%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP766-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:11:57 AM UTC 2026
% Result : Unsatisfiable 125.69s 16.33s
% Output : CNFRefutation 129.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 19
% Syntax : Number of clauses : 572 ( 572 unt; 0 nHn; 4 RR)
% Number of literals : 572 ( 571 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 1038 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
difference(A,product(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(c3,plain,
difference(X,product(X,quotient(product(eta(X3),product(X2,X)),X))) = quotient(product(eta(X3),product(X2,X)),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
quotient(product(eta(X3),product(X2,X)),X) = difference(X,product(X,quotient(product(eta(X3),product(X2,X)),X))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
difference(A2,product(product(A2,B2),C)) = quotient(product(B2,product(C,A2)),A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
cnf(c6,plain,
difference(X2,product(product(X2,X),X3)) = quotient(product(X,product(X3,X2)),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
quotient(product(X,product(X3,X2)),X2) = difference(X2,product(product(X2,X),X3)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
product(quotient(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(c9,plain,
product(quotient(difference(X3,product(product(X3,X2),X)),X),X) = difference(X3,product(product(X3,X2),X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
difference(X3,product(product(X3,X2),X)) = product(quotient(difference(X3,product(product(X3,X2),X)),X),X),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
difference(X3,product(product(X3,X2),X)) = quotient(product(X2,product(X,X3)),X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c12,plain,
quotient(difference(X3,product(product(X3,X2),X)),X) = quotient(quotient(product(X2,product(X,X3)),X3),X),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,axiom,
difference(product(A2,B2),product(A2,product(B2,C2))) = quotient(quotient(product(C2,product(A2,B2)),B2),A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
cnf(c14,plain,
difference(product(X,X3),product(X,product(X3,X2))) = quotient(quotient(product(X2,product(X,X3)),X3),X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
quotient(quotient(product(X2,product(X,X3)),X3),X) = difference(product(X,X3),product(X,product(X3,X2))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,axiom,
l(A2,B2,C2) = difference(product(A2,B2),product(A2,product(B2,C2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
cnf(c17,plain,
l(X,X3,X2) = difference(product(X,X3),product(X,product(X3,X2))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
difference(product(X,X3),product(X,product(X3,X2))) = l(X,X3,X2),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
quotient(quotient(product(X2,product(X,X3)),X3),X) = l(X,X3,X2),
inference(transitivity,[status(thm)],[c15,c18]) ).
cnf(c20,plain,
quotient(difference(X3,product(product(X3,X2),X)),X) = l(X,X3,X2),
inference(transitivity,[status(thm)],[c12,c19]) ).
cnf(c21,plain,
product(quotient(difference(X3,product(product(X3,X2),X)),X),X) = product(l(X,X3,X2),X),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
difference(X3,product(product(X3,X2),X)) = product(l(X,X3,X2),X),
inference(transitivity,[status(thm)],[c10,c21]) ).
cnf(c23,plain,
difference(X2,product(product(X2,X),X3)) = product(l(X3,X2,X),X3),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
quotient(product(X,product(X3,X2)),X2) = product(l(X3,X2,X),X3),
inference(transitivity,[status(thm)],[c7,c23]) ).
cnf(c25,plain,
quotient(product(X2,product(X,X3)),X3) = product(l(X,X3,X2),X),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
product(X3,quotient(product(X2,product(X,X3)),X3)) = product(X3,product(l(X,X3,X2),X)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
difference(X3,product(product(X3,X),X2)) = product(l(X2,X3,X),X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c28,plain,
product(l(X2,X3,X),X2) = difference(X3,product(product(X3,X),X2)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
product(X3,product(l(X2,X3,X),X2)) = product(X3,difference(X3,product(product(X3,X),X2))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,axiom,
product(A2,difference(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(c31,plain,
product(X3,difference(X3,product(product(X3,X),X2))) = product(product(X3,X),X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
product(X3,product(l(X2,X3,X),X2)) = product(product(X3,X),X2),
inference(transitivity,[status(thm)],[c29,c31]) ).
cnf(c33,plain,
product(X3,product(l(X,X3,X2),X)) = product(product(X3,X2),X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
product(X3,quotient(product(X2,product(X,X3)),X3)) = product(product(X3,X2),X),
inference(transitivity,[status(thm)],[c26,c33]) ).
cnf(c35,plain,
product(X3,quotient(product(eta(X2),product(X,X3)),X3)) = product(product(X3,eta(X2)),X),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,axiom,
product(one,A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
cnf(c37,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
X = product(one,X),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
difference(one,X) = difference(one,product(one,X)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
difference(one,product(one,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c41,plain,
difference(one,X) = X,
inference(transitivity,[status(thm)],[c39,c40]) ).
cnf(c42,plain,
difference(one,t(eta(X),X2)) = t(eta(X),X2),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
t(eta(X),X2) = difference(one,t(eta(X),X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
quotient(quotient(X2,eta(X)),t(eta(X),X2)) = quotient(quotient(X2,eta(X)),difference(one,t(eta(X),X2))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
difference(X,product(X,eta(eta(X)))) = eta(eta(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c46,plain,
eta(eta(X)) = difference(X,product(X,eta(eta(X)))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,axiom,
eta(A2) = product(i(A2),A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
cnf(c48,plain,
eta(eta(X)) = product(i(eta(X)),eta(X)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
product(X,eta(eta(X))) = product(X,product(i(eta(X)),eta(X))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,axiom,
product(A2,product(B2,eta(A2))) = product(product(A2,B2),eta(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos17) ).
cnf(c51,plain,
product(X,product(i(eta(X)),eta(X))) = product(product(X,i(eta(X))),eta(X)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,axiom,
i(A2) = difference(A2,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
cnf(c53,plain,
i(j(X)) = difference(j(X),one),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,axiom,
j(A2) = quotient(one,A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
cnf(c55,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
product(j(X),X) = product(quotient(one,X),X),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
product(quotient(one,X),X) = one,
inference(substitution,[status(thm)],[c8]) ).
cnf(c58,plain,
product(j(X),X) = one,
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
one = product(j(X),X),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
difference(j(X),one) = difference(j(X),product(j(X),X)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
difference(j(X),product(j(X),X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c62,plain,
difference(j(X),one) = X,
inference(transitivity,[status(thm)],[c60,c61]) ).
cnf(c63,plain,
i(j(X)) = X,
inference(transitivity,[status(thm)],[c53,c62]) ).
cnf(c64,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
product(X,i(eta(X))) = product(i(j(X)),i(eta(X))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
i(j(j(X))) = j(X),
inference(substitution,[status(thm)],[c63]) ).
cnf(c67,plain,
j(X) = i(j(j(X))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
i(j(X)) = i(i(j(j(X)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
product(i(j(X)),i(eta(X))) = product(i(i(j(j(X)))),i(eta(X))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,axiom,
product(i(i(A2)),B2) = product(eta(A2),product(A2,B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
cnf(c71,plain,
product(i(i(j(j(X)))),i(eta(X))) = product(eta(j(j(X))),product(j(j(X)),i(eta(X)))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,axiom,
product(A2,product(eta(A2),B2)) = product(j(j(A2)),B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
cnf(c73,plain,
product(X,product(eta(X),i(eta(X)))) = product(j(j(X)),i(eta(X))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
product(j(j(X)),i(eta(X))) = product(X,product(eta(X),i(eta(X)))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
i(X) = difference(X,one),
inference(substitution,[status(thm)],[c52]) ).
cnf(c76,plain,
product(X,i(X)) = product(X,difference(X,one)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
product(X,difference(X,one)) = one,
inference(substitution,[status(thm)],[c30]) ).
cnf(c78,plain,
product(X,i(X)) = one,
inference(transitivity,[status(thm)],[c76,c77]) ).
cnf(c79,plain,
product(eta(X),i(eta(X))) = one,
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
product(X,product(eta(X),i(eta(X)))) = product(X,one),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,axiom,
product(A2,one) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
cnf(c82,plain,
product(X,one) = X,
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,plain,
product(X,product(eta(X),i(eta(X)))) = X,
inference(transitivity,[status(thm)],[c80,c82]) ).
cnf(c84,plain,
product(j(j(X)),i(eta(X))) = X,
inference(transitivity,[status(thm)],[c74,c83]) ).
cnf(c85,plain,
product(eta(j(j(X))),product(j(j(X)),i(eta(X)))) = product(eta(j(j(X))),X),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
eta(j(X)) = product(i(j(X)),j(X)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c87,plain,
product(i(j(X)),j(X)) = product(X,j(X)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c88,axiom,
product(i(A2),A2) = product(A2,j(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
cnf(c89,plain,
product(i(X),X) = product(X,j(X)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
product(X,j(X)) = product(i(X),X),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c47]) ).
cnf(c92,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
product(X,j(X)) = eta(X),
inference(transitivity,[status(thm)],[c90,c92]) ).
cnf(c94,plain,
product(i(j(X)),j(X)) = eta(X),
inference(transitivity,[status(thm)],[c87,c93]) ).
cnf(c95,plain,
eta(j(X)) = eta(X),
inference(transitivity,[status(thm)],[c86,c94]) ).
cnf(c96,plain,
eta(j(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
product(eta(j(j(X))),X) = product(eta(j(X)),X),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
product(eta(j(X)),X) = product(eta(X),X),
inference(congruence,[status(thm)],[c95]) ).
cnf(c99,plain,
product(X,one) = X,
inference(substitution,[status(thm)],[c81]) ).
cnf(c100,plain,
X = product(X,one),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
product(eta(X),X) = product(eta(X),product(X,one)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
product(i(i(X)),one) = product(eta(X),product(X,one)),
inference(substitution,[status(thm)],[c70]) ).
cnf(c103,plain,
product(eta(X),product(X,one)) = product(i(i(X)),one),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
product(i(i(X)),one) = i(i(X)),
inference(substitution,[status(thm)],[c81]) ).
cnf(c105,plain,
product(eta(X),product(X,one)) = i(i(X)),
inference(transitivity,[status(thm)],[c103,c104]) ).
cnf(c106,plain,
product(eta(X),X) = i(i(X)),
inference(transitivity,[status(thm)],[c101,c105]) ).
cnf(c107,plain,
product(eta(j(X)),X) = i(i(X)),
inference(transitivity,[status(thm)],[c98,c106]) ).
cnf(c108,plain,
product(eta(j(j(X))),X) = i(i(X)),
inference(transitivity,[status(thm)],[c97,c107]) ).
cnf(c109,plain,
product(eta(j(j(X))),product(j(j(X)),i(eta(X)))) = i(i(X)),
inference(transitivity,[status(thm)],[c85,c108]) ).
cnf(c110,plain,
product(i(i(j(j(X)))),i(eta(X))) = i(i(X)),
inference(transitivity,[status(thm)],[c71,c109]) ).
cnf(c111,plain,
product(i(j(X)),i(eta(X))) = i(i(X)),
inference(transitivity,[status(thm)],[c69,c110]) ).
cnf(c112,plain,
product(X,i(eta(X))) = i(i(X)),
inference(transitivity,[status(thm)],[c65,c111]) ).
cnf(c113,plain,
product(product(X,i(eta(X))),eta(X)) = product(i(i(X)),eta(X)),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
product(i(i(X)),eta(X)) = product(eta(X),product(X,eta(X))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c115,plain,
product(eta(X),one) = eta(X),
inference(substitution,[status(thm)],[c81]) ).
cnf(c116,plain,
eta(X) = product(eta(X),one),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
product(X,eta(X)) = product(X,product(eta(X),one)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
product(X,product(eta(X),one)) = product(j(j(X)),one),
inference(substitution,[status(thm)],[c72]) ).
cnf(c119,plain,
product(j(j(X)),one) = j(j(X)),
inference(substitution,[status(thm)],[c81]) ).
cnf(c120,plain,
product(X,product(eta(X),one)) = j(j(X)),
inference(transitivity,[status(thm)],[c118,c119]) ).
cnf(c121,plain,
product(X,eta(X)) = j(j(X)),
inference(transitivity,[status(thm)],[c117,c120]) ).
cnf(c122,plain,
product(eta(X),product(X,eta(X))) = product(eta(X),j(j(X))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
j(j(X)) = product(X,eta(X)),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c124,plain,
product(eta(X),j(j(X))) = product(eta(X),product(X,eta(X))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
eta(i(X)) = product(i(i(X)),i(X)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c126,plain,
product(i(i(X)),i(X)) = product(eta(X),product(X,i(X))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c127,plain,
product(eta(X),product(X,i(X))) = product(eta(X),one),
inference(congruence,[status(thm)],[c78]) ).
cnf(c128,plain,
product(eta(X),one) = eta(X),
inference(substitution,[status(thm)],[c81]) ).
cnf(c129,plain,
product(eta(X),product(X,i(X))) = eta(X),
inference(transitivity,[status(thm)],[c127,c128]) ).
cnf(c130,plain,
product(i(i(X)),i(X)) = eta(X),
inference(transitivity,[status(thm)],[c126,c129]) ).
cnf(c131,plain,
eta(i(X)) = eta(X),
inference(transitivity,[status(thm)],[c125,c130]) ).
cnf(c132,plain,
eta(X) = eta(i(X)),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
product(X,eta(X)) = product(X,eta(i(X))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
product(eta(X),product(X,eta(X))) = product(eta(X),product(X,eta(i(X)))),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
eta(i(i(X))) = eta(i(X)),
inference(substitution,[status(thm)],[c131]) ).
cnf(c136,plain,
eta(i(X)) = eta(i(i(X))),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
product(X,eta(i(X))) = product(X,eta(i(i(X)))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
product(eta(X),product(X,eta(i(X)))) = product(eta(X),product(X,eta(i(i(X))))),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
product(i(i(X)),eta(i(i(X)))) = product(eta(X),product(X,eta(i(i(X))))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c140,plain,
product(eta(X),product(X,eta(i(i(X))))) = product(i(i(X)),eta(i(i(X)))),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
product(i(i(X)),eta(i(i(X)))) = j(j(i(i(X)))),
inference(substitution,[status(thm)],[c121]) ).
cnf(c142,plain,
j(i(X)) = quotient(one,i(X)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c143,plain,
one = product(X,i(X)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c144,plain,
quotient(one,i(X)) = quotient(product(X,i(X)),i(X)),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,axiom,
quotient(product(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(c146,plain,
quotient(product(X,i(X)),i(X)) = X,
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
quotient(one,i(X)) = X,
inference(transitivity,[status(thm)],[c144,c146]) ).
cnf(c148,plain,
j(i(X)) = X,
inference(transitivity,[status(thm)],[c142,c147]) ).
cnf(c149,plain,
j(i(i(X))) = i(X),
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
j(j(i(i(X)))) = j(i(X)),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
j(j(i(i(X)))) = X,
inference(transitivity,[status(thm)],[c150,c148]) ).
cnf(c152,plain,
product(i(i(X)),eta(i(i(X)))) = X,
inference(transitivity,[status(thm)],[c141,c151]) ).
cnf(c153,plain,
product(eta(X),product(X,eta(i(i(X))))) = X,
inference(transitivity,[status(thm)],[c140,c152]) ).
cnf(c154,plain,
product(eta(X),product(X,eta(i(X)))) = X,
inference(transitivity,[status(thm)],[c138,c153]) ).
cnf(c155,plain,
product(eta(X),product(X,eta(X))) = X,
inference(transitivity,[status(thm)],[c134,c154]) ).
cnf(c156,plain,
product(eta(X),j(j(X))) = X,
inference(transitivity,[status(thm)],[c124,c155]) ).
cnf(c157,plain,
product(eta(X),product(X,eta(X))) = X,
inference(transitivity,[status(thm)],[c122,c156]) ).
cnf(c158,plain,
product(i(i(X)),eta(X)) = X,
inference(transitivity,[status(thm)],[c114,c157]) ).
cnf(c159,plain,
product(product(X,i(eta(X))),eta(X)) = X,
inference(transitivity,[status(thm)],[c113,c158]) ).
cnf(c160,plain,
product(X,product(i(eta(X)),eta(X))) = X,
inference(transitivity,[status(thm)],[c51,c159]) ).
cnf(c161,plain,
product(X,eta(eta(X))) = X,
inference(transitivity,[status(thm)],[c49,c160]) ).
cnf(c162,plain,
difference(X,product(X,eta(eta(X)))) = difference(X,X),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
product(X,one) = X,
inference(substitution,[status(thm)],[c81]) ).
cnf(c164,plain,
X = product(X,one),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
difference(X,X) = difference(X,product(X,one)),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
difference(X,product(X,one)) = one,
inference(substitution,[status(thm)],[c2]) ).
cnf(c167,plain,
difference(X,X) = one,
inference(transitivity,[status(thm)],[c165,c166]) ).
cnf(c168,plain,
difference(X,product(X,eta(eta(X)))) = one,
inference(transitivity,[status(thm)],[c162,c167]) ).
cnf(c169,plain,
eta(eta(X)) = one,
inference(transitivity,[status(thm)],[c46,c168]) ).
cnf(c170,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
difference(one,t(eta(X),X2)) = difference(eta(eta(X)),t(eta(X),X2)),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
quotient(quotient(X2,eta(X)),difference(one,t(eta(X),X2))) = quotient(quotient(X2,eta(X)),difference(eta(eta(X)),t(eta(X),X2))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
eta(j(eta(X))) = eta(eta(X)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c174,plain,
eta(eta(X)) = eta(j(eta(X))),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
difference(eta(eta(X)),t(eta(X),X2)) = difference(eta(j(eta(X))),t(eta(X),X2)),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
quotient(quotient(X2,eta(X)),difference(eta(eta(X)),t(eta(X),X2))) = quotient(quotient(X2,eta(X)),difference(eta(j(eta(X))),t(eta(X),X2))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,axiom,
t(A2,B2) = quotient(product(A2,B2),A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos18) ).
cnf(c178,plain,
t(X2,difference(X2,X)) = quotient(product(X2,difference(X2,X)),X2),
inference(substitution,[status(thm)],[c177]) ).
cnf(c179,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c180,plain,
quotient(product(X2,difference(X2,X)),X2) = quotient(X,X2),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
t(X2,difference(X2,X)) = quotient(X,X2),
inference(transitivity,[status(thm)],[c178,c180]) ).
cnf(c182,plain,
t(eta(X),difference(eta(X),X2)) = quotient(X2,eta(X)),
inference(substitution,[status(thm)],[c181]) ).
cnf(c183,plain,
quotient(X2,eta(X)) = t(eta(X),difference(eta(X),X2)),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
quotient(quotient(X2,eta(X)),difference(eta(j(eta(X))),t(eta(X),X2))) = quotient(t(eta(X),difference(eta(X),X2)),difference(eta(j(eta(X))),t(eta(X),X2))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
difference(one,product(j(eta(X2)),X)) = product(j(eta(X2)),X),
inference(substitution,[status(thm)],[c41]) ).
cnf(c186,plain,
product(j(eta(X2)),X) = difference(one,product(j(eta(X2)),X)),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
product(j(eta(X)),eta(X)) = one,
inference(substitution,[status(thm)],[c58]) ).
cnf(c188,plain,
one = product(j(eta(X)),eta(X)),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
difference(one,product(j(eta(X2)),X)) = difference(product(j(eta(X2)),eta(X2)),product(j(eta(X2)),X)),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c191,plain,
X = product(X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
product(X3,X) = product(X3,product(X2,difference(X2,X))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
difference(product(X3,X2),product(X3,X)) = difference(product(X3,X2),product(X3,product(X2,difference(X2,X)))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
l(X3,X2,difference(X2,X)) = difference(product(X3,X2),product(X3,product(X2,difference(X2,X)))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c195,plain,
difference(product(X3,X2),product(X3,product(X2,difference(X2,X)))) = l(X3,X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
difference(product(X3,X2),product(X3,X)) = l(X3,X2,difference(X2,X)),
inference(transitivity,[status(thm)],[c193,c195]) ).
cnf(c197,plain,
difference(product(j(eta(X2)),eta(X2)),product(j(eta(X2)),X)) = l(j(eta(X2)),eta(X2),difference(eta(X2),X)),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
difference(X2,product(product(X2,X),j(X2))) = quotient(product(X,product(j(X2),X2)),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c199,plain,
product(X,product(j(X2),X2)) = product(X,one),
inference(congruence,[status(thm)],[c58]) ).
cnf(c200,plain,
quotient(product(X,product(j(X2),X2)),X2) = quotient(product(X,one),X2),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
product(X,one) = X,
inference(substitution,[status(thm)],[c81]) ).
cnf(c202,plain,
quotient(product(X,one),X2) = quotient(X,X2),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
quotient(product(X,product(j(X2),X2)),X2) = quotient(X,X2),
inference(transitivity,[status(thm)],[c200,c202]) ).
cnf(c204,plain,
difference(X2,product(product(X2,X),j(X2))) = quotient(X,X2),
inference(transitivity,[status(thm)],[c198,c203]) ).
cnf(c205,plain,
difference(X,product(product(X,X2),j(X))) = quotient(X2,X),
inference(substitution,[status(thm)],[c204]) ).
cnf(c206,plain,
quotient(X2,X) = difference(X,product(product(X,X2),j(X))),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
quotient(quotient(X2,X),j(X)) = quotient(difference(X,product(product(X,X2),j(X))),j(X)),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c209,plain,
X = product(X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c208]) ).
cnf(c210,plain,
product(X,X3) = product(product(X2,difference(X2,X)),X3),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
difference(X2,product(X,X3)) = difference(X2,product(product(X2,difference(X2,X)),X3)),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
quotient(difference(X2,product(X,X3)),X3) = quotient(difference(X2,product(product(X2,difference(X2,X)),X3)),X3),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
quotient(difference(X2,product(product(X2,difference(X2,X)),X3)),X3) = l(X3,X2,difference(X2,X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c214,plain,
quotient(difference(X2,product(X,X3)),X3) = l(X3,X2,difference(X2,X)),
inference(transitivity,[status(thm)],[c212,c213]) ).
cnf(c215,plain,
quotient(difference(X,product(product(X,X2),j(X))),j(X)) = l(j(X),X,difference(X,product(X,X2))),
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
difference(product(j(X2),X2),product(j(X2),X)) = l(j(X2),X2,difference(X2,X)),
inference(substitution,[status(thm)],[c196]) ).
cnf(c217,plain,
l(j(X2),X2,difference(X2,X)) = difference(product(j(X2),X2),product(j(X2),X)),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
difference(product(j(X2),X2),product(j(X2),X)) = difference(one,product(j(X2),X)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c219,plain,
difference(one,product(j(X2),X)) = product(j(X2),X),
inference(substitution,[status(thm)],[c41]) ).
cnf(c220,plain,
difference(product(j(X2),X2),product(j(X2),X)) = product(j(X2),X),
inference(transitivity,[status(thm)],[c218,c219]) ).
cnf(c221,plain,
l(j(X2),X2,difference(X2,X)) = product(j(X2),X),
inference(transitivity,[status(thm)],[c217,c220]) ).
cnf(c222,plain,
l(j(X),X,difference(X,product(X,X2))) = product(j(X),product(X,X2)),
inference(substitution,[status(thm)],[c221]) ).
cnf(c223,plain,
difference(one,product(j(X2),product(X2,X))) = product(j(X2),product(X2,X)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c224,plain,
product(j(X2),product(X2,X)) = difference(one,product(j(X2),product(X2,X))),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
one = product(j(X),X),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c226,plain,
difference(one,product(j(X2),product(X2,X))) = difference(product(j(X2),X2),product(j(X2),product(X2,X))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
l(j(X2),X2,X) = difference(product(j(X2),X2),product(j(X2),product(X2,X))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c228,plain,
difference(product(j(X2),X2),product(j(X2),product(X2,X))) = l(j(X2),X2,X),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
difference(one,product(j(X2),product(X2,X))) = l(j(X2),X2,X),
inference(transitivity,[status(thm)],[c226,c228]) ).
cnf(c230,plain,
product(j(X2),product(X2,X)) = l(j(X2),X2,X),
inference(transitivity,[status(thm)],[c224,c229]) ).
cnf(c231,plain,
product(j(X),product(X,X2)) = l(j(X),X,X2),
inference(substitution,[status(thm)],[c230]) ).
cnf(c232,plain,
l(j(X),X,difference(X,product(X,X2))) = l(j(X),X,X2),
inference(transitivity,[status(thm)],[c222,c231]) ).
cnf(c233,plain,
quotient(difference(X,product(product(X,X2),j(X))),j(X)) = l(j(X),X,X2),
inference(transitivity,[status(thm)],[c215,c232]) ).
cnf(c234,plain,
quotient(quotient(X2,X),j(X)) = l(j(X),X,X2),
inference(transitivity,[status(thm)],[c207,c233]) ).
cnf(c235,plain,
quotient(quotient(X,eta(X2)),j(eta(X2))) = l(j(eta(X2)),eta(X2),X),
inference(substitution,[status(thm)],[c234]) ).
cnf(c236,plain,
l(j(eta(X2)),eta(X2),X) = quotient(quotient(X,eta(X2)),j(eta(X2))),
inference(symmetry,[status(thm)],[c235]) ).
cnf(c237,plain,
product(quotient(product(X2,j(eta(X))),eta(X)),eta(X)) = product(X2,j(eta(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c238,plain,
product(X2,j(eta(X))) = product(quotient(product(X2,j(eta(X))),eta(X)),eta(X)),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
t(eta(X2),difference(eta(X2),X)) = quotient(X,eta(X2)),
inference(substitution,[status(thm)],[c181]) ).
cnf(c240,plain,
quotient(X,eta(X2)) = t(eta(X2),difference(eta(X2),X)),
inference(symmetry,[status(thm)],[c239]) ).
cnf(c241,plain,
product(eta(X2),quotient(X,eta(X2))) = product(eta(X2),t(eta(X2),difference(eta(X2),X))),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
t(X,X) = quotient(product(X,X),X),
inference(substitution,[status(thm)],[c177]) ).
cnf(c243,plain,
quotient(product(X,X),X) = X,
inference(substitution,[status(thm)],[c145]) ).
cnf(c244,plain,
t(X,X) = X,
inference(transitivity,[status(thm)],[c242,c243]) ).
cnf(c245,plain,
t(eta(X),eta(X)) = eta(X),
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
eta(X) = t(eta(X),eta(X)),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
product(eta(X2),t(eta(X2),X)) = product(t(eta(X2),eta(X2)),t(eta(X2),X)),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,axiom,
t(eta(A2),product(B2,C2)) = product(t(eta(A2),B2),t(eta(A2),C2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos19) ).
cnf(c249,plain,
t(eta(X2),product(eta(X2),X)) = product(t(eta(X2),eta(X2)),t(eta(X2),X)),
inference(substitution,[status(thm)],[c248]) ).
cnf(c250,plain,
product(t(eta(X2),eta(X2)),t(eta(X2),X)) = t(eta(X2),product(eta(X2),X)),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
product(eta(X2),t(eta(X2),X)) = t(eta(X2),product(eta(X2),X)),
inference(transitivity,[status(thm)],[c247,c250]) ).
cnf(c252,plain,
product(eta(X2),t(eta(X2),difference(eta(X2),X))) = t(eta(X2),product(eta(X2),difference(eta(X2),X))),
inference(substitution,[status(thm)],[c251]) ).
cnf(c253,plain,
product(eta(X2),difference(eta(X2),X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c254,plain,
t(eta(X2),product(eta(X2),difference(eta(X2),X))) = t(eta(X2),X),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
product(eta(X2),t(eta(X2),difference(eta(X2),X))) = t(eta(X2),X),
inference(transitivity,[status(thm)],[c252,c254]) ).
cnf(c256,plain,
product(eta(X2),quotient(X,eta(X2))) = t(eta(X2),X),
inference(transitivity,[status(thm)],[c241,c255]) ).
cnf(c257,plain,
t(eta(X2),X) = product(eta(X2),quotient(X,eta(X2))),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
difference(eta(X2),t(eta(X2),X)) = difference(eta(X2),product(eta(X2),quotient(X,eta(X2)))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
difference(eta(X2),product(eta(X2),quotient(X,eta(X2)))) = quotient(X,eta(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c260,plain,
difference(eta(X2),t(eta(X2),X)) = quotient(X,eta(X2)),
inference(transitivity,[status(thm)],[c258,c259]) ).
cnf(c261,plain,
difference(eta(X),t(eta(X),product(X2,j(eta(X))))) = quotient(product(X2,j(eta(X))),eta(X)),
inference(substitution,[status(thm)],[c260]) ).
cnf(c262,plain,
quotient(product(X2,j(eta(X))),eta(X)) = difference(eta(X),t(eta(X),product(X2,j(eta(X))))),
inference(symmetry,[status(thm)],[c261]) ).
cnf(c263,plain,
i(eta(X)) = difference(eta(X),one),
inference(substitution,[status(thm)],[c52]) ).
cnf(c264,plain,
one = eta(eta(X)),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c265,plain,
difference(eta(X),one) = difference(eta(X),eta(eta(X))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
eta(X) = product(X,j(X)),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c267,plain,
difference(X,eta(X)) = difference(X,product(X,j(X))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
difference(X,product(X,j(X))) = j(X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c269,plain,
difference(X,eta(X)) = j(X),
inference(transitivity,[status(thm)],[c267,c268]) ).
cnf(c270,plain,
difference(eta(X),eta(eta(X))) = j(eta(X)),
inference(substitution,[status(thm)],[c269]) ).
cnf(c271,plain,
difference(eta(X),one) = j(eta(X)),
inference(transitivity,[status(thm)],[c265,c270]) ).
cnf(c272,plain,
i(eta(X)) = j(eta(X)),
inference(transitivity,[status(thm)],[c263,c271]) ).
cnf(c273,plain,
j(eta(X)) = i(eta(X)),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c274,plain,
product(t(eta(X2),X),j(eta(X2))) = product(t(eta(X2),X),i(eta(X2))),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
t(X,j(X)) = quotient(product(X,j(X)),X),
inference(substitution,[status(thm)],[c177]) ).
cnf(c276,plain,
quotient(product(X,j(X)),X) = quotient(eta(X),X),
inference(congruence,[status(thm)],[c93]) ).
cnf(c277,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c47]) ).
cnf(c278,plain,
quotient(eta(X),X) = quotient(product(i(X),X),X),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
quotient(product(i(X),X),X) = i(X),
inference(substitution,[status(thm)],[c145]) ).
cnf(c280,plain,
quotient(eta(X),X) = i(X),
inference(transitivity,[status(thm)],[c278,c279]) ).
cnf(c281,plain,
quotient(product(X,j(X)),X) = i(X),
inference(transitivity,[status(thm)],[c276,c280]) ).
cnf(c282,plain,
t(X,j(X)) = i(X),
inference(transitivity,[status(thm)],[c275,c281]) ).
cnf(c283,plain,
t(eta(X),j(eta(X))) = i(eta(X)),
inference(substitution,[status(thm)],[c282]) ).
cnf(c284,plain,
i(eta(X)) = t(eta(X),j(eta(X))),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
product(t(eta(X2),X),i(eta(X2))) = product(t(eta(X2),X),t(eta(X2),j(eta(X2)))),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
t(eta(X2),product(X,j(eta(X2)))) = product(t(eta(X2),X),t(eta(X2),j(eta(X2)))),
inference(substitution,[status(thm)],[c248]) ).
cnf(c287,plain,
product(t(eta(X2),X),t(eta(X2),j(eta(X2)))) = t(eta(X2),product(X,j(eta(X2)))),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
product(t(eta(X2),X),i(eta(X2))) = t(eta(X2),product(X,j(eta(X2)))),
inference(transitivity,[status(thm)],[c285,c287]) ).
cnf(c289,plain,
product(t(eta(X2),X),j(eta(X2))) = t(eta(X2),product(X,j(eta(X2)))),
inference(transitivity,[status(thm)],[c274,c288]) ).
cnf(c290,plain,
product(t(eta(X),X2),j(eta(X))) = t(eta(X),product(X2,j(eta(X)))),
inference(substitution,[status(thm)],[c289]) ).
cnf(c291,plain,
t(eta(X),product(X2,j(eta(X)))) = product(t(eta(X),X2),j(eta(X))),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
difference(eta(X),t(eta(X),product(X2,j(eta(X))))) = difference(eta(X),product(t(eta(X),X2),j(eta(X)))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c294,plain,
X = product(X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
product(X,j(X2)) = product(product(X2,difference(X2,X)),j(X2)),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
difference(X2,product(X,j(X2))) = difference(X2,product(product(X2,difference(X2,X)),j(X2))),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
difference(X2,product(product(X2,difference(X2,X)),j(X2))) = quotient(difference(X2,X),X2),
inference(substitution,[status(thm)],[c204]) ).
cnf(c298,plain,
difference(X2,product(X,j(X2))) = quotient(difference(X2,X),X2),
inference(transitivity,[status(thm)],[c296,c297]) ).
cnf(c299,plain,
difference(eta(X),product(t(eta(X),X2),j(eta(X)))) = quotient(difference(eta(X),t(eta(X),X2)),eta(X)),
inference(substitution,[status(thm)],[c298]) ).
cnf(c300,plain,
difference(eta(X2),t(eta(X2),difference(eta(X2),X))) = quotient(difference(eta(X2),X),eta(X2)),
inference(substitution,[status(thm)],[c260]) ).
cnf(c301,plain,
quotient(difference(eta(X2),X),eta(X2)) = difference(eta(X2),t(eta(X2),difference(eta(X2),X))),
inference(symmetry,[status(thm)],[c300]) ).
cnf(c302,plain,
t(eta(X2),difference(eta(X2),X)) = quotient(X,eta(X2)),
inference(substitution,[status(thm)],[c181]) ).
cnf(c303,plain,
difference(eta(X2),t(eta(X2),difference(eta(X2),X))) = difference(eta(X2),quotient(X,eta(X2))),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
quotient(difference(eta(X2),X),eta(X2)) = difference(eta(X2),quotient(X,eta(X2))),
inference(transitivity,[status(thm)],[c301,c303]) ).
cnf(c305,plain,
quotient(difference(eta(X),t(eta(X),X2)),eta(X)) = difference(eta(X),quotient(t(eta(X),X2),eta(X))),
inference(substitution,[status(thm)],[c304]) ).
cnf(c306,plain,
t(eta(X2),X) = product(eta(X2),quotient(X,eta(X2))),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c307,plain,
quotient(t(eta(X2),X),eta(X2)) = quotient(product(eta(X2),quotient(X,eta(X2))),eta(X2)),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
t(eta(X2),quotient(X,eta(X2))) = quotient(product(eta(X2),quotient(X,eta(X2))),eta(X2)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c309,plain,
quotient(product(eta(X2),quotient(X,eta(X2))),eta(X2)) = t(eta(X2),quotient(X,eta(X2))),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c310,plain,
quotient(t(eta(X2),X),eta(X2)) = t(eta(X2),quotient(X,eta(X2))),
inference(transitivity,[status(thm)],[c307,c309]) ).
cnf(c311,plain,
quotient(t(eta(X),X2),eta(X)) = t(eta(X),quotient(X2,eta(X))),
inference(substitution,[status(thm)],[c310]) ).
cnf(c312,plain,
difference(eta(X),quotient(t(eta(X),X2),eta(X))) = difference(eta(X),t(eta(X),quotient(X2,eta(X)))),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
difference(eta(X),t(eta(X),quotient(X2,eta(X)))) = quotient(quotient(X2,eta(X)),eta(X)),
inference(substitution,[status(thm)],[c260]) ).
cnf(c314,plain,
difference(eta(X),quotient(t(eta(X),X2),eta(X))) = quotient(quotient(X2,eta(X)),eta(X)),
inference(transitivity,[status(thm)],[c312,c313]) ).
cnf(c315,plain,
quotient(difference(eta(X),t(eta(X),X2)),eta(X)) = quotient(quotient(X2,eta(X)),eta(X)),
inference(transitivity,[status(thm)],[c305,c314]) ).
cnf(c316,plain,
difference(eta(X),product(t(eta(X),X2),j(eta(X)))) = quotient(quotient(X2,eta(X)),eta(X)),
inference(transitivity,[status(thm)],[c299,c315]) ).
cnf(c317,plain,
difference(eta(X),t(eta(X),product(X2,j(eta(X))))) = quotient(quotient(X2,eta(X)),eta(X)),
inference(transitivity,[status(thm)],[c292,c316]) ).
cnf(c318,plain,
quotient(product(X2,j(eta(X))),eta(X)) = quotient(quotient(X2,eta(X)),eta(X)),
inference(transitivity,[status(thm)],[c262,c317]) ).
cnf(c319,plain,
product(quotient(product(X2,j(eta(X))),eta(X)),eta(X)) = product(quotient(quotient(X2,eta(X)),eta(X)),eta(X)),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
product(quotient(quotient(X2,eta(X)),eta(X)),eta(X)) = quotient(X2,eta(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c321,plain,
product(quotient(product(X2,j(eta(X))),eta(X)),eta(X)) = quotient(X2,eta(X)),
inference(transitivity,[status(thm)],[c319,c320]) ).
cnf(c322,plain,
product(X2,j(eta(X))) = quotient(X2,eta(X)),
inference(transitivity,[status(thm)],[c238,c321]) ).
cnf(c323,plain,
product(X,j(eta(X2))) = quotient(X,eta(X2)),
inference(substitution,[status(thm)],[c322]) ).
cnf(c324,plain,
quotient(X,eta(X2)) = product(X,j(eta(X2))),
inference(symmetry,[status(thm)],[c323]) ).
cnf(c325,plain,
quotient(quotient(X,eta(X2)),j(eta(X2))) = quotient(product(X,j(eta(X2))),j(eta(X2))),
inference(congruence,[status(thm)],[c324]) ).
cnf(c326,plain,
quotient(product(X,j(eta(X2))),j(eta(X2))) = X,
inference(substitution,[status(thm)],[c145]) ).
cnf(c327,plain,
quotient(quotient(X,eta(X2)),j(eta(X2))) = X,
inference(transitivity,[status(thm)],[c325,c326]) ).
cnf(c328,plain,
l(j(eta(X2)),eta(X2),X) = X,
inference(transitivity,[status(thm)],[c236,c327]) ).
cnf(c329,plain,
l(j(eta(X2)),eta(X2),difference(eta(X2),X)) = difference(eta(X2),X),
inference(substitution,[status(thm)],[c328]) ).
cnf(c330,plain,
difference(product(j(eta(X2)),eta(X2)),product(j(eta(X2)),X)) = difference(eta(X2),X),
inference(transitivity,[status(thm)],[c197,c329]) ).
cnf(c331,plain,
difference(one,product(j(eta(X2)),X)) = difference(eta(X2),X),
inference(transitivity,[status(thm)],[c189,c330]) ).
cnf(c332,plain,
product(j(eta(X2)),X) = difference(eta(X2),X),
inference(transitivity,[status(thm)],[c186,c331]) ).
cnf(c333,plain,
product(j(eta(X)),X2) = difference(eta(X),X2),
inference(substitution,[status(thm)],[c332]) ).
cnf(c334,plain,
difference(eta(X),X2) = product(j(eta(X)),X2),
inference(symmetry,[status(thm)],[c333]) ).
cnf(c335,plain,
t(eta(X),difference(eta(X),X2)) = t(eta(X),product(j(eta(X)),X2)),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
quotient(t(eta(X),difference(eta(X),X2)),difference(eta(j(eta(X))),t(eta(X),X2))) = quotient(t(eta(X),product(j(eta(X)),X2)),difference(eta(j(eta(X))),t(eta(X),X2))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
j(eta(X)) = i(eta(X)),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c338,plain,
product(j(eta(X2)),t(eta(X2),X)) = product(i(eta(X2)),t(eta(X2),X)),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
t(eta(X),j(eta(X))) = i(eta(X)),
inference(substitution,[status(thm)],[c282]) ).
cnf(c340,plain,
i(eta(X)) = t(eta(X),j(eta(X))),
inference(symmetry,[status(thm)],[c339]) ).
cnf(c341,plain,
product(i(eta(X2)),t(eta(X2),X)) = product(t(eta(X2),j(eta(X2))),t(eta(X2),X)),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
t(eta(X2),product(j(eta(X2)),X)) = product(t(eta(X2),j(eta(X2))),t(eta(X2),X)),
inference(substitution,[status(thm)],[c248]) ).
cnf(c343,plain,
product(t(eta(X2),j(eta(X2))),t(eta(X2),X)) = t(eta(X2),product(j(eta(X2)),X)),
inference(symmetry,[status(thm)],[c342]) ).
cnf(c344,plain,
product(i(eta(X2)),t(eta(X2),X)) = t(eta(X2),product(j(eta(X2)),X)),
inference(transitivity,[status(thm)],[c341,c343]) ).
cnf(c345,plain,
product(j(eta(X2)),t(eta(X2),X)) = t(eta(X2),product(j(eta(X2)),X)),
inference(transitivity,[status(thm)],[c338,c344]) ).
cnf(c346,plain,
product(j(eta(X)),t(eta(X),X2)) = t(eta(X),product(j(eta(X)),X2)),
inference(substitution,[status(thm)],[c345]) ).
cnf(c347,plain,
t(eta(X),product(j(eta(X)),X2)) = product(j(eta(X)),t(eta(X),X2)),
inference(symmetry,[status(thm)],[c346]) ).
cnf(c348,plain,
quotient(t(eta(X),product(j(eta(X)),X2)),difference(eta(j(eta(X))),t(eta(X),X2))) = quotient(product(j(eta(X)),t(eta(X),X2)),difference(eta(j(eta(X))),t(eta(X),X2))),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
product(X2,product(eta(X2),difference(eta(X2),X))) = product(j(j(X2)),difference(eta(X2),X)),
inference(substitution,[status(thm)],[c72]) ).
cnf(c350,plain,
product(j(j(X2)),difference(eta(X2),X)) = product(X2,product(eta(X2),difference(eta(X2),X))),
inference(symmetry,[status(thm)],[c349]) ).
cnf(c351,plain,
product(eta(X2),difference(eta(X2),X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c352,plain,
product(X2,product(eta(X2),difference(eta(X2),X))) = product(X2,X),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
product(j(j(X2)),difference(eta(X2),X)) = product(X2,X),
inference(transitivity,[status(thm)],[c350,c352]) ).
cnf(c354,plain,
product(X2,X) = product(j(j(X2)),difference(eta(X2),X)),
inference(symmetry,[status(thm)],[c353]) ).
cnf(c355,plain,
quotient(product(X2,X),difference(eta(X2),X)) = quotient(product(j(j(X2)),difference(eta(X2),X)),difference(eta(X2),X)),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
quotient(product(j(j(X2)),difference(eta(X2),X)),difference(eta(X2),X)) = j(j(X2)),
inference(substitution,[status(thm)],[c145]) ).
cnf(c357,plain,
quotient(product(X2,X),difference(eta(X2),X)) = j(j(X2)),
inference(transitivity,[status(thm)],[c355,c356]) ).
cnf(c358,plain,
quotient(product(j(eta(X)),t(eta(X),X2)),difference(eta(j(eta(X))),t(eta(X),X2))) = j(j(j(eta(X)))),
inference(substitution,[status(thm)],[c357]) ).
cnf(c359,plain,
product(eta(X),eta(eta(X))) = j(j(eta(X))),
inference(substitution,[status(thm)],[c121]) ).
cnf(c360,plain,
j(j(eta(X))) = product(eta(X),eta(eta(X))),
inference(symmetry,[status(thm)],[c359]) ).
cnf(c361,plain,
product(eta(X),eta(eta(X))) = product(eta(X),one),
inference(congruence,[status(thm)],[c169]) ).
cnf(c362,plain,
product(eta(X),one) = eta(X),
inference(substitution,[status(thm)],[c81]) ).
cnf(c363,plain,
product(eta(X),eta(eta(X))) = eta(X),
inference(transitivity,[status(thm)],[c361,c362]) ).
cnf(c364,plain,
j(j(eta(X))) = eta(X),
inference(transitivity,[status(thm)],[c360,c363]) ).
cnf(c365,plain,
j(j(j(eta(X)))) = j(eta(X)),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
quotient(product(j(eta(X)),t(eta(X),X2)),difference(eta(j(eta(X))),t(eta(X),X2))) = j(eta(X)),
inference(transitivity,[status(thm)],[c358,c365]) ).
cnf(c367,plain,
quotient(t(eta(X),product(j(eta(X)),X2)),difference(eta(j(eta(X))),t(eta(X),X2))) = j(eta(X)),
inference(transitivity,[status(thm)],[c348,c366]) ).
cnf(c368,plain,
quotient(t(eta(X),difference(eta(X),X2)),difference(eta(j(eta(X))),t(eta(X),X2))) = j(eta(X)),
inference(transitivity,[status(thm)],[c336,c367]) ).
cnf(c369,plain,
quotient(quotient(X2,eta(X)),difference(eta(j(eta(X))),t(eta(X),X2))) = j(eta(X)),
inference(transitivity,[status(thm)],[c184,c368]) ).
cnf(c370,plain,
quotient(quotient(X2,eta(X)),difference(eta(eta(X)),t(eta(X),X2))) = j(eta(X)),
inference(transitivity,[status(thm)],[c176,c369]) ).
cnf(c371,plain,
quotient(quotient(X2,eta(X)),difference(one,t(eta(X),X2))) = j(eta(X)),
inference(transitivity,[status(thm)],[c172,c370]) ).
cnf(c372,plain,
quotient(quotient(X2,eta(X)),t(eta(X),X2)) = j(eta(X)),
inference(transitivity,[status(thm)],[c44,c371]) ).
cnf(c373,plain,
quotient(quotient(X,eta(X2)),t(eta(X2),X)) = j(eta(X2)),
inference(substitution,[status(thm)],[c372]) ).
cnf(c374,plain,
j(eta(X2)) = quotient(quotient(X,eta(X2)),t(eta(X2),X)),
inference(symmetry,[status(thm)],[c373]) ).
cnf(c375,plain,
t(j(eta(X2)),t(eta(X2),X)) = t(quotient(quotient(X,eta(X2)),t(eta(X2),X)),t(eta(X2),X)),
inference(congruence,[status(thm)],[c374]) ).
cnf(c376,plain,
product(quotient(X2,X),X) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c377,plain,
X2 = product(quotient(X2,X),X),
inference(symmetry,[status(thm)],[c376]) ).
cnf(c378,plain,
quotient(X2,quotient(X2,X)) = quotient(product(quotient(X2,X),X),quotient(X2,X)),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
t(quotient(X2,X),X) = quotient(product(quotient(X2,X),X),quotient(X2,X)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c380,plain,
quotient(product(quotient(X2,X),X),quotient(X2,X)) = t(quotient(X2,X),X),
inference(symmetry,[status(thm)],[c379]) ).
cnf(c381,plain,
quotient(X2,quotient(X2,X)) = t(quotient(X2,X),X),
inference(transitivity,[status(thm)],[c378,c380]) ).
cnf(c382,plain,
quotient(quotient(X,eta(X2)),quotient(quotient(X,eta(X2)),t(eta(X2),X))) = t(quotient(quotient(X,eta(X2)),t(eta(X2),X)),t(eta(X2),X)),
inference(substitution,[status(thm)],[c381]) ).
cnf(c383,plain,
t(quotient(quotient(X,eta(X2)),t(eta(X2),X)),t(eta(X2),X)) = quotient(quotient(X,eta(X2)),quotient(quotient(X,eta(X2)),t(eta(X2),X))),
inference(symmetry,[status(thm)],[c382]) ).
cnf(c384,plain,
quotient(quotient(X,eta(X2)),t(eta(X2),X)) = j(eta(X2)),
inference(substitution,[status(thm)],[c372]) ).
cnf(c385,plain,
quotient(quotient(X,eta(X2)),quotient(quotient(X,eta(X2)),t(eta(X2),X))) = quotient(quotient(X,eta(X2)),j(eta(X2))),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
quotient(quotient(X,eta(X2)),j(eta(X2))) = l(j(eta(X2)),eta(X2),X),
inference(substitution,[status(thm)],[c234]) ).
cnf(c387,plain,
quotient(quotient(X,eta(X2)),j(eta(X2))) = X,
inference(transitivity,[status(thm)],[c386,c328]) ).
cnf(c388,plain,
quotient(quotient(X,eta(X2)),quotient(quotient(X,eta(X2)),t(eta(X2),X))) = X,
inference(transitivity,[status(thm)],[c385,c387]) ).
cnf(c389,plain,
t(quotient(quotient(X,eta(X2)),t(eta(X2),X)),t(eta(X2),X)) = X,
inference(transitivity,[status(thm)],[c383,c388]) ).
cnf(c390,plain,
t(j(eta(X2)),t(eta(X2),X)) = X,
inference(transitivity,[status(thm)],[c375,c389]) ).
cnf(c391,plain,
t(j(eta(X2)),t(eta(X2),product(product(X3,eta(X2)),X))) = product(product(X3,eta(X2)),X),
inference(substitution,[status(thm)],[c390]) ).
cnf(c392,plain,
product(product(X3,eta(X2)),X) = t(j(eta(X2)),t(eta(X2),product(product(X3,eta(X2)),X))),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
t(eta(X2),difference(eta(X2),X)) = quotient(X,eta(X2)),
inference(substitution,[status(thm)],[c181]) ).
cnf(c394,plain,
quotient(X,eta(X2)) = t(eta(X2),difference(eta(X2),X)),
inference(symmetry,[status(thm)],[c393]) ).
cnf(c395,plain,
t(j(eta(X2)),quotient(X,eta(X2))) = t(j(eta(X2)),t(eta(X2),difference(eta(X2),X))),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
t(j(eta(X2)),t(eta(X2),difference(eta(X2),X))) = difference(eta(X2),X),
inference(substitution,[status(thm)],[c390]) ).
cnf(c397,plain,
t(j(eta(X2)),quotient(X,eta(X2))) = difference(eta(X2),X),
inference(transitivity,[status(thm)],[c395,c396]) ).
cnf(c398,plain,
t(j(eta(X2)),quotient(product(X,eta(X2)),eta(X2))) = difference(eta(X2),product(X,eta(X2))),
inference(substitution,[status(thm)],[c397]) ).
cnf(c399,plain,
difference(eta(X2),product(X,eta(X2))) = t(j(eta(X2)),quotient(product(X,eta(X2)),eta(X2))),
inference(symmetry,[status(thm)],[c398]) ).
cnf(c400,plain,
quotient(product(X,eta(X2)),eta(X2)) = X,
inference(substitution,[status(thm)],[c145]) ).
cnf(c401,plain,
t(j(eta(X2)),quotient(product(X,eta(X2)),eta(X2))) = t(j(eta(X2)),X),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
difference(eta(X2),product(X,eta(X2))) = t(j(eta(X2)),X),
inference(transitivity,[status(thm)],[c399,c401]) ).
cnf(c403,plain,
difference(eta(X2),product(t(eta(X2),product(product(X3,eta(X2)),X)),eta(X2))) = t(j(eta(X2)),t(eta(X2),product(product(X3,eta(X2)),X))),
inference(substitution,[status(thm)],[c402]) ).
cnf(c404,plain,
t(j(eta(X2)),t(eta(X2),product(product(X3,eta(X2)),X))) = difference(eta(X2),product(t(eta(X2),product(product(X3,eta(X2)),X)),eta(X2))),
inference(symmetry,[status(thm)],[c403]) ).
cnf(c405,plain,
eta(X) = eta(j(X)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c406,plain,
product(difference(eta(X2),X),eta(X2)) = product(difference(eta(X2),X),eta(j(X2))),
inference(congruence,[status(thm)],[c405]) ).
cnf(c407,plain,
eta(j(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c408,plain,
eta(j(X)) = eta(j(j(X))),
inference(symmetry,[status(thm)],[c407]) ).
cnf(c409,plain,
product(difference(eta(X2),X),eta(j(X2))) = product(difference(eta(X2),X),eta(j(j(X2)))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
product(i(i(X2)),X) = product(eta(X2),product(X2,X)),
inference(substitution,[status(thm)],[c70]) ).
cnf(c411,plain,
eta(X) = eta(j(X)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c412,plain,
product(eta(X2),product(X2,X)) = product(eta(j(X2)),product(X2,X)),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
eta(j(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c414,plain,
eta(j(X)) = eta(j(j(X))),
inference(symmetry,[status(thm)],[c413]) ).
cnf(c415,plain,
product(eta(j(X2)),product(X2,X)) = product(eta(j(j(X2))),product(X2,X)),
inference(congruence,[status(thm)],[c414]) ).
cnf(c416,plain,
product(X2,X) = product(j(j(X2)),difference(eta(X2),X)),
inference(symmetry,[status(thm)],[c353]) ).
cnf(c417,plain,
product(eta(j(j(X2))),product(X2,X)) = product(eta(j(j(X2))),product(j(j(X2)),difference(eta(X2),X))),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
product(i(i(j(j(X2)))),difference(eta(X2),X)) = product(eta(j(j(X2))),product(j(j(X2)),difference(eta(X2),X))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c419,plain,
product(eta(j(j(X2))),product(j(j(X2)),difference(eta(X2),X))) = product(i(i(j(j(X2)))),difference(eta(X2),X)),
inference(symmetry,[status(thm)],[c418]) ).
cnf(c420,plain,
i(j(j(X))) = j(X),
inference(substitution,[status(thm)],[c63]) ).
cnf(c421,plain,
i(i(j(j(X)))) = i(j(X)),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
product(i(i(j(j(X2)))),difference(eta(X2),X)) = product(i(j(X2)),difference(eta(X2),X)),
inference(congruence,[status(thm)],[c421]) ).
cnf(c423,plain,
product(i(j(X2)),difference(eta(X2),X)) = product(X2,difference(eta(X2),X)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c424,plain,
product(i(i(j(j(X2)))),difference(eta(X2),X)) = product(X2,difference(eta(X2),X)),
inference(transitivity,[status(thm)],[c422,c423]) ).
cnf(c425,plain,
product(eta(j(j(X2))),product(j(j(X2)),difference(eta(X2),X))) = product(X2,difference(eta(X2),X)),
inference(transitivity,[status(thm)],[c419,c424]) ).
cnf(c426,plain,
product(eta(j(j(X2))),product(X2,X)) = product(X2,difference(eta(X2),X)),
inference(transitivity,[status(thm)],[c417,c425]) ).
cnf(c427,plain,
product(eta(j(X2)),product(X2,X)) = product(X2,difference(eta(X2),X)),
inference(transitivity,[status(thm)],[c415,c426]) ).
cnf(c428,plain,
product(eta(X2),product(X2,X)) = product(X2,difference(eta(X2),X)),
inference(transitivity,[status(thm)],[c412,c427]) ).
cnf(c429,plain,
product(i(i(X2)),X) = product(X2,difference(eta(X2),X)),
inference(transitivity,[status(thm)],[c410,c428]) ).
cnf(c430,plain,
product(X2,difference(eta(X2),X)) = product(i(i(X2)),X),
inference(symmetry,[status(thm)],[c429]) ).
cnf(c431,plain,
difference(eta(X2),product(X2,difference(eta(X2),X))) = difference(eta(X2),product(i(i(X2)),X)),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
product(i(i(X2)),X) = product(eta(X2),product(X2,X)),
inference(substitution,[status(thm)],[c70]) ).
cnf(c433,plain,
difference(eta(X2),product(i(i(X2)),X)) = difference(eta(X2),product(eta(X2),product(X2,X))),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
difference(eta(X2),product(eta(X2),product(X2,X))) = product(X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c435,plain,
difference(eta(X2),product(i(i(X2)),X)) = product(X2,X),
inference(transitivity,[status(thm)],[c433,c434]) ).
cnf(c436,plain,
difference(eta(X2),product(X2,difference(eta(X2),X))) = product(X2,X),
inference(transitivity,[status(thm)],[c431,c435]) ).
cnf(c437,plain,
difference(eta(j(j(X2))),product(j(j(X2)),difference(eta(j(j(X2))),X))) = product(j(j(X2)),X),
inference(substitution,[status(thm)],[c436]) ).
cnf(c438,plain,
product(j(j(X2)),X) = difference(eta(j(j(X2))),product(j(j(X2)),difference(eta(j(j(X2))),X))),
inference(symmetry,[status(thm)],[c437]) ).
cnf(c439,plain,
product(X2,product(eta(X2),difference(eta(j(j(X2))),X))) = product(j(j(X2)),difference(eta(j(j(X2))),X)),
inference(substitution,[status(thm)],[c72]) ).
cnf(c440,plain,
product(j(j(X2)),difference(eta(j(j(X2))),X)) = product(X2,product(eta(X2),difference(eta(j(j(X2))),X))),
inference(symmetry,[status(thm)],[c439]) ).
cnf(c441,plain,
difference(eta(j(j(X2))),product(j(j(X2)),difference(eta(j(j(X2))),X))) = difference(eta(j(j(X2))),product(X2,product(eta(X2),difference(eta(j(j(X2))),X)))),
inference(congruence,[status(thm)],[c440]) ).
cnf(c442,plain,
eta(j(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c443,plain,
difference(eta(j(j(X2))),product(X2,product(eta(X2),difference(eta(j(j(X2))),X)))) = difference(eta(j(X2)),product(X2,product(eta(X2),difference(eta(j(j(X2))),X)))),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
eta(j(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c445,plain,
difference(eta(j(j(X2))),X) = difference(eta(j(X2)),X),
inference(congruence,[status(thm)],[c444]) ).
cnf(c446,plain,
product(eta(X2),difference(eta(j(j(X2))),X)) = product(eta(X2),difference(eta(j(X2)),X)),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
product(X2,product(eta(X2),difference(eta(j(j(X2))),X))) = product(X2,product(eta(X2),difference(eta(j(X2)),X))),
inference(congruence,[status(thm)],[c446]) ).
cnf(c448,plain,
difference(eta(j(X2)),product(X2,product(eta(X2),difference(eta(j(j(X2))),X)))) = difference(eta(j(X2)),product(X2,product(eta(X2),difference(eta(j(X2)),X)))),
inference(congruence,[status(thm)],[c447]) ).
cnf(c449,plain,
difference(eta(j(X2)),product(X2,product(eta(X2),difference(eta(j(X2)),X)))) = difference(eta(X2),product(X2,product(eta(X2),difference(eta(j(X2)),X)))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c450,plain,
difference(eta(j(X2)),X) = difference(eta(X2),X),
inference(congruence,[status(thm)],[c95]) ).
cnf(c451,plain,
product(eta(X2),difference(eta(j(X2)),X)) = product(eta(X2),difference(eta(X2),X)),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
product(X2,product(eta(X2),difference(eta(j(X2)),X))) = product(X2,product(eta(X2),difference(eta(X2),X))),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
difference(eta(X2),product(X2,product(eta(X2),difference(eta(j(X2)),X)))) = difference(eta(X2),product(X2,product(eta(X2),difference(eta(X2),X)))),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
product(eta(X2),difference(eta(X2),X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c455,plain,
product(X2,product(eta(X2),difference(eta(X2),X))) = product(X2,X),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
difference(eta(X2),product(X2,product(eta(X2),difference(eta(X2),X)))) = difference(eta(X2),product(X2,X)),
inference(congruence,[status(thm)],[c455]) ).
cnf(c457,plain,
difference(eta(X2),product(X2,product(eta(X2),difference(eta(j(X2)),X)))) = difference(eta(X2),product(X2,X)),
inference(transitivity,[status(thm)],[c453,c456]) ).
cnf(c458,plain,
difference(eta(j(X2)),product(X2,product(eta(X2),difference(eta(j(X2)),X)))) = difference(eta(X2),product(X2,X)),
inference(transitivity,[status(thm)],[c449,c457]) ).
cnf(c459,plain,
difference(eta(j(X2)),product(X2,product(eta(X2),difference(eta(j(j(X2))),X)))) = difference(eta(X2),product(X2,X)),
inference(transitivity,[status(thm)],[c448,c458]) ).
cnf(c460,plain,
difference(eta(j(j(X2))),product(X2,product(eta(X2),difference(eta(j(j(X2))),X)))) = difference(eta(X2),product(X2,X)),
inference(transitivity,[status(thm)],[c443,c459]) ).
cnf(c461,plain,
difference(eta(j(j(X2))),product(j(j(X2)),difference(eta(j(j(X2))),X))) = difference(eta(X2),product(X2,X)),
inference(transitivity,[status(thm)],[c441,c460]) ).
cnf(c462,plain,
product(j(j(X2)),X) = difference(eta(X2),product(X2,X)),
inference(transitivity,[status(thm)],[c438,c461]) ).
cnf(c463,plain,
product(j(j(X2)),difference(X2,X)) = difference(eta(X2),product(X2,difference(X2,X))),
inference(substitution,[status(thm)],[c462]) ).
cnf(c464,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c465,plain,
difference(eta(X2),product(X2,difference(X2,X))) = difference(eta(X2),X),
inference(congruence,[status(thm)],[c464]) ).
cnf(c466,plain,
product(j(j(X2)),difference(X2,X)) = difference(eta(X2),X),
inference(transitivity,[status(thm)],[c463,c465]) ).
cnf(c467,plain,
difference(eta(X2),X) = product(j(j(X2)),difference(X2,X)),
inference(symmetry,[status(thm)],[c466]) ).
cnf(c468,plain,
product(difference(eta(X2),X),eta(j(j(X2)))) = product(product(j(j(X2)),difference(X2,X)),eta(j(j(X2)))),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
product(j(j(X2)),product(difference(X2,X),eta(j(j(X2))))) = product(product(j(j(X2)),difference(X2,X)),eta(j(j(X2)))),
inference(substitution,[status(thm)],[c50]) ).
cnf(c470,plain,
product(product(j(j(X2)),difference(X2,X)),eta(j(j(X2)))) = product(j(j(X2)),product(difference(X2,X),eta(j(j(X2))))),
inference(symmetry,[status(thm)],[c469]) ).
cnf(c471,plain,
eta(j(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c472,plain,
product(difference(X2,X),eta(j(j(X2)))) = product(difference(X2,X),eta(j(X2))),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
product(j(j(X2)),product(difference(X2,X),eta(j(j(X2))))) = product(j(j(X2)),product(difference(X2,X),eta(j(X2)))),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
product(difference(X2,X),eta(j(X2))) = product(difference(X2,X),eta(X2)),
inference(congruence,[status(thm)],[c95]) ).
cnf(c475,plain,
product(j(j(X2)),product(difference(X2,X),eta(j(X2)))) = product(j(j(X2)),product(difference(X2,X),eta(X2))),
inference(congruence,[status(thm)],[c474]) ).
cnf(c476,plain,
difference(X2,product(X2,product(difference(X2,X),eta(X2)))) = product(difference(X2,X),eta(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c477,plain,
product(difference(X2,X),eta(X2)) = difference(X2,product(X2,product(difference(X2,X),eta(X2)))),
inference(symmetry,[status(thm)],[c476]) ).
cnf(c478,plain,
product(X2,product(difference(X2,X),eta(X2))) = product(product(X2,difference(X2,X)),eta(X2)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c479,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c480,plain,
product(product(X2,difference(X2,X)),eta(X2)) = product(X,eta(X2)),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
product(X2,product(difference(X2,X),eta(X2))) = product(X,eta(X2)),
inference(transitivity,[status(thm)],[c478,c480]) ).
cnf(c482,plain,
difference(X2,product(X2,product(difference(X2,X),eta(X2)))) = difference(X2,product(X,eta(X2))),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
product(difference(X2,X),eta(X2)) = difference(X2,product(X,eta(X2))),
inference(transitivity,[status(thm)],[c477,c482]) ).
cnf(c484,plain,
product(j(j(X2)),product(difference(X2,X),eta(X2))) = product(j(j(X2)),difference(X2,product(X,eta(X2)))),
inference(congruence,[status(thm)],[c483]) ).
cnf(c485,plain,
product(j(j(X2)),difference(X2,product(X,eta(X2)))) = difference(eta(X2),product(X,eta(X2))),
inference(substitution,[status(thm)],[c466]) ).
cnf(c486,plain,
product(j(j(X2)),product(difference(X2,X),eta(X2))) = difference(eta(X2),product(X,eta(X2))),
inference(transitivity,[status(thm)],[c484,c485]) ).
cnf(c487,plain,
product(j(j(X2)),product(difference(X2,X),eta(j(X2)))) = difference(eta(X2),product(X,eta(X2))),
inference(transitivity,[status(thm)],[c475,c486]) ).
cnf(c488,plain,
product(j(j(X2)),product(difference(X2,X),eta(j(j(X2))))) = difference(eta(X2),product(X,eta(X2))),
inference(transitivity,[status(thm)],[c473,c487]) ).
cnf(c489,plain,
product(product(j(j(X2)),difference(X2,X)),eta(j(j(X2)))) = difference(eta(X2),product(X,eta(X2))),
inference(transitivity,[status(thm)],[c470,c488]) ).
cnf(c490,plain,
product(difference(eta(X2),X),eta(j(j(X2)))) = difference(eta(X2),product(X,eta(X2))),
inference(transitivity,[status(thm)],[c468,c489]) ).
cnf(c491,plain,
product(difference(eta(X2),X),eta(j(X2))) = difference(eta(X2),product(X,eta(X2))),
inference(transitivity,[status(thm)],[c409,c490]) ).
cnf(c492,plain,
product(difference(eta(X2),X),eta(X2)) = difference(eta(X2),product(X,eta(X2))),
inference(transitivity,[status(thm)],[c406,c491]) ).
cnf(c493,plain,
product(difference(eta(X2),t(eta(X2),product(product(X3,eta(X2)),X))),eta(X2)) = difference(eta(X2),product(t(eta(X2),product(product(X3,eta(X2)),X)),eta(X2))),
inference(substitution,[status(thm)],[c492]) ).
cnf(c494,plain,
difference(eta(X2),product(t(eta(X2),product(product(X3,eta(X2)),X)),eta(X2))) = product(difference(eta(X2),t(eta(X2),product(product(X3,eta(X2)),X))),eta(X2)),
inference(symmetry,[status(thm)],[c493]) ).
cnf(c495,plain,
difference(X2,product(product(X2,X2),X)) = quotient(product(X2,product(X,X2)),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c496,plain,
t(X2,product(X,X2)) = quotient(product(X2,product(X,X2)),X2),
inference(substitution,[status(thm)],[c177]) ).
cnf(c497,plain,
quotient(product(X2,product(X,X2)),X2) = t(X2,product(X,X2)),
inference(symmetry,[status(thm)],[c496]) ).
cnf(c498,plain,
difference(X2,product(product(X2,X2),X)) = t(X2,product(X,X2)),
inference(transitivity,[status(thm)],[c495,c497]) ).
cnf(c499,plain,
difference(X2,product(product(X2,X2),l(X2,X2,X))) = t(X2,product(l(X2,X2,X),X2)),
inference(substitution,[status(thm)],[c498]) ).
cnf(c500,plain,
t(X2,product(l(X2,X2,X),X2)) = difference(X2,product(product(X2,X2),l(X2,X2,X))),
inference(symmetry,[status(thm)],[c499]) ).
cnf(c501,plain,
l(X3,X2,X) = difference(product(X3,X2),product(X3,product(X2,X))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c502,plain,
product(product(X3,X2),l(X3,X2,X)) = product(product(X3,X2),difference(product(X3,X2),product(X3,product(X2,X)))),
inference(congruence,[status(thm)],[c501]) ).
cnf(c503,plain,
product(product(X3,X2),difference(product(X3,X2),product(X3,product(X2,X)))) = product(X3,product(X2,X)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c504,plain,
product(product(X3,X2),l(X3,X2,X)) = product(X3,product(X2,X)),
inference(transitivity,[status(thm)],[c502,c503]) ).
cnf(c505,plain,
product(product(X2,X2),l(X2,X2,X)) = product(X2,product(X2,X)),
inference(substitution,[status(thm)],[c504]) ).
cnf(c506,plain,
difference(X2,product(product(X2,X2),l(X2,X2,X))) = difference(X2,product(X2,product(X2,X))),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
difference(X2,product(X2,product(X2,X))) = product(X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c508,plain,
difference(X2,product(product(X2,X2),l(X2,X2,X))) = product(X2,X),
inference(transitivity,[status(thm)],[c506,c507]) ).
cnf(c509,plain,
t(X2,product(l(X2,X2,X),X2)) = product(X2,X),
inference(transitivity,[status(thm)],[c500,c508]) ).
cnf(c510,plain,
t(eta(X2),product(l(eta(X2),eta(X2),X),eta(X2))) = product(eta(X2),X),
inference(substitution,[status(thm)],[c509]) ).
cnf(c511,plain,
product(eta(X2),X) = t(eta(X2),product(l(eta(X2),eta(X2),X),eta(X2))),
inference(symmetry,[status(thm)],[c510]) ).
cnf(c512,plain,
product(product(eta(X3),X2),t(eta(X3),X)) = product(t(eta(X3),product(l(eta(X3),eta(X3),X2),eta(X3))),t(eta(X3),X)),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
t(eta(X3),product(product(l(eta(X3),eta(X3),X2),eta(X3)),X)) = product(t(eta(X3),product(l(eta(X3),eta(X3),X2),eta(X3))),t(eta(X3),X)),
inference(substitution,[status(thm)],[c248]) ).
cnf(c514,plain,
product(t(eta(X3),product(l(eta(X3),eta(X3),X2),eta(X3))),t(eta(X3),X)) = t(eta(X3),product(product(l(eta(X3),eta(X3),X2),eta(X3)),X)),
inference(symmetry,[status(thm)],[c513]) ).
cnf(c515,plain,
quotient(difference(eta(X2),product(product(eta(X2),X),eta(X2))),eta(X2)) = l(eta(X2),eta(X2),X),
inference(substitution,[status(thm)],[c20]) ).
cnf(c516,plain,
l(eta(X2),eta(X2),X) = quotient(difference(eta(X2),product(product(eta(X2),X),eta(X2))),eta(X2)),
inference(symmetry,[status(thm)],[c515]) ).
cnf(c517,plain,
t(eta(X2),product(X,eta(X2))) = product(t(eta(X2),X),t(eta(X2),eta(X2))),
inference(substitution,[status(thm)],[c248]) ).
cnf(c518,plain,
t(eta(X),eta(X)) = eta(X),
inference(substitution,[status(thm)],[c244]) ).
cnf(c519,plain,
product(t(eta(X2),X),t(eta(X2),eta(X2))) = product(t(eta(X2),X),eta(X2)),
inference(congruence,[status(thm)],[c518]) ).
cnf(c520,plain,
t(X2,X) = quotient(product(X2,X),X2),
inference(substitution,[status(thm)],[c177]) ).
cnf(c521,plain,
product(t(X2,X),X2) = product(quotient(product(X2,X),X2),X2),
inference(congruence,[status(thm)],[c520]) ).
cnf(c522,plain,
product(quotient(product(X2,X),X2),X2) = product(X2,X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c523,plain,
product(t(X2,X),X2) = product(X2,X),
inference(transitivity,[status(thm)],[c521,c522]) ).
cnf(c524,plain,
product(t(eta(X2),X),eta(X2)) = product(eta(X2),X),
inference(substitution,[status(thm)],[c523]) ).
cnf(c525,plain,
product(t(eta(X2),X),t(eta(X2),eta(X2))) = product(eta(X2),X),
inference(transitivity,[status(thm)],[c519,c524]) ).
cnf(c526,plain,
t(eta(X2),product(X,eta(X2))) = product(eta(X2),X),
inference(transitivity,[status(thm)],[c517,c525]) ).
cnf(c527,plain,
product(eta(X2),X) = t(eta(X2),product(X,eta(X2))),
inference(symmetry,[status(thm)],[c526]) ).
cnf(c528,plain,
product(product(eta(X2),X),eta(X2)) = product(t(eta(X2),product(X,eta(X2))),eta(X2)),
inference(congruence,[status(thm)],[c527]) ).
cnf(c529,plain,
product(t(eta(X2),product(X,eta(X2))),eta(X2)) = product(eta(X2),product(X,eta(X2))),
inference(substitution,[status(thm)],[c523]) ).
cnf(c530,plain,
product(product(eta(X2),X),eta(X2)) = product(eta(X2),product(X,eta(X2))),
inference(transitivity,[status(thm)],[c528,c529]) ).
cnf(c531,plain,
difference(eta(X2),product(product(eta(X2),X),eta(X2))) = difference(eta(X2),product(eta(X2),product(X,eta(X2)))),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
quotient(difference(eta(X2),product(product(eta(X2),X),eta(X2))),eta(X2)) = quotient(difference(eta(X2),product(eta(X2),product(X,eta(X2)))),eta(X2)),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
difference(eta(X2),product(eta(X2),product(X,eta(X2)))) = product(X,eta(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c534,plain,
quotient(difference(eta(X2),product(eta(X2),product(X,eta(X2)))),eta(X2)) = quotient(product(X,eta(X2)),eta(X2)),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
quotient(product(X,eta(X2)),eta(X2)) = X,
inference(substitution,[status(thm)],[c145]) ).
cnf(c536,plain,
quotient(difference(eta(X2),product(eta(X2),product(X,eta(X2)))),eta(X2)) = X,
inference(transitivity,[status(thm)],[c534,c535]) ).
cnf(c537,plain,
quotient(difference(eta(X2),product(product(eta(X2),X),eta(X2))),eta(X2)) = X,
inference(transitivity,[status(thm)],[c532,c536]) ).
cnf(c538,plain,
l(eta(X2),eta(X2),X) = X,
inference(transitivity,[status(thm)],[c516,c537]) ).
cnf(c539,plain,
product(l(eta(X2),eta(X2),X),eta(X2)) = product(X,eta(X2)),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
product(product(l(eta(X3),eta(X3),X2),eta(X3)),X) = product(product(X2,eta(X3)),X),
inference(congruence,[status(thm)],[c539]) ).
cnf(c541,plain,
t(eta(X3),product(product(l(eta(X3),eta(X3),X2),eta(X3)),X)) = t(eta(X3),product(product(X2,eta(X3)),X)),
inference(congruence,[status(thm)],[c540]) ).
cnf(c542,plain,
product(t(eta(X3),product(l(eta(X3),eta(X3),X2),eta(X3))),t(eta(X3),X)) = t(eta(X3),product(product(X2,eta(X3)),X)),
inference(transitivity,[status(thm)],[c514,c541]) ).
cnf(c543,plain,
product(product(eta(X3),X2),t(eta(X3),X)) = t(eta(X3),product(product(X2,eta(X3)),X)),
inference(transitivity,[status(thm)],[c512,c542]) ).
cnf(c544,plain,
product(product(eta(X2),X3),t(eta(X2),X)) = t(eta(X2),product(product(X3,eta(X2)),X)),
inference(substitution,[status(thm)],[c543]) ).
cnf(c545,plain,
t(eta(X2),product(product(X3,eta(X2)),X)) = product(product(eta(X2),X3),t(eta(X2),X)),
inference(symmetry,[status(thm)],[c544]) ).
cnf(c546,plain,
difference(eta(X2),t(eta(X2),product(product(X3,eta(X2)),X))) = difference(eta(X2),product(product(eta(X2),X3),t(eta(X2),X))),
inference(congruence,[status(thm)],[c545]) ).
cnf(c547,plain,
product(difference(eta(X2),t(eta(X2),product(product(X3,eta(X2)),X))),eta(X2)) = product(difference(eta(X2),product(product(eta(X2),X3),t(eta(X2),X))),eta(X2)),
inference(congruence,[status(thm)],[c546]) ).
cnf(c548,plain,
difference(X3,product(product(X3,X2),X)) = quotient(product(X2,product(X,X3)),X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c549,plain,
product(difference(X3,product(product(X3,X2),X)),X3) = product(quotient(product(X2,product(X,X3)),X3),X3),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
product(quotient(product(X2,product(X,X3)),X3),X3) = product(X2,product(X,X3)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c551,plain,
product(difference(X3,product(product(X3,X2),X)),X3) = product(X2,product(X,X3)),
inference(transitivity,[status(thm)],[c549,c550]) ).
cnf(c552,plain,
product(difference(eta(X2),product(product(eta(X2),X3),t(eta(X2),X))),eta(X2)) = product(X3,product(t(eta(X2),X),eta(X2))),
inference(substitution,[status(thm)],[c551]) ).
cnf(c553,plain,
product(t(eta(X2),X),eta(X2)) = product(eta(X2),X),
inference(substitution,[status(thm)],[c523]) ).
cnf(c554,plain,
product(X3,product(t(eta(X2),X),eta(X2))) = product(X3,product(eta(X2),X)),
inference(congruence,[status(thm)],[c553]) ).
cnf(c555,plain,
product(difference(eta(X2),product(product(eta(X2),X3),t(eta(X2),X))),eta(X2)) = product(X3,product(eta(X2),X)),
inference(transitivity,[status(thm)],[c552,c554]) ).
cnf(c556,plain,
product(difference(eta(X2),t(eta(X2),product(product(X3,eta(X2)),X))),eta(X2)) = product(X3,product(eta(X2),X)),
inference(transitivity,[status(thm)],[c547,c555]) ).
cnf(c557,plain,
difference(eta(X2),product(t(eta(X2),product(product(X3,eta(X2)),X)),eta(X2))) = product(X3,product(eta(X2),X)),
inference(transitivity,[status(thm)],[c494,c556]) ).
cnf(c558,plain,
t(j(eta(X2)),t(eta(X2),product(product(X3,eta(X2)),X))) = product(X3,product(eta(X2),X)),
inference(transitivity,[status(thm)],[c404,c557]) ).
cnf(c559,plain,
product(product(X3,eta(X2)),X) = product(X3,product(eta(X2),X)),
inference(transitivity,[status(thm)],[c392,c558]) ).
cnf(c560,plain,
product(X3,quotient(product(eta(X2),product(X,X3)),X3)) = product(X3,product(eta(X2),X)),
inference(transitivity,[status(thm)],[c35,c559]) ).
cnf(c561,plain,
product(X,quotient(product(eta(X3),product(X2,X)),X)) = product(X,product(eta(X3),X2)),
inference(substitution,[status(thm)],[c560]) ).
cnf(c562,plain,
difference(X,product(X,quotient(product(eta(X3),product(X2,X)),X))) = difference(X,product(X,product(eta(X3),X2))),
inference(congruence,[status(thm)],[c561]) ).
cnf(c563,plain,
difference(X,product(X,product(eta(X3),X2))) = product(eta(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c564,plain,
difference(X,product(X,quotient(product(eta(X3),product(X2,X)),X))) = product(eta(X3),X2),
inference(transitivity,[status(thm)],[c562,c563]) ).
cnf(c565,plain,
quotient(product(eta(X3),product(X2,X)),X) = product(eta(X3),X2),
inference(transitivity,[status(thm)],[c4,c564]) ).
cnf(c566,plain,
product(eta(X3),X2) = quotient(product(eta(X3),product(X2,X)),X),
inference(symmetry,[status(thm)],[c565]) ).
cnf(c567,plain,
product(product(eta(X3),X2),X) = product(quotient(product(eta(X3),product(X2,X)),X),X),
inference(congruence,[status(thm)],[c566]) ).
cnf(c568,plain,
product(quotient(product(eta(X3),product(X2,X)),X),X) = product(eta(X3),product(X2,X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c569,plain,
product(product(eta(X3),X2),X) = product(eta(X3),product(X2,X)),
inference(transitivity,[status(thm)],[c567,c568]) ).
cnf(c570,plain,
product(product(eta(x0),x1),x2) = product(eta(x0),product(x1,x2)),
inference(substitution,[status(thm)],[c569]) ).
cnf(c571,plain,
product(eta(x0),product(x1,x2)) = product(product(eta(x0),x1),x2),
inference(symmetry,[status(thm)],[c570]) ).
cnf(c572,plain,
$false,
inference(resolution,[status(thm)],[c1,c571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP766-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:43:24 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 125.69/16.33 Command-line arguments: --flatten --complete-subsets
% 125.69/16.33
% 125.69/16.33 % SZS status Unsatisfiable
% 125.69/16.33
% 125.69/16.40 % SZS output start CNFRefutation
% See solution above
% 129.68/16.86
% 129.68/16.86 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------