i(X2),X))),product(X2,X)) = difference(X,j(X2)),
inference(transitivity,[status(thm)],[c2389,c2436]) ).
cnf(c2438,plain,
quotient(eta(difference(product(X2,X),i(quotient(product(X2,X),product(X2,difference(i(X2),X)))))),product(X2,X)) = difference(X,j(X2)),
inference(transitivity,[status(thm)],[c2387,c2437]) ).
cnf(c2439,plain,
quotient(eta(difference(product(X2,X),i(j(X2)))),product(X2,X)) = difference(X,j(X2)),
inference(transitivity,[status(thm)],[c2386,c2438]) ).
cnf(c2440,plain,
quotient(eta(difference(product(X2,X),j(X2))),product(X2,X)) = difference(X,j(X2)),
inference(transitivity,[status(thm)],[c2313,c2439]) ).
cnf(c2441,plain,
quotient(eta(difference(product(X2,X),X2)),product(X2,X)) = difference(X,j(X2)),
inference(transitivity,[status(thm)],[c2310,c2440]) ).
cnf(c2442,plain,
difference(difference(i(X2),product(X2,X)),X2) = difference(X,j(X2)),
inference(transitivity,[status(thm)],[c2307,c2441]) ).
cnf(c2443,plain,
difference(X,j(X2)) = difference(difference(i(X2),product(X2,X)),X2),
inference(symmetry,[status(thm)],[c2442]) ).
cnf(c2444,plain,
quotient(X2,difference(X,j(X2))) = quotient(X2,difference(difference(i(X2),product(X2,X)),X2)),
inference(congruence,[status(thm)],[c2443]) ).
cnf(c2445,plain,
quotient(X2,difference(difference(i(X2),product(X2,X)),X2)) = difference(i(X2),product(X2,X)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c2446,plain,
quotient(X2,difference(X,j(X2))) = difference(i(X2),product(X2,X)),
inference(transitivity,[status(thm)],[c2444,c2445]) ).
cnf(c2447,plain,
difference(i(X2),product(X2,X)) = quotient(X2,difference(X,j(X2))),
inference(symmetry,[status(thm)],[c2446]) ).
cnf(c2448,plain,
difference(X2,difference(i(X2),product(X2,X))) = difference(X2,quotient(X2,difference(X,j(X2)))),
inference(congruence,[status(thm)],[c2447]) ).
cnf(c2449,plain,
product(X,difference(X,X2)) = X2,
inference(substitution,[status(thm)],[c7]) ).
cnf(c2450,plain,
X2 = product(X,difference(X,X2)),
inference(symmetry,[status(thm)],[c2449]) ).
cnf(c2451,plain,
difference(X2,X) = difference(product(X,difference(X,X2)),X),
inference(congruence,[status(thm)],[c2450]) ).
cnf(c2452,plain,
product(difference(X2,X),X) = product(difference(product(X,difference(X,X2)),X),X),
inference(congruence,[status(thm)],[c2451]) ).
cnf(c2453,plain,
product(difference(product(X,difference(X,X2)),X),X) = difference(difference(X,X2),X),
inference(substitution,[status(thm)],[c238]) ).
cnf(c2454,plain,
product(difference(X2,X),X) = difference(difference(X,X2),X),
inference(transitivity,[status(thm)],[c2452,c2453]) ).
cnf(c2455,plain,
product(difference(quotient(X2,X),X2),X2) = difference(difference(X2,quotient(X2,X)),X2),
inference(substitution,[status(thm)],[c2454]) ).
cnf(c2456,plain,
difference(difference(X2,quotient(X2,X)),X2) = product(difference(quotient(X2,X),X2),X2),
inference(symmetry,[status(thm)],[c2455]) ).
cnf(c2457,plain,
product(difference(quotient(X2,X),X2),X2) = product(X,X2),
inference(congruence,[status(thm)],[c209]) ).
cnf(c2458,plain,
difference(difference(X2,quotient(X2,X)),X2) = product(X,X2),
inference(transitivity,[status(thm)],[c2456,c2457]) ).
cnf(c2459,plain,
product(X,X2) = difference(difference(X2,quotient(X2,X)),X2),
inference(symmetry,[status(thm)],[c2458]) ).
cnf(c2460,plain,
quotient(X2,product(X,X2)) = quotient(X2,difference(difference(X2,quotient(X2,X)),X2)),
inference(congruence,[status(thm)],[c2459]) ).
cnf(c2461,plain,
quotient(X2,difference(difference(X2,quotient(X2,X)),X2)) = difference(X2,quotient(X2,X)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c2462,plain,
quotient(X2,product(X,X2)) = difference(X2,quotient(X2,X)),
inference(transitivity,[status(thm)],[c2460,c2461]) ).
cnf(c2463,plain,
quotient(X2,product(difference(X,j(X2)),X2)) = difference(X2,quotient(X2,difference(X,j(X2)))),
inference(substitution,[status(thm)],[c2462]) ).
cnf(c2464,plain,
difference(X2,quotient(X2,difference(X,j(X2)))) = quotient(X2,product(difference(X,j(X2)),X2)),
inference(symmetry,[status(thm)],[c2463]) ).
cnf(c2465,plain,
product(difference(X,j(X2)),X2) = difference(difference(X2,X),i(X2)),
inference(substitution,[status(thm)],[c1131]) ).
cnf(c2466,plain,
quotient(X2,product(difference(X,j(X2)),X2)) = quotient(X2,difference(difference(X2,X),i(X2))),
inference(congruence,[status(thm)],[c2465]) ).
cnf(c2467,plain,
product(i(eta(X)),j(i(i(i(i(X)))))) = j(quotient(i(i(i(i(X)))),i(eta(X)))),
inference(substitution,[status(thm)],[c809]) ).
cnf(c2468,plain,
j(quotient(i(i(i(i(X)))),i(eta(X)))) = product(i(eta(X)),j(i(i(i(i(X)))))),
inference(symmetry,[status(thm)],[c2467]) ).
cnf(c2469,plain,
i(eta(X)) = j(eta(X)),
inference(symmetry,[status(thm)],[c788]) ).
cnf(c2470,plain,
product(i(i(X)),i(eta(X))) = product(i(i(X)),j(eta(X))),
inference(congruence,[status(thm)],[c2469]) ).
cnf(c2471,plain,
quotient(eta(i(i(X))),quotient(eta(X),i(i(X)))) = product(i(i(X)),j(eta(X))),
inference(substitution,[status(thm)],[c1230]) ).
cnf(c2472,plain,
product(i(i(X)),j(eta(X))) = quotient(eta(i(i(X))),quotient(eta(X),i(i(X)))),
inference(symmetry,[status(thm)],[c2471]) ).
cnf(c2473,plain,
i(i(i(X))) = product(eta(X),i(X)),
inference(symmetry,[status(thm)],[c2355]) ).
cnf(c2474,plain,
difference(i(i(i(X))),eta(X)) = difference(product(eta(X),i(X)),eta(X)),
inference(congruence,[status(thm)],[c2473]) ).
cnf(c2475,plain,
quotient(difference(i(X),eta(X)),eta(X)) = difference(product(eta(X),i(X)),eta(X)),
inference(substitution,[status(thm)],[c233]) ).
cnf(c2476,plain,
difference(product(eta(X),i(X)),eta(X)) = quotient(difference(i(X),eta(X)),eta(X)),
inference(symmetry,[status(thm)],[c2475]) ).
cnf(c2477,plain,
quotient(difference(i(X),eta(X)),eta(X)) = quotient(X,eta(X)),
inference(congruence,[status(thm)],[c497]) ).
cnf(c2478,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c2479,plain,
quotient(X,eta(X)) = quotient(X,eta(i(X))),
inference(congruence,[status(thm)],[c2478]) ).
cnf(c2480,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c2481,plain,
quotient(X,eta(i(X))) = quotient(j(i(X)),eta(i(X))),
inference(congruence,[status(thm)],[c2480]) ).
cnf(c2482,plain,
quotient(j(i(X)),eta(i(X))) = i(i(X)),
inference(substitution,[status(thm)],[c501]) ).
cnf(c2483,plain,
quotient(X,eta(i(X))) = i(i(X)),
inference(transitivity,[status(thm)],[c2481,c2482]) ).
cnf(c2484,plain,
quotient(X,eta(X)) = i(i(X)),
inference(transitivity,[status(thm)],[c2479,c2483]) ).
cnf(c2485,plain,
quotient(difference(i(X),eta(X)),eta(X)) = i(i(X)),
inference(transitivity,[status(thm)],[c2477,c2484]) ).
cnf(c2486,plain,
difference(product(eta(X),i(X)),eta(X)) = i(i(X)),
inference(transitivity,[status(thm)],[c2476,c2485]) ).
cnf(c2487,plain,
difference(i(i(i(X))),eta(X)) = i(i(X)),
inference(transitivity,[status(thm)],[c2474,c2486]) ).
cnf(c2488,plain,
i(i(X)) = difference(i(i(i(X))),eta(X)),
inference(symmetry,[status(thm)],[c2487]) ).
cnf(c2489,plain,
quotient(eta(X),i(i(X))) = quotient(eta(X),difference(i(i(i(X))),eta(X))),
inference(congruence,[status(thm)],[c2488]) ).
cnf(c2490,plain,
quotient(eta(X),difference(i(i(i(X))),eta(X))) = i(i(i(X))),
inference(substitution,[status(thm)],[c86]) ).
cnf(c2491,plain,
quotient(eta(X),i(i(X))) = i(i(i(X))),
inference(transitivity,[status(thm)],[c2489,c2490]) ).
cnf(c2492,plain,
quotient(eta(i(i(X))),quotient(eta(X),i(i(X)))) = quotient(eta(i(i(X))),i(i(i(X)))),
inference(congruence,[status(thm)],[c2491]) ).
cnf(c2493,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c2494,plain,
quotient(eta(X),i(X)) = quotient(eta(i(X)),i(X)),
inference(congruence,[status(thm)],[c2493]) ).
cnf(c2495,plain,
quotient(eta(i(X)),i(X)) = i(i(X)),
inference(substitution,[status(thm)],[c1660]) ).
cnf(c2496,plain,
quotient(eta(X),i(X)) = i(i(X)),
inference(transitivity,[status(thm)],[c2494,c2495]) ).
cnf(c2497,plain,
quotient(eta(i(i(X))),i(i(i(X)))) = i(i(i(i(X)))),
inference(substitution,[status(thm)],[c2496]) ).
cnf(c2498,plain,
quotient(eta(i(i(X))),quotient(eta(X),i(i(X)))) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2492,c2497]) ).
cnf(c2499,plain,
product(i(i(X)),j(eta(X))) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2472,c2498]) ).
cnf(c2500,plain,
product(i(i(X)),i(eta(X))) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2470,c2499]) ).
cnf(c2501,plain,
i(i(i(i(X)))) = product(i(i(X)),i(eta(X))),
inference(symmetry,[status(thm)],[c2500]) ).
cnf(c2502,plain,
j(i(i(i(i(X))))) = j(product(i(i(X)),i(eta(X)))),
inference(congruence,[status(thm)],[c2501]) ).
cnf(c2503,plain,
product(i(eta(X)),j(i(i(i(i(X)))))) = product(i(eta(X)),j(product(i(i(X)),i(eta(X))))),
inference(congruence,[status(thm)],[c2502]) ).
cnf(c2504,plain,
product(i(eta(X)),j(product(i(i(X)),i(eta(X))))) = quotient(eta(i(eta(X))),i(i(X))),
inference(substitution,[status(thm)],[c1235]) ).
cnf(c2505,plain,
eta(i(eta(X))) = eta(eta(X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c2506,plain,
quotient(eta(i(eta(X))),i(i(X))) = quotient(eta(eta(X)),i(i(X))),
inference(congruence,[status(thm)],[c2505]) ).
cnf(c2507,plain,
quotient(eta(eta(X)),i(i(X))) = quotient(one,i(i(X))),
inference(congruence,[status(thm)],[c507]) ).
cnf(c2508,plain,
j(i(i(X))) = quotient(one,i(i(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c2509,plain,
quotient(one,i(i(X))) = j(i(i(X))),
inference(symmetry,[status(thm)],[c2508]) ).
cnf(c2510,plain,
j(i(i(X))) = i(X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c2511,plain,
quotient(one,i(i(X))) = i(X),
inference(transitivity,[status(thm)],[c2509,c2510]) ).
cnf(c2512,plain,
quotient(eta(eta(X)),i(i(X))) = i(X),
inference(transitivity,[status(thm)],[c2507,c2511]) ).
cnf(c2513,plain,
quotient(eta(i(eta(X))),i(i(X))) = i(X),
inference(transitivity,[status(thm)],[c2506,c2512]) ).
cnf(c2514,plain,
product(i(eta(X)),j(product(i(i(X)),i(eta(X))))) = i(X),
inference(transitivity,[status(thm)],[c2504,c2513]) ).
cnf(c2515,plain,
product(i(eta(X)),j(i(i(i(i(X)))))) = i(X),
inference(transitivity,[status(thm)],[c2503,c2514]) ).
cnf(c2516,plain,
j(quotient(i(i(i(i(X)))),i(eta(X)))) = i(X),
inference(transitivity,[status(thm)],[c2468,c2515]) ).
cnf(c2517,plain,
i(X) = j(quotient(i(i(i(i(X)))),i(eta(X)))),
inference(symmetry,[status(thm)],[c2516]) ).
cnf(c2518,plain,
difference(X,i(X2)) = difference(X,j(quotient(i(i(i(i(X2)))),i(eta(X2))))),
inference(congruence,[status(thm)],[c2517]) ).
cnf(c2519,plain,
quotient(X2,difference(X,i(X2))) = quotient(X2,difference(X,j(quotient(i(i(i(i(X2)))),i(eta(X2)))))),
inference(congruence,[status(thm)],[c2518]) ).
cnf(c2520,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c2521,plain,
quotient(X2,difference(X,j(quotient(i(i(i(i(X2)))),i(eta(X2)))))) = quotient(j(i(X2)),difference(X,j(quotient(i(i(i(i(X2)))),i(eta(X2)))))),
inference(congruence,[status(thm)],[c2520]) ).
cnf(c2522,plain,
i(X) = j(quotient(i(i(i(i(X)))),i(eta(X)))),
inference(symmetry,[status(thm)],[c2516]) ).
cnf(c2523,plain,
j(i(X)) = j(j(quotient(i(i(i(i(X)))),i(eta(X))))),
inference(congruence,[status(thm)],[c2522]) ).
cnf(c2524,plain,
quotient(j(i(X2)),difference(X,j(quotient(i(i(i(i(X2)))),i(eta(X2)))))) = quotient(j(j(quotient(i(i(i(i(X2)))),i(eta(X2))))),difference(X,j(quotient(i(i(i(i(X2)))),i(eta(X2)))))),
inference(congruence,[status(thm)],[c2523]) ).
cnf(c2525,plain,
quotient(eta(X),product(X2,X)) = difference(X,j(X2)),
inference(substitution,[status(thm)],[c1159]) ).
cnf(c2526,plain,
difference(X,j(X2)) = quotient(eta(X),product(X2,X)),
inference(symmetry,[status(thm)],[c2525]) ).
cnf(c2527,plain,
quotient(j(j(X2)),difference(X,j(X2))) = quotient(j(j(X2)),quotient(eta(X),product(X2,X))),
inference(congruence,[status(thm)],[c2526]) ).
cnf(c2528,plain,
eta(X) = eta(difference(X2,difference(i(X2),X))),
inference(symmetry,[status(thm)],[c2433]) ).
cnf(c2529,plain,
quotient(eta(X),product(X2,X)) = quotient(eta(difference(X2,difference(i(X2),X))),product(X2,X)),
inference(congruence,[status(thm)],[c2528]) ).
cnf(c2530,plain,
quotient(j(j(X2)),quotient(eta(X),product(X2,X))) = quotient(j(j(X2)),quotient(eta(difference(X2,difference(i(X2),X))),product(X2,X))),
inference(congruence,[status(thm)],[c2529]) ).
cnf(c2531,plain,
eta(product(X2,difference(i(X2),X))) = eta(difference(X2,difference(i(X2),X))),
inference(substitution,[status(thm)],[c1641]) ).
cnf(c2532,plain,
eta(difference(X2,difference(i(X2),X))) = eta(product(X2,difference(i(X2),X))),
inference(symmetry,[status(thm)],[c2531]) ).
cnf(c2533,plain,
quotient(eta(difference(X2,difference(i(X2),X))),product(X2,X)) = quotient(eta(product(X2,difference(i(X2),X))),product(X2,X)),
inference(congruence,[status(thm)],[c2532]) ).
cnf(c2534,plain,
quotient(j(j(X2)),quotient(eta(difference(X2,difference(i(X2),X))),product(X2,X))) = quotient(j(j(X2)),quotient(eta(product(X2,difference(i(X2),X))),product(X2,X))),
inference(congruence,[status(thm)],[c2533]) ).
cnf(c2535,plain,
j(X2) = quotient(product(X2,X),product(X2,difference(i(X2),X))),
inference(symmetry,[status(thm)],[c2381]) ).
cnf(c2536,plain,
j(j(X2)) = j(quotient(product(X2,X),product(X2,difference(i(X2),X)))),
inference(congruence,[status(thm)],[c2535]) ).
cnf(c2537,plain,
quotient(j(j(X2)),quotient(eta(product(X2,difference(i(X2),X))),product(X2,X))) = quotient(j(quotient(product(X2,X),product(X2,difference(i(X2),X)))),quotient(eta(product(X2,difference(i(X2),X))),product(X2,X))),
inference(congruence,[status(thm)],[c2536]) ).
cnf(c2538,plain,
product(X,quotient(eta(X),X2)) = j(quotient(X2,X)),
inference(substitution,[status(thm)],[c582]) ).
cnf(c2539,plain,
j(quotient(X2,X)) = product(X,quotient(eta(X),X2)),
inference(symmetry,[status(thm)],[c2538]) ).
cnf(c2540,plain,
quotient(j(quotient(X2,X)),quotient(eta(X),X2)) = quotient(product(X,quotient(eta(X),X2)),quotient(eta(X),X2)),
inference(congruence,[status(thm)],[c2539]) ).
cnf(c2541,plain,
quotient(product(X,quotient(eta(X),X2)),quotient(eta(X),X2)) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c2542,plain,
quotient(j(quotient(X2,X)),quotient(eta(X),X2)) = X,
inference(transitivity,[status(thm)],[c2540,c2541]) ).
cnf(c2543,plain,
quotient(j(quotient(product(X2,X),product(X2,difference(i(X2),X)))),quotient(eta(product(X2,difference(i(X2),X))),product(X2,X))) = product(X2,difference(i(X2),X)),
inference(substitution,[status(thm)],[c2542]) ).
cnf(c2544,plain,
quotient(j(j(X2)),quotient(eta(product(X2,difference(i(X2),X))),product(X2,X))) = product(X2,difference(i(X2),X)),
inference(transitivity,[status(thm)],[c2537,c2543]) ).
cnf(c2545,plain,
quotient(j(j(X2)),quotient(eta(difference(X2,difference(i(X2),X))),product(X2,X))) = product(X2,difference(i(X2),X)),
inference(transitivity,[status(thm)],[c2534,c2544]) ).
cnf(c2546,plain,
quotient(j(j(X2)),quotient(eta(X),product(X2,X))) = product(X2,difference(i(X2),X)),
inference(transitivity,[status(thm)],[c2530,c2545]) ).
cnf(c2547,plain,
quotient(j(j(X2)),difference(X,j(X2))) = product(X2,difference(i(X2),X)),
inference(transitivity,[status(thm)],[c2527,c2546]) ).
cnf(c2548,plain,
quotient(j(j(quotient(i(i(i(i(X2)))),i(eta(X2))))),difference(X,j(quotient(i(i(i(i(X2)))),i(eta(X2)))))) = product(quotient(i(i(i(i(X2)))),i(eta(X2))),difference(i(quotient(i(i(i(i(X2)))),i(eta(X2)))),X)),
inference(substitution,[status(thm)],[c2547]) ).
cnf(c2549,plain,
difference(difference(i(eta(X)),X2),eta(X)) = i(X2),
inference(substitution,[status(thm)],[c1666]) ).
cnf(c2550,plain,
i(X2) = difference(difference(i(eta(X)),X2),eta(X)),
inference(symmetry,[status(thm)],[c2549]) ).
cnf(c2551,plain,
quotient(i(X2),i(eta(X))) = quotient(difference(difference(i(eta(X)),X2),eta(X)),i(eta(X))),
inference(congruence,[status(thm)],[c2550]) ).
cnf(c2552,plain,
quotient(difference(i(X2),X),X2) = product(X2,quotient(X,X2)),
inference(symmetry,[status(thm)],[c432]) ).
cnf(c2553,plain,
difference(product(X3,X2),quotient(difference(i(X3),X),X3)) = difference(product(X3,X2),product(X3,quotient(X,X3))),
inference(congruence,[status(thm)],[c2552]) ).
cnf(c2554,plain,
quotient(difference(X2,product(quotient(X,X3),X3)),X3) = difference(product(X3,X2),product(X3,quotient(X,X3))),
inference(substitution,[status(thm)],[c69]) ).
cnf(c2555,plain,
difference(product(X3,X2),product(X3,quotient(X,X3))) = quotient(difference(X2,product(quotient(X,X3),X3)),X3),
inference(symmetry,[status(thm)],[c2554]) ).
cnf(c2556,plain,
product(quotient(X,X2),X2) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c2557,plain,
difference(X2,product(quotient(X,X3),X3)) = difference(X2,X),
inference(congruence,[status(thm)],[c2556]) ).
cnf(c2558,plain,
quotient(difference(X2,product(quotient(X,X3),X3)),X3) = quotient(difference(X2,X),X3),
inference(congruence,[status(thm)],[c2557]) ).
cnf(c2559,plain,
difference(product(X3,X2),product(X3,quotient(X,X3))) = quotient(difference(X2,X),X3),
inference(transitivity,[status(thm)],[c2555,c2558]) ).
cnf(c2560,plain,
difference(product(X3,X2),quotient(difference(i(X3),X),X3)) = quotient(difference(X2,X),X3),
inference(transitivity,[status(thm)],[c2553,c2559]) ).
cnf(c2561,plain,
difference(product(X3,difference(X3,X2)),quotient(difference(i(X3),X),X3)) = quotient(difference(difference(X3,X2),X),X3),
inference(substitution,[status(thm)],[c2560]) ).
cnf(c2562,plain,
quotient(difference(difference(X3,X2),X),X3) = difference(product(X3,difference(X3,X2)),quotient(difference(i(X3),X),X3)),
inference(symmetry,[status(thm)],[c2561]) ).
cnf(c2563,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c2564,plain,
difference(product(X3,difference(X3,X2)),quotient(difference(i(X3),X),X3)) = difference(X2,quotient(difference(i(X3),X),X3)),
inference(congruence,[status(thm)],[c2563]) ).
cnf(c2565,plain,
quotient(difference(difference(X3,X2),X),X3) = difference(X2,quotient(difference(i(X3),X),X3)),
inference(transitivity,[status(thm)],[c2562,c2564]) ).
cnf(c2566,plain,
quotient(difference(difference(i(eta(X)),X2),eta(X)),i(eta(X))) = difference(X2,quotient(difference(i(i(eta(X))),eta(X)),i(eta(X)))),
inference(substitution,[status(thm)],[c2565]) ).
cnf(c2567,plain,
X = product(i(i(X)),eta(X)),
inference(symmetry,[status(thm)],[c514]) ).
cnf(c2568,plain,
difference(X2,X) = difference(X2,product(i(i(X)),eta(X))),
inference(congruence,[status(thm)],[c2567]) ).
cnf(c2569,plain,
quotient(difference(X2,X),i(X)) = quotient(difference(X2,product(i(i(X)),eta(X))),i(X)),
inference(congruence,[status(thm)],[c2568]) ).
cnf(c2570,plain,
difference(product(X2,X3),quotient(difference(i(X2),product(i(X2),X)),X2)) = quotient(difference(X3,product(i(X2),X)),X2),
inference(substitution,[status(thm)],[c2560]) ).
cnf(c2571,plain,
quotient(difference(X3,product(i(X2),X)),X2) = difference(product(X2,X3),quotient(difference(i(X2),product(i(X2),X)),X2)),
inference(symmetry,[status(thm)],[c2570]) ).
cnf(c2572,plain,
difference(i(X2),product(i(X2),X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c2573,plain,
quotient(difference(i(X2),product(i(X2),X)),X2) = quotient(X,X2),
inference(congruence,[status(thm)],[c2572]) ).
cnf(c2574,plain,
difference(product(X2,X3),quotient(difference(i(X2),product(i(X2),X)),X2)) = difference(product(X2,X3),quotient(X,X2)),
inference(congruence,[status(thm)],[c2573]) ).
cnf(c2575,plain,
quotient(difference(X3,product(i(X2),X)),X2) = difference(product(X2,X3),quotient(X,X2)),
inference(transitivity,[status(thm)],[c2571,c2574]) ).
cnf(c2576,plain,
quotient(difference(X2,product(i(i(X)),eta(X))),i(X)) = difference(product(i(X),X2),quotient(eta(X),i(X))),
inference(substitution,[status(thm)],[c2575]) ).
cnf(c2577,plain,
difference(product(i(X),X2),quotient(eta(X),i(X))) = difference(product(i(X),X2),i(i(X))),
inference(congruence,[status(thm)],[c2496]) ).
cnf(c2578,plain,
quotient(difference(X2,product(i(i(X)),eta(X))),i(X)) = difference(product(i(X),X2),i(i(X))),
inference(transitivity,[status(thm)],[c2576,c2577]) ).
cnf(c2579,plain,
quotient(difference(X2,X),i(X)) = difference(product(i(X),X2),i(i(X))),
inference(transitivity,[status(thm)],[c2569,c2578]) ).
cnf(c2580,plain,
quotient(difference(i(i(eta(X))),eta(X)),i(eta(X))) = difference(product(i(eta(X)),i(i(eta(X)))),i(i(eta(X)))),
inference(substitution,[status(thm)],[c2579]) ).
cnf(c2581,plain,
difference(X2,quotient(difference(i(i(eta(X))),eta(X)),i(eta(X)))) = difference(X2,difference(product(i(eta(X)),i(i(eta(X)))),i(i(eta(X))))),
inference(congruence,[status(thm)],[c2580]) ).
cnf(c2582,plain,
product(i(eta(X)),i(i(eta(X)))) = difference(eta(X),i(i(eta(X)))),
inference(substitution,[status(thm)],[c2067]) ).
cnf(c2583,plain,
difference(product(i(eta(X)),i(i(eta(X)))),i(i(eta(X)))) = difference(difference(eta(X),i(i(eta(X)))),i(i(eta(X)))),
inference(congruence,[status(thm)],[c2582]) ).
cnf(c2584,plain,
difference(X2,difference(product(i(eta(X)),i(i(eta(X)))),i(i(eta(X))))) = difference(X2,difference(difference(eta(X),i(i(eta(X)))),i(i(eta(X))))),
inference(congruence,[status(thm)],[c2583]) ).
cnf(c2585,plain,
difference(eta(X),i(i(eta(X)))) = i(eta(eta(X))),
inference(substitution,[status(thm)],[c2191]) ).
cnf(c2586,plain,
difference(difference(eta(X),i(i(eta(X)))),i(i(eta(X)))) = difference(i(eta(eta(X))),i(i(eta(X)))),
inference(congruence,[status(thm)],[c2585]) ).
cnf(c2587,plain,
difference(X2,difference(difference(eta(X),i(i(eta(X)))),i(i(eta(X))))) = difference(X2,difference(i(eta(eta(X))),i(i(eta(X))))),
inference(congruence,[status(thm)],[c2586]) ).
cnf(c2588,plain,
i(eta(X)) = j(eta(X)),
inference(symmetry,[status(thm)],[c788]) ).
cnf(c2589,plain,
difference(i(eta(X)),i(i(X))) = difference(j(eta(X)),i(i(X))),
inference(congruence,[status(thm)],[c2588]) ).
cnf(c2590,plain,
product(eta(X),difference(i(eta(X)),difference(eta(X),i(i(X))))) = difference(j(eta(X)),i(i(X))),
inference(substitution,[status(thm)],[c2103]) ).
cnf(c2591,plain,
difference(j(eta(X)),i(i(X))) = product(eta(X),difference(i(eta(X)),difference(eta(X),i(i(X))))),
inference(symmetry,[status(thm)],[c2590]) ).
cnf(c2592,plain,
eta(X) = quotient(i(i(X)),X),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c2593,plain,
difference(eta(X),i(i(X))) = difference(quotient(i(i(X)),X),i(i(X))),
inference(congruence,[status(thm)],[c2592]) ).
cnf(c2594,plain,
difference(quotient(i(i(X)),X),i(i(X))) = X,
inference(substitution,[status(thm)],[c209]) ).
cnf(c2595,plain,
difference(eta(X),i(i(X))) = X,
inference(transitivity,[status(thm)],[c2593,c2594]) ).
cnf(c2596,plain,
difference(i(eta(X)),difference(eta(X),i(i(X)))) = difference(i(eta(X)),X),
inference(congruence,[status(thm)],[c2595]) ).
cnf(c2597,plain,
product(eta(X),difference(i(eta(X)),difference(eta(X),i(i(X))))) = product(eta(X),difference(i(eta(X)),X)),
inference(congruence,[status(thm)],[c2596]) ).
cnf(c2598,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c2599,plain,
i(eta(X)) = i(eta(i(X))),
inference(congruence,[status(thm)],[c2598]) ).
cnf(c2600,plain,
difference(i(eta(X)),X) = difference(i(eta(i(X))),X),
inference(congruence,[status(thm)],[c2599]) ).
cnf(c2601,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c2602,plain,
difference(i(eta(i(X))),X) = difference(i(eta(i(X))),j(i(X))),
inference(congruence,[status(thm)],[c2601]) ).
cnf(c2603,plain,
j(X) = product(i(eta(X)),i(X)),
inference(symmetry,[status(thm)],[c2180]) ).
cnf(c2604,plain,
difference(i(eta(X)),j(X)) = difference(i(eta(X)),product(i(eta(X)),i(X))),
inference(congruence,[status(thm)],[c2603]) ).
cnf(c2605,plain,
difference(i(eta(X)),product(i(eta(X)),i(X))) = i(X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c2606,plain,
difference(i(eta(X)),j(X)) = i(X),
inference(transitivity,[status(thm)],[c2604,c2605]) ).
cnf(c2607,plain,
difference(i(eta(i(X))),j(i(X))) = i(i(X)),
inference(substitution,[status(thm)],[c2606]) ).
cnf(c2608,plain,
difference(i(eta(i(X))),X) = i(i(X)),
inference(transitivity,[status(thm)],[c2602,c2607]) ).
cnf(c2609,plain,
difference(i(eta(X)),X) = i(i(X)),
inference(transitivity,[status(thm)],[c2600,c2608]) ).
cnf(c2610,plain,
product(eta(X),difference(i(eta(X)),X)) = product(eta(X),i(i(X))),
inference(congruence,[status(thm)],[c2609]) ).
cnf(c2611,plain,
j(i(i(i(X)))) = i(i(X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c2612,plain,
i(i(X)) = j(i(i(i(X)))),
inference(symmetry,[status(thm)],[c2611]) ).
cnf(c2613,plain,
product(eta(X),i(i(X))) = product(eta(X),j(i(i(i(X))))),
inference(congruence,[status(thm)],[c2612]) ).
cnf(c2614,plain,
product(i(i(i(X))),quotient(difference(i(i(i(X))),eta(X)),i(i(i(X))))) = product(eta(X),j(i(i(i(X))))),
inference(substitution,[status(thm)],[c2086]) ).
cnf(c2615,plain,
product(eta(X),j(i(i(i(X))))) = product(i(i(i(X))),quotient(difference(i(i(i(X))),eta(X)),i(i(i(X))))),
inference(symmetry,[status(thm)],[c2614]) ).
cnf(c2616,plain,
quotient(difference(i(i(i(X))),eta(X)),i(i(i(X)))) = quotient(i(i(X)),i(i(i(X)))),
inference(congruence,[status(thm)],[c2487]) ).
cnf(c2617,plain,
product(i(i(i(X))),quotient(difference(i(i(i(X))),eta(X)),i(i(i(X))))) = product(i(i(i(X))),quotient(i(i(X)),i(i(i(X))))),
inference(congruence,[status(thm)],[c2616]) ).
cnf(c2618,plain,
difference(i(X),product(product(i(X),X),j(i(X)))) = quotient(X,i(X)),
inference(substitution,[status(thm)],[c418]) ).
cnf(c2619,plain,
quotient(X,i(X)) = difference(i(X),product(product(i(X),X),j(i(X)))),
inference(symmetry,[status(thm)],[c2618]) ).
cnf(c2620,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c2621,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c2620]) ).
cnf(c2622,plain,
product(product(i(X),X),j(i(X))) = product(eta(X),j(i(X))),
inference(congruence,[status(thm)],[c2621]) ).
cnf(c2623,plain,
difference(i(X),product(product(i(X),X),j(i(X)))) = difference(i(X),product(eta(X),j(i(X)))),
inference(congruence,[status(thm)],[c2622]) ).
cnf(c2624,plain,
product(eta(X),j(i(X))) = product(eta(X),X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c2625,plain,
difference(i(X),product(eta(X),j(i(X)))) = difference(i(X),product(eta(X),X)),
inference(congruence,[status(thm)],[c2624]) ).
cnf(c2626,plain,
difference(i(X),product(eta(X),X)) = difference(i(X),i(i(X))),
inference(congruence,[status(thm)],[c490]) ).
cnf(c2627,plain,
difference(i(X),product(eta(X),j(i(X)))) = difference(i(X),i(i(X))),
inference(transitivity,[status(thm)],[c2625,c2626]) ).
cnf(c2628,plain,
difference(i(X),product(product(i(X),X),j(i(X)))) = difference(i(X),i(i(X))),
inference(transitivity,[status(thm)],[c2623,c2627]) ).
cnf(c2629,plain,
quotient(X,i(X)) = difference(i(X),i(i(X))),
inference(transitivity,[status(thm)],[c2619,c2628]) ).
cnf(c2630,plain,
quotient(i(i(X)),i(i(i(X)))) = difference(i(i(i(X))),i(i(i(i(X))))),
inference(substitution,[status(thm)],[c2629]) ).
cnf(c2631,plain,
product(i(i(i(X))),quotient(i(i(X)),i(i(i(X))))) = product(i(i(i(X))),difference(i(i(i(X))),i(i(i(i(X)))))),
inference(congruence,[status(thm)],[c2630]) ).
cnf(c2632,plain,
product(i(i(i(X))),difference(i(i(i(X))),i(i(i(i(X)))))) = i(i(i(i(X)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c2633,plain,
product(i(i(i(X))),quotient(i(i(X)),i(i(i(X))))) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2631,c2632]) ).
cnf(c2634,plain,
product(i(i(i(X))),quotient(difference(i(i(i(X))),eta(X)),i(i(i(X))))) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2617,c2633]) ).
cnf(c2635,plain,
product(eta(X),j(i(i(i(X))))) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2615,c2634]) ).
cnf(c2636,plain,
product(eta(X),i(i(X))) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2613,c2635]) ).
cnf(c2637,plain,
product(eta(X),difference(i(eta(X)),X)) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2610,c2636]) ).
cnf(c2638,plain,
product(eta(X),difference(i(eta(X)),difference(eta(X),i(i(X))))) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2597,c2637]) ).
cnf(c2639,plain,
difference(j(eta(X)),i(i(X))) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2591,c2638]) ).
cnf(c2640,plain,
difference(i(eta(X)),i(i(X))) = i(i(i(i(X)))),
inference(transitivity,[status(thm)],[c2589,c2639]) ).
cnf(c2641,plain,
difference(i(eta(eta(X))),i(i(eta(X)))) = i(i(i(i(eta(X))))),
inference(substitution,[status(thm)],[c2640]) ).
cnf(c2642,plain,
difference(X2,difference(i(eta(eta(X))),i(i(eta(X))))) = difference(X2,i(i(i(i(eta(X)))))),
inference(congruence,[status(thm)],[c2641]) ).
cnf(c2643,plain,
i(i(i(eta(X)))) = i(eta(X)),
inference(congruence,[status(thm)],[c726]) ).
cnf(c2644,plain,
i(i(i(i(eta(X))))) = i(i(eta(X))),
inference(congruence,[status(thm)],[c2643]) ).
cnf(c2645,plain,
difference(X2,i(i(i(i(eta(X)))))) = difference(X2,i(i(eta(X)))),
inference(congruence,[status(thm)],[c2644]) ).
cnf(c2646,plain,
difference(X2,i(i(eta(X)))) = difference(X2,eta(X)),
inference(congruence,[status(thm)],[c726]) ).
cnf(c2647,plain,
difference(X2,i(i(i(i(eta(X)))))) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c2645,c2646]) ).
cnf(c2648,plain,
difference(X2,difference(i(eta(eta(X))),i(i(eta(X))))) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c2642,c2647]) ).
cnf(c2649,plain,
difference(X2,difference(difference(eta(X),i(i(eta(X)))),i(i(eta(X))))) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c2587,c2648]) ).
cnf(c2650,plain,
difference(X2,difference(product(i(eta(X)),i(i(eta(X)))),i(i(eta(X))))) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c2584,c2649]) ).
cnf(c2651,plain,
difference(X2,quotient(difference(i(i(eta(X))),eta(X)),i(eta(X)))) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c2581,c2650]) ).
cnf(c2652,plain,
quotient(difference(difference(i(eta(X)),X2),eta(X)),i(eta(X))) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c2566,c2651]) ).
cnf(c2653,plain,
quotient(i(X2),i(eta(X))) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c2551,c2652]) ).
cnf(c2654,plain,
quotient(i(i(i(i(X)))),i(eta(X))) = difference(i(i(i(X))),eta(X)),
inference(substitution,[status(thm)],[c2653]) ).
cnf(c2655,plain,
product(quotient(i(i(i(i(X2)))),i(eta(X2))),difference(i(quotient(i(i(i(i(X2)))),i(eta(X2)))),X)) = product(difference(i(i(i(X2))),eta(X2)),difference(i(quotient(i(i(i(i(X2)))),i(eta(X2)))),X)),
inference(congruence,[status(thm)],[c2654]) ).
cnf(c2656,plain,
quotient(i(i(i(i(X)))),i(eta(X))) = difference(i(i(i(X))),eta(X)),
inference(substitution,[status(thm)],[c2653]) ).
cnf(c2657,plain,
i(quotient(i(i(i(i(X)))),i(eta(X)))) = i(difference(i(i(i(X))),eta(X))),
inference(congruence,[status(thm)],[c2656]) ).
cnf(c2658,plain,
difference(i(quotient(i(i(i(i(X2)))),i(eta(X2)))),X) = difference(i(difference(i(i(i(X2))),eta(X2))),X),
inference(congruence,[status(thm)],[c2657]) ).
cnf(c2659,plain,
product(difference(i(i(i(X2))),eta(X2)),difference(i(quotient(i(i(i(i(X2)))),i(eta(X2)))),X)) = product(difference(i(i(i(X2))),eta(X2)),difference(i(difference(i(i(i(X2))),eta(X2))),X)),
inference(congruence,[status(thm)],[c2658]) ).
cnf(c2660,plain,
product(difference(i(i(i(X2))),eta(X2)),difference(i(difference(i(i(i(X2))),eta(X2))),X)) = product(i(i(X2)),difference(i(difference(i(i(i(X2))),eta(X2))),X)),
inference(congruence,[status(thm)],[c2487]) ).
cnf(c2661,plain,
i(difference(i(i(i(X))),eta(X))) = i(i(i(X))),
inference(congruence,[status(thm)],[c2487]) ).
cnf(c2662,plain,
difference(i(difference(i(i(i(X2))),eta(X2))),X) = difference(i(i(i(X2))),X),
inference(congruence,[status(thm)],[c2661]) ).
cnf(c2663,plain,
product(i(i(X2)),difference(i(difference(i(i(i(X2))),eta(X2))),X)) = product(i(i(X2)),difference(i(i(i(X2))),X)),
inference(congruence,[status(thm)],[c2662]) ).
cnf(c2664,plain,
product(X2,difference(i(X2),difference(X2,product(X2,X)))) = difference(j(X2),product(X2,X)),
inference(substitution,[status(thm)],[c2103]) ).
cnf(c2665,plain,
difference(j(X2),product(X2,X)) = product(X2,difference(i(X2),difference(X2,product(X2,X)))),
inference(symmetry,[status(thm)],[c2664]) ).
cnf(c2666,plain,
difference(X2,product(X2,X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c2667,plain,
difference(i(X2),difference(X2,product(X2,X))) = difference(i(X2),X),
inference(congruence,[status(thm)],[c2666]) ).
cnf(c2668,plain,
product(X2,difference(i(X2),difference(X2,product(X2,X)))) = product(X2,difference(i(X2),X)),
inference(congruence,[status(thm)],[c2667]) ).
cnf(c2669,plain,
difference(j(X2),product(X2,X)) = product(X2,difference(i(X2),X)),
inference(transitivity,[status(thm)],[c2665,c2668]) ).
cnf(c2670,plain,
difference(j(i(X2)),product(i(X2),X)) = product(i(X2),difference(i(i(X2)),X)),
inference(substitution,[status(thm)],[c2669]) ).
cnf(c2671,plain,
product(i(X2),difference(i(i(X2)),X)) = difference(j(i(X2)),product(i(X2),X)),
inference(symmetry,[status(thm)],[c2670]) ).
cnf(c2672,plain,
difference(j(i(X2)),product(i(X2),X)) = difference(X2,product(i(X2),X)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c2673,plain,
product(i(X2),difference(i(i(X2)),X)) = difference(X2,product(i(X2),X)),
inference(transitivity,[status(thm)],[c2671,c2672]) ).
cnf(c2674,plain,
product(i(i(X2)),difference(i(i(i(X2))),X)) = difference(i(X2),product(i(i(X2)),X)),
inference(substitution,[status(thm)],[c2673]) ).
cnf(c2675,plain,
product(i(i(X2)),difference(i(difference(i(i(i(X2))),eta(X2))),X)) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2663,c2674]) ).
cnf(c2676,plain,
product(difference(i(i(i(X2))),eta(X2)),difference(i(difference(i(i(i(X2))),eta(X2))),X)) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2660,c2675]) ).
cnf(c2677,plain,
product(difference(i(i(i(X2))),eta(X2)),difference(i(quotient(i(i(i(i(X2)))),i(eta(X2)))),X)) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2659,c2676]) ).
cnf(c2678,plain,
product(quotient(i(i(i(i(X2)))),i(eta(X2))),difference(i(quotient(i(i(i(i(X2)))),i(eta(X2)))),X)) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2655,c2677]) ).
cnf(c2679,plain,
quotient(j(j(quotient(i(i(i(i(X2)))),i(eta(X2))))),difference(X,j(quotient(i(i(i(i(X2)))),i(eta(X2)))))) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2548,c2678]) ).
cnf(c2680,plain,
quotient(j(i(X2)),difference(X,j(quotient(i(i(i(i(X2)))),i(eta(X2)))))) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2524,c2679]) ).
cnf(c2681,plain,
quotient(X2,difference(X,j(quotient(i(i(i(i(X2)))),i(eta(X2)))))) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2521,c2680]) ).
cnf(c2682,plain,
quotient(X2,difference(X,i(X2))) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2519,c2681]) ).
cnf(c2683,plain,
quotient(X2,difference(difference(X2,X),i(X2))) = difference(i(X2),product(i(i(X2)),difference(X2,X))),
inference(substitution,[status(thm)],[c2682]) ).
cnf(c2684,plain,
product(i(X2),difference(i(X2),difference(X2,X))) = difference(X2,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c2685,plain,
difference(X2,X) = product(i(X2),difference(i(X2),difference(X2,X))),
inference(symmetry,[status(thm)],[c2684]) ).
cnf(c2686,plain,
product(i(i(X2)),difference(X2,X)) = product(i(i(X2)),product(i(X2),difference(i(X2),difference(X2,X)))),
inference(congruence,[status(thm)],[c2685]) ).
cnf(c2687,plain,
quotient(eta(X2),i(quotient(X,i(X2)))) = difference(i(eta(X2)),quotient(X,i(X2))),
inference(substitution,[status(thm)],[c1856]) ).
cnf(c2688,plain,
difference(i(eta(X2)),quotient(X,i(X2))) = quotient(eta(X2),i(quotient(X,i(X2)))),
inference(symmetry,[status(thm)],[c2687]) ).
cnf(c2689,plain,
quotient(difference(i(eta(X2)),quotient(X,i(X2))),X2) = quotient(quotient(eta(X2),i(quotient(X,i(X2)))),X2),
inference(congruence,[status(thm)],[c2688]) ).
cnf(c2690,plain,
product(eta(X2),quotient(X,i(X2))) = quotient(eta(X2),i(quotient(X,i(X2)))),
inference(substitution,[status(thm)],[c1387]) ).
cnf(c2691,plain,
quotient(eta(X2),i(quotient(X,i(X2)))) = product(eta(X2),quotient(X,i(X2))),
inference(symmetry,[status(thm)],[c2690]) ).
cnf(c2692,plain,
quotient(quotient(eta(X2),i(quotient(X,i(X2)))),X2) = quotient(product(eta(X2),quotient(X,i(X2))),X2),
inference(congruence,[status(thm)],[c2691]) ).
cnf(c2693,plain,
product(i(X2),product(X2,product(quotient(X,i(X2)),i(X2)))) = quotient(product(eta(X2),quotient(X,i(X2))),X2),
inference(substitution,[status(thm)],[c2148]) ).
cnf(c2694,plain,
quotient(product(eta(X2),quotient(X,i(X2))),X2) = product(i(X2),product(X2,product(quotient(X,i(X2)),i(X2)))),
inference(symmetry,[status(thm)],[c2693]) ).
cnf(c2695,plain,
product(quotient(X,i(X2)),i(X2)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c2696,plain,
product(X2,product(quotient(X,i(X2)),i(X2))) = product(X2,X),
inference(congruence,[status(thm)],[c2695]) ).
cnf(c2697,plain,
product(i(X2),product(X2,product(quotient(X,i(X2)),i(X2)))) = product(i(X2),product(X2,X)),
inference(congruence,[status(thm)],[c2696]) ).
cnf(c2698,plain,
quotient(product(eta(X2),quotient(X,i(X2))),X2) = product(i(X2),product(X2,X)),
inference(transitivity,[status(thm)],[c2694,c2697]) ).
cnf(c2699,plain,
quotient(quotient(eta(X2),i(quotient(X,i(X2)))),X2) = product(i(X2),product(X2,X)),
inference(transitivity,[status(thm)],[c2692,c2698]) ).
cnf(c2700,plain,
quotient(difference(i(eta(X2)),quotient(X,i(X2))),X2) = product(i(X2),product(X2,X)),
inference(transitivity,[status(thm)],[c2689,c2699]) ).
cnf(c2701,plain,
quotient(difference(i(eta(i(X2))),quotient(difference(i(X2),difference(X2,X)),i(i(X2)))),i(X2)) = product(i(i(X2)),product(i(X2),difference(i(X2),difference(X2,X)))),
inference(substitution,[status(thm)],[c2700]) ).
cnf(c2702,plain,
product(i(i(X2)),product(i(X2),difference(i(X2),difference(X2,X)))) = quotient(difference(i(eta(i(X2))),quotient(difference(i(X2),difference(X2,X)),i(i(X2)))),i(X2)),
inference(symmetry,[status(thm)],[c2701]) ).
cnf(c2703,plain,
difference(i(eta(i(X2))),quotient(difference(i(X2),difference(X2,X)),i(i(X2)))) = difference(i(eta(i(X2))),product(X,i(X2))),
inference(congruence,[status(thm)],[c1371]) ).
cnf(c2704,plain,
quotient(difference(i(eta(i(X2))),quotient(difference(i(X2),difference(X2,X)),i(i(X2)))),i(X2)) = quotient(difference(i(eta(i(X2))),product(X,i(X2))),i(X2)),
inference(congruence,[status(thm)],[c2703]) ).
cnf(c2705,plain,
quotient(difference(i(eta(i(X2))),product(X,i(X2))),i(X2)) = difference(product(i(X2),i(eta(i(X2)))),product(i(X2),X)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c2706,plain,
product(i(X),i(eta(i(X)))) = i(i(i(X))),
inference(substitution,[status(thm)],[c2195]) ).
cnf(c2707,plain,
difference(product(i(X2),i(eta(i(X2)))),product(i(X2),X)) = difference(i(i(i(X2))),product(i(X2),X)),
inference(congruence,[status(thm)],[c2706]) ).
cnf(c2708,plain,
quotient(difference(i(eta(i(X2))),product(X,i(X2))),i(X2)) = difference(i(i(i(X2))),product(i(X2),X)),
inference(transitivity,[status(thm)],[c2705,c2707]) ).
cnf(c2709,plain,
quotient(difference(i(eta(i(X2))),quotient(difference(i(X2),difference(X2,X)),i(i(X2)))),i(X2)) = difference(i(i(i(X2))),product(i(X2),X)),
inference(transitivity,[status(thm)],[c2704,c2708]) ).
cnf(c2710,plain,
product(i(i(X2)),product(i(X2),difference(i(X2),difference(X2,X)))) = difference(i(i(i(X2))),product(i(X2),X)),
inference(transitivity,[status(thm)],[c2702,c2709]) ).
cnf(c2711,plain,
product(i(i(X2)),difference(X2,X)) = difference(i(i(i(X2))),product(i(X2),X)),
inference(transitivity,[status(thm)],[c2686,c2710]) ).
cnf(c2712,plain,
difference(i(X2),product(i(i(X2)),difference(X2,X))) = difference(i(X2),difference(i(i(i(X2))),product(i(X2),X))),
inference(congruence,[status(thm)],[c2711]) ).
cnf(c2713,plain,
difference(i(i(i(X2))),product(i(X2),X)) = product(i(i(X2)),difference(X2,X)),
inference(symmetry,[status(thm)],[c2711]) ).
cnf(c2714,plain,
difference(i(X2),difference(i(i(i(X2))),product(i(X2),X))) = difference(i(X2),product(i(i(X2)),difference(X2,X))),
inference(congruence,[status(thm)],[c2713]) ).
cnf(c2715,plain,
j(i(difference(i(X2),X))) = difference(i(X2),X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c2716,plain,
difference(i(X2),X) = j(i(difference(i(X2),X))),
inference(symmetry,[status(thm)],[c2715]) ).
cnf(c2717,plain,
product(X2,difference(i(X2),X)) = product(X2,j(i(difference(i(X2),X)))),
inference(congruence,[status(thm)],[c2716]) ).
cnf(c2718,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c2719,plain,
product(X2,j(i(difference(i(X2),X)))) = product(j(i(X2)),j(i(difference(i(X2),X)))),
inference(congruence,[status(thm)],[c2718]) ).
cnf(c2720,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c2721,plain,
difference(X2,eta(X)) = difference(X2,eta(i(X))),
inference(congruence,[status(thm)],[c2720]) ).
cnf(c2722,plain,
product(difference(X2,eta(X)),i(X)) = product(difference(X2,eta(i(X))),i(X)),
inference(congruence,[status(thm)],[c2721]) ).
cnf(c2723,plain,
product(difference(X2,eta(i(X))),i(X)) = i(difference(i(X),X2)),
inference(substitution,[status(thm)],[c143]) ).
cnf(c2724,plain,
product(difference(X2,eta(X)),i(X)) = i(difference(i(X),X2)),
inference(transitivity,[status(thm)],[c2722,c2723]) ).
cnf(c2725,plain,
product(difference(X,eta(X2)),i(X2)) = i(difference(i(X2),X)),
inference(substitution,[status(thm)],[c2724]) ).
cnf(c2726,plain,
i(difference(i(X2),X)) = product(difference(X,eta(X2)),i(X2)),
inference(symmetry,[status(thm)],[c2725]) ).
cnf(c2727,plain,
j(i(difference(i(X2),X))) = j(product(difference(X,eta(X2)),i(X2))),
inference(congruence,[status(thm)],[c2726]) ).
cnf(c2728,plain,
product(j(i(X2)),j(i(difference(i(X2),X)))) = product(j(i(X2)),j(product(difference(X,eta(X2)),i(X2)))),
inference(congruence,[status(thm)],[c2727]) ).
cnf(c2729,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c2730,plain,
product(X,X2) = product(X,i(j(X2))),
inference(congruence,[status(thm)],[c2729]) ).
cnf(c2731,plain,
j(product(X,X2)) = j(product(X,i(j(X2)))),
inference(congruence,[status(thm)],[c2730]) ).
cnf(c2732,plain,
product(j(X2),j(product(X,X2))) = product(j(X2),j(product(X,i(j(X2))))),
inference(congruence,[status(thm)],[c2731]) ).
cnf(c2733,plain,
quotient(eta(j(X2)),product(quotient(X,X2),j(X2))) = difference(j(X2),j(quotient(X,X2))),
inference(substitution,[status(thm)],[c1159]) ).
cnf(c2734,plain,
difference(j(X2),j(quotient(X,X2))) = quotient(eta(j(X2)),product(quotient(X,X2),j(X2))),
inference(symmetry,[status(thm)],[c2733]) ).
cnf(c2735,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c2736,plain,
j(X) = j(j(i(X))),
inference(congruence,[status(thm)],[c2735]) ).
cnf(c2737,plain,
product(quotient(X2,X),j(X)) = product(quotient(X2,X),j(j(i(X)))),
inference(congruence,[status(thm)],[c2736]) ).
cnf(c2738,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c2739,plain,
quotient(X2,X) = quotient(X2,j(i(X))),
inference(congruence,[status(thm)],[c2738]) ).
cnf(c2740,plain,
product(quotient(X2,X),j(j(i(X)))) = product(quotient(X2,j(i(X))),j(j(i(X)))),
inference(congruence,[status(thm)],[c2739]) ).
cnf(c2741,plain,
product(j(X),quotient(difference(j(X),quotient(X2,j(X))),j(X))) = product(quotient(X2,j(X)),j(j(X))),
inference(substitution,[status(thm)],[c2086]) ).
cnf(c2742,plain,
product(quotient(X2,j(X)),j(j(X))) = product(j(X),quotient(difference(j(X),quotient(X2,j(X))),j(X))),
inference(symmetry,[status(thm)],[c2741]) ).
cnf(c2743,plain,
difference(j(X),quotient(X2,j(X))) = product(X,product(X2,X)),
inference(substitution,[status(thm)],[c931]) ).
cnf(c2744,plain,
quotient(difference(j(X),quotient(X2,j(X))),j(X)) = quotient(product(X,product(X2,X)),j(X)),
inference(congruence,[status(thm)],[c2743]) ).
cnf(c2745,plain,
product(j(X),quotient(difference(j(X),quotient(X2,j(X))),j(X))) = product(j(X),quotient(product(X,product(X2,X)),j(X))),
inference(congruence,[status(thm)],[c2744]) ).
cnf(c2746,plain,
product(j(X),quotient(product(X,product(X2,X)),j(X))) = quotient(difference(i(j(X)),product(X,product(X2,X))),j(X)),
inference(substitution,[status(thm)],[c432]) ).
cnf(c2747,plain,
difference(i(j(X)),product(X,product(X2,X))) = difference(X,product(X,product(X2,X))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c2748,plain,
quotient(difference(i(j(X)),product(X,product(X2,X))),j(X)) = quotient(difference(X,product(X,product(X2,X))),j(X)),
inference(congruence,[status(thm)],[c2747]) ).
cnf(c2749,plain,
difference(X,product(X,product(X2,X))) = product(X2,X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c2750,plain,
quotient(difference(X,product(X,product(X2,X))),j(X)) = quotient(product(X2,X),j(X)),
inference(congruence,[status(thm)],[c2749]) ).
cnf(c2751,plain,
quotient(difference(i(j(X)),product(X,product(X2,X))),j(X)) = quotient(product(X2,X),j(X)),
inference(transitivity,[status(thm)],[c2748,c2750]) ).
cnf(c2752,plain,
product(j(X),quotient(product(X,product(X2,X)),j(X))) = quotient(product(X2,X),j(X)),
inference(transitivity,[status(thm)],[c2746,c2751]) ).
cnf(c2753,plain,
product(j(X),quotient(difference(j(X),quotient(X2,j(X))),j(X))) = quotient(product(X2,X),j(X)),
inference(transitivity,[status(thm)],[c2745,c2752]) ).
cnf(c2754,plain,
product(quotient(X2,j(X)),j(j(X))) = quotient(product(X2,X),j(X)),
inference(transitivity,[status(thm)],[c2742,c2753]) ).
cnf(c2755,plain,
product(quotient(X2,j(i(X))),j(j(i(X)))) = quotient(product(X2,i(X)),j(i(X))),
inference(substitution,[status(thm)],[c2754]) ).
cnf(c2756,plain,
quotient(product(X2,i(X)),j(i(X))) = quotient(product(X2,i(X)),X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c2757,plain,
product(quotient(X2,j(i(X))),j(j(i(X)))) = quotient(product(X2,i(X)),X),
inference(transitivity,[status(thm)],[c2755,c2756]) ).
cnf(c2758,plain,
product(quotient(X2,X),j(j(i(X)))) = quotient(product(X2,i(X)),X),
inference(transitivity,[status(thm)],[c2740,c2757]) ).
cnf(c2759,plain,
product(quotient(X2,X),j(X)) = quotient(product(X2,i(X)),X),
inference(transitivity,[status(thm)],[c2737,c2758]) ).
cnf(c2760,plain,
product(quotient(X,X2),j(X2)) = quotient(product(X,i(X2)),X2),
inference(substitution,[status(thm)],[c2759]) ).
cnf(c2761,plain,
quotient(eta(j(X2)),product(quotient(X,X2),j(X2))) = quotient(eta(j(X2)),quotient(product(X,i(X2)),X2)),
inference(congruence,[status(thm)],[c2760]) ).
cnf(c2762,plain,
quotient(eta(j(X2)),quotient(product(X,i(X2)),X2)) = quotient(eta(X2),quotient(product(X,i(X2)),X2)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c2763,plain,
quotient(eta(X2),quotient(product(X,i(X2)),X2)) = product(X2,j(product(X,i(X2)))),
inference(substitution,[status(thm)],[c1230]) ).
cnf(c2764,plain,
quotient(eta(j(X2)),quotient(product(X,i(X2)),X2)) = product(X2,j(product(X,i(X2)))),
inference(transitivity,[status(thm)],[c2762,c2763]) ).
cnf(c2765,plain,
quotient(eta(j(X2)),product(quotient(X,X2),j(X2))) = product(X2,j(product(X,i(X2)))),
inference(transitivity,[status(thm)],[c2761,c2764]) ).
cnf(c2766,plain,
difference(j(X2),j(quotient(X,X2))) = product(X2,j(product(X,i(X2)))),
inference(transitivity,[status(thm)],[c2734,c2765]) ).
cnf(c2767,plain,
difference(j(j(X2)),j(quotient(X,j(X2)))) = product(j(X2),j(product(X,i(j(X2))))),
inference(substitution,[status(thm)],[c2766]) ).
cnf(c2768,plain,
product(j(X2),j(product(X,i(j(X2))))) = difference(j(j(X2)),j(quotient(X,j(X2)))),
inference(symmetry,[status(thm)],[c2767]) ).
cnf(c2769,plain,
j(quotient(X,j(X2))) = product(j(X2),quotient(eta(X2),X)),
inference(symmetry,[status(thm)],[c802]) ).
cnf(c2770,plain,
difference(j(j(X2)),j(quotient(X,j(X2)))) = difference(j(j(X2)),product(j(X2),quotient(eta(X2),X))),
inference(congruence,[status(thm)],[c2769]) ).
cnf(c2771,plain,
difference(j(j(X2)),product(j(X2),quotient(eta(X2),X))) = product(j(X2),difference(i(j(X2)),quotient(eta(X2),X))),
inference(substitution,[status(thm)],[c2669]) ).
cnf(c2772,plain,
difference(i(j(X2)),quotient(eta(X2),X)) = difference(X2,quotient(eta(X2),X)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c2773,plain,
product(j(X2),difference(i(j(X2)),quotient(eta(X2),X))) = product(j(X2),difference(X2,quotient(eta(X2),X))),
inference(congruence,[status(thm)],[c2772]) ).
cnf(c2774,plain,
quotient(quotient(difference(X2,X),X2),j(X2)) = quotient(quotient(difference(X2,X),i(X2)),X2),
inference(substitution,[status(thm)],[c1920]) ).
cnf(c2775,plain,
quotient(quotient(difference(X2,X),i(X2)),X2) = quotient(quotient(difference(X2,X),X2),j(X2)),
inference(symmetry,[status(thm)],[c2774]) ).
cnf(c2776,plain,
quotient(difference(X2,X),X2) = difference(X2,product(X,j(X2))),
inference(symmetry,[status(thm)],[c1329]) ).
cnf(c2777,plain,
quotient(quotient(difference(X2,X),X2),j(X2)) = quotient(difference(X2,product(X,j(X2))),j(X2)),
inference(congruence,[status(thm)],[c2776]) ).
cnf(c2778,plain,
quotient(difference(X2,product(X,j(X2))),j(X2)) = difference(product(j(X2),X2),product(j(X2),X)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c2779,plain,
difference(product(j(X2),X2),product(j(X2),X)) = difference(one,product(j(X2),X)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c2780,plain,
difference(one,product(j(X2),X)) = product(j(X2),X),
inference(substitution,[status(thm)],[c190]) ).
cnf(c2781,plain,
difference(product(j(X2),X2),product(j(X2),X)) = product(j(X2),X),
inference(transitivity,[status(thm)],[c2779,c2780]) ).
cnf(c2782,plain,
quotient(difference(X2,product(X,j(X2))),j(X2)) = product(j(X2),X),
inference(transitivity,[status(thm)],[c2778,c2781]) ).
cnf(c2783,plain,
quotient(quotient(difference(X2,X),X2),j(X2)) = product(j(X2),X),
inference(transitivity,[status(thm)],[c2777,c2782]) ).
cnf(c2784,plain,
quotient(quotient(difference(X2,X),i(X2)),X2) = product(j(X2),X),
inference(transitivity,[status(thm)],[c2775,c2783]) ).
cnf(c2785,plain,
quotient(quotient(difference(X2,difference(X2,X)),i(X2)),X2) = product(j(X2),difference(X2,X)),
inference(substitution,[status(thm)],[c2784]) ).
cnf(c2786,plain,
product(j(X2),difference(X2,X)) = quotient(quotient(difference(X2,difference(X2,X)),i(X2)),X2),
inference(symmetry,[status(thm)],[c2785]) ).
cnf(c2787,plain,
quotient(quotient(difference(X2,difference(X2,X)),i(i(X2))),i(X2)) = quotient(quotient(difference(X2,difference(X2,X)),i(X2)),X2),
inference(substitution,[status(thm)],[c2234]) ).
cnf(c2788,plain,
quotient(quotient(difference(X2,difference(X2,X)),i(X2)),X2) = quotient(quotient(difference(X2,difference(X2,X)),i(i(X2))),i(X2)),
inference(symmetry,[status(thm)],[c2787]) ).
cnf(c2789,plain,
quotient(quotient(difference(X2,difference(X2,X)),i(i(i(X2)))),i(i(X2))) = quotient(quotient(difference(X2,difference(X2,X)),i(i(X2))),i(X2)),
inference(substitution,[status(thm)],[c2234]) ).
cnf(c2790,plain,
quotient(quotient(difference(X2,difference(X2,X)),i(i(X2))),i(X2)) = quotient(quotient(difference(X2,difference(X2,X)),i(i(i(X2)))),i(i(X2))),
inference(symmetry,[status(thm)],[c2789]) ).
cnf(c2791,plain,
quotient(i(X2),difference(X,i(X2))) = X,
inference(substitution,[status(thm)],[c86]) ).
cnf(c2792,plain,
X = quotient(i(X2),difference(X,i(X2))),
inference(symmetry,[status(thm)],[c2791]) ).
cnf(c2793,plain,
difference(i(i(X2)),X) = difference(i(i(X2)),quotient(i(X2),difference(X,i(X2)))),
inference(congruence,[status(thm)],[c2792]) ).
cnf(c2794,plain,
difference(i(i(X2)),difference(i(i(X2)),X)) = difference(i(i(X2)),difference(i(i(X2)),quotient(i(X2),difference(X,i(X2))))),
inference(congruence,[status(thm)],[c2793]) ).
cnf(c2795,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c2796,plain,
product(X,X2) = product(X,j(i(X2))),
inference(congruence,[status(thm)],[c2795]) ).
cnf(c2797,plain,
quotient(i(X2),product(X,X2)) = quotient(i(X2),product(X,j(i(X2)))),
inference(congruence,[status(thm)],[c2796]) ).
cnf(c2798,plain,
quotient(eta(X),quotient(X2,X)) = product(X,j(X2)),
inference(substitution,[status(thm)],[c1230]) ).
cnf(c2799,plain,
product(X,j(X2)) = quotient(eta(X),quotient(X2,X)),
inference(symmetry,[status(thm)],[c2798]) ).
cnf(c2800,plain,
quotient(X2,product(X,j(X2))) = quotient(X2,quotient(eta(X),quotient(X2,X))),
inference(congruence,[status(thm)],[c2799]) ).
cnf(c2801,plain,
eta(X) = eta(difference(X2,quotient(X,X2))),
inference(symmetry,[status(thm)],[c1564]) ).
cnf(c2802,plain,
quotient(eta(X),quotient(X2,X)) = quotient(eta(difference(X2,quotient(X,X2))),quotient(X2,X)),
inference(congruence,[status(thm)],[c2801]) ).
cnf(c2803,plain,
quotient(X2,quotient(eta(X),quotient(X2,X))) = quotient(X2,quotient(eta(difference(X2,quotient(X,X2))),quotient(X2,X))),
inference(congruence,[status(thm)],[c2802]) ).
cnf(c2804,plain,
eta(quotient(X2,quotient(X,X2))) = eta(difference(X2,quotient(X,X2))),
inference(substitution,[status(thm)],[c1270]) ).
cnf(c2805,plain,
eta(difference(X2,quotient(X,X2))) = eta(quotient(X2,quotient(X,X2))),
inference(symmetry,[status(thm)],[c2804]) ).
cnf(c2806,plain,
quotient(eta(difference(X2,quotient(X,X2))),quotient(X2,X)) = quotient(eta(quotient(X2,quotient(X,X2))),quotient(X2,X)),
inference(congruence,[status(thm)],[c2805]) ).
cnf(c2807,plain,
quotient(X2,quotient(eta(difference(X2,quotient(X,X2))),quotient(X2,X))) = quotient(X2,quotient(eta(quotient(X2,quotient(X,X2))),quotient(X2,X))),
inference(congruence,[status(thm)],[c2806]) ).
cnf(c2808,plain,
quotient(X2,quotient(X,X2)) = product(X2,quotient(X2,X)),
inference(symmetry,[status(thm)],[c1110]) ).
cnf(c2809,plain,
difference(X2,quotient(X2,quotient(X,X2))) = difference(X2,product(X2,quotient(X2,X))),
inference(congruence,[status(thm)],[c2808]) ).
cnf(c2810,plain,
difference(X2,product(X2,quotient(X2,X))) = quotient(X2,X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c2811,plain,
difference(X2,quotient(X2,quotient(X,X2))) = quotient(X2,X),
inference(transitivity,[status(thm)],[c2809,c2810]) ).
cnf(c2812,plain,
quotient(X2,X) = difference(X2,quotient(X2,quotient(X,X2))),
inference(symmetry,[status(thm)],[c2811]) ).
cnf(c2813,plain,
quotient(eta(quotient(X2,quotient(X,X2))),quotient(X2,X)) = quotient(eta(quotient(X2,quotient(X,X2))),difference(X2,quotient(X2,quotient(X,X2)))),
inference(congruence,[status(thm)],[c2812]) ).
cnf(c2814,plain,
quotient(X2,quotient(eta(quotient(X2,quotient(X,X2))),quotient(X2,X))) = quotient(X2,quotient(eta(quotient(X2,quotient(X,X2))),difference(X2,quotient(X2,quotient(X,X2))))),
inference(congruence,[status(thm)],[c2813]) ).
cnf(c2815,plain,
quotient(eta(difference(difference(X,X2),X)),difference(X,X2)) = difference(difference(i(X),difference(X,X2)),X),
inference(substitution,[status(thm)],[c2305]) ).
cnf(c2816,plain,
difference(difference(i(X),difference(X,X2)),X) = quotient(eta(difference(difference(X,X2),X)),difference(X,X2)),
inference(symmetry,[status(thm)],[c2815]) ).
cnf(c2817,plain,
difference(difference(X,X2),quotient(difference(i(difference(X,X2)),eta(difference(difference(X,X2),X))),difference(X,X2))) = quotient(eta(difference(difference(X,X2),X)),difference(X,X2)),
inference(substitution,[status(thm)],[c905]) ).
cnf(c2818,plain,
quotient(eta(difference(difference(X,X2),X)),difference(X,X2)) = difference(difference(X,X2),quotient(difference(i(difference(X,X2)),eta(difference(difference(X,X2),X))),difference(X,X2))),
inference(symmetry,[status(thm)],[c2817]) ).
cnf(c2819,plain,
eta(difference(X2,X)) = eta(difference(X,X2)),
inference(substitution,[status(thm)],[c1442]) ).
cnf(c2820,plain,
difference(i(X2),eta(difference(X2,X))) = difference(i(X2),eta(difference(X,X2))),
inference(congruence,[status(thm)],[c2819]) ).
cnf(c2821,plain,
quotient(difference(i(X2),eta(difference(X2,X))),X2) = quotient(difference(i(X2),eta(difference(X,X2))),X2),
inference(congruence,[status(thm)],[c2820]) ).
cnf(c2822,plain,
eta(product(X,X2)) = eta(difference(X,X2)),
inference(substitution,[status(thm)],[c1641]) ).
cnf(c2823,plain,
eta(difference(X,X2)) = eta(product(X,X2)),
inference(symmetry,[status(thm)],[c2822]) ).
cnf(c2824,plain,
difference(i(X2),eta(difference(X,X2))) = difference(i(X2),eta(product(X,X2))),
inference(congruence,[status(thm)],[c2823]) ).
cnf(c2825,plain,
quotient(difference(i(X2),eta(difference(X,X2))),X2) = quotient(difference(i(X2),eta(product(X,X2))),X2),
inference(congruence,[status(thm)],[c2824]) ).
cnf(c2826,plain,
product(product(X2,quotient(eta(product(X,X2)),product(X,X2))),X) = quotient(difference(i(X2),eta(product(X,X2))),X2),
inference(substitution,[status(thm)],[c434]) ).
cnf(c2827,plain,
quotient(difference(i(X2),eta(product(X,X2))),X2) = product(product(X2,quotient(eta(product(X,X2)),product(X,X2))),X),
inference(symmetry,[status(thm)],[c2826]) ).
cnf(c2828,plain,
quotient(eta(product(X,X2)),product(X,X2)) = i(product(X,X2)),
inference(substitution,[status(thm)],[c1660]) ).
cnf(c2829,plain,
product(X2,quotient(eta(product(X,X2)),product(X,X2))) = product(X2,i(product(X,X2))),
inference(congruence,[status(thm)],[c2828]) ).
cnf(c2830,plain,
product(product(X2,quotient(eta(product(X,X2)),product(X,X2))),X) = product(product(X2,i(product(X,X2))),X),
inference(congruence,[status(thm)],[c2829]) ).
cnf(c2831,plain,
quotient(difference(i(X2),eta(product(X,X2))),X2) = product(product(X2,i(product(X,X2))),X),
inference(transitivity,[status(thm)],[c2827,c2830]) ).
cnf(c2832,plain,
quotient(difference(i(X2),eta(difference(X,X2))),X2) = product(product(X2,i(product(X,X2))),X),
inference(transitivity,[status(thm)],[c2825,c2831]) ).
cnf(c2833,plain,
quotient(difference(i(X2),eta(difference(X2,X))),X2) = product(product(X2,i(product(X,X2))),X),
inference(transitivity,[status(thm)],[c2821,c2832]) ).
cnf(c2834,plain,
quotient(difference(i(difference(X,X2)),eta(difference(difference(X,X2),X))),difference(X,X2)) = product(product(difference(X,X2),i(product(X,difference(X,X2)))),X),
inference(substitution,[status(thm)],[c2833]) ).
cnf(c2835,plain,
difference(difference(X,X2),quotient(difference(i(difference(X,X2)),eta(difference(difference(X,X2),X))),difference(X,X2))) = difference(difference(X,X2),product(product(difference(X,X2),i(product(X,difference(X,X2)))),X)),
inference(congruence,[status(thm)],[c2834]) ).
cnf(c2836,plain,
difference(difference(X3,X2),product(product(difference(X3,X2),X),X3)) = quotient(product(X,product(X3,difference(X3,X2))),difference(X3,X2)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c2837,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c2838,plain,
product(X,product(X3,difference(X3,X2))) = product(X,X2),
inference(congruence,[status(thm)],[c2837]) ).
cnf(c2839,plain,
quotient(product(X,product(X3,difference(X3,X2))),difference(X3,X2)) = quotient(product(X,X2),difference(X3,X2)),
inference(congruence,[status(thm)],[c2838]) ).
cnf(c2840,plain,
difference(difference(X3,X2),product(product(difference(X3,X2),X),X3)) = quotient(product(X,X2),difference(X3,X2)),
inference(transitivity,[status(thm)],[c2836,c2839]) ).
cnf(c2841,plain,
difference(difference(X,X2),product(product(difference(X,X2),i(product(X,difference(X,X2)))),X)) = quotient(product(i(product(X,difference(X,X2))),X2),difference(X,X2)),
inference(substitution,[status(thm)],[c2840]) ).
cnf(c2842,plain,
product(X,difference(X,X2)) = X2,
inference(substitution,[status(thm)],[c7]) ).
cnf(c2843,plain,
i(product(X,difference(X,X2))) = i(X2),
inference(congruence,[status(thm)],[c2842]) ).
cnf(c2844,plain,
product(i(product(X,difference(X,X2))),X2) = product(i(X2),X2),
inference(congruence,[status(thm)],[c2843]) ).
cnf(c2845,plain,
quotient(product(i(product(X,difference(X,X2))),X2),difference(X,X2)) = quotient(product(i(X2),X2),difference(X,X2)),
inference(congruence,[status(thm)],[c2844]) ).
cnf(c2846,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c2847,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c2846]) ).
cnf(c2848,plain,
quotient(product(i(X2),X2),difference(X,X2)) = quotient(eta(X2),difference(X,X2)),
inference(congruence,[status(thm)],[c2847]) ).
cnf(c2849,plain,
quotient(product(i(product(X,difference(X,X2))),X2),difference(X,X2)) = quotient(eta(X2),difference(X,X2)),
inference(transitivity,[status(thm)],[c2845,c2848]) ).
cnf(c2850,plain,
difference(difference(X,X2),product(product(difference(X,X2),i(product(X,difference(X,X2)))),X)) = quotient(eta(X2),difference(X,X2)),
inference(transitivity,[status(thm)],[c2841,c2849]) ).
cnf(c2851,plain,
difference(difference(X,X2),quotient(difference(i(difference(X,X2)),eta(difference(difference(X,X2),X))),difference(X,X2))) = quotient(eta(X2),difference(X,X2)),
inference(transitivity,[status(thm)],[c2835,c2850]) ).
cnf(c2852,plain,
quotient(eta(difference(difference(X,X2),X)),difference(X,X2)) = quotient(eta(X2),difference(X,X2)),
inference(transitivity,[status(thm)],[c2818,c2851]) ).
cnf(c2853,plain,
difference(difference(i(X),difference(X,X2)),X) = quotient(eta(X2),difference(X,X2)),
inference(transitivity,[status(thm)],[c2816,c2852]) ).
cnf(c2854,plain,
difference(difference(i(X2),difference(X2,X)),X2) = quotient(eta(X),difference(X2,X)),
inference(substitution,[status(thm)],[c2853]) ).
cnf(c2855,plain,
quotient(eta(X),difference(X2,X)) = difference(difference(i(X2),difference(X2,X)),X2),
inference(symmetry,[status(thm)],[c2854]) ).
cnf(c2856,plain,
quotient(X2,quotient(eta(X),difference(X2,X))) = quotient(X2,difference(difference(i(X2),difference(X2,X)),X2)),
inference(congruence,[status(thm)],[c2855]) ).
cnf(c2857,plain,
quotient(X2,difference(difference(i(X2),difference(X2,X)),X2)) = difference(i(X2),difference(X2,X)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c2858,plain,
quotient(X2,quotient(eta(X),difference(X2,X))) = difference(i(X2),difference(X2,X)),
inference(transitivity,[status(thm)],[c2856,c2857]) ).
cnf(c2859,plain,
quotient(X2,quotient(eta(quotient(X2,quotient(X,X2))),difference(X2,quotient(X2,quotient(X,X2))))) = difference(i(X2),difference(X2,quotient(X2,quotient(X,X2)))),
inference(substitution,[status(thm)],[c2858]) ).
cnf(c2860,plain,
difference(i(X2),difference(X2,quotient(X2,quotient(X,X2)))) = difference(i(X2),quotient(X2,X)),
inference(congruence,[status(thm)],[c2811]) ).
cnf(c2861,plain,
quotient(X2,quotient(eta(quotient(X2,quotient(X,X2))),difference(X2,quotient(X2,quotient(X,X2))))) = difference(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c2859,c2860]) ).
cnf(c2862,plain,
quotient(X2,quotient(eta(quotient(X2,quotient(X,X2))),quotient(X2,X))) = difference(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c2814,c2861]) ).
cnf(c2863,plain,
quotient(X2,quotient(eta(difference(X2,quotient(X,X2))),quotient(X2,X))) = difference(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c2807,c2862]) ).
cnf(c2864,plain,
quotient(X2,quotient(eta(X),quotient(X2,X))) = difference(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c2803,c2863]) ).
cnf(c2865,plain,
quotient(X2,product(X,j(X2))) = difference(i(X2),quotient(X2,X)),
inference(transitivity,[status(thm)],[c2800,c2864]) ).
cnf(c2866,plain,
quotient(i(X2),product(X,j(i(X2)))) = difference(i(i(X2)),quotient(i(X2),X)),
inference(substitution,[status(thm)],[c2865]) ).
cnf(c2867,plain,
quotient(i(X2),product(X,X2)) = difference(i(i(X2)),quotient(i(X2),X)),
inference(transitivity,[status(thm)],[c2797,c2866]) ).
cnf(c2868,plain,
quotient(i(X2),product(difference(X,i(X2)),X2)) = difference(i(i(X2)),quotient(i(X2),difference(X,i(X2)))),
inference(substitution,[status(thm)],[c2867]) ).
cnf(c2869,plain,
difference(i(i(X2)),quotient(i(X2),difference(X,i(X2)))) = quotient(i(X2),product(difference(X,i(X2)),X2)),
inference(symmetry,[status(thm)],[c2868]) ).
cnf(c2870,plain,
difference(i(i(X2)),difference(i(i(X2)),quotient(i(X2),difference(X,i(X2))))) = difference(i(i(X2)),quotient(i(X2),product(difference(X,i(X2)),X2))),
inference(congruence,[status(thm)],[c2869]) ).
cnf(c2871,plain,
j(X) = product(X,difference(i(i(X)),i(X))),
inference(symmetry,[status(thm)],[c1088]) ).
cnf(c2872,plain,
quotient(j(X2),X) = quotient(product(X2,difference(i(i(X2)),i(X2))),X),
inference(congruence,[status(thm)],[c2871]) ).
cnf(c2873,plain,
difference(X2,quotient(j(X2),X)) = difference(X2,quotient(product(X2,difference(i(i(X2)),i(X2))),X)),
inference(congruence,[status(thm)],[c2872]) ).
cnf(c2874,plain,
quotient(product(X3,X2),difference(product(X3,quotient(product(X2,X3),X)),product(X3,X2))) = product(X3,quotient(product(X2,X3),X)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c2875,plain,
product(X3,quotient(product(X2,X3),X)) = quotient(product(X3,X2),difference(product(X3,quotient(product(X2,X3),X)),product(X3,X2))),
inference(symmetry,[status(thm)],[c2874]) ).
cnf(c2876,plain,
quotient(difference(quotient(product(X2,X3),X),product(X2,X3)),X3) = difference(product(X3,quotient(product(X2,X3),X)),product(X3,X2)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c2877,plain,
difference(product(X3,quotient(product(X2,X3),X)),product(X3,X2)) = quotient(difference(quotient(product(X2,X3),X),product(X2,X3)),X3),
inference(symmetry,[status(thm)],[c2876]) ).
cnf(c2878,plain,
difference(quotient(product(X2,X3),X),product(X2,X3)) = X,
inference(substitution,[status(thm)],[c209]) ).
cnf(c2879,plain,
quotient(difference(quotient(product(X2,X3),X),product(X2,X3)),X3) = quotient(X,X3),
inference(congruence,[status(thm)],[c2878]) ).
cnf(c2880,plain,
difference(product(X3,quotient(product(X2,X3),X)),product(X3,X2)) = quotient(X,X3),
inference(transitivity,[status(thm)],[c2877,c2879]) ).
cnf(c2881,plain,
quotient(product(X3,X2),difference(product(X3,quotient(product(X2,X3),X)),product(X3,X2))) = quotient(product(X3,X2),quotient(X,X3)),
inference(congruence,[status(thm)],[c2880]) ).
cnf(c2882,plain,
product(X3,quotient(product(X2,X3),X)) = quotient(product(X3,X2),quotient(X,X3)),
inference(transitivity,[status(thm)],[c2875,c2881]) ).
cnf(c2883,plain,
quotient(product(X3,X2),quotient(X,X3)) = product(X3,quotient(product(X2,X3),X)),
inference(symmetry,[status(thm)],[c2882]) ).
cnf(c2884,plain,
difference(X3,quotient(product(X3,X2),quotient(X,X3))) = difference(X3,product(X3,quotient(product(X2,X3),X))),
inference(congruence,[status(thm)],[c2883]) ).
cnf(c2885,plain,
difference(X3,product(X3,quotient(product(X2,X3),X))) = quotient(product(X2,X3),X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c2886,plain,
difference(X3,quotient(product(X3,X2),quotient(X,X3))) = quotient(product(X2,X3),X),
inference(transitivity,[status(thm)],[c2884,c2885]) ).
cnf(c2887,plain,
difference(X2,quotient(product(X2,X3),quotient(product(X,X2),X2))) = quotient(product(X3,X2),product(X,X2)),
inference(substitution,[status(thm)],[c2886]) ).
cnf(c2888,plain,
quotient(product(X3,X2),product(X,X2)) = difference(X2,quotient(product(X2,X3),quotient(product(X,X2),X2))),
inference(symmetry,[status(thm)],[c2887]) ).
cnf(c2889,plain,
quotient(product(X,X2),X2) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c2890,plain,
quotient(product(X2,X3),quotient(product(X,X2),X2)) = quotient(product(X2,X3),X),
inference(congruence,[status(thm)],[c2889]) ).
cnf(c2891,plain,
difference(X2,quotient(product(X2,X3),quotient(product(X,X2),X2))) = difference(X2,quotient(product(X2,X3),X)),
inference(congruence,[status(thm)],[c2890]) ).
cnf(c2892,plain,
quotient(product(X3,X2),product(X,X2)) = difference(X2,quotient(product(X2,X3),X)),
inference(transitivity,[status(thm)],[c2888,c2891]) ).
cnf(c2893,plain,
quotient(product(difference(i(i(X2)),i(X2)),X2),product(X,X2)) = difference(X2,quotient(product(X2,difference(i(i(X2)),i(X2))),X)),
inference(substitution,[status(thm)],[c2892]) ).
cnf(c2894,plain,
difference(X2,quotient(product(X2,difference(i(i(X2)),i(X2))),X)) = quotient(product(difference(i(i(X2)),i(X2)),X2),product(X,X2)),
inference(symmetry,[status(thm)],[c2893]) ).
cnf(c2895,plain,
quotient(product(difference(i(i(X2)),i(X2)),X2),product(X,X2)) = quotient(i(X2),product(X,X2)),
inference(congruence,[status(thm)],[c1128]) ).
cnf(c2896,plain,
quotient(product(difference(i(i(X2)),i(X2)),X2),product(X,X2)) = difference(i(i(X2)),quotient(i(X2),X)),
inference(transitivity,[status(thm)],[c2895,c2867]) ).
cnf(c2897,plain,
difference(X2,quotient(product(X2,difference(i(i(X2)),i(X2))),X)) = difference(i(i(X2)),quotient(i(X2),X)),
inference(transitivity,[status(thm)],[c2894,c2896]) ).
cnf(c2898,plain,
difference(X2,quotient(j(X2),X)) = difference(i(i(X2)),quotient(i(X2),X)),
inference(transitivity,[status(thm)],[c2873,c2897]) ).
cnf(c2899,plain,
difference(X2,quotient(j(X2),product(difference(X,i(X2)),X2))) = difference(i(i(X2)),quotient(i(X2),product(difference(X,i(X2)),X2))),
inference(substitution,[status(thm)],[c2898]) ).
cnf(c2900,plain,
difference(i(i(X2)),quotient(i(X2),product(difference(X,i(X2)),X2))) = difference(X2,quotient(j(X2),product(difference(X,i(X2)),X2))),
inference(symmetry,[status(thm)],[c2899]) ).
cnf(c2901,plain,
product(difference(X,i(X2)),X2) = difference(difference(X2,X),j(X2)),
inference(symmetry,[status(thm)],[c1876]) ).
cnf(c2902,plain,
quotient(j(X2),product(difference(X,i(X2)),X2)) = quotient(j(X2),difference(difference(X2,X),j(X2))),
inference(congruence,[status(thm)],[c2901]) ).
cnf(c2903,plain,
quotient(j(X2),difference(difference(X2,X),j(X2))) = difference(X2,X),
inference(substitution,[status(thm)],[c86]) ).
cnf(c2904,plain,
quotient(j(X2),product(difference(X,i(X2)),X2)) = difference(X2,X),
inference(transitivity,[status(thm)],[c2902,c2903]) ).
cnf(c2905,plain,
difference(X2,quotient(j(X2),product(difference(X,i(X2)),X2))) = difference(X2,difference(X2,X)),
inference(congruence,[status(thm)],[c2904]) ).
cnf(c2906,plain,
difference(i(i(X2)),quotient(i(X2),product(difference(X,i(X2)),X2))) = difference(X2,difference(X2,X)),
inference(transitivity,[status(thm)],[c2900,c2905]) ).
cnf(c2907,plain,
difference(i(i(X2)),difference(i(i(X2)),quotient(i(X2),difference(X,i(X2))))) = difference(X2,difference(X2,X)),
inference(transitivity,[status(thm)],[c2870,c2906]) ).
cnf(c2908,plain,
difference(i(i(X2)),difference(i(i(X2)),X)) = difference(X2,difference(X2,X)),
inference(transitivity,[status(thm)],[c2794,c2907]) ).
cnf(c2909,plain,
difference(X2,difference(X2,X)) = difference(i(i(X2)),difference(i(i(X2)),X)),
inference(symmetry,[status(thm)],[c2908]) ).
cnf(c2910,plain,
quotient(difference(X2,difference(X2,X)),i(i(i(X2)))) = quotient(difference(i(i(X2)),difference(i(i(X2)),X)),i(i(i(X2)))),
inference(congruence,[status(thm)],[c2909]) ).
cnf(c2911,plain,
quotient(quotient(difference(X2,difference(X2,X)),i(i(i(X2)))),i(i(X2))) = quotient(quotient(difference(i(i(X2)),difference(i(i(X2)),X)),i(i(i(X2)))),i(i(X2))),
inference(congruence,[status(thm)],[c2910]) ).
cnf(c2912,plain,
quotient(quotient(difference(i(i(X2)),difference(i(i(X2)),X)),i(i(i(X2)))),i(i(X2))) = product(j(i(i(X2))),difference(i(i(X2)),X)),
inference(substitution,[status(thm)],[c2784]) ).
cnf(c2913,plain,
j(i(i(X))) = i(X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c2914,plain,
product(j(i(i(X2))),difference(i(i(X2)),X)) = product(i(X2),difference(i(i(X2)),X)),
inference(congruence,[status(thm)],[c2913]) ).
cnf(c2915,plain,
product(j(i(i(X2))),difference(i(i(X2)),X)) = difference(X2,product(i(X2),X)),
inference(transitivity,[status(thm)],[c2914,c2673]) ).
cnf(c2916,plain,
quotient(quotient(difference(i(i(X2)),difference(i(i(X2)),X)),i(i(i(X2)))),i(i(X2))) = difference(X2,product(i(X2),X)),
inference(transitivity,[status(thm)],[c2912,c2915]) ).
cnf(c2917,plain,
quotient(quotient(difference(X2,difference(X2,X)),i(i(i(X2)))),i(i(X2))) = difference(X2,product(i(X2),X)),
inference(transitivity,[status(thm)],[c2911,c2916]) ).
cnf(c2918,plain,
quotient(quotient(difference(X2,difference(X2,X)),i(i(X2))),i(X2)) = difference(X2,product(i(X2),X)),
inference(transitivity,[status(thm)],[c2790,c2917]) ).
cnf(c2919,plain,
quotient(quotient(difference(X2,difference(X2,X)),i(X2)),X2) = difference(X2,product(i(X2),X)),
inference(transitivity,[status(thm)],[c2788,c2918]) ).
cnf(c2920,plain,
product(j(X2),difference(X2,X)) = difference(X2,product(i(X2),X)),
inference(transitivity,[status(thm)],[c2786,c2919]) ).
cnf(c2921,plain,
product(j(X2),difference(X2,quotient(eta(X2),X))) = difference(X2,product(i(X2),quotient(eta(X2),X))),
inference(substitution,[status(thm)],[c2920]) ).
cnf(c2922,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c2923,plain,
quotient(eta(X2),X) = quotient(eta(i(X2)),X),
inference(congruence,[status(thm)],[c2922]) ).
cnf(c2924,plain,
product(i(X2),quotient(eta(X2),X)) = product(i(X2),quotient(eta(i(X2)),X)),
inference(congruence,[status(thm)],[c2923]) ).
cnf(c2925,plain,
product(i(X2),quotient(eta(i(X2)),X)) = j(quotient(X,i(X2))),
inference(substitution,[status(thm)],[c582]) ).
cnf(c2926,plain,
product(i(X2),quotient(eta(X2),X)) = j(quotient(X,i(X2))),
inference(transitivity,[status(thm)],[c2924,c2925]) ).
cnf(c2927,plain,
difference(X2,product(i(X2),quotient(eta(X2),X))) = difference(X2,j(quotient(X,i(X2)))),
inference(congruence,[status(thm)],[c2926]) ).
cnf(c2928,plain,
product(j(X2),difference(X2,quotient(eta(X2),X))) = difference(X2,j(quotient(X,i(X2)))),
inference(transitivity,[status(thm)],[c2921,c2927]) ).
cnf(c2929,plain,
product(j(X2),difference(i(j(X2)),quotient(eta(X2),X))) = difference(X2,j(quotient(X,i(X2)))),
inference(transitivity,[status(thm)],[c2773,c2928]) ).
cnf(c2930,plain,
difference(j(j(X2)),product(j(X2),quotient(eta(X2),X))) = difference(X2,j(quotient(X,i(X2)))),
inference(transitivity,[status(thm)],[c2771,c2929]) ).
cnf(c2931,plain,
difference(j(j(X2)),j(quotient(X,j(X2)))) = difference(X2,j(quotient(X,i(X2)))),
inference(transitivity,[status(thm)],[c2770,c2930]) ).
cnf(c2932,plain,
product(j(X2),j(product(X,i(j(X2))))) = difference(X2,j(quotient(X,i(X2)))),
inference(transitivity,[status(thm)],[c2768,c2931]) ).
cnf(c2933,plain,
product(j(X2),j(product(X,X2))) = difference(X2,j(quotient(X,i(X2)))),
inference(transitivity,[status(thm)],[c2732,c2932]) ).
cnf(c2934,plain,
product(j(i(X2)),j(product(difference(X,eta(X2)),i(X2)))) = difference(i(X2),j(quotient(difference(X,eta(X2)),i(i(X2))))),
inference(substitution,[status(thm)],[c2933]) ).
cnf(c2935,plain,
difference(product(i(i(X)),X2),quotient(difference(i(i(i(X))),eta(X)),i(i(X)))) = quotient(difference(X2,eta(X)),i(i(X))),
inference(substitution,[status(thm)],[c2560]) ).
cnf(c2936,plain,
quotient(difference(X2,eta(X)),i(i(X))) = difference(product(i(i(X)),X2),quotient(difference(i(i(i(X))),eta(X)),i(i(X)))),
inference(symmetry,[status(thm)],[c2935]) ).
cnf(c2937,plain,
quotient(difference(i(i(i(X))),eta(X)),i(i(X))) = quotient(i(i(X)),i(i(X))),
inference(congruence,[status(thm)],[c2487]) ).
cnf(c2938,plain,
difference(product(i(i(X)),X2),quotient(difference(i(i(i(X))),eta(X)),i(i(X)))) = difference(product(i(i(X)),X2),quotient(i(i(X)),i(i(X)))),
inference(congruence,[status(thm)],[c2937]) ).
cnf(c2939,plain,
quotient(i(i(X)),i(i(X))) = one,
inference(substitution,[status(thm)],[c1116]) ).
cnf(c2940,plain,
difference(product(i(i(X)),X2),quotient(i(i(X)),i(i(X)))) = difference(product(i(i(X)),X2),one),
inference(congruence,[status(thm)],[c2939]) ).
cnf(c2941,plain,
i(product(i(i(X)),X2)) = difference(product(i(i(X)),X2),one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c2942,plain,
difference(product(i(i(X)),X2),one) = i(product(i(i(X)),X2)),
inference(symmetry,[status(thm)],[c2941]) ).
cnf(c2943,plain,
difference(product(i(i(X)),X2),quotient(i(i(X)),i(i(X)))) = i(product(i(i(X)),X2)),
inference(transitivity,[status(thm)],[c2940,c2942]) ).
cnf(c2944,plain,
difference(product(i(i(X)),X2),quotient(difference(i(i(i(X))),eta(X)),i(i(X)))) = i(product(i(i(X)),X2)),
inference(transitivity,[status(thm)],[c2938,c2943]) ).
cnf(c2945,plain,
quotient(difference(X2,eta(X)),i(i(X))) = i(product(i(i(X)),X2)),
inference(transitivity,[status(thm)],[c2936,c2944]) ).
cnf(c2946,plain,
quotient(difference(X,eta(X2)),i(i(X2))) = i(product(i(i(X2)),X)),
inference(substitution,[status(thm)],[c2945]) ).
cnf(c2947,plain,
j(quotient(difference(X,eta(X2)),i(i(X2)))) = j(i(product(i(i(X2)),X))),
inference(congruence,[status(thm)],[c2946]) ).
cnf(c2948,plain,
difference(i(X2),j(quotient(difference(X,eta(X2)),i(i(X2))))) = difference(i(X2),j(i(product(i(i(X2)),X)))),
inference(congruence,[status(thm)],[c2947]) ).
cnf(c2949,plain,
j(i(product(i(i(X2)),X))) = product(i(i(X2)),X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c2950,plain,
difference(i(X2),j(i(product(i(i(X2)),X)))) = difference(i(X2),product(i(i(X2)),X)),
inference(congruence,[status(thm)],[c2949]) ).
cnf(c2951,plain,
difference(i(X2),j(quotient(difference(X,eta(X2)),i(i(X2))))) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2948,c2950]) ).
cnf(c2952,plain,
product(j(i(X2)),j(product(difference(X,eta(X2)),i(X2)))) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2934,c2951]) ).
cnf(c2953,plain,
product(j(i(X2)),j(i(difference(i(X2),X)))) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2728,c2952]) ).
cnf(c2954,plain,
product(X2,j(i(difference(i(X2),X)))) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2719,c2953]) ).
cnf(c2955,plain,
product(X2,difference(i(X2),X)) = difference(i(X2),product(i(i(X2)),X)),
inference(transitivity,[status(thm)],[c2717,c2954]) ).
cnf(c2956,plain,
product(X2,difference(i(X2),difference(X2,X))) = difference(i(X2),product(i(i(X2)),difference(X2,X))),
inference(substitution,[status(thm)],[c2955]) ).
cnf(c2957,plain,
difference(i(X2),product(i(i(X2)),difference(X2,X))) = product(X2,difference(i(X2),difference(X2,X))),
inference(symmetry,[status(thm)],[c2956]) ).
cnf(c2958,plain,
product(product(X,j(X2)),X2) = difference(i(X2),difference(X2,X)),
inference(substitution,[status(thm)],[c2094]) ).
cnf(c2959,plain,
difference(i(X2),difference(X2,X)) = product(product(X,j(X2)),X2),
inference(symmetry,[status(thm)],[c2958]) ).
cnf(c2960,plain,
product(X2,difference(i(X2),difference(X2,X))) = product(X2,product(product(X,j(X2)),X2)),
inference(congruence,[status(thm)],[c2959]) ).
cnf(c2961,plain,
difference(j(X2),quotient(product(X,j(X2)),j(X2))) = product(X2,product(product(X,j(X2)),X2)),
inference(substitution,[status(thm)],[c931]) ).
cnf(c2962,plain,
product(X2,product(product(X,j(X2)),X2)) = difference(j(X2),quotient(product(X,j(X2)),j(X2))),
inference(symmetry,[status(thm)],[c2961]) ).
cnf(c2963,plain,
quotient(product(X,j(X2)),j(X2)) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c2964,plain,
difference(j(X2),quotient(product(X,j(X2)),j(X2))) = difference(j(X2),X),
inference(congruence,[status(thm)],[c2963]) ).
cnf(c2965,plain,
product(X2,product(product(X,j(X2)),X2)) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2962,c2964]) ).
cnf(c2966,plain,
product(X2,difference(i(X2),difference(X2,X))) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2960,c2965]) ).
cnf(c2967,plain,
difference(i(X2),product(i(i(X2)),difference(X2,X))) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2957,c2966]) ).
cnf(c2968,plain,
difference(i(X2),difference(i(i(i(X2))),product(i(X2),X))) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2714,c2967]) ).
cnf(c2969,plain,
difference(i(X2),product(i(i(X2)),difference(X2,X))) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2712,c2968]) ).
cnf(c2970,plain,
quotient(X2,difference(difference(X2,X),i(X2))) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2683,c2969]) ).
cnf(c2971,plain,
quotient(X2,product(difference(X,j(X2)),X2)) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2466,c2970]) ).
cnf(c2972,plain,
difference(X2,quotient(X2,difference(X,j(X2)))) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2464,c2971]) ).
cnf(c2973,plain,
difference(X2,difference(i(X2),product(X2,X))) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c2448,c2972]) ).
cnf(c2974,plain,
difference(X2,difference(i(X2),product(X2,product(X,X2)))) = difference(j(X2),product(X,X2)),
inference(substitution,[status(thm)],[c2973]) ).
cnf(c2975,plain,
difference(j(X2),product(X,X2)) = difference(X2,difference(i(X2),product(X2,product(X,X2)))),
inference(symmetry,[status(thm)],[c2974]) ).
cnf(c2976,plain,
difference(i(X),X) = product(X,X),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c2977,plain,
product(difference(i(X2),X2),X) = product(product(X2,X2),X),
inference(congruence,[status(thm)],[c2976]) ).
cnf(c2978,plain,
product(product(difference(i(X2),X2),X),X2) = product(product(product(X2,X2),X),X2),
inference(congruence,[status(thm)],[c2977]) ).
cnf(c2979,plain,
difference(i(X3),product(i(X3),product(product(product(X3,X2),X),X3))) = product(product(product(X3,X2),X),X3),
inference(substitution,[status(thm)],[c43]) ).
cnf(c2980,plain,
product(product(product(X3,X2),X),X3) = difference(i(X3),product(i(X3),product(product(product(X3,X2),X),X3))),
inference(symmetry,[status(thm)],[c2979]) ).
cnf(c2981,plain,
product(difference(X3,product(product(X3,X2),X)),X3) = product(i(X3),product(product(product(X3,X2),X),X3)),
inference(substitution,[status(thm)],[c322]) ).
cnf(c2982,plain,
product(i(X3),product(product(product(X3,X2),X),X3)) = product(difference(X3,product(product(X3,X2),X)),X3),
inference(symmetry,[status(thm)],[c2981]) ).
cnf(c2983,plain,
difference(X3,product(product(X3,X2),X)) = quotient(product(X2,product(X,X3)),X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c2984,plain,
product(difference(X3,product(product(X3,X2),X)),X3) = product(quotient(product(X2,product(X,X3)),X3),X3),
inference(congruence,[status(thm)],[c2983]) ).
cnf(c2985,plain,
product(quotient(product(X2,product(X,X3)),X3),X3) = product(X2,product(X,X3)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c2986,plain,
product(difference(X3,product(product(X3,X2),X)),X3) = product(X2,product(X,X3)),
inference(transitivity,[status(thm)],[c2984,c2985]) ).
cnf(c2987,plain,
product(i(X3),product(product(product(X3,X2),X),X3)) = product(X2,product(X,X3)),
inference(transitivity,[status(thm)],[c2982,c2986]) ).
cnf(c2988,plain,
difference(i(X3),product(i(X3),product(product(product(X3,X2),X),X3))) = difference(i(X3),product(X2,product(X,X3))),
inference(congruence,[status(thm)],[c2987]) ).
cnf(c2989,plain,
product(product(product(X3,X2),X),X3) = difference(i(X3),product(X2,product(X,X3))),
inference(transitivity,[status(thm)],[c2980,c2988]) ).
cnf(c2990,plain,
product(product(product(X2,X2),X),X2) = difference(i(X2),product(X2,product(X,X2))),
inference(substitution,[status(thm)],[c2989]) ).
cnf(c2991,plain,
product(product(difference(i(X2),X2),X),X2) = difference(i(X2),product(X2,product(X,X2))),
inference(transitivity,[status(thm)],[c2978,c2990]) ).
cnf(c2992,plain,
difference(i(X2),product(X2,product(X,X2))) = product(product(difference(i(X2),X2),X),X2),
inference(symmetry,[status(thm)],[c2991]) ).
cnf(c2993,plain,
difference(X2,difference(i(X2),product(X2,product(X,X2)))) = difference(X2,product(product(difference(i(X2),X2),X),X2)),
inference(congruence,[status(thm)],[c2992]) ).
cnf(c2994,plain,
X = difference(one,X),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c2995,plain,
product(product(difference(i(X2),X2),X),X2) = product(product(difference(i(X2),X2),X),difference(one,X2)),
inference(congruence,[status(thm)],[c2994]) ).
cnf(c2996,plain,
difference(X2,product(product(difference(i(X2),X2),X),X2)) = difference(X2,product(product(difference(i(X2),X2),X),difference(one,X2))),
inference(congruence,[status(thm)],[c2995]) ).
cnf(c2997,plain,
one = product(X,i(X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c2998,plain,
difference(one,X) = difference(product(X,i(X)),X),
inference(congruence,[status(thm)],[c2997]) ).
cnf(c2999,plain,
product(product(difference(i(X2),X2),X),difference(one,X2)) = product(product(difference(i(X2),X2),X),difference(product(X2,i(X2)),X2)),
inference(congruence,[status(thm)],[c2998]) ).
cnf(c3000,plain,
difference(X2,product(product(difference(i(X2),X2),X),difference(one,X2))) = difference(X2,product(product(difference(i(X2),X2),X),difference(product(X2,i(X2)),X2))),
inference(congruence,[status(thm)],[c2999]) ).
cnf(c3001,plain,
quotient(difference(i(X),X),X) = difference(product(X,i(X)),X),
inference(substitution,[status(thm)],[c233]) ).
cnf(c3002,plain,
difference(product(X,i(X)),X) = quotient(difference(i(X),X),X),
inference(symmetry,[status(thm)],[c3001]) ).
cnf(c3003,plain,
product(product(difference(i(X2),X2),X),difference(product(X2,i(X2)),X2)) = product(product(difference(i(X2),X2),X),quotient(difference(i(X2),X2),X2)),
inference(congruence,[status(thm)],[c3002]) ).
cnf(c3004,plain,
difference(X2,product(product(difference(i(X2),X2),X),difference(product(X2,i(X2)),X2))) = difference(X2,product(product(difference(i(X2),X2),X),quotient(difference(i(X2),X2),X2))),
inference(congruence,[status(thm)],[c3003]) ).
cnf(c3005,plain,
product(difference(X2,product(X3,X)),X3) = difference(difference(X3,X2),product(X,X3)),
inference(substitution,[status(thm)],[c1097]) ).
cnf(c3006,plain,
difference(difference(X3,X2),product(X,X3)) = product(difference(X2,product(X3,X)),X3),
inference(symmetry,[status(thm)],[c3005]) ).
cnf(c3007,plain,
quotient(difference(difference(X3,X2),product(X,X3)),X2) = quotient(product(difference(X2,product(X3,X)),X3),X2),
inference(congruence,[status(thm)],[c3006]) ).
cnf(c3008,plain,
quotient(product(difference(X2,product(X3,X)),X3),X2) = difference(X2,product(product(X3,X),quotient(X3,X2))),
inference(substitution,[status(thm)],[c963]) ).
cnf(c3009,plain,
quotient(difference(difference(X3,X2),product(X,X3)),X2) = difference(X2,product(product(X3,X),quotient(X3,X2))),
inference(transitivity,[status(thm)],[c3007,c3008]) ).
cnf(c3010,plain,
quotient(difference(difference(difference(i(X2),X2),X2),product(X,difference(i(X2),X2))),X2) = difference(X2,product(product(difference(i(X2),X2),X),quotient(difference(i(X2),X2),X2))),
inference(substitution,[status(thm)],[c3009]) ).
cnf(c3011,plain,
difference(X2,product(product(difference(i(X2),X2),X),quotient(difference(i(X2),X2),X2))) = quotient(difference(difference(difference(i(X2),X2),X2),product(X,difference(i(X2),X2))),X2),
inference(symmetry,[status(thm)],[c3010]) ).
cnf(c3012,plain,
difference(i(X),X) = product(X,X),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c3013,plain,
difference(difference(i(X),X),X) = difference(product(X,X),X),
inference(congruence,[status(thm)],[c3012]) ).
cnf(c3014,plain,
difference(difference(i(X),X),X) = j(X),
inference(transitivity,[status(thm)],[c3013,c1070]) ).
cnf(c3015,plain,
difference(difference(difference(i(X2),X2),X2),product(X,difference(i(X2),X2))) = difference(j(X2),product(X,difference(i(X2),X2))),
inference(congruence,[status(thm)],[c3014]) ).
cnf(c3016,plain,
quotient(difference(difference(difference(i(X2),X2),X2),product(X,difference(i(X2),X2))),X2) = quotient(difference(j(X2),product(X,difference(i(X2),X2))),X2),
inference(congruence,[status(thm)],[c3015]) ).
cnf(c3017,plain,
eta(X) = product(X,j(X)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c3018,plain,
difference(eta(X2),quotient(difference(i(X2),X),X2)) = difference(product(X2,j(X2)),quotient(difference(i(X2),X),X2)),
inference(congruence,[status(thm)],[c3017]) ).
cnf(c3019,plain,
difference(product(X2,j(X2)),quotient(difference(i(X2),X),X2)) = quotient(difference(j(X2),X),X2),
inference(substitution,[status(thm)],[c2560]) ).
cnf(c3020,plain,
difference(eta(X2),quotient(difference(i(X2),X),X2)) = quotient(difference(j(X2),X),X2),
inference(transitivity,[status(thm)],[c3018,c3019]) ).
cnf(c3021,plain,
quotient(difference(j(X2),X),X2) = difference(eta(X2),quotient(difference(i(X2),X),X2)),
inference(symmetry,[status(thm)],[c3020]) ).
cnf(c3022,plain,
quotient(X2,quotient(eta(eta(X)),difference(X2,eta(X)))) = difference(i(X2),difference(X2,eta(X))),
inference(substitution,[status(thm)],[c2858]) ).
cnf(c3023,plain,
difference(i(X2),difference(X2,eta(X))) = quotient(X2,quotient(eta(eta(X)),difference(X2,eta(X)))),
inference(symmetry,[status(thm)],[c3022]) ).
cnf(c3024,plain,
quotient(eta(eta(X)),difference(X2,eta(X))) = quotient(one,difference(X2,eta(X))),
inference(congruence,[status(thm)],[c507]) ).
cnf(c3025,plain,
quotient(X2,quotient(eta(eta(X)),difference(X2,eta(X)))) = quotient(X2,quotient(one,difference(X2,eta(X)))),
inference(congruence,[status(thm)],[c3024]) ).
cnf(c3026,plain,
j(difference(X2,eta(X))) = quotient(one,difference(X2,eta(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c3027,plain,
quotient(one,difference(X2,eta(X))) = j(difference(X2,eta(X))),
inference(symmetry,[status(thm)],[c3026]) ).
cnf(c3028,plain,
quotient(X2,quotient(one,difference(X2,eta(X)))) = quotient(X2,j(difference(X2,eta(X)))),
inference(congruence,[status(thm)],[c3027]) ).
cnf(c3029,plain,
quotient(X2,j(difference(X2,eta(X)))) = quotient(X2,difference(eta(X),X2)),
inference(congruence,[status(thm)],[c1178]) ).
cnf(c3030,plain,
quotient(X2,difference(eta(X),X2)) = eta(X),
inference(substitution,[status(thm)],[c86]) ).
cnf(c3031,plain,
quotient(X2,j(difference(X2,eta(X)))) = eta(X),
inference(transitivity,[status(thm)],[c3029,c3030]) ).
cnf(c3032,plain,
quotient(X2,quotient(one,difference(X2,eta(X)))) = eta(X),
inference(transitivity,[status(thm)],[c3028,c3031]) ).
cnf(c3033,plain,
quotient(X2,quotient(eta(eta(X)),difference(X2,eta(X)))) = eta(X),
inference(transitivity,[status(thm)],[c3025,c3032]) ).
cnf(c3034,plain,
difference(i(X2),difference(X2,eta(X))) = eta(X),
inference(transitivity,[status(thm)],[c3023,c3033]) ).
cnf(c3035,plain,
difference(i(quotient(difference(i(X2),X),X2)),difference(quotient(difference(i(X2),X),X2),eta(X2))) = eta(X2),
inference(substitution,[status(thm)],[c3034]) ).
cnf(c3036,plain,
eta(X2) = difference(i(quotient(difference(i(X2),X),X2)),difference(quotient(difference(i(X2),X),X2),eta(X2))),
inference(symmetry,[status(thm)],[c3035]) ).
cnf(c3037,plain,
difference(eta(X2),quotient(difference(i(X2),X),X2)) = difference(difference(i(quotient(difference(i(X2),X),X2)),difference(quotient(difference(i(X2),X),X2),eta(X2))),quotient(difference(i(X2),X),X2)),
inference(congruence,[status(thm)],[c3036]) ).
cnf(c3038,plain,
difference(difference(i(quotient(difference(i(X2),X),X2)),difference(quotient(difference(i(X2),X),X2),eta(X2))),quotient(difference(i(X2),X),X2)) = quotient(eta(eta(X2)),difference(quotient(difference(i(X2),X),X2),eta(X2))),
inference(substitution,[status(thm)],[c2853]) ).
cnf(c3039,plain,
quotient(i(difference(X2,quotient(difference(i(X2),X),X2))),X2) = difference(quotient(difference(i(X2),X),X2),eta(X2)),
inference(substitution,[status(thm)],[c138]) ).
cnf(c3040,plain,
difference(quotient(difference(i(X2),X),X2),eta(X2)) = quotient(i(difference(X2,quotient(difference(i(X2),X),X2))),X2),
inference(symmetry,[status(thm)],[c3039]) ).
cnf(c3041,plain,
i(difference(X2,quotient(difference(i(X2),X),X2))) = i(quotient(X,X2)),
inference(congruence,[status(thm)],[c905]) ).
cnf(c3042,plain,
quotient(i(difference(X2,quotient(difference(i(X2),X),X2))),X2) = quotient(i(quotient(X,X2)),X2),
inference(congruence,[status(thm)],[c3041]) ).
cnf(c3043,plain,
difference(quotient(difference(i(X2),X),X2),eta(X2)) = quotient(i(quotient(X,X2)),X2),
inference(transitivity,[status(thm)],[c3040,c3042]) ).
cnf(c3044,plain,
quotient(eta(eta(X2)),difference(quotient(difference(i(X2),X),X2),eta(X2))) = quotient(eta(eta(X2)),quotient(i(quotient(X,X2)),X2)),
inference(congruence,[status(thm)],[c3043]) ).
cnf(c3045,plain,
quotient(eta(eta(X2)),quotient(i(quotient(X,X2)),X2)) = quotient(one,quotient(i(quotient(X,X2)),X2)),
inference(congruence,[status(thm)],[c507]) ).
cnf(c3046,plain,
j(quotient(i(quotient(X,X2)),X2)) = quotient(one,quotient(i(quotient(X,X2)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c3047,plain,
quotient(one,quotient(i(quotient(X,X2)),X2)) = j(quotient(i(quotient(X,X2)),X2)),
inference(symmetry,[status(thm)],[c3046]) ).
cnf(c3048,plain,
quotient(eta(eta(X2)),quotient(i(quotient(X,X2)),X2)) = j(quotient(i(quotient(X,X2)),X2)),
inference(transitivity,[status(thm)],[c3045,c3047]) ).
cnf(c3049,plain,
quotient(eta(eta(X2)),difference(quotient(difference(i(X2),X),X2),eta(X2))) = j(quotient(i(quotient(X,X2)),X2)),
inference(transitivity,[status(thm)],[c3044,c3048]) ).
cnf(c3050,plain,
difference(difference(i(quotient(difference(i(X2),X),X2)),difference(quotient(difference(i(X2),X),X2),eta(X2))),quotient(difference(i(X2),X),X2)) = j(quotient(i(quotient(X,X2)),X2)),
inference(transitivity,[status(thm)],[c3038,c3049]) ).
cnf(c3051,plain,
difference(eta(X2),quotient(difference(i(X2),X),X2)) = j(quotient(i(quotient(X,X2)),X2)),
inference(transitivity,[status(thm)],[c3037,c3050]) ).
cnf(c3052,plain,
quotient(difference(j(X2),X),X2) = j(quotient(i(quotient(X,X2)),X2)),
inference(transitivity,[status(thm)],[c3021,c3051]) ).
cnf(c3053,plain,
quotient(difference(j(X2),product(X,difference(i(X2),X2))),X2) = j(quotient(i(quotient(product(X,difference(i(X2),X2)),X2)),X2)),
inference(substitution,[status(thm)],[c3052]) ).
cnf(c3054,plain,
difference(i(X),X) = product(X,X),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c3055,plain,
product(X2,difference(i(X),X)) = product(X2,product(X,X)),
inference(congruence,[status(thm)],[c3054]) ).
cnf(c3056,plain,
quotient(product(X2,difference(i(X),X)),X) = quotient(product(X2,product(X,X)),X),
inference(congruence,[status(thm)],[c3055]) ).
cnf(c3057,plain,
difference(X,product(product(X,X2),X)) = quotient(product(X2,product(X,X)),X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c3058,plain,
quotient(product(X2,product(X,X)),X) = difference(X,product(product(X,X2),X)),
inference(symmetry,[status(thm)],[c3057]) ).
cnf(c3059,plain,
product(product(X,X2),X) = difference(i(X),product(X2,X)),
inference(substitution,[status(thm)],[c696]) ).
cnf(c3060,plain,
difference(X,product(product(X,X2),X)) = difference(X,difference(i(X),product(X2,X))),
inference(congruence,[status(thm)],[c3059]) ).
cnf(c3061,plain,
quotient(product(X2,product(X,X)),X) = difference(X,difference(i(X),product(X2,X))),
inference(transitivity,[status(thm)],[c3058,c3060]) ).
cnf(c3062,plain,
quotient(product(X2,difference(i(X),X)),X) = difference(X,difference(i(X),product(X2,X))),
inference(transitivity,[status(thm)],[c3056,c3061]) ).
cnf(c3063,plain,
quotient(product(X,difference(i(X2),X2)),X2) = difference(X2,difference(i(X2),product(X,X2))),
inference(substitution,[status(thm)],[c3062]) ).
cnf(c3064,plain,
i(quotient(product(X,difference(i(X2),X2)),X2)) = i(difference(X2,difference(i(X2),product(X,X2)))),
inference(congruence,[status(thm)],[c3063]) ).
cnf(c3065,plain,
quotient(i(quotient(product(X,difference(i(X2),X2)),X2)),X2) = quotient(i(difference(X2,difference(i(X2),product(X,X2)))),X2),
inference(congruence,[status(thm)],[c3064]) ).
cnf(c3066,plain,
j(quotient(i(quotient(product(X,difference(i(X2),X2)),X2)),X2)) = j(quotient(i(difference(X2,difference(i(X2),product(X,X2)))),X2)),
inference(congruence,[status(thm)],[c3065]) ).
cnf(c3067,plain,
quotient(i(difference(X2,difference(i(X2),product(X,X2)))),X2) = difference(difference(i(X2),product(X,X2)),eta(X2)),
inference(substitution,[status(thm)],[c138]) ).
cnf(c3068,plain,
j(quotient(i(difference(X2,difference(i(X2),product(X,X2)))),X2)) = j(difference(difference(i(X2),product(X,X2)),eta(X2))),
inference(congruence,[status(thm)],[c3067]) ).
cnf(c3069,plain,
j(difference(difference(i(X2),product(X,X2)),eta(X2))) = difference(eta(X2),difference(i(X2),product(X,X2))),
inference(substitution,[status(thm)],[c1178]) ).
cnf(c3070,plain,
difference(i(difference(i(X2),X)),difference(difference(i(X2),X),eta(X2))) = eta(X2),
inference(substitution,[status(thm)],[c3034]) ).
cnf(c3071,plain,
eta(X2) = difference(i(difference(i(X2),X)),difference(difference(i(X2),X),eta(X2))),
inference(symmetry,[status(thm)],[c3070]) ).
cnf(c3072,plain,
difference(eta(X2),difference(i(X2),X)) = difference(difference(i(difference(i(X2),X)),difference(difference(i(X2),X),eta(X2))),difference(i(X2),X)),
inference(congruence,[status(thm)],[c3071]) ).
cnf(c3073,plain,
difference(difference(i(difference(i(X2),X)),difference(difference(i(X2),X),eta(X2))),difference(i(X2),X)) = quotient(eta(eta(X2)),difference(difference(i(X2),X),eta(X2))),
inference(substitution,[status(thm)],[c2853]) ).
cnf(c3074,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c3075,plain,
difference(difference(i(X2),X),eta(X2)) = difference(difference(i(X2),X),eta(i(X2))),
inference(congruence,[status(thm)],[c3074]) ).
cnf(c3076,plain,
difference(difference(i(X2),X),eta(i(X2))) = product(i(X),i(X2)),
inference(substitution,[status(thm)],[c459]) ).
cnf(c3077,plain,
difference(difference(i(X2),X),eta(X2)) = product(i(X),i(X2)),
inference(transitivity,[status(thm)],[c3075,c3076]) ).
cnf(c3078,plain,
quotient(eta(eta(X2)),difference(difference(i(X2),X),eta(X2))) = quotient(eta(eta(X2)),product(i(X),i(X2))),
inference(congruence,[status(thm)],[c3077]) ).
cnf(c3079,plain,
quotient(eta(eta(X2)),product(i(X),i(X2))) = quotient(one,product(i(X),i(X2))),
inference(congruence,[status(thm)],[c507]) ).
cnf(c3080,plain,
j(product(i(X),i(X2))) = quotient(one,product(i(X),i(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c3081,plain,
quotient(one,product(i(X),i(X2))) = j(product(i(X),i(X2))),
inference(symmetry,[status(thm)],[c3080]) ).
cnf(c3082,plain,
quotient(eta(eta(X2)),product(i(X),i(X2))) = j(product(i(X),i(X2))),
inference(transitivity,[status(thm)],[c3079,c3081]) ).
cnf(c3083,plain,
quotient(eta(eta(X2)),difference(difference(i(X2),X),eta(X2))) = j(product(i(X),i(X2))),
inference(transitivity,[status(thm)],[c3078,c3082]) ).
cnf(c3084,plain,
difference(difference(i(difference(i(X2),X)),difference(difference(i(X2),X),eta(X2))),difference(i(X2),X)) = j(product(i(X),i(X2))),
inference(transitivity,[status(thm)],[c3073,c3083]) ).
cnf(c3085,plain,
difference(eta(X2),difference(i(X2),X)) = j(product(i(X),i(X2))),
inference(transitivity,[status(thm)],[c3072,c3084]) ).
cnf(c3086,plain,
difference(eta(X2),difference(i(X2),product(X,X2))) = j(product(i(product(X,X2)),i(X2))),
inference(substitution,[status(thm)],[c3085]) ).
cnf(c3087,plain,
j(difference(difference(i(X2),product(X,X2)),eta(X2))) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c3069,c3086]) ).
cnf(c3088,plain,
j(quotient(i(difference(X2,difference(i(X2),product(X,X2)))),X2)) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c3068,c3087]) ).
cnf(c3089,plain,
j(quotient(i(quotient(product(X,difference(i(X2),X2)),X2)),X2)) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c3066,c3088]) ).
cnf(c3090,plain,
quotient(difference(j(X2),product(X,difference(i(X2),X2))),X2) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c3053,c3089]) ).
cnf(c3091,plain,
quotient(difference(difference(difference(i(X2),X2),X2),product(X,difference(i(X2),X2))),X2) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c3016,c3090]) ).
cnf(c3092,plain,
difference(X2,product(product(difference(i(X2),X2),X),quotient(difference(i(X2),X2),X2))) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c3011,c3091]) ).
cnf(c3093,plain,
difference(X2,product(product(difference(i(X2),X2),X),difference(product(X2,i(X2)),X2))) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c3004,c3092]) ).
cnf(c3094,plain,
difference(X2,product(product(difference(i(X2),X2),X),difference(one,X2))) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c3000,c3093]) ).
cnf(c3095,plain,
difference(X2,product(product(difference(i(X2),X2),X),X2)) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c2996,c3094]) ).
cnf(c3096,plain,
difference(X2,difference(i(X2),product(X2,product(X,X2)))) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c2993,c3095]) ).
cnf(c3097,plain,
difference(j(X2),product(X,X2)) = j(product(i(product(X,X2)),i(X2))),
inference(transitivity,[status(thm)],[c2975,c3096]) ).
cnf(c3098,plain,
difference(j(i(X2)),product(product(X2,X),i(X2))) = j(product(i(product(product(X2,X),i(X2))),i(i(X2)))),
inference(substitution,[status(thm)],[c3097]) ).
cnf(c3099,plain,
i(product(product(X2,X),i(X2))) = i(quotient(difference(i(X2),X),i(i(X2)))),
inference(congruence,[status(thm)],[c1366]) ).
cnf(c3100,plain,
product(i(product(product(X2,X),i(X2))),i(i(X2))) = product(i(quotient(difference(i(X2),X),i(i(X2)))),i(i(X2))),
inference(congruence,[status(thm)],[c3099]) ).
cnf(c3101,plain,
j(product(i(product(product(X2,X),i(X2))),i(i(X2)))) = j(product(i(quotient(difference(i(X2),X),i(i(X2)))),i(i(X2)))),
inference(congruence,[status(thm)],[c3100]) ).
cnf(c3102,plain,
difference(difference(X,quotient(X2,X)),eta(X)) = product(i(quotient(X2,X)),X),
inference(substitution,[status(thm)],[c459]) ).
cnf(c3103,plain,
product(i(quotient(X2,X)),X) = difference(difference(X,quotient(X2,X)),eta(X)),
inference(symmetry,[status(thm)],[c3102]) ).
cnf(c3104,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c3105,plain,
difference(difference(X,quotient(X2,X)),eta(X)) = difference(difference(X,quotient(X2,X)),eta(i(X))),
inference(congruence,[status(thm)],[c3104]) ).
cnf(c3106,plain,
product(i(X),product(X2,i(X))) = difference(X,quotient(X2,X)),
inference(substitution,[status(thm)],[c911]) ).
cnf(c3107,plain,
difference(X,quotient(X2,X)) = product(i(X),product(X2,i(X))),
inference(symmetry,[status(thm)],[c3106]) ).
cnf(c3108,plain,
difference(difference(X,quotient(X2,X)),eta(i(X))) = difference(product(i(X),product(X2,i(X))),eta(i(X))),
inference(congruence,[status(thm)],[c3107]) ).
cnf(c3109,plain,
difference(product(i(X),product(X2,i(X))),eta(i(X))) = quotient(i(product(X2,i(X))),i(X)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c3110,plain,
difference(difference(X,quotient(X2,X)),eta(i(X))) = quotient(i(product(X2,i(X))),i(X)),
inference(transitivity,[status(thm)],[c3108,c3109]) ).
cnf(c3111,plain,
difference(difference(X,quotient(X2,X)),eta(X)) = quotient(i(product(X2,i(X))),i(X)),
inference(transitivity,[status(thm)],[c3105,c3110]) ).
cnf(c3112,plain,
product(i(quotient(X2,X)),X) = quotient(i(product(X2,i(X))),i(X)),
inference(transitivity,[status(thm)],[c3103,c3111]) ).
cnf(c3113,plain,
product(i(quotient(difference(i(X2),X),i(i(X2)))),i(i(X2))) = quotient(i(product(difference(i(X2),X),i(i(i(X2))))),i(i(i(X2)))),
inference(substitution,[status(thm)],[c3112]) ).
cnf(c3114,plain,
j(product(i(quotient(difference(i(X2),X),i(i(X2)))),i(i(X2)))) = j(quotient(i(product(difference(i(X2),X),i(i(i(X2))))),i(i(i(X2))))),
inference(congruence,[status(thm)],[c3113]) ).
cnf(c3115,plain,
product(i(quotient(X2,i(X))),i(X)) = quotient(i(product(X2,i(i(X)))),i(i(X))),
inference(substitution,[status(thm)],[c3112]) ).
cnf(c3116,plain,
quotient(i(product(X2,i(i(X)))),i(i(X))) = product(i(quotient(X2,i(X))),i(X)),
inference(symmetry,[status(thm)],[c3115]) ).
cnf(c3117,plain,
j(quotient(i(product(X2,i(i(X)))),i(i(X)))) = j(product(i(quotient(X2,i(X))),i(X))),
inference(congruence,[status(thm)],[c3116]) ).
cnf(c3118,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c3119,plain,
quotient(eta(X2),X) = quotient(eta(i(X2)),X),
inference(congruence,[status(thm)],[c3118]) ).
cnf(c3120,plain,
difference(i(X2),quotient(eta(X2),X)) = difference(i(X2),quotient(eta(i(X2)),X)),
inference(congruence,[status(thm)],[c3119]) ).
cnf(c3121,plain,
difference(i(X2),quotient(eta(i(X2)),X)) = j(product(X,i(X2))),
inference(substitution,[status(thm)],[c1632]) ).
cnf(c3122,plain,
difference(i(X2),quotient(eta(X2),X)) = j(product(X,i(X2))),
inference(transitivity,[status(thm)],[c3120,c3121]) ).
cnf(c3123,plain,
difference(i(X),quotient(eta(X),i(quotient(X2,i(X))))) = j(product(i(quotient(X2,i(X))),i(X))),
inference(substitution,[status(thm)],[c3122]) ).
cnf(c3124,plain,
j(product(i(quotient(X2,i(X))),i(X))) = difference(i(X),quotient(eta(X),i(quotient(X2,i(X))))),
inference(symmetry,[status(thm)],[c3123]) ).
cnf(c3125,plain,
product(eta(X),quotient(X2,i(X))) = quotient(eta(X),i(quotient(X2,i(X)))),
inference(substitution,[status(thm)],[c1387]) ).
cnf(c3126,plain,
quotient(eta(X),i(quotient(X2,i(X)))) = product(eta(X),quotient(X2,i(X))),
inference(symmetry,[status(thm)],[c3125]) ).
cnf(c3127,plain,
difference(i(X),quotient(eta(X),i(quotient(X2,i(X))))) = difference(i(X),product(eta(X),quotient(X2,i(X)))),
inference(congruence,[status(thm)],[c3126]) ).
cnf(c3128,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c3129,plain,
product(eta(X),quotient(X2,i(X))) = product(product(i(X),X),quotient(X2,i(X))),
inference(congruence,[status(thm)],[c3128]) ).
cnf(c3130,plain,
difference(i(X),product(eta(X),quotient(X2,i(X)))) = difference(i(X),product(product(i(X),X),quotient(X2,i(X)))),
inference(congruence,[status(thm)],[c3129]) ).
cnf(c3131,plain,
difference(i(X),product(product(i(X),X),quotient(X2,i(X)))) = quotient(product(X,X2),i(X)),
inference(substitution,[status(thm)],[c445]) ).
cnf(c3132,plain,
difference(i(X),product(eta(X),quotient(X2,i(X)))) = quotient(product(X,X2),i(X)),
inference(transitivity,[status(thm)],[c3130,c3131]) ).
cnf(c3133,plain,
difference(i(X),quotient(eta(X),i(quotient(X2,i(X))))) = quotient(product(X,X2),i(X)),
inference(transitivity,[status(thm)],[c3127,c3132]) ).
cnf(c3134,plain,
j(product(i(quotient(X2,i(X))),i(X))) = quotient(product(X,X2),i(X)),
inference(transitivity,[status(thm)],[c3124,c3133]) ).
cnf(c3135,plain,
j(quotient(i(product(X2,i(i(X)))),i(i(X)))) = quotient(product(X,X2),i(X)),
inference(transitivity,[status(thm)],[c3117,c3134]) ).
cnf(c3136,plain,
j(quotient(i(product(difference(i(X2),X),i(i(i(X2))))),i(i(i(X2))))) = quotient(product(i(X2),difference(i(X2),X)),i(i(X2))),
inference(substitution,[status(thm)],[c3135]) ).
cnf(c3137,plain,
product(i(X2),difference(i(X2),X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c3138,plain,
quotient(product(i(X2),difference(i(X2),X)),i(i(X2))) = quotient(X,i(i(X2))),
inference(congruence,[status(thm)],[c3137]) ).
cnf(c3139,plain,
j(quotient(i(product(difference(i(X2),X),i(i(i(X2))))),i(i(i(X2))))) = quotient(X,i(i(X2))),
inference(transitivity,[status(thm)],[c3136,c3138]) ).
cnf(c3140,plain,
j(product(i(quotient(difference(i(X2),X),i(i(X2)))),i(i(X2)))) = quotient(X,i(i(X2))),
inference(transitivity,[status(thm)],[c3114,c3139]) ).
cnf(c3141,plain,
j(product(i(product(product(X2,X),i(X2))),i(i(X2)))) = quotient(X,i(i(X2))),
inference(transitivity,[status(thm)],[c3101,c3140]) ).
cnf(c3142,plain,
difference(j(i(X2)),product(product(X2,X),i(X2))) = quotient(X,i(i(X2))),
inference(transitivity,[status(thm)],[c3098,c3141]) ).
cnf(c3143,plain,
difference(j(i(X2)),quotient(difference(i(X2),X),i(i(X2)))) = quotient(X,i(i(X2))),
inference(transitivity,[status(thm)],[c2287,c3142]) ).
cnf(c3144,plain,
quotient(product(X,eta(i(X2))),j(i(X2))) = quotient(X,i(i(X2))),
inference(transitivity,[status(thm)],[c2285,c3143]) ).
cnf(c3145,plain,
quotient(quotient(X,i(eta(i(X2)))),j(i(X2))) = quotient(X,i(i(X2))),
inference(transitivity,[status(thm)],[c2283,c3144]) ).
cnf(c3146,plain,
i(product(j(i(X2)),j(X))) = quotient(X,i(i(X2))),
inference(transitivity,[status(thm)],[c2280,c3145]) ).
cnf(c3147,plain,
i(product(X2,j(X))) = quotient(X,i(i(X2))),
inference(transitivity,[status(thm)],[c100,c3146]) ).
cnf(c3148,plain,
i(product(X2,j(i(X)))) = quotient(i(X),i(i(X2))),
inference(substitution,[status(thm)],[c3147]) ).
cnf(c3149,plain,
i(product(X2,X)) = quotient(i(X),i(i(X2))),
inference(transitivity,[status(thm)],[c97,c3148]) ).
cnf(c3150,plain,
i(product(x0,x1)) = quotient(i(x1),i(i(x0))),
inference(substitution,[status(thm)],[c3149]) ).
cnf(c3151,plain,
quotient(i(x1),i(i(x0))) = i(product(x0,x1)),
inference(symmetry,[status(thm)],[c3150]) ).
cnf(c3152,plain,
quotient(eta(x0),quotient(i(x1),i(i(x0)))) = quotient(eta(x0),i(product(x0,x1))),
inference(congruence,[status(thm)],[c3151]) ).
cnf(c3153,plain,
product(eta(x0),product(x0,x1)) = quotient(eta(x0),i(product(x0,x1))),
inference(substitution,[status(thm)],[c1387]) ).
cnf(c3154,plain,
quotient(eta(x0),i(product(x0,x1))) = product(eta(x0),product(x0,x1)),
inference(symmetry,[status(thm)],[c3153]) ).
cnf(c3155,plain,
quotient(eta(x0),quotient(i(x1),i(i(x0)))) = product(eta(x0),product(x0,x1)),
inference(transitivity,[status(thm)],[c3152,c3154]) ).
cnf(c3156,plain,
product(i(i(x0)),j(i(x1))) = product(eta(x0),product(x0,x1)),
inference(transitivity,[status(thm)],[c94,c3155]) ).
cnf(c3157,plain,
product(i(i(x0)),x1) = product(eta(x0),product(x0,x1)),
inference(transitivity,[status(thm)],[c18,c3156]) ).
cnf(c3158,plain,
$false,
inference(resolution,[status(thm)],[c1,c3157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP765-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.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 10:42:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 194.98/25.06 Command-line arguments: --no-flatten-goal
% 194.98/25.06
% 194.98/25.06 % SZS status Unsatisfiable
% 194.98/25.06
% 196.57/25.29 % SZS output start CNFRefutation
% See solution above
% 213.98/27.47
% 213.98/27.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------