%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP770-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 10:11:58 AM UTC 2026
% Result : Unsatisfiable 144.45s 18.61s
% Output : CNFRefutation 146.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 18
% Syntax : Number of clauses : 460 ( 460 unt; 0 nHn; 7 RR)
% Number of literals : 460 ( 459 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 885 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
product(x0,product(x1,x2)) != product(quotient(product(x0,x1),x0),product(x0,x2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
product(j(product(A,B)),A) = j(B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos24) ).
cnf(c3,plain,
product(j(product(X,i(X))),X) = j(i(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
j(i(X)) = product(j(product(X,i(X))),X),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
i(A2) = difference(A2,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
cnf(c6,plain,
i(X) = difference(X,one),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
product(X,i(X)) = product(X,difference(X,one)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
product(A2,difference(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
cnf(c9,plain,
product(X,difference(X,one)) = one,
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
product(X,i(X)) = one,
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
j(product(X,i(X))) = j(one),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
product(j(product(X,i(X))),X) = product(j(one),X),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,axiom,
j(A2) = quotient(one,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
cnf(c14,plain,
j(one) = quotient(one,one),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,axiom,
product(one,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
cnf(c16,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
X = product(one,X),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
quotient(X,X) = quotient(product(one,X),X),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
quotient(product(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
cnf(c20,plain,
quotient(product(one,X),X) = one,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
quotient(X,X) = one,
inference(transitivity,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
quotient(one,one) = one,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
j(one) = one,
inference(transitivity,[status(thm)],[c14,c22]) ).
cnf(c24,plain,
product(j(one),X) = product(one,X),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c26,plain,
product(j(one),X) = X,
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
product(j(product(X,i(X))),X) = X,
inference(transitivity,[status(thm)],[c12,c26]) ).
cnf(c28,plain,
j(i(X)) = X,
inference(transitivity,[status(thm)],[c4,c27]) ).
cnf(c29,plain,
j(i(product(quotient(product(X,X3),X),product(X,X2)))) = product(quotient(product(X,X3),X),product(X,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
product(quotient(product(X3,X2),X3),product(X3,X)) = j(i(product(quotient(product(X3,X2),X3),product(X3,X)))),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
quotient(product(i(product(quotient(product(X3,X2),X3),product(X3,X))),X3),X3) = i(product(quotient(product(X3,X2),X3),product(X3,X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c32,plain,
i(product(quotient(product(X3,X2),X3),product(X3,X))) = quotient(product(i(product(quotient(product(X3,X2),X3),product(X3,X))),X3),X3),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,axiom,
difference(A2,product(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
cnf(c34,plain,
difference(X3,product(X3,product(i(product(quotient(X2,X),product(X,X3))),X))) = product(i(product(quotient(X2,X),product(X,X3))),X),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
product(i(product(quotient(X2,X),product(X,X3))),X) = difference(X3,product(X3,product(i(product(quotient(X2,X),product(X,X3))),X))),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,axiom,
difference(A2,product(product(A2,B2),C)) = quotient(product(B2,product(C,A2)),A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
cnf(c37,plain,
difference(X3,product(product(X3,X2),X)) = quotient(product(X2,product(X,X3)),X3),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
product(difference(X3,product(product(X3,X2),X)),X3) = product(quotient(product(X2,product(X,X3)),X3),X3),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
product(quotient(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
cnf(c40,plain,
product(quotient(product(X2,product(X,X3)),X3),X3) = product(X2,product(X,X3)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
product(difference(X3,product(product(X3,X2),X)),X3) = product(X2,product(X,X3)),
inference(transitivity,[status(thm)],[c38,c40]) ).
cnf(c42,plain,
product(difference(X,product(product(X,X3),i(product(quotient(X2,X),product(X,X3))))),X) = product(X3,product(i(product(quotient(X2,X),product(X,X3))),X)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
product(X3,product(i(product(quotient(X2,X),product(X,X3))),X)) = product(difference(X,product(product(X,X3),i(product(quotient(X2,X),product(X,X3))))),X),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,axiom,
product(A2,i(product(B2,A2))) = i(B2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos23) ).
cnf(c45,plain,
product(product(X,X3),i(product(quotient(X2,X),product(X,X3)))) = i(quotient(X2,X)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
difference(X,product(product(X,X3),i(product(quotient(X2,X),product(X,X3))))) = difference(X,i(quotient(X2,X))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
product(difference(X,product(product(X,X3),i(product(quotient(X2,X),product(X,X3))))),X) = product(difference(X,i(quotient(X2,X))),X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
product(X2,i(product(X,X2))) = i(X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c49,plain,
i(X) = product(X2,i(product(X,X2))),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
difference(X2,i(X)) = difference(X2,product(X2,i(product(X,X2)))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
difference(X2,product(X2,i(product(X,X2)))) = i(product(X,X2)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c52,plain,
difference(X2,i(X)) = i(product(X,X2)),
inference(transitivity,[status(thm)],[c50,c51]) ).
cnf(c53,plain,
difference(X,i(quotient(X2,X))) = i(product(quotient(X2,X),X)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
product(difference(X,i(quotient(X2,X))),X) = product(i(product(quotient(X2,X),X)),X),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
product(quotient(X2,X),X) = X2,
inference(substitution,[status(thm)],[c39]) ).
cnf(c56,plain,
i(product(quotient(X2,X),X)) = i(X2),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
product(i(product(quotient(X2,X),X)),X) = product(i(X2),X),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
product(difference(X,i(quotient(X2,X))),X) = product(i(X2),X),
inference(transitivity,[status(thm)],[c54,c57]) ).
cnf(c59,plain,
product(difference(X,product(product(X,X3),i(product(quotient(X2,X),product(X,X3))))),X) = product(i(X2),X),
inference(transitivity,[status(thm)],[c47,c58]) ).
cnf(c60,plain,
product(X3,product(i(product(quotient(X2,X),product(X,X3))),X)) = product(i(X2),X),
inference(transitivity,[status(thm)],[c43,c59]) ).
cnf(c61,plain,
difference(X3,product(X3,product(i(product(quotient(X2,X),product(X,X3))),X))) = difference(X3,product(i(X2),X)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
product(i(product(quotient(X2,X),product(X,X3))),X) = difference(X3,product(i(X2),X)),
inference(transitivity,[status(thm)],[c35,c61]) ).
cnf(c63,plain,
product(i(product(quotient(product(X3,X2),X3),product(X3,X))),X3) = difference(X,product(i(product(X3,X2)),X3)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
i(j(X)) = difference(j(X),one),
inference(substitution,[status(thm)],[c5]) ).
cnf(c65,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c66,plain,
product(j(X),X) = product(quotient(one,X),X),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
product(quotient(one,X),X) = one,
inference(substitution,[status(thm)],[c39]) ).
cnf(c68,plain,
product(j(X),X) = one,
inference(transitivity,[status(thm)],[c66,c67]) ).
cnf(c69,plain,
one = product(j(X),X),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
difference(j(X),one) = difference(j(X),product(j(X),X)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
difference(j(X),product(j(X),X)) = X,
inference(substitution,[status(thm)],[c33]) ).
cnf(c72,plain,
difference(j(X),one) = X,
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
i(j(X)) = X,
inference(transitivity,[status(thm)],[c64,c72]) ).
cnf(c74,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
product(X2,X) = product(X2,i(j(X))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
i(product(X2,X)) = i(product(X2,i(j(X)))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
product(i(product(X2,X)),X2) = product(i(product(X2,i(j(X)))),X2),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
product(X,i(product(quotient(X2,X),X))) = i(quotient(X2,X)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c79,plain,
i(quotient(X2,X)) = product(X,i(product(quotient(X2,X),X))),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
product(quotient(X2,X),X) = X2,
inference(substitution,[status(thm)],[c39]) ).
cnf(c81,plain,
i(product(quotient(X2,X),X)) = i(X2),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
product(X,i(product(quotient(X2,X),X))) = product(X,i(X2)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
i(quotient(X2,X)) = product(X,i(X2)),
inference(transitivity,[status(thm)],[c79,c82]) ).
cnf(c84,plain,
i(quotient(X,X2)) = product(X2,i(X)),
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
product(X2,i(X)) = i(quotient(X,X2)),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
i(product(X2,i(X))) = i(i(quotient(X,X2))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
product(i(product(X2,i(X))),X2) = product(i(i(quotient(X,X2))),X2),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,axiom,
product(i(i(A2)),B2) = product(eta(A2),product(A2,B2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).
cnf(c89,plain,
product(i(i(quotient(X,X2))),X2) = product(eta(quotient(X,X2)),product(quotient(X,X2),X2)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
product(quotient(X,X2),X2) = X,
inference(substitution,[status(thm)],[c39]) ).
cnf(c91,plain,
product(eta(quotient(X,X2)),product(quotient(X,X2),X2)) = product(eta(quotient(X,X2)),X),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
i(quotient(X,X2)) = product(X2,i(X)),
inference(substitution,[status(thm)],[c83]) ).
cnf(c93,plain,
product(X2,i(X)) = i(quotient(X,X2)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
eta(product(X2,i(X))) = eta(i(quotient(X,X2))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,axiom,
eta(A2) = product(i(A2),A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
cnf(c96,plain,
eta(i(X)) = product(i(i(X)),i(X)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
product(i(i(X)),i(X)) = product(eta(X),product(X,i(X))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c98,plain,
product(eta(X),product(X,i(X))) = product(eta(X),one),
inference(congruence,[status(thm)],[c10]) ).
cnf(c99,axiom,
product(A2,one) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
cnf(c100,plain,
product(eta(X),one) = eta(X),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
product(eta(X),product(X,i(X))) = eta(X),
inference(transitivity,[status(thm)],[c98,c100]) ).
cnf(c102,plain,
product(i(i(X)),i(X)) = eta(X),
inference(transitivity,[status(thm)],[c97,c101]) ).
cnf(c103,plain,
eta(i(X)) = eta(X),
inference(transitivity,[status(thm)],[c96,c102]) ).
cnf(c104,plain,
eta(i(quotient(X,X2))) = eta(quotient(X,X2)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
eta(product(X2,i(X))) = eta(quotient(X,X2)),
inference(transitivity,[status(thm)],[c94,c104]) ).
cnf(c106,plain,
eta(product(X,i(X2))) = eta(quotient(X2,X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
eta(quotient(X2,X)) = eta(product(X,i(X2))),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,axiom,
product(i(A2),A2) = product(A2,j(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
cnf(c109,plain,
product(i(X),X) = product(X,j(X)),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
product(X,j(X)) = product(i(X),X),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c95]) ).
cnf(c112,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
product(X,j(X)) = eta(X),
inference(transitivity,[status(thm)],[c110,c112]) ).
cnf(c114,plain,
product(product(X2,X),j(product(X2,X))) = eta(product(X2,X)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
eta(product(X2,X)) = product(product(X2,X),j(product(X2,X))),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
difference(X2,eta(product(X2,X))) = difference(X2,product(product(X2,X),j(product(X2,X)))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
difference(X2,product(product(X2,X),j(product(X2,X)))) = quotient(product(X,product(j(product(X2,X)),X2)),X2),
inference(substitution,[status(thm)],[c36]) ).
cnf(c118,plain,
product(j(product(X2,X)),X2) = j(X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c119,plain,
product(X,product(j(product(X2,X)),X2)) = product(X,j(X)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
quotient(product(X,product(j(product(X2,X)),X2)),X2) = quotient(product(X,j(X)),X2),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
quotient(product(X,j(X)),X2) = quotient(eta(X),X2),
inference(congruence,[status(thm)],[c113]) ).
cnf(c122,plain,
quotient(product(X,product(j(product(X2,X)),X2)),X2) = quotient(eta(X),X2),
inference(transitivity,[status(thm)],[c120,c121]) ).
cnf(c123,plain,
difference(X2,product(product(X2,X),j(product(X2,X)))) = quotient(eta(X),X2),
inference(transitivity,[status(thm)],[c117,c122]) ).
cnf(c124,plain,
difference(X2,eta(product(X2,X))) = quotient(eta(X),X2),
inference(transitivity,[status(thm)],[c116,c123]) ).
cnf(c125,plain,
quotient(eta(X),X2) = difference(X2,eta(product(X2,X))),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
product(X2,quotient(eta(X),X2)) = product(X2,difference(X2,eta(product(X2,X)))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
product(X2,difference(X2,eta(product(X2,X)))) = eta(product(X2,X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c128,plain,
product(X2,quotient(eta(X),X2)) = eta(product(X2,X)),
inference(transitivity,[status(thm)],[c126,c127]) ).
cnf(c129,plain,
product(X,quotient(eta(i(X2)),X)) = eta(product(X,i(X2))),
inference(substitution,[status(thm)],[c128]) ).
cnf(c130,plain,
eta(product(X,i(X2))) = product(X,quotient(eta(i(X2)),X)),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
quotient(eta(i(X2)),X) = quotient(eta(X2),X),
inference(congruence,[status(thm)],[c103]) ).
cnf(c132,plain,
product(X,quotient(eta(i(X2)),X)) = product(X,quotient(eta(X2),X)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
product(X,quotient(eta(X2),X)) = eta(product(X,X2)),
inference(substitution,[status(thm)],[c128]) ).
cnf(c134,plain,
product(X,quotient(eta(i(X2)),X)) = eta(product(X,X2)),
inference(transitivity,[status(thm)],[c132,c133]) ).
cnf(c135,plain,
eta(product(X,i(X2))) = eta(product(X,X2)),
inference(transitivity,[status(thm)],[c130,c134]) ).
cnf(c136,plain,
eta(quotient(X2,X)) = eta(product(X,X2)),
inference(transitivity,[status(thm)],[c107,c135]) ).
cnf(c137,plain,
eta(quotient(X,X2)) = eta(product(X2,X)),
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
product(eta(quotient(X,X2)),X) = product(eta(product(X2,X)),X),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
eta(quotient(X,X2)) = eta(product(X2,X)),
inference(substitution,[status(thm)],[c136]) ).
cnf(c140,plain,
eta(product(X2,X)) = eta(quotient(X,X2)),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
product(eta(product(X2,X)),X) = product(eta(quotient(X,X2)),X),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
eta(quotient(X,X2)) = eta(product(X2,i(X))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c143,plain,
product(eta(quotient(X,X2)),X) = product(eta(product(X2,i(X))),X),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c145,plain,
product(eta(product(X2,i(X))),X) = product(eta(product(X2,i(X))),j(i(X))),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
eta(quotient(X,i(X2))) = eta(product(i(X2),X)),
inference(substitution,[status(thm)],[c136]) ).
cnf(c147,plain,
eta(product(i(X2),X)) = eta(quotient(X,i(X2))),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
eta(product(i(X2),i(X))) = eta(quotient(X,i(X2))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c149,plain,
eta(quotient(X,i(X2))) = eta(product(i(X2),i(X))),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c8]) ).
cnf(c151,plain,
X = product(X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
i(X) = i(product(X2,difference(X2,X))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
product(difference(X2,X),i(X)) = product(difference(X2,X),i(product(X2,difference(X2,X)))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
product(difference(X2,X),i(product(X2,difference(X2,X)))) = i(X2),
inference(substitution,[status(thm)],[c44]) ).
cnf(c155,plain,
product(difference(X2,X),i(X)) = i(X2),
inference(transitivity,[status(thm)],[c153,c154]) ).
cnf(c156,plain,
product(difference(X,X2),i(X2)) = i(X),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
i(X) = product(difference(X,X2),i(X2)),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
product(i(X2),i(X)) = product(i(X2),product(difference(X,X2),i(X2))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
eta(product(i(X2),i(X))) = eta(product(i(X2),product(difference(X,X2),i(X2)))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
product(X2,quotient(eta(product(X,X2)),X2)) = eta(product(X2,product(X,X2))),
inference(substitution,[status(thm)],[c128]) ).
cnf(c161,plain,
eta(product(X2,product(X,X2))) = product(X2,quotient(eta(product(X,X2)),X2)),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
eta(i(product(X,X2))) = eta(product(X,X2)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c163,plain,
eta(product(X,X2)) = eta(i(product(X,X2))),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
quotient(eta(product(X,X2)),X2) = quotient(eta(i(product(X,X2))),X2),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
difference(X2,eta(product(X2,i(product(X,X2))))) = quotient(eta(i(product(X,X2))),X2),
inference(substitution,[status(thm)],[c124]) ).
cnf(c166,plain,
quotient(eta(i(product(X,X2))),X2) = difference(X2,eta(product(X2,i(product(X,X2))))),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
product(X2,i(product(X,X2))) = i(X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c168,plain,
eta(product(X2,i(product(X,X2)))) = eta(i(X)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
difference(X2,eta(product(X2,i(product(X,X2))))) = difference(X2,eta(i(X))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
difference(X2,eta(i(X))) = difference(X2,eta(X)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c171,plain,
difference(X2,eta(product(X2,i(product(X,X2))))) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c169,c170]) ).
cnf(c172,plain,
quotient(eta(i(product(X,X2))),X2) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c166,c171]) ).
cnf(c173,plain,
quotient(eta(product(X,X2)),X2) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c164,c172]) ).
cnf(c174,plain,
product(X2,quotient(eta(product(X,X2)),X2)) = product(X2,difference(X2,eta(X))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
product(X2,difference(X2,eta(X))) = eta(X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c176,plain,
product(X2,quotient(eta(product(X,X2)),X2)) = eta(X),
inference(transitivity,[status(thm)],[c174,c175]) ).
cnf(c177,plain,
eta(product(X2,product(X,X2))) = eta(X),
inference(transitivity,[status(thm)],[c161,c176]) ).
cnf(c178,plain,
eta(product(i(X2),product(difference(X,X2),i(X2)))) = eta(difference(X,X2)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c179,plain,
eta(j(X)) = product(i(j(X)),j(X)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c180,plain,
product(i(j(X)),j(X)) = product(X,j(X)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c181,plain,
product(i(j(X)),j(X)) = eta(X),
inference(transitivity,[status(thm)],[c180,c113]) ).
cnf(c182,plain,
eta(j(X)) = eta(X),
inference(transitivity,[status(thm)],[c179,c181]) ).
cnf(c183,plain,
eta(j(difference(X2,X))) = eta(difference(X2,X)),
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
eta(difference(X2,X)) = eta(j(difference(X2,X))),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
product(j(product(X2,difference(X2,X))),X2) = j(difference(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c186,plain,
j(difference(X2,X)) = product(j(product(X2,difference(X2,X))),X2),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c8]) ).
cnf(c188,plain,
j(product(X2,difference(X2,X))) = j(X),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
product(j(product(X2,difference(X2,X))),X2) = product(j(X),X2),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
j(difference(X2,X)) = product(j(X),X2),
inference(transitivity,[status(thm)],[c186,c189]) ).
cnf(c191,plain,
eta(j(difference(X2,X))) = eta(product(j(X),X2)),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
eta(difference(X2,X)) = eta(product(j(X),X2)),
inference(transitivity,[status(thm)],[c184,c191]) ).
cnf(c193,plain,
eta(difference(X,X2)) = eta(product(j(X2),X)),
inference(substitution,[status(thm)],[c192]) ).
cnf(c194,plain,
eta(product(i(X2),product(difference(X,X2),i(X2)))) = eta(product(j(X2),X)),
inference(transitivity,[status(thm)],[c178,c193]) ).
cnf(c195,plain,
eta(product(i(X2),i(X))) = eta(product(j(X2),X)),
inference(transitivity,[status(thm)],[c159,c194]) ).
cnf(c196,plain,
eta(quotient(X,i(X2))) = eta(product(j(X2),X)),
inference(transitivity,[status(thm)],[c149,c195]) ).
cnf(c197,plain,
eta(product(i(X2),X)) = eta(product(j(X2),X)),
inference(transitivity,[status(thm)],[c147,c196]) ).
cnf(c198,plain,
eta(product(j(X2),X)) = eta(product(i(X2),X)),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
difference(X2,eta(X)) = quotient(eta(product(X,X2)),X2),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c200,plain,
product(difference(X2,eta(X)),X2) = product(quotient(eta(product(X,X2)),X2),X2),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
product(quotient(eta(product(X,X2)),X2),X2) = eta(product(X,X2)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c202,plain,
product(difference(X2,eta(X)),X2) = eta(product(X,X2)),
inference(transitivity,[status(thm)],[c200,c201]) ).
cnf(c203,plain,
product(difference(X,eta(i(X2))),X) = eta(product(i(X2),X)),
inference(substitution,[status(thm)],[c202]) ).
cnf(c204,plain,
eta(product(i(X2),X)) = product(difference(X,eta(i(X2))),X),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
difference(X,eta(i(X2))) = difference(X,eta(X2)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c206,plain,
product(difference(X,eta(i(X2))),X) = product(difference(X,eta(X2)),X),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
product(difference(X,eta(X2)),X) = eta(product(X2,X)),
inference(substitution,[status(thm)],[c202]) ).
cnf(c208,plain,
product(difference(X,eta(i(X2))),X) = eta(product(X2,X)),
inference(transitivity,[status(thm)],[c206,c207]) ).
cnf(c209,plain,
eta(product(i(X2),X)) = eta(product(X2,X)),
inference(transitivity,[status(thm)],[c204,c208]) ).
cnf(c210,plain,
eta(product(j(X2),X)) = eta(product(X2,X)),
inference(transitivity,[status(thm)],[c198,c209]) ).
cnf(c211,plain,
eta(product(X2,X)) = eta(product(j(X2),X)),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
product(eta(product(X2,X)),j(X)) = product(eta(product(j(X2),X)),j(X)),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
eta(difference(X,X2)) = eta(product(j(X2),X)),
inference(substitution,[status(thm)],[c192]) ).
cnf(c214,plain,
eta(product(j(X2),X)) = eta(difference(X,X2)),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
product(eta(product(j(X2),X)),j(X)) = product(eta(difference(X,X2)),j(X)),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,axiom,
product(j(j(A2)),j(product(B2,A2))) = j(B2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos22) ).
cnf(c217,plain,
product(j(j(X)),j(product(j(eta(X)),X))) = j(j(eta(X))),
inference(substitution,[status(thm)],[c216]) ).
cnf(c218,plain,
j(j(eta(X))) = product(j(j(X)),j(product(j(eta(X)),X))),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
eta(X) = product(X,j(X)),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c220,plain,
j(eta(X)) = j(product(X,j(X))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
product(j(eta(X)),X) = product(j(product(X,j(X))),X),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
product(j(product(X,j(X))),X) = j(j(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c223,plain,
product(j(eta(X)),X) = j(j(X)),
inference(transitivity,[status(thm)],[c221,c222]) ).
cnf(c224,plain,
j(product(j(eta(X)),X)) = j(j(j(X))),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
product(j(j(X)),j(product(j(eta(X)),X))) = product(j(j(X)),j(j(j(X)))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
product(j(j(X)),j(j(j(X)))) = eta(j(j(X))),
inference(substitution,[status(thm)],[c113]) ).
cnf(c227,plain,
eta(j(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c182]) ).
cnf(c228,plain,
eta(j(j(X))) = eta(X),
inference(transitivity,[status(thm)],[c227,c182]) ).
cnf(c229,plain,
product(j(j(X)),j(j(j(X)))) = eta(X),
inference(transitivity,[status(thm)],[c226,c228]) ).
cnf(c230,plain,
product(j(j(X)),j(product(j(eta(X)),X))) = eta(X),
inference(transitivity,[status(thm)],[c225,c229]) ).
cnf(c231,plain,
j(j(eta(X))) = eta(X),
inference(transitivity,[status(thm)],[c218,c230]) ).
cnf(c232,plain,
eta(X) = j(j(eta(X))),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
quotient(eta(X2),X) = quotient(j(j(eta(X2))),X),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
quotient(product(j(product(X2,X)),X2),X2) = j(product(X2,X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c235,plain,
j(product(X2,X)) = quotient(product(j(product(X2,X)),X2),X2),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
product(j(product(X2,X)),X2) = j(X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c237,plain,
quotient(product(j(product(X2,X)),X2),X2) = quotient(j(X),X2),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
j(product(X2,X)) = quotient(j(X),X2),
inference(transitivity,[status(thm)],[c235,c237]) ).
cnf(c239,plain,
j(product(X,j(eta(X2)))) = quotient(j(j(eta(X2))),X),
inference(substitution,[status(thm)],[c238]) ).
cnf(c240,plain,
quotient(j(j(eta(X2))),X) = j(product(X,j(eta(X2)))),
inference(symmetry,[status(thm)],[c239]) ).
cnf(c241,plain,
quotient(product(X2,j(eta(X))),j(eta(X))) = X2,
inference(substitution,[status(thm)],[c19]) ).
cnf(c242,plain,
X2 = quotient(product(X2,j(eta(X))),j(eta(X))),
inference(symmetry,[status(thm)],[c241]) ).
cnf(c243,plain,
quotient(X2,eta(X)) = quotient(quotient(product(X2,j(eta(X))),j(eta(X))),eta(X)),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
eta(X) = j(j(eta(X))),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c245,plain,
difference(j(X2),eta(X)) = difference(j(X2),j(j(eta(X)))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
product(quotient(X2,X),X) = X2,
inference(substitution,[status(thm)],[c39]) ).
cnf(c247,plain,
X2 = product(quotient(X2,X),X),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
j(X2) = j(product(quotient(X2,X),X)),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
product(j(X2),quotient(X2,X)) = product(j(product(quotient(X2,X),X)),quotient(X2,X)),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
product(j(product(quotient(X2,X),X)),quotient(X2,X)) = j(X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c251,plain,
product(j(X2),quotient(X2,X)) = j(X),
inference(transitivity,[status(thm)],[c249,c250]) ).
cnf(c252,plain,
j(X) = product(j(X2),quotient(X2,X)),
inference(symmetry,[status(thm)],[c251]) ).
cnf(c253,plain,
difference(j(X2),j(X)) = difference(j(X2),product(j(X2),quotient(X2,X))),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
difference(j(X2),product(j(X2),quotient(X2,X))) = quotient(X2,X),
inference(substitution,[status(thm)],[c33]) ).
cnf(c255,plain,
difference(j(X2),j(X)) = quotient(X2,X),
inference(transitivity,[status(thm)],[c253,c254]) ).
cnf(c256,plain,
difference(j(X2),j(j(eta(X)))) = quotient(X2,j(eta(X))),
inference(substitution,[status(thm)],[c255]) ).
cnf(c257,plain,
difference(j(X2),eta(X)) = quotient(X2,j(eta(X))),
inference(transitivity,[status(thm)],[c245,c256]) ).
cnf(c258,plain,
quotient(X2,j(eta(X))) = difference(j(X2),eta(X)),
inference(symmetry,[status(thm)],[c257]) ).
cnf(c259,plain,
quotient(quotient(X2,j(eta(X))),eta(X)) = quotient(difference(j(X2),eta(X)),eta(X)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
product(one,difference(one,X)) = difference(one,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c261,plain,
difference(one,X) = product(one,difference(one,X)),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c262,plain,
product(one,difference(one,X)) = X,
inference(substitution,[status(thm)],[c8]) ).
cnf(c263,plain,
difference(one,X) = X,
inference(transitivity,[status(thm)],[c261,c262]) ).
cnf(c264,plain,
difference(one,product(X2,product(i(X2),X))) = product(X2,product(i(X2),X)),
inference(substitution,[status(thm)],[c263]) ).
cnf(c265,plain,
product(X2,product(i(X2),X)) = difference(one,product(X2,product(i(X2),X))),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
one = product(X,i(X)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c267,plain,
difference(one,product(X2,product(i(X2),X))) = difference(product(X2,i(X2)),product(X2,product(i(X2),X))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,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(c269,plain,
difference(product(X2,i(X2)),product(X2,product(i(X2),X))) = quotient(quotient(product(X,product(X2,i(X2))),i(X2)),X2),
inference(substitution,[status(thm)],[c268]) ).
cnf(c270,plain,
difference(j(X2),j(i(X))) = quotient(X2,i(X)),
inference(substitution,[status(thm)],[c255]) ).
cnf(c271,plain,
quotient(X2,i(X)) = difference(j(X2),j(i(X))),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
difference(j(X2),j(i(X))) = difference(j(X2),X),
inference(congruence,[status(thm)],[c28]) ).
cnf(c273,plain,
quotient(X2,i(X)) = difference(j(X2),X),
inference(transitivity,[status(thm)],[c271,c272]) ).
cnf(c274,plain,
quotient(product(X,product(X2,i(X2))),i(X2)) = difference(j(product(X,product(X2,i(X2)))),X2),
inference(substitution,[status(thm)],[c273]) ).
cnf(c275,plain,
quotient(quotient(product(X,product(X2,i(X2))),i(X2)),X2) = quotient(difference(j(product(X,product(X2,i(X2)))),X2),X2),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
j(product(X,product(X2,i(X2)))) = quotient(j(product(X2,i(X2))),X),
inference(substitution,[status(thm)],[c238]) ).
cnf(c277,plain,
difference(j(product(X,product(X2,i(X2)))),X2) = difference(quotient(j(product(X2,i(X2))),X),X2),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
quotient(difference(j(product(X,product(X2,i(X2)))),X2),X2) = quotient(difference(quotient(j(product(X2,i(X2))),X),X2),X2),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
j(product(X,i(X))) = quotient(j(i(X)),X),
inference(substitution,[status(thm)],[c238]) ).
cnf(c280,plain,
quotient(j(product(X2,i(X2))),X) = quotient(quotient(j(i(X2)),X2),X),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
difference(quotient(j(product(X2,i(X2))),X),X2) = difference(quotient(quotient(j(i(X2)),X2),X),X2),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
quotient(difference(quotient(j(product(X2,i(X2))),X),X2),X2) = quotient(difference(quotient(quotient(j(i(X2)),X2),X),X2),X2),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
quotient(j(i(X)),X) = quotient(X,X),
inference(congruence,[status(thm)],[c28]) ).
cnf(c284,plain,
quotient(quotient(j(i(X2)),X2),X) = quotient(quotient(X2,X2),X),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
difference(quotient(quotient(j(i(X2)),X2),X),X2) = difference(quotient(quotient(X2,X2),X),X2),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
quotient(difference(quotient(quotient(j(i(X2)),X2),X),X2),X2) = quotient(difference(quotient(quotient(X2,X2),X),X2),X2),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
quotient(quotient(X2,X2),X) = quotient(one,X),
inference(congruence,[status(thm)],[c21]) ).
cnf(c288,plain,
difference(quotient(quotient(X2,X2),X),X2) = difference(quotient(one,X),X2),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
quotient(difference(quotient(quotient(X2,X2),X),X2),X2) = quotient(difference(quotient(one,X),X2),X2),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c291,plain,
quotient(one,X) = j(X),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
difference(quotient(one,X),X2) = difference(j(X),X2),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
quotient(difference(quotient(one,X),X2),X2) = quotient(difference(j(X),X2),X2),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
quotient(difference(quotient(quotient(X2,X2),X),X2),X2) = quotient(difference(j(X),X2),X2),
inference(transitivity,[status(thm)],[c289,c293]) ).
cnf(c295,plain,
quotient(difference(quotient(quotient(j(i(X2)),X2),X),X2),X2) = quotient(difference(j(X),X2),X2),
inference(transitivity,[status(thm)],[c286,c294]) ).
cnf(c296,plain,
quotient(difference(quotient(j(product(X2,i(X2))),X),X2),X2) = quotient(difference(j(X),X2),X2),
inference(transitivity,[status(thm)],[c282,c295]) ).
cnf(c297,plain,
quotient(difference(j(product(X,product(X2,i(X2)))),X2),X2) = quotient(difference(j(X),X2),X2),
inference(transitivity,[status(thm)],[c278,c296]) ).
cnf(c298,plain,
quotient(quotient(product(X,product(X2,i(X2))),i(X2)),X2) = quotient(difference(j(X),X2),X2),
inference(transitivity,[status(thm)],[c275,c297]) ).
cnf(c299,plain,
difference(product(X2,i(X2)),product(X2,product(i(X2),X))) = quotient(difference(j(X),X2),X2),
inference(transitivity,[status(thm)],[c269,c298]) ).
cnf(c300,plain,
difference(one,product(X2,product(i(X2),X))) = quotient(difference(j(X),X2),X2),
inference(transitivity,[status(thm)],[c267,c299]) ).
cnf(c301,plain,
product(X2,product(i(X2),X)) = quotient(difference(j(X),X2),X2),
inference(transitivity,[status(thm)],[c265,c300]) ).
cnf(c302,plain,
product(eta(X),product(i(eta(X)),X2)) = quotient(difference(j(X2),eta(X)),eta(X)),
inference(substitution,[status(thm)],[c301]) ).
cnf(c303,plain,
quotient(difference(j(X2),eta(X)),eta(X)) = product(eta(X),product(i(eta(X)),X2)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,axiom,
product(eta(A2),product(B2,C2)) = product(product(eta(A2),B2),C2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).
cnf(c305,plain,
product(eta(X),product(i(eta(X)),X2)) = product(product(eta(X),i(eta(X))),X2),
inference(substitution,[status(thm)],[c304]) ).
cnf(c306,plain,
product(eta(X),i(eta(X))) = one,
inference(substitution,[status(thm)],[c10]) ).
cnf(c307,plain,
product(product(eta(X),i(eta(X))),X2) = product(one,X2),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c309,plain,
product(product(eta(X),i(eta(X))),X2) = X2,
inference(transitivity,[status(thm)],[c307,c308]) ).
cnf(c310,plain,
product(eta(X),product(i(eta(X)),X2)) = X2,
inference(transitivity,[status(thm)],[c305,c309]) ).
cnf(c311,plain,
quotient(difference(j(X2),eta(X)),eta(X)) = X2,
inference(transitivity,[status(thm)],[c303,c310]) ).
cnf(c312,plain,
quotient(quotient(X2,j(eta(X))),eta(X)) = X2,
inference(transitivity,[status(thm)],[c259,c311]) ).
cnf(c313,plain,
quotient(quotient(product(X2,j(eta(X))),j(eta(X))),eta(X)) = product(X2,j(eta(X))),
inference(substitution,[status(thm)],[c312]) ).
cnf(c314,plain,
quotient(X2,eta(X)) = product(X2,j(eta(X))),
inference(transitivity,[status(thm)],[c243,c313]) ).
cnf(c315,plain,
quotient(X,eta(X2)) = product(X,j(eta(X2))),
inference(substitution,[status(thm)],[c314]) ).
cnf(c316,plain,
product(X,j(eta(X2))) = quotient(X,eta(X2)),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
j(product(X,j(eta(X2)))) = j(quotient(X,eta(X2))),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
product(j(j(X)),j(product(quotient(X2,X),X))) = j(quotient(X2,X)),
inference(substitution,[status(thm)],[c216]) ).
cnf(c319,plain,
j(quotient(X2,X)) = product(j(j(X)),j(product(quotient(X2,X),X))),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
product(quotient(X2,X),X) = X2,
inference(substitution,[status(thm)],[c39]) ).
cnf(c321,plain,
j(product(quotient(X2,X),X)) = j(X2),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
product(j(j(X)),j(product(quotient(X2,X),X))) = product(j(j(X)),j(X2)),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
j(quotient(X2,X)) = product(j(j(X)),j(X2)),
inference(transitivity,[status(thm)],[c319,c322]) ).
cnf(c324,plain,
j(quotient(X,eta(X2))) = product(j(j(eta(X2))),j(X)),
inference(substitution,[status(thm)],[c323]) ).
cnf(c325,plain,
product(j(j(eta(X2))),j(X)) = product(eta(X2),j(X)),
inference(congruence,[status(thm)],[c231]) ).
cnf(c326,plain,
j(quotient(X,eta(X2))) = product(eta(X2),j(X)),
inference(transitivity,[status(thm)],[c324,c325]) ).
cnf(c327,plain,
j(product(X,j(eta(X2)))) = product(eta(X2),j(X)),
inference(transitivity,[status(thm)],[c317,c326]) ).
cnf(c328,plain,
quotient(j(j(eta(X2))),X) = product(eta(X2),j(X)),
inference(transitivity,[status(thm)],[c240,c327]) ).
cnf(c329,plain,
quotient(eta(X2),X) = product(eta(X2),j(X)),
inference(transitivity,[status(thm)],[c233,c328]) ).
cnf(c330,plain,
quotient(eta(difference(X,X2)),X) = product(eta(difference(X,X2)),j(X)),
inference(substitution,[status(thm)],[c329]) ).
cnf(c331,plain,
product(eta(difference(X,X2)),j(X)) = quotient(eta(difference(X,X2)),X),
inference(symmetry,[status(thm)],[c330]) ).
cnf(c332,plain,
difference(X,eta(product(X,difference(X,X2)))) = quotient(eta(difference(X,X2)),X),
inference(substitution,[status(thm)],[c124]) ).
cnf(c333,plain,
quotient(eta(difference(X,X2)),X) = difference(X,eta(product(X,difference(X,X2)))),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
product(X,difference(X,X2)) = X2,
inference(substitution,[status(thm)],[c8]) ).
cnf(c335,plain,
eta(product(X,difference(X,X2))) = eta(X2),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
difference(X,eta(product(X,difference(X,X2)))) = difference(X,eta(X2)),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
quotient(eta(difference(X,X2)),X) = difference(X,eta(X2)),
inference(transitivity,[status(thm)],[c333,c336]) ).
cnf(c338,plain,
product(eta(difference(X,X2)),j(X)) = difference(X,eta(X2)),
inference(transitivity,[status(thm)],[c331,c337]) ).
cnf(c339,plain,
product(eta(product(j(X2),X)),j(X)) = difference(X,eta(X2)),
inference(transitivity,[status(thm)],[c215,c338]) ).
cnf(c340,plain,
product(eta(product(X2,X)),j(X)) = difference(X,eta(X2)),
inference(transitivity,[status(thm)],[c212,c339]) ).
cnf(c341,plain,
product(eta(product(X2,i(X))),j(i(X))) = difference(i(X),eta(X2)),
inference(substitution,[status(thm)],[c340]) ).
cnf(c342,plain,
product(eta(product(X2,i(X))),X) = difference(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c145,c341]) ).
cnf(c343,plain,
product(eta(quotient(X,X2)),X) = difference(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c143,c342]) ).
cnf(c344,plain,
product(eta(product(X2,X)),X) = difference(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c141,c343]) ).
cnf(c345,plain,
product(eta(quotient(X,X2)),X) = difference(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c138,c344]) ).
cnf(c346,plain,
product(eta(quotient(X,X2)),product(quotient(X,X2),X2)) = difference(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c91,c345]) ).
cnf(c347,plain,
product(i(i(quotient(X,X2))),X2) = difference(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c89,c346]) ).
cnf(c348,plain,
product(i(product(X2,i(X))),X2) = difference(i(X),eta(X2)),
inference(transitivity,[status(thm)],[c87,c347]) ).
cnf(c349,plain,
product(i(product(X2,i(j(X)))),X2) = difference(i(j(X)),eta(X2)),
inference(substitution,[status(thm)],[c348]) ).
cnf(c350,plain,
difference(i(j(X)),eta(X2)) = difference(X,eta(X2)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c351,plain,
product(i(product(X2,i(j(X)))),X2) = difference(X,eta(X2)),
inference(transitivity,[status(thm)],[c349,c350]) ).
cnf(c352,plain,
product(i(product(X2,X)),X2) = difference(X,eta(X2)),
inference(transitivity,[status(thm)],[c77,c351]) ).
cnf(c353,plain,
difference(X,product(i(product(X3,X2)),X3)) = difference(X,difference(X2,eta(X3))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
product(quotient(quotient(X2,j(eta(X))),eta(X)),eta(X)) = quotient(X2,j(eta(X))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c355,plain,
quotient(X2,j(eta(X))) = product(quotient(quotient(X2,j(eta(X))),eta(X)),eta(X)),
inference(symmetry,[status(thm)],[c354]) ).
cnf(c356,plain,
product(quotient(quotient(X2,j(eta(X))),eta(X)),eta(X)) = product(X2,eta(X)),
inference(congruence,[status(thm)],[c312]) ).
cnf(c357,plain,
quotient(X2,j(eta(X))) = product(X2,eta(X)),
inference(transitivity,[status(thm)],[c355,c356]) ).
cnf(c358,plain,
quotient(i(X2),j(eta(X))) = product(i(X2),eta(X)),
inference(substitution,[status(thm)],[c357]) ).
cnf(c359,plain,
product(i(X2),eta(X)) = quotient(i(X2),j(eta(X))),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c360,plain,
difference(j(i(X2)),j(X)) = quotient(i(X2),X),
inference(substitution,[status(thm)],[c255]) ).
cnf(c361,plain,
quotient(i(X2),X) = difference(j(i(X2)),j(X)),
inference(symmetry,[status(thm)],[c360]) ).
cnf(c362,plain,
difference(j(i(X2)),j(X)) = difference(X2,j(X)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c363,plain,
quotient(i(X2),X) = difference(X2,j(X)),
inference(transitivity,[status(thm)],[c361,c362]) ).
cnf(c364,plain,
quotient(i(X2),j(eta(X))) = difference(X2,j(j(eta(X)))),
inference(substitution,[status(thm)],[c363]) ).
cnf(c365,plain,
difference(X2,j(j(eta(X)))) = difference(X2,eta(X)),
inference(congruence,[status(thm)],[c231]) ).
cnf(c366,plain,
quotient(i(X2),j(eta(X))) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c364,c365]) ).
cnf(c367,plain,
product(i(X2),eta(X)) = difference(X2,eta(X)),
inference(transitivity,[status(thm)],[c359,c366]) ).
cnf(c368,plain,
product(i(product(X3,X2)),eta(X)) = difference(product(X3,X2),eta(X)),
inference(substitution,[status(thm)],[c367]) ).
cnf(c369,plain,
difference(product(X3,X2),eta(X)) = product(i(product(X3,X2)),eta(X)),
inference(symmetry,[status(thm)],[c368]) ).
cnf(c370,plain,
eta(X) = j(j(eta(X))),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c371,plain,
difference(eta(X2),X) = difference(j(j(eta(X2))),X),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
quotient(j(eta(X2)),i(X)) = difference(j(j(eta(X2))),X),
inference(substitution,[status(thm)],[c273]) ).
cnf(c373,plain,
difference(j(j(eta(X2))),X) = quotient(j(eta(X2)),i(X)),
inference(symmetry,[status(thm)],[c372]) ).
cnf(c374,plain,
j(product(i(X),eta(X2))) = quotient(j(eta(X2)),i(X)),
inference(substitution,[status(thm)],[c238]) ).
cnf(c375,plain,
quotient(j(eta(X2)),i(X)) = j(product(i(X),eta(X2))),
inference(symmetry,[status(thm)],[c374]) ).
cnf(c376,plain,
product(i(X),eta(X2)) = difference(X,eta(X2)),
inference(substitution,[status(thm)],[c367]) ).
cnf(c377,plain,
j(product(i(X),eta(X2))) = j(difference(X,eta(X2))),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
j(difference(X,eta(X2))) = product(j(eta(X2)),X),
inference(substitution,[status(thm)],[c190]) ).
cnf(c379,plain,
j(product(i(X),eta(X2))) = product(j(eta(X2)),X),
inference(transitivity,[status(thm)],[c377,c378]) ).
cnf(c380,plain,
quotient(j(eta(X2)),i(X)) = product(j(eta(X2)),X),
inference(transitivity,[status(thm)],[c375,c379]) ).
cnf(c381,plain,
difference(j(j(eta(X2))),X) = product(j(eta(X2)),X),
inference(transitivity,[status(thm)],[c373,c380]) ).
cnf(c382,plain,
difference(eta(X2),X) = product(j(eta(X2)),X),
inference(transitivity,[status(thm)],[c371,c381]) ).
cnf(c383,plain,
product(j(eta(X2)),X) = difference(eta(X2),X),
inference(symmetry,[status(thm)],[c382]) ).
cnf(c384,plain,
product(product(j(eta(X3)),X2),X) = product(difference(eta(X3),X2),X),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,plain,
product(eta(X3),product(product(j(eta(X3)),X2),X)) = product(eta(X3),product(difference(eta(X3),X2),X)),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
product(eta(X3),product(difference(eta(X3),X2),X)) = product(product(eta(X3),difference(eta(X3),X2)),X),
inference(substitution,[status(thm)],[c304]) ).
cnf(c387,plain,
product(eta(X2),difference(eta(X2),X)) = X,
inference(substitution,[status(thm)],[c8]) ).
cnf(c388,plain,
product(product(eta(X3),difference(eta(X3),X2)),X) = product(X2,X),
inference(congruence,[status(thm)],[c387]) ).
cnf(c389,plain,
product(eta(X3),product(difference(eta(X3),X2),X)) = product(X2,X),
inference(transitivity,[status(thm)],[c386,c388]) ).
cnf(c390,plain,
product(eta(X3),product(product(j(eta(X3)),X2),X)) = product(X2,X),
inference(transitivity,[status(thm)],[c385,c389]) ).
cnf(c391,plain,
product(eta(X),product(product(j(eta(X)),X3),X2)) = product(X3,X2),
inference(substitution,[status(thm)],[c390]) ).
cnf(c392,plain,
product(X3,X2) = product(eta(X),product(product(j(eta(X)),X3),X2)),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
i(product(X3,X2)) = i(product(eta(X),product(product(j(eta(X)),X3),X2))),
inference(congruence,[status(thm)],[c392]) ).
cnf(c394,plain,
product(i(product(X3,X2)),eta(X)) = product(i(product(eta(X),product(product(j(eta(X)),X3),X2))),eta(X)),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
product(i(product(eta(X),product(product(j(eta(X)),X3),X2))),eta(X)) = difference(product(product(j(eta(X)),X3),X2),eta(eta(X))),
inference(substitution,[status(thm)],[c352]) ).
cnf(c396,plain,
eta(j(eta(X))) = eta(eta(X)),
inference(substitution,[status(thm)],[c182]) ).
cnf(c397,plain,
eta(eta(X)) = eta(j(eta(X))),
inference(symmetry,[status(thm)],[c396]) ).
cnf(c398,plain,
product(j(eta(X)),j(j(eta(X)))) = eta(j(eta(X))),
inference(substitution,[status(thm)],[c113]) ).
cnf(c399,plain,
eta(j(eta(X))) = product(j(eta(X)),j(j(eta(X)))),
inference(symmetry,[status(thm)],[c398]) ).
cnf(c400,plain,
product(j(eta(X)),j(j(eta(X)))) = product(j(eta(X)),eta(X)),
inference(congruence,[status(thm)],[c231]) ).
cnf(c401,plain,
product(j(eta(X)),eta(X)) = one,
inference(substitution,[status(thm)],[c68]) ).
cnf(c402,plain,
product(j(eta(X)),j(j(eta(X)))) = one,
inference(transitivity,[status(thm)],[c400,c401]) ).
cnf(c403,plain,
eta(j(eta(X))) = one,
inference(transitivity,[status(thm)],[c399,c402]) ).
cnf(c404,plain,
eta(eta(X)) = one,
inference(transitivity,[status(thm)],[c397,c403]) ).
cnf(c405,plain,
difference(product(product(j(eta(X)),X3),X2),eta(eta(X))) = difference(product(product(j(eta(X)),X3),X2),one),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
i(product(product(j(eta(X)),X3),X2)) = difference(product(product(j(eta(X)),X3),X2),one),
inference(substitution,[status(thm)],[c5]) ).
cnf(c407,plain,
difference(product(product(j(eta(X)),X3),X2),one) = i(product(product(j(eta(X)),X3),X2)),
inference(symmetry,[status(thm)],[c406]) ).
cnf(c408,plain,
j(difference(X,X2)) = product(j(X2),X),
inference(substitution,[status(thm)],[c190]) ).
cnf(c409,plain,
product(j(X2),X) = j(difference(X,X2)),
inference(symmetry,[status(thm)],[c408]) ).
cnf(c410,plain,
product(product(j(X3),X2),X) = product(j(difference(X2,X3)),X),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
i(product(product(j(X3),X2),X)) = i(product(j(difference(X2,X3)),X)),
inference(congruence,[status(thm)],[c410]) ).
cnf(c412,plain,
j(difference(X,X2)) = product(j(X2),X),
inference(substitution,[status(thm)],[c190]) ).
cnf(c413,plain,
product(j(X2),X) = j(difference(X,X2)),
inference(symmetry,[status(thm)],[c412]) ).
cnf(c414,plain,
i(product(j(X2),X)) = i(j(difference(X,X2))),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
i(j(difference(X,X2))) = difference(X,X2),
inference(substitution,[status(thm)],[c73]) ).
cnf(c416,plain,
i(product(j(X2),X)) = difference(X,X2),
inference(transitivity,[status(thm)],[c414,c415]) ).
cnf(c417,plain,
i(product(j(difference(X2,X3)),X)) = difference(X,difference(X2,X3)),
inference(substitution,[status(thm)],[c416]) ).
cnf(c418,plain,
i(product(product(j(X3),X2),X)) = difference(X,difference(X2,X3)),
inference(transitivity,[status(thm)],[c411,c417]) ).
cnf(c419,plain,
i(product(product(j(eta(X)),X3),X2)) = difference(X2,difference(X3,eta(X))),
inference(substitution,[status(thm)],[c418]) ).
cnf(c420,plain,
difference(product(product(j(eta(X)),X3),X2),one) = difference(X2,difference(X3,eta(X))),
inference(transitivity,[status(thm)],[c407,c419]) ).
cnf(c421,plain,
difference(product(product(j(eta(X)),X3),X2),eta(eta(X))) = difference(X2,difference(X3,eta(X))),
inference(transitivity,[status(thm)],[c405,c420]) ).
cnf(c422,plain,
product(i(product(eta(X),product(product(j(eta(X)),X3),X2))),eta(X)) = difference(X2,difference(X3,eta(X))),
inference(transitivity,[status(thm)],[c395,c421]) ).
cnf(c423,plain,
product(i(product(X3,X2)),eta(X)) = difference(X2,difference(X3,eta(X))),
inference(transitivity,[status(thm)],[c394,c422]) ).
cnf(c424,plain,
difference(product(X3,X2),eta(X)) = difference(X2,difference(X3,eta(X))),
inference(transitivity,[status(thm)],[c369,c423]) ).
cnf(c425,plain,
difference(product(X2,X),eta(X3)) = difference(X,difference(X2,eta(X3))),
inference(substitution,[status(thm)],[c424]) ).
cnf(c426,plain,
difference(X,difference(X2,eta(X3))) = difference(product(X2,X),eta(X3)),
inference(symmetry,[status(thm)],[c425]) ).
cnf(c427,plain,
quotient(eta(product(X3,product(X2,X))),product(X2,X)) = difference(product(X2,X),eta(X3)),
inference(substitution,[status(thm)],[c173]) ).
cnf(c428,plain,
difference(product(X2,X),eta(X3)) = quotient(eta(product(X3,product(X2,X))),product(X2,X)),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
quotient(eta(product(X3,product(X2,X))),product(X2,X)) = product(eta(product(X3,product(X2,X))),j(product(X2,X))),
inference(substitution,[status(thm)],[c329]) ).
cnf(c430,plain,
eta(j(product(X2,X))) = eta(product(X2,X)),
inference(substitution,[status(thm)],[c182]) ).
cnf(c431,plain,
eta(product(X2,X)) = eta(j(product(X2,X))),
inference(symmetry,[status(thm)],[c430]) ).
cnf(c432,plain,
product(eta(product(X2,X)),j(X)) = product(eta(j(product(X2,X))),j(X)),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
product(j(product(X2,X)),X2) = j(X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c434,plain,
j(X) = product(j(product(X2,X)),X2),
inference(symmetry,[status(thm)],[c433]) ).
cnf(c435,plain,
product(eta(j(product(X2,X))),j(X)) = product(eta(j(product(X2,X))),product(j(product(X2,X)),X2)),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
product(i(i(j(product(X2,X)))),X2) = product(eta(j(product(X2,X))),product(j(product(X2,X)),X2)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c437,plain,
product(eta(j(product(X2,X))),product(j(product(X2,X)),X2)) = product(i(i(j(product(X2,X)))),X2),
inference(symmetry,[status(thm)],[c436]) ).
cnf(c438,plain,
i(j(product(X2,X))) = product(X2,X),
inference(substitution,[status(thm)],[c73]) ).
cnf(c439,plain,
i(i(j(product(X2,X)))) = i(product(X2,X)),
inference(congruence,[status(thm)],[c438]) ).
cnf(c440,plain,
product(i(i(j(product(X2,X)))),X2) = product(i(product(X2,X)),X2),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
product(eta(j(product(X2,X))),product(j(product(X2,X)),X2)) = product(i(product(X2,X)),X2),
inference(transitivity,[status(thm)],[c437,c440]) ).
cnf(c442,plain,
product(eta(j(product(X2,X))),j(X)) = product(i(product(X2,X)),X2),
inference(transitivity,[status(thm)],[c435,c441]) ).
cnf(c443,plain,
product(eta(product(X2,X)),j(X)) = product(i(product(X2,X)),X2),
inference(transitivity,[status(thm)],[c432,c442]) ).
cnf(c444,plain,
product(eta(product(X3,product(X2,X))),j(product(X2,X))) = product(i(product(X3,product(X2,X))),X3),
inference(substitution,[status(thm)],[c443]) ).
cnf(c445,plain,
quotient(eta(product(X3,product(X2,X))),product(X2,X)) = product(i(product(X3,product(X2,X))),X3),
inference(transitivity,[status(thm)],[c429,c444]) ).
cnf(c446,plain,
difference(product(X2,X),eta(X3)) = product(i(product(X3,product(X2,X))),X3),
inference(transitivity,[status(thm)],[c428,c445]) ).
cnf(c447,plain,
difference(X,difference(X2,eta(X3))) = product(i(product(X3,product(X2,X))),X3),
inference(transitivity,[status(thm)],[c426,c446]) ).
cnf(c448,plain,
difference(X,product(i(product(X3,X2)),X3)) = product(i(product(X3,product(X2,X))),X3),
inference(transitivity,[status(thm)],[c353,c447]) ).
cnf(c449,plain,
product(i(product(quotient(product(X3,X2),X3),product(X3,X))),X3) = product(i(product(X3,product(X2,X))),X3),
inference(transitivity,[status(thm)],[c63,c448]) ).
cnf(c450,plain,
quotient(product(i(product(quotient(product(X3,X2),X3),product(X3,X))),X3),X3) = quotient(product(i(product(X3,product(X2,X))),X3),X3),
inference(congruence,[status(thm)],[c449]) ).
cnf(c451,plain,
quotient(product(i(product(X3,product(X2,X))),X3),X3) = i(product(X3,product(X2,X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c452,plain,
quotient(product(i(product(quotient(product(X3,X2),X3),product(X3,X))),X3),X3) = i(product(X3,product(X2,X))),
inference(transitivity,[status(thm)],[c450,c451]) ).
cnf(c453,plain,
i(product(quotient(product(X3,X2),X3),product(X3,X))) = i(product(X3,product(X2,X))),
inference(transitivity,[status(thm)],[c32,c452]) ).
cnf(c454,plain,
j(i(product(quotient(product(X3,X2),X3),product(X3,X)))) = j(i(product(X3,product(X2,X)))),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
j(i(product(X3,product(X2,X)))) = product(X3,product(X2,X)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c456,plain,
j(i(product(quotient(product(X3,X2),X3),product(X3,X)))) = product(X3,product(X2,X)),
inference(transitivity,[status(thm)],[c454,c455]) ).
cnf(c457,plain,
product(quotient(product(X3,X2),X3),product(X3,X)) = product(X3,product(X2,X)),
inference(transitivity,[status(thm)],[c30,c456]) ).
cnf(c458,plain,
product(quotient(product(x0,x1),x0),product(x0,x2)) = product(x0,product(x1,x2)),
inference(substitution,[status(thm)],[c457]) ).
cnf(c459,plain,
product(x0,product(x1,x2)) = product(quotient(product(x0,x1),x0),product(x0,x2)),
inference(symmetry,[status(thm)],[c458]) ).
cnf(c460,plain,
$false,
inference(resolution,[status(thm)],[c1,c459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP770-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:46:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 144.45/18.61 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 144.45/18.61
% 144.45/18.61 % SZS status Unsatisfiable
% 144.45/18.61
% 144.45/18.65 % SZS output start CNFRefutation
% See solution above
% 146.06/18.86
% 146.06/18.86 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------