%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 10:11:59 AM UTC 2026
% Result : Theorem 3.86s 1.02s
% Output : CNFRefutation 7.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 10
% Syntax : Number of formulae : 590 ( 590 unt; 0 def)
% Number of atoms : 590 ( 589 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 1033 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,conjecture,
bigC(a,b,X0) = bigC(c,c,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2] : bigC(a,b,X0_2) = bigC(c,c,X0_2),
inference(negate_conjecture,[status(cth)],[c1]) ).
cnf(c3,plain,
bigC(a,b,x0) != bigC(c,c,x0),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,axiom,
bigC(A,B,C) = product(product(A,B),product(C,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
cnf(c5,plain,
bigC(X3,X,X2) = product(product(X3,X),product(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,axiom,
product(product(A2,B2),product(C2,D)) = product(product(A2,C2),product(B2,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
cnf(c7,plain,
product(product(X3,X2),product(X,X3)) = product(product(X3,X),product(X2,X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
product(product(X3,X),product(X2,X3)) = product(product(X3,X2),product(X,X3)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
bigC(X3,X2,X) = product(product(X3,X2),product(X,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c10,plain,
product(product(X3,X2),product(X,X3)) = bigC(X3,X2,X),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
product(product(X3,X),product(X2,X3)) = bigC(X3,X2,X),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
bigC(X3,X,X2) = bigC(X3,X2,X),
inference(transitivity,[status(thm)],[c5,c11]) ).
cnf(c13,plain,
bigC(X2,X,X3) = bigC(X2,X3,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
bigC(X2,X3,X) = product(product(X2,X3),product(X,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c15,axiom,
quotient(product(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
cnf(c16,plain,
quotient(product(X,X2),X2) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
X = quotient(product(X,X2),X2),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
product(X,X2) = product(X,quotient(product(X2,X3),X3)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
product(product(X2,X3),product(X,X2)) = product(product(X2,X3),product(X,quotient(product(X2,X3),X3))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
product(product(X3,X3),product(X2,X)) = product(product(X3,X2),product(X3,X)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c21,plain,
product(product(X3,X2),product(X3,X)) = product(product(X3,X3),product(X2,X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
product(A2,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
cnf(c23,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
product(product(X3,X3),product(X2,X)) = product(X3,product(X2,X)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
product(product(X3,X2),product(X3,X)) = product(X3,product(X2,X)),
inference(transitivity,[status(thm)],[c21,c24]) ).
cnf(c26,plain,
product(product(X3,X2),product(X3,quotient(X3,X))) = product(X3,product(X2,quotient(X3,X))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
product(X3,product(X2,quotient(X3,X))) = product(product(X3,X2),product(X3,quotient(X3,X))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
product(product(X3,X),product(X2,X2)) = product(product(X3,X2),product(X,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c29,plain,
product(product(X3,X2),product(X,X2)) = product(product(X3,X),product(X2,X2)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c31,plain,
product(product(X3,X),product(X2,X2)) = product(product(X3,X),X2),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
product(product(X3,X2),product(X,X2)) = product(product(X3,X),X2),
inference(transitivity,[status(thm)],[c29,c31]) ).
cnf(c33,plain,
product(product(X3,X2),product(difference(X2,X),X2)) = product(product(X3,difference(X2,X)),X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
product(product(X3,difference(X2,X)),X2) = product(product(X3,X2),product(difference(X2,X),X2)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
bigC(X3,difference(X3,X2),X) = bigC(X3,X,difference(X3,X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c36,plain,
bigC(X3,X2,difference(X3,X)) = bigC(X3,difference(X3,X),X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c37,plain,
bigC(X3,difference(X3,X),X2) = product(product(X3,difference(X3,X)),product(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c38,axiom,
product(A2,difference(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
cnf(c39,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
product(product(X3,difference(X3,X)),product(X2,X3)) = product(X,product(X2,X3)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
bigC(X3,difference(X3,X),X2) = product(X,product(X2,X3)),
inference(transitivity,[status(thm)],[c37,c40]) ).
cnf(c42,plain,
bigC(X3,X2,difference(X3,X)) = product(X,product(X2,X3)),
inference(transitivity,[status(thm)],[c36,c41]) ).
cnf(c43,plain,
bigC(X3,X,difference(X3,X2)) = product(X2,product(X,X3)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
bigC(X3,difference(X3,X2),X) = product(X2,product(X,X3)),
inference(transitivity,[status(thm)],[c35,c43]) ).
cnf(c45,plain,
bigC(X2,difference(X2,X3),difference(X2,X)) = product(X3,product(difference(X2,X),X2)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
product(X3,product(difference(X2,X),X2)) = bigC(X2,difference(X2,X3),difference(X2,X)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
bigC(X2,difference(X2,X3),difference(X2,X)) = product(X,product(difference(X2,X3),X2)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c48,plain,
product(X3,product(difference(X2,X),X2)) = product(X,product(difference(X2,X3),X2)),
inference(transitivity,[status(thm)],[c46,c47]) ).
cnf(c49,plain,
product(X,product(difference(X2,product(X3,X2)),X2)) = product(product(X3,X2),product(difference(X2,X),X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
product(product(X3,X2),product(difference(X2,X),X2)) = product(X,product(difference(X2,product(X3,X2)),X2)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c52,plain,
X = product(X,X),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
product(X,X2) = product(X,product(X2,X2)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
difference(X2,product(X,X2)) = difference(X2,product(X,product(X2,X2))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
bigC(X2,X2,difference(X2,X)) = product(X,product(X2,X2)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c56,plain,
product(X,product(X2,X2)) = bigC(X2,X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
difference(X2,product(X,product(X2,X2))) = difference(X2,bigC(X2,X2,difference(X2,X))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c59,plain,
X = product(X,X),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
product(X2,product(X,X2)) = product(product(X2,X2),product(X,X2)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
bigC(X2,X2,X) = product(product(X2,X2),product(X,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c62,plain,
product(product(X2,X2),product(X,X2)) = bigC(X2,X2,X),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
product(X2,product(X,X2)) = bigC(X2,X2,X),
inference(transitivity,[status(thm)],[c60,c62]) ).
cnf(c64,plain,
bigC(X2,X2,X) = product(X2,product(X,X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
difference(X2,bigC(X2,X2,X)) = difference(X2,product(X2,product(X,X2))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,axiom,
difference(A2,product(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
cnf(c67,plain,
difference(X2,product(X2,product(X,X2))) = product(X,X2),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
difference(X2,bigC(X2,X2,X)) = product(X,X2),
inference(transitivity,[status(thm)],[c65,c67]) ).
cnf(c69,plain,
difference(X2,bigC(X2,X2,difference(X2,X))) = product(difference(X2,X),X2),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
difference(X2,product(X,product(X2,X2))) = product(difference(X2,X),X2),
inference(transitivity,[status(thm)],[c57,c69]) ).
cnf(c71,plain,
difference(X2,product(X,X2)) = product(difference(X2,X),X2),
inference(transitivity,[status(thm)],[c54,c70]) ).
cnf(c72,plain,
difference(X,product(X2,X)) = product(difference(X,X2),X),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
product(difference(X,product(X2,X)),X) = product(product(difference(X,X2),X),X),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
product(X,product(difference(X2,product(X3,X2)),X2)) = product(X,product(product(difference(X2,X3),X2),X2)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,axiom,
product(product(product(A2,B2),B2),product(B2,product(B2,A2))) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
cnf(c76,plain,
product(product(product(X,X2),X2),product(X2,product(X2,X))) = X2,
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
X2 = product(product(product(X,X2),X2),product(X2,product(X2,X))),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
quotient(X2,product(X2,product(X2,X))) = quotient(product(product(product(X,X2),X2),product(X2,product(X2,X))),product(X2,product(X2,X))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
quotient(product(product(product(X,X2),X2),product(X2,product(X2,X))),product(X2,product(X2,X))) = product(product(X,X2),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c80,plain,
quotient(X2,product(X2,product(X2,X))) = product(product(X,X2),X2),
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
quotient(X2,product(X2,product(X2,difference(X2,X)))) = product(product(difference(X2,X),X2),X2),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
product(product(difference(X2,X),X2),X2) = quotient(X2,product(X2,product(X2,difference(X2,X)))),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c84,plain,
product(X2,product(X2,difference(X2,X))) = product(X2,X),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
quotient(X2,product(X2,product(X2,difference(X2,X)))) = quotient(X2,product(X2,X)),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
product(product(difference(X2,X),X2),X2) = quotient(X2,product(X2,X)),
inference(transitivity,[status(thm)],[c82,c85]) ).
cnf(c87,plain,
quotient(X2,product(X2,X)) = product(product(difference(X2,X),X2),X2),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
product(X2,quotient(X2,product(X2,X))) = product(X2,product(product(difference(X2,X),X2),X2)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
product(X2,product(product(difference(X2,X),X2),X2)) = bigC(X2,X2,product(difference(X2,X),X2)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c90,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c91,plain,
X = product(X,X),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
product(product(X2,X),X2) = product(product(X2,X),product(X2,X2)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
bigC(X2,X,X2) = product(product(X2,X),product(X2,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c94,plain,
product(product(X2,X),product(X2,X2)) = bigC(X2,X,X2),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
bigC(X2,X2,X) = bigC(X2,X,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c96,plain,
bigC(X2,X,X2) = bigC(X2,X2,X),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
product(product(X2,X),product(X2,X2)) = bigC(X2,X2,X),
inference(transitivity,[status(thm)],[c94,c96]) ).
cnf(c98,plain,
product(product(X2,X),X2) = bigC(X2,X2,X),
inference(transitivity,[status(thm)],[c92,c97]) ).
cnf(c99,plain,
product(product(X2,product(X,X2)),X2) = bigC(X2,X2,product(X,X2)),
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
bigC(X2,X2,product(X,X2)) = product(product(X2,product(X,X2)),X2),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
product(product(X2,product(X,X2)),X2) = product(bigC(X2,X2,X),X2),
inference(congruence,[status(thm)],[c63]) ).
cnf(c102,plain,
bigC(X2,X2,product(X,X2)) = product(bigC(X2,X2,X),X2),
inference(transitivity,[status(thm)],[c100,c101]) ).
cnf(c103,plain,
bigC(X2,X2,product(difference(X2,X),X2)) = product(bigC(X2,X2,difference(X2,X)),X2),
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
bigC(X2,X2,difference(X2,X)) = product(X,product(X2,X2)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c105,plain,
product(bigC(X2,X2,difference(X2,X)),X2) = product(product(X,product(X2,X2)),X2),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c107,plain,
product(X,product(X2,X2)) = product(X,X2),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
product(product(X,product(X2,X2)),X2) = product(product(X,X2),X2),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
product(bigC(X2,X2,difference(X2,X)),X2) = product(product(X,X2),X2),
inference(transitivity,[status(thm)],[c105,c108]) ).
cnf(c110,plain,
bigC(X2,X2,product(difference(X2,X),X2)) = product(product(X,X2),X2),
inference(transitivity,[status(thm)],[c103,c109]) ).
cnf(c111,plain,
product(X2,product(product(difference(X2,X),X2),X2)) = product(product(X,X2),X2),
inference(transitivity,[status(thm)],[c89,c110]) ).
cnf(c112,plain,
product(X2,quotient(X2,product(X2,X))) = product(product(X,X2),X2),
inference(transitivity,[status(thm)],[c88,c111]) ).
cnf(c113,plain,
product(X2,quotient(X2,product(X2,difference(X2,X)))) = product(product(difference(X2,X),X2),X2),
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
product(product(difference(X2,X),X2),X2) = product(X2,quotient(X2,product(X2,difference(X2,X)))),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c116,plain,
quotient(X2,product(X2,difference(X2,X))) = quotient(X2,X),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
product(X2,quotient(X2,product(X2,difference(X2,X)))) = product(X2,quotient(X2,X)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
product(product(difference(X2,X),X2),X2) = product(X2,quotient(X2,X)),
inference(transitivity,[status(thm)],[c114,c117]) ).
cnf(c119,plain,
product(product(difference(X,X2),X),X) = product(X,quotient(X,X2)),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
product(X,product(product(difference(X2,X3),X2),X2)) = product(X,product(X2,quotient(X2,X3))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
product(X,product(difference(X2,product(X3,X2)),X2)) = product(X,product(X2,quotient(X2,X3))),
inference(transitivity,[status(thm)],[c74,c120]) ).
cnf(c122,plain,
product(product(X3,X2),product(difference(X2,X),X2)) = product(X,product(X2,quotient(X2,X3))),
inference(transitivity,[status(thm)],[c50,c121]) ).
cnf(c123,plain,
product(product(X3,difference(X2,X)),X2) = product(X,product(X2,quotient(X2,X3))),
inference(transitivity,[status(thm)],[c34,c122]) ).
cnf(c124,plain,
product(product(X,difference(X3,product(X3,X2))),X3) = product(product(X3,X2),product(X3,quotient(X3,X))),
inference(substitution,[status(thm)],[c123]) ).
cnf(c125,plain,
product(product(X3,X2),product(X3,quotient(X3,X))) = product(product(X,difference(X3,product(X3,X2))),X3),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
difference(X2,product(X2,X)) = X,
inference(substitution,[status(thm)],[c66]) ).
cnf(c127,plain,
product(X,difference(X3,product(X3,X2))) = product(X,X2),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
product(product(X,difference(X3,product(X3,X2))),X3) = product(product(X,X2),X3),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
product(product(X3,X2),product(X3,quotient(X3,X))) = product(product(X,X2),X3),
inference(transitivity,[status(thm)],[c125,c128]) ).
cnf(c130,plain,
product(X3,product(X2,quotient(X3,X))) = product(product(X,X2),X3),
inference(transitivity,[status(thm)],[c27,c129]) ).
cnf(c131,plain,
product(product(X2,X3),product(X,quotient(product(X2,X3),X3))) = product(product(X3,X),product(X2,X3)),
inference(substitution,[status(thm)],[c130]) ).
cnf(c132,plain,
bigC(X3,X,X2) = product(product(X3,X),product(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c133,plain,
product(product(X3,X),product(X2,X3)) = bigC(X3,X,X2),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
bigC(X3,X2,X) = bigC(X3,X,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c135,plain,
bigC(X3,X,X2) = bigC(X3,X2,X),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
product(product(X3,X),product(X2,X3)) = bigC(X3,X2,X),
inference(transitivity,[status(thm)],[c133,c135]) ).
cnf(c137,plain,
product(product(X2,X3),product(X,quotient(product(X2,X3),X3))) = bigC(X3,X2,X),
inference(transitivity,[status(thm)],[c131,c136]) ).
cnf(c138,plain,
product(product(X2,X3),product(X,X2)) = bigC(X3,X2,X),
inference(transitivity,[status(thm)],[c19,c137]) ).
cnf(c139,plain,
bigC(X2,X3,X) = bigC(X3,X2,X),
inference(transitivity,[status(thm)],[c14,c138]) ).
cnf(c140,plain,
bigC(X2,X,X3) = bigC(X3,X2,X),
inference(transitivity,[status(thm)],[c13,c139]) ).
cnf(c141,plain,
bigC(X3,X,X2) = bigC(X2,X3,X),
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
bigC(X2,X3,X) = bigC(X3,X,X2),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
bigC(X3,X2,X) = bigC(X3,X,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c144,plain,
bigC(X3,X,X2) = bigC(X3,X2,X),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
bigC(X2,X3,X) = bigC(X3,X2,X),
inference(transitivity,[status(thm)],[c142,c144]) ).
cnf(c146,plain,
bigC(b,a,X) = bigC(a,b,X),
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
bigC(a,b,X) = bigC(b,a,X),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
bigC(b,a,X) = bigC(b,X,a),
inference(substitution,[status(thm)],[c12]) ).
cnf(c149,plain,
bigC(b,X,a) = product(product(b,X),product(a,b)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c150,plain,
product(product(c,difference(b,X)),c) = bigC(c,c,difference(b,X)),
inference(substitution,[status(thm)],[c98]) ).
cnf(c151,plain,
bigC(c,c,difference(b,X)) = product(product(c,difference(b,X)),c),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
product(product(X3,X2),product(X3,difference(X3,X))) = product(X3,product(X2,difference(X3,X))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c153,plain,
product(X3,product(X2,difference(X3,X))) = product(product(X3,X2),product(X3,difference(X3,X))),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c155,plain,
product(product(X3,X2),product(X3,difference(X3,X))) = product(product(X3,X2),X),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
product(X3,product(X2,difference(X3,X))) = product(product(X3,X2),X),
inference(transitivity,[status(thm)],[c153,c155]) ).
cnf(c157,plain,
product(product(X3,X2),X) = product(X3,product(X2,difference(X3,X))),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
difference(X3,product(product(X3,X2),X)) = difference(X3,product(X3,product(X2,difference(X3,X)))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
difference(X3,product(X3,product(X2,difference(X3,X)))) = product(X2,difference(X3,X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c160,plain,
difference(X3,product(product(X3,X2),X)) = product(X2,difference(X3,X)),
inference(transitivity,[status(thm)],[c158,c159]) ).
cnf(c161,plain,
difference(c,product(product(c,a),X)) = product(a,difference(c,X)),
inference(substitution,[status(thm)],[c160]) ).
cnf(c162,plain,
product(a,difference(c,X)) = difference(c,product(product(c,a),X)),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
bigC(X3,quotient(X2,X3),X) = bigC(X3,X,quotient(X2,X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c164,plain,
bigC(X3,X2,quotient(X,X3)) = product(product(X3,X2),product(quotient(X,X3),X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c165,axiom,
product(quotient(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
cnf(c166,plain,
product(quotient(X,X2),X2) = X,
inference(substitution,[status(thm)],[c165]) ).
cnf(c167,plain,
product(product(X3,X2),product(quotient(X,X3),X3)) = product(product(X3,X2),X),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
bigC(X3,X2,quotient(X,X3)) = product(product(X3,X2),X),
inference(transitivity,[status(thm)],[c164,c167]) ).
cnf(c169,plain,
bigC(X3,X,quotient(X2,X3)) = product(product(X3,X),X2),
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
bigC(X3,quotient(X2,X3),X) = product(product(X3,X),X2),
inference(transitivity,[status(thm)],[c163,c169]) ).
cnf(c171,plain,
bigC(c,quotient(X,c),a) = product(product(c,a),X),
inference(substitution,[status(thm)],[c170]) ).
cnf(c172,plain,
product(product(c,a),X) = bigC(c,quotient(X,c),a),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
difference(c,product(product(c,a),X)) = difference(c,bigC(c,quotient(X,c),a)),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
product(product(quotient(X3,X2),X2),product(X,X2)) = product(product(quotient(X3,X2),X),X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c175,plain,
product(product(quotient(X3,X2),X),X2) = product(product(quotient(X3,X2),X2),product(X,X2)),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
product(quotient(X2,X),X) = X2,
inference(substitution,[status(thm)],[c165]) ).
cnf(c177,plain,
product(product(quotient(X3,X2),X2),product(X,X2)) = product(X3,product(X,X2)),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
product(product(quotient(X3,X2),X),X2) = product(X3,product(X,X2)),
inference(transitivity,[status(thm)],[c175,c177]) ).
cnf(c179,plain,
product(product(quotient(X3,X),X2),X) = product(X3,product(X2,X)),
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
product(X3,product(X2,X)) = product(product(quotient(X3,X),X2),X),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
quotient(product(X3,product(X2,X)),X) = quotient(product(product(quotient(X3,X),X2),X),X),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
quotient(product(product(quotient(X3,X),X2),X),X) = product(quotient(X3,X),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c183,plain,
quotient(product(X3,product(X2,X)),X) = product(quotient(X3,X),X2),
inference(transitivity,[status(thm)],[c181,c182]) ).
cnf(c184,plain,
quotient(product(product(a,c),product(c,b)),b) = product(quotient(product(a,c),b),c),
inference(substitution,[status(thm)],[c183]) ).
cnf(c185,plain,
product(quotient(product(a,c),b),c) = quotient(product(product(a,c),product(c,b)),b),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c187,plain,
quotient(product(product(a,c),product(c,b)),b) = quotient(product(a,b),b),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
quotient(product(a,b),b) = a,
inference(substitution,[status(thm)],[c15]) ).
cnf(c189,plain,
quotient(product(product(a,c),product(c,b)),b) = a,
inference(transitivity,[status(thm)],[c187,c188]) ).
cnf(c190,plain,
product(quotient(product(a,c),b),c) = a,
inference(transitivity,[status(thm)],[c185,c189]) ).
cnf(c191,plain,
a = product(quotient(product(a,c),b),c),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
bigC(c,X,a) = bigC(c,X,product(quotient(product(a,c),b),c)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
difference(c,bigC(c,X,a)) = difference(c,bigC(c,X,product(quotient(product(a,c),b),c))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
product(difference(X2,X),X2) = difference(X2,product(X,X2)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c195,plain,
product(X3,product(difference(X2,X),X2)) = product(X3,difference(X2,product(X,X2))),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
difference(X2,product(product(X2,X3),product(X,X2))) = product(X3,difference(X2,product(X,X2))),
inference(substitution,[status(thm)],[c160]) ).
cnf(c197,plain,
product(X3,difference(X2,product(X,X2))) = difference(X2,product(product(X2,X3),product(X,X2))),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
bigC(X2,X3,X) = product(product(X2,X3),product(X,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c199,plain,
product(product(X2,X3),product(X,X2)) = bigC(X2,X3,X),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
difference(X2,product(product(X2,X3),product(X,X2))) = difference(X2,bigC(X2,X3,X)),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
product(X3,difference(X2,product(X,X2))) = difference(X2,bigC(X2,X3,X)),
inference(transitivity,[status(thm)],[c197,c200]) ).
cnf(c202,plain,
product(X3,product(difference(X2,X),X2)) = difference(X2,bigC(X2,X3,X)),
inference(transitivity,[status(thm)],[c195,c201]) ).
cnf(c203,plain,
product(X2,product(difference(X3,product(X,X3)),X3)) = difference(X3,bigC(X3,X2,product(X,X3))),
inference(substitution,[status(thm)],[c202]) ).
cnf(c204,plain,
difference(X3,bigC(X3,X2,product(X,X3))) = product(X2,product(difference(X3,product(X,X3)),X3)),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
product(product(X,X3),product(difference(X3,X2),X3)) = product(X2,product(difference(X3,product(X,X3)),X3)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c206,plain,
product(X2,product(difference(X3,product(X,X3)),X3)) = product(product(X,X3),product(difference(X3,X2),X3)),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
product(product(X,X3),product(difference(X3,X2),X3)) = product(product(X,difference(X3,X2)),X3),
inference(substitution,[status(thm)],[c32]) ).
cnf(c208,plain,
product(product(X,difference(X3,X2)),X3) = product(X2,product(X3,quotient(X3,X))),
inference(substitution,[status(thm)],[c123]) ).
cnf(c209,plain,
product(product(X,X3),product(difference(X3,X2),X3)) = product(X2,product(X3,quotient(X3,X))),
inference(transitivity,[status(thm)],[c207,c208]) ).
cnf(c210,plain,
product(X2,product(difference(X3,product(X,X3)),X3)) = product(X2,product(X3,quotient(X3,X))),
inference(transitivity,[status(thm)],[c206,c209]) ).
cnf(c211,plain,
difference(X3,bigC(X3,X2,product(X,X3))) = product(X2,product(X3,quotient(X3,X))),
inference(transitivity,[status(thm)],[c204,c210]) ).
cnf(c212,plain,
difference(c,bigC(c,X,product(quotient(product(a,c),b),c))) = product(X,product(c,quotient(c,quotient(product(a,c),b)))),
inference(substitution,[status(thm)],[c211]) ).
cnf(c213,plain,
quotient(product(quotient(product(a,c),b),c),c) = quotient(product(a,c),b),
inference(substitution,[status(thm)],[c15]) ).
cnf(c214,plain,
quotient(product(a,c),b) = quotient(product(quotient(product(a,c),b),c),c),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
quotient(product(quotient(product(a,c),b),c),c) = quotient(a,c),
inference(congruence,[status(thm)],[c190]) ).
cnf(c216,plain,
quotient(product(a,c),b) = quotient(a,c),
inference(transitivity,[status(thm)],[c214,c215]) ).
cnf(c217,plain,
quotient(c,quotient(product(a,c),b)) = quotient(c,quotient(a,c)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
product(c,quotient(c,quotient(product(a,c),b))) = product(c,quotient(c,quotient(a,c))),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
product(X,product(c,quotient(c,quotient(product(a,c),b)))) = product(X,product(c,quotient(c,quotient(a,c)))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c221,plain,
X = product(X,X),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
product(X2,X) = product(product(X2,X2),X),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
quotient(product(X2,X),X2) = quotient(product(product(X2,X2),X),X2),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
bigC(X2,X2,quotient(X,X2)) = product(product(X2,X2),X),
inference(substitution,[status(thm)],[c168]) ).
cnf(c225,plain,
product(product(X2,X2),X) = bigC(X2,X2,quotient(X,X2)),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
quotient(product(product(X2,X2),X),X2) = quotient(bigC(X2,X2,quotient(X,X2)),X2),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
bigC(X2,X2,X) = product(product(X2,X),X2),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c228,plain,
quotient(bigC(X2,X2,X),X2) = quotient(product(product(X2,X),X2),X2),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
quotient(product(product(X2,X),X2),X2) = product(X2,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c230,plain,
quotient(bigC(X2,X2,X),X2) = product(X2,X),
inference(transitivity,[status(thm)],[c228,c229]) ).
cnf(c231,plain,
quotient(bigC(X2,X2,quotient(X,X2)),X2) = product(X2,quotient(X,X2)),
inference(substitution,[status(thm)],[c230]) ).
cnf(c232,plain,
quotient(product(product(X2,X2),X),X2) = product(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c226,c231]) ).
cnf(c233,plain,
quotient(product(X2,X),X2) = product(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c223,c232]) ).
cnf(c234,plain,
quotient(product(c,a),c) = product(c,quotient(a,c)),
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
product(c,quotient(a,c)) = quotient(product(c,a),c),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
quotient(product(c,product(c,b)),b) = product(quotient(c,b),c),
inference(substitution,[status(thm)],[c183]) ).
cnf(c237,plain,
product(quotient(c,b),c) = quotient(product(c,product(c,b)),b),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
product(c,product(a,difference(c,b))) = product(product(c,a),b),
inference(substitution,[status(thm)],[c156]) ).
cnf(c239,plain,
product(product(c,a),b) = product(c,product(a,difference(c,b))),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
difference(c,product(c,difference(a,product(c,b)))) = difference(a,product(c,b)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c241,plain,
difference(a,product(c,b)) = difference(c,product(c,difference(a,product(c,b)))),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
difference(a,product(product(a,c),product(c,b))) = product(c,difference(a,product(c,b))),
inference(substitution,[status(thm)],[c160]) ).
cnf(c243,plain,
product(c,difference(a,product(c,b))) = difference(a,product(product(a,c),product(c,b))),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
difference(a,product(product(a,c),product(c,b))) = difference(a,product(a,b)),
inference(congruence,[status(thm)],[c186]) ).
cnf(c245,plain,
difference(a,product(a,b)) = b,
inference(substitution,[status(thm)],[c66]) ).
cnf(c246,plain,
difference(a,product(product(a,c),product(c,b))) = b,
inference(transitivity,[status(thm)],[c244,c245]) ).
cnf(c247,plain,
product(c,difference(a,product(c,b))) = b,
inference(transitivity,[status(thm)],[c243,c246]) ).
cnf(c248,plain,
difference(c,product(c,difference(a,product(c,b)))) = difference(c,b),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
difference(a,product(c,b)) = difference(c,b),
inference(transitivity,[status(thm)],[c241,c248]) ).
cnf(c250,plain,
difference(c,b) = difference(a,product(c,b)),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
product(a,difference(c,b)) = product(a,difference(a,product(c,b))),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
product(a,difference(a,product(c,b))) = product(c,b),
inference(substitution,[status(thm)],[c38]) ).
cnf(c253,plain,
product(a,difference(c,b)) = product(c,b),
inference(transitivity,[status(thm)],[c251,c252]) ).
cnf(c254,plain,
product(c,product(a,difference(c,b))) = product(c,product(c,b)),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
product(product(c,a),b) = product(c,product(c,b)),
inference(transitivity,[status(thm)],[c239,c254]) ).
cnf(c256,plain,
product(c,product(c,b)) = product(product(c,a),b),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c257,plain,
quotient(product(c,product(c,b)),b) = quotient(product(product(c,a),b),b),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
quotient(product(product(c,a),b),b) = product(c,a),
inference(substitution,[status(thm)],[c15]) ).
cnf(c259,plain,
quotient(product(c,product(c,b)),b) = product(c,a),
inference(transitivity,[status(thm)],[c257,c258]) ).
cnf(c260,plain,
product(quotient(c,b),c) = product(c,a),
inference(transitivity,[status(thm)],[c237,c259]) ).
cnf(c261,plain,
product(c,a) = product(quotient(c,b),c),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c262,plain,
quotient(product(c,a),c) = quotient(product(quotient(c,b),c),c),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
quotient(product(quotient(c,b),c),c) = quotient(c,b),
inference(substitution,[status(thm)],[c15]) ).
cnf(c264,plain,
quotient(product(c,a),c) = quotient(c,b),
inference(transitivity,[status(thm)],[c262,c263]) ).
cnf(c265,plain,
product(c,quotient(a,c)) = quotient(c,b),
inference(transitivity,[status(thm)],[c235,c264]) ).
cnf(c266,plain,
quotient(c,b) = product(c,quotient(a,c)),
inference(symmetry,[status(thm)],[c265]) ).
cnf(c267,plain,
difference(c,quotient(c,b)) = difference(c,product(c,quotient(a,c))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
difference(c,product(c,quotient(a,c))) = quotient(a,c),
inference(substitution,[status(thm)],[c66]) ).
cnf(c269,plain,
difference(c,quotient(c,b)) = quotient(a,c),
inference(transitivity,[status(thm)],[c267,c268]) ).
cnf(c270,plain,
quotient(a,c) = difference(c,quotient(c,b)),
inference(symmetry,[status(thm)],[c269]) ).
cnf(c271,plain,
quotient(c,quotient(a,c)) = quotient(c,difference(c,quotient(c,b))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
difference(X2,product(X2,quotient(X2,difference(X2,X)))) = quotient(X2,difference(X2,X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c273,plain,
quotient(X2,difference(X2,X)) = difference(X2,product(X2,quotient(X2,difference(X2,X)))),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c274,plain,
product(product(difference(X2,difference(X2,X)),X2),X2) = product(X2,quotient(X2,difference(X2,X))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c275,plain,
product(X2,quotient(X2,difference(X2,X))) = product(product(difference(X2,difference(X2,X)),X2),X2),
inference(symmetry,[status(thm)],[c274]) ).
cnf(c276,plain,
difference(X2,product(difference(X2,X),X2)) = product(difference(X2,difference(X2,X)),X2),
inference(substitution,[status(thm)],[c71]) ).
cnf(c277,plain,
product(difference(X2,difference(X2,X)),X2) = difference(X2,product(difference(X2,X),X2)),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
product(product(difference(X2,difference(X2,X)),X2),X2) = product(difference(X2,product(difference(X2,X),X2)),X2),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
difference(X2,product(product(difference(X2,X),X2),X2)) = product(difference(X2,product(difference(X2,X),X2)),X2),
inference(substitution,[status(thm)],[c71]) ).
cnf(c280,plain,
product(difference(X2,product(difference(X2,X),X2)),X2) = difference(X2,product(product(difference(X2,X),X2),X2)),
inference(symmetry,[status(thm)],[c279]) ).
cnf(c281,plain,
difference(X2,product(product(difference(X2,X),X2),X2)) = difference(X2,quotient(X2,product(X2,X))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c282,plain,
quotient(X2,product(X2,X)) = product(product(difference(X2,X),X2),X2),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c283,plain,
quotient(X2,product(X2,X)) = product(X2,quotient(X2,X)),
inference(transitivity,[status(thm)],[c282,c118]) ).
cnf(c284,plain,
difference(X2,quotient(X2,product(X2,X))) = difference(X2,product(X2,quotient(X2,X))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
difference(X2,product(X2,quotient(X2,X))) = quotient(X2,X),
inference(substitution,[status(thm)],[c66]) ).
cnf(c286,plain,
difference(X2,quotient(X2,product(X2,X))) = quotient(X2,X),
inference(transitivity,[status(thm)],[c284,c285]) ).
cnf(c287,plain,
difference(X2,product(product(difference(X2,X),X2),X2)) = quotient(X2,X),
inference(transitivity,[status(thm)],[c281,c286]) ).
cnf(c288,plain,
product(difference(X2,product(difference(X2,X),X2)),X2) = quotient(X2,X),
inference(transitivity,[status(thm)],[c280,c287]) ).
cnf(c289,plain,
product(product(difference(X2,difference(X2,X)),X2),X2) = quotient(X2,X),
inference(transitivity,[status(thm)],[c278,c288]) ).
cnf(c290,plain,
product(X2,quotient(X2,difference(X2,X))) = quotient(X2,X),
inference(transitivity,[status(thm)],[c275,c289]) ).
cnf(c291,plain,
difference(X2,product(X2,quotient(X2,difference(X2,X)))) = difference(X2,quotient(X2,X)),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
quotient(X2,difference(X2,X)) = difference(X2,quotient(X2,X)),
inference(transitivity,[status(thm)],[c273,c291]) ).
cnf(c293,plain,
quotient(c,difference(c,quotient(c,b))) = difference(c,quotient(c,quotient(c,b))),
inference(substitution,[status(thm)],[c292]) ).
cnf(c294,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c295,plain,
X = product(X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c296,plain,
difference(difference(X2,X),X) = difference(difference(X2,X),product(X2,difference(X2,X))),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
product(product(X2,X),product(X2,quotient(X2,X))) = product(X2,product(X,quotient(X2,X))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c298,plain,
product(X2,product(X,quotient(X2,X))) = product(product(X2,X),product(X2,quotient(X2,X))),
inference(symmetry,[status(thm)],[c297]) ).
cnf(c299,plain,
product(X2,quotient(X2,X)) = quotient(X2,product(X2,X)),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c300,plain,
product(product(X2,X),product(X2,quotient(X2,X))) = product(product(X2,X),quotient(X2,product(X2,X))),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
product(product(difference(X2,X),X2),product(difference(X2,X),X2)) = product(difference(X2,X),X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c302,plain,
product(difference(X2,X),X2) = product(product(difference(X2,X),X2),product(difference(X2,X),X2)),
inference(symmetry,[status(thm)],[c301]) ).
cnf(c303,plain,
product(product(difference(X2,X),X2),product(difference(X2,X),X2)) = product(X,product(difference(X2,product(difference(X2,X),X2)),X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c304,plain,
difference(X2,product(difference(X2,X),X2)) = product(difference(X2,difference(X2,X)),X2),
inference(substitution,[status(thm)],[c71]) ).
cnf(c305,plain,
product(difference(X2,product(difference(X2,X),X2)),X2) = product(product(difference(X2,difference(X2,X)),X2),X2),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
product(X,product(difference(X2,product(difference(X2,X),X2)),X2)) = product(X,product(product(difference(X2,difference(X2,X)),X2),X2)),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
product(product(difference(X2,difference(X2,X)),X2),X2) = product(X2,quotient(X2,difference(X2,X))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c308,plain,
product(X,product(product(difference(X2,difference(X2,X)),X2),X2)) = product(X,product(X2,quotient(X2,difference(X2,X)))),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
product(X,product(X2,quotient(X2,difference(X2,X)))) = product(X,quotient(X2,X)),
inference(congruence,[status(thm)],[c290]) ).
cnf(c310,plain,
product(X,product(product(difference(X2,difference(X2,X)),X2),X2)) = product(X,quotient(X2,X)),
inference(transitivity,[status(thm)],[c308,c309]) ).
cnf(c311,plain,
product(X,product(difference(X2,product(difference(X2,X),X2)),X2)) = product(X,quotient(X2,X)),
inference(transitivity,[status(thm)],[c306,c310]) ).
cnf(c312,plain,
product(product(difference(X2,X),X2),product(difference(X2,X),X2)) = product(X,quotient(X2,X)),
inference(transitivity,[status(thm)],[c303,c311]) ).
cnf(c313,plain,
product(difference(X2,X),X2) = product(X,quotient(X2,X)),
inference(transitivity,[status(thm)],[c302,c312]) ).
cnf(c314,plain,
product(difference(X2,product(X2,X)),X2) = product(product(X2,X),quotient(X2,product(X2,X))),
inference(substitution,[status(thm)],[c313]) ).
cnf(c315,plain,
product(product(X2,X),quotient(X2,product(X2,X))) = product(difference(X2,product(X2,X)),X2),
inference(symmetry,[status(thm)],[c314]) ).
cnf(c316,plain,
difference(X2,product(X2,X)) = X,
inference(substitution,[status(thm)],[c66]) ).
cnf(c317,plain,
product(difference(X2,product(X2,X)),X2) = product(X,X2),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
product(product(X2,X),quotient(X2,product(X2,X))) = product(X,X2),
inference(transitivity,[status(thm)],[c315,c317]) ).
cnf(c319,plain,
product(product(X2,X),product(X2,quotient(X2,X))) = product(X,X2),
inference(transitivity,[status(thm)],[c300,c318]) ).
cnf(c320,plain,
product(X2,product(X,quotient(X2,X))) = product(X,X2),
inference(transitivity,[status(thm)],[c298,c319]) ).
cnf(c321,plain,
product(X,product(X2,quotient(X,X2))) = product(X2,X),
inference(substitution,[status(thm)],[c320]) ).
cnf(c322,plain,
product(X2,X) = product(X,product(X2,quotient(X,X2))),
inference(symmetry,[status(thm)],[c321]) ).
cnf(c323,plain,
difference(X,product(X2,X)) = difference(X,product(X,product(X2,quotient(X,X2)))),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
difference(X,product(X,product(X2,quotient(X,X2)))) = product(X2,quotient(X,X2)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c325,plain,
difference(X,product(X2,X)) = product(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c323,c324]) ).
cnf(c326,plain,
difference(difference(X2,X),product(X2,difference(X2,X))) = product(X2,quotient(difference(X2,X),X2)),
inference(substitution,[status(thm)],[c325]) ).
cnf(c327,plain,
difference(X2,product(quotient(X,X2),X2)) = product(difference(X2,quotient(X,X2)),X2),
inference(substitution,[status(thm)],[c71]) ).
cnf(c328,plain,
product(difference(X2,quotient(X,X2)),X2) = difference(X2,product(quotient(X,X2),X2)),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c329,plain,
product(quotient(X,X2),X2) = X,
inference(substitution,[status(thm)],[c165]) ).
cnf(c330,plain,
difference(X2,product(quotient(X,X2),X2)) = difference(X2,X),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
product(difference(X2,quotient(X,X2)),X2) = difference(X2,X),
inference(transitivity,[status(thm)],[c328,c330]) ).
cnf(c332,plain,
difference(X2,X) = product(difference(X2,quotient(X,X2)),X2),
inference(symmetry,[status(thm)],[c331]) ).
cnf(c333,plain,
quotient(difference(X2,X),X2) = quotient(product(difference(X2,quotient(X,X2)),X2),X2),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
quotient(product(difference(X2,quotient(X,X2)),X2),X2) = difference(X2,quotient(X,X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c335,plain,
quotient(difference(X2,X),X2) = difference(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c333,c334]) ).
cnf(c336,plain,
product(X2,quotient(difference(X2,X),X2)) = product(X2,difference(X2,quotient(X,X2))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
product(X2,difference(X2,quotient(X,X2))) = quotient(X,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c338,plain,
product(X2,quotient(difference(X2,X),X2)) = quotient(X,X2),
inference(transitivity,[status(thm)],[c336,c337]) ).
cnf(c339,plain,
difference(difference(X2,X),product(X2,difference(X2,X))) = quotient(X,X2),
inference(transitivity,[status(thm)],[c326,c338]) ).
cnf(c340,plain,
difference(difference(X2,X),X) = quotient(X,X2),
inference(transitivity,[status(thm)],[c296,c339]) ).
cnf(c341,plain,
difference(difference(quotient(X2,X),X2),X2) = quotient(X2,quotient(X2,X)),
inference(substitution,[status(thm)],[c340]) ).
cnf(c342,plain,
quotient(X2,quotient(X2,X)) = difference(difference(quotient(X2,X),X2),X2),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
product(quotient(X2,X),X) = X2,
inference(substitution,[status(thm)],[c165]) ).
cnf(c344,plain,
X2 = product(quotient(X2,X),X),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
difference(quotient(X2,X),X2) = difference(quotient(X2,X),product(quotient(X2,X),X)),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
difference(quotient(X2,X),product(quotient(X2,X),X)) = X,
inference(substitution,[status(thm)],[c66]) ).
cnf(c347,plain,
difference(quotient(X2,X),X2) = X,
inference(transitivity,[status(thm)],[c345,c346]) ).
cnf(c348,plain,
difference(difference(quotient(X2,X),X2),X2) = difference(X,X2),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
quotient(X2,quotient(X2,X)) = difference(X,X2),
inference(transitivity,[status(thm)],[c342,c348]) ).
cnf(c350,plain,
quotient(c,quotient(c,b)) = difference(b,c),
inference(substitution,[status(thm)],[c349]) ).
cnf(c351,plain,
difference(c,quotient(c,quotient(c,b))) = difference(c,difference(b,c)),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
quotient(c,difference(c,quotient(c,b))) = difference(c,difference(b,c)),
inference(transitivity,[status(thm)],[c293,c351]) ).
cnf(c353,plain,
quotient(c,quotient(a,c)) = difference(c,difference(b,c)),
inference(transitivity,[status(thm)],[c271,c352]) ).
cnf(c354,plain,
product(c,quotient(c,quotient(a,c))) = product(c,difference(c,difference(b,c))),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
product(X,product(c,quotient(c,quotient(a,c)))) = product(X,product(c,difference(c,difference(b,c)))),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
product(c,difference(c,difference(b,c))) = difference(b,c),
inference(substitution,[status(thm)],[c38]) ).
cnf(c357,plain,
product(X,product(c,difference(c,difference(b,c)))) = product(X,difference(b,c)),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
product(X,product(c,quotient(c,quotient(a,c)))) = product(X,difference(b,c)),
inference(transitivity,[status(thm)],[c355,c357]) ).
cnf(c359,plain,
product(X,product(c,quotient(c,quotient(product(a,c),b)))) = product(X,difference(b,c)),
inference(transitivity,[status(thm)],[c219,c358]) ).
cnf(c360,plain,
difference(c,bigC(c,X,product(quotient(product(a,c),b),c))) = product(X,difference(b,c)),
inference(transitivity,[status(thm)],[c212,c359]) ).
cnf(c361,plain,
difference(c,bigC(c,X,a)) = product(X,difference(b,c)),
inference(transitivity,[status(thm)],[c193,c360]) ).
cnf(c362,plain,
difference(c,bigC(c,quotient(X,c),a)) = product(quotient(X,c),difference(b,c)),
inference(substitution,[status(thm)],[c361]) ).
cnf(c363,plain,
difference(X,product(product(X,quotient(X3,X2)),X2)) = product(quotient(X3,X2),difference(X,X2)),
inference(substitution,[status(thm)],[c160]) ).
cnf(c364,plain,
product(quotient(X3,X2),difference(X,X2)) = difference(X,product(product(X,quotient(X3,X2)),X2)),
inference(symmetry,[status(thm)],[c363]) ).
cnf(c365,plain,
product(product(X3,X),product(quotient(X2,X),X)) = product(product(X3,quotient(X2,X)),X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c366,plain,
product(product(X3,quotient(X2,X)),X) = product(product(X3,X),product(quotient(X2,X),X)),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c367,plain,
product(quotient(X2,X),X) = X2,
inference(substitution,[status(thm)],[c165]) ).
cnf(c368,plain,
product(product(X3,X),product(quotient(X2,X),X)) = product(product(X3,X),X2),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
product(product(X3,quotient(X2,X)),X) = product(product(X3,X),X2),
inference(transitivity,[status(thm)],[c366,c368]) ).
cnf(c370,plain,
product(product(X,quotient(X3,X2)),X2) = product(product(X,X2),X3),
inference(substitution,[status(thm)],[c369]) ).
cnf(c371,plain,
difference(X,product(product(X,quotient(X3,X2)),X2)) = difference(X,product(product(X,X2),X3)),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
difference(X,product(product(X,X2),X3)) = product(X2,difference(X,X3)),
inference(substitution,[status(thm)],[c160]) ).
cnf(c373,plain,
difference(X,product(product(X,quotient(X3,X2)),X2)) = product(X2,difference(X,X3)),
inference(transitivity,[status(thm)],[c371,c372]) ).
cnf(c374,plain,
product(quotient(X3,X2),difference(X,X2)) = product(X2,difference(X,X3)),
inference(transitivity,[status(thm)],[c364,c373]) ).
cnf(c375,plain,
product(quotient(X,c),difference(b,c)) = product(c,difference(b,X)),
inference(substitution,[status(thm)],[c374]) ).
cnf(c376,plain,
difference(c,bigC(c,quotient(X,c),a)) = product(c,difference(b,X)),
inference(transitivity,[status(thm)],[c362,c375]) ).
cnf(c377,plain,
difference(c,product(product(c,a),X)) = product(c,difference(b,X)),
inference(transitivity,[status(thm)],[c173,c376]) ).
cnf(c378,plain,
product(a,difference(c,X)) = product(c,difference(b,X)),
inference(transitivity,[status(thm)],[c162,c377]) ).
cnf(c379,plain,
product(c,difference(b,X)) = product(a,difference(c,X)),
inference(symmetry,[status(thm)],[c378]) ).
cnf(c380,plain,
product(product(c,difference(b,X)),c) = product(product(a,difference(c,X)),c),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
product(product(a,difference(c,X)),c) = product(X,product(c,quotient(c,a))),
inference(substitution,[status(thm)],[c123]) ).
cnf(c382,plain,
quotient(c,quotient(c,b)) = difference(b,c),
inference(substitution,[status(thm)],[c349]) ).
cnf(c383,plain,
difference(b,c) = quotient(c,quotient(c,b)),
inference(symmetry,[status(thm)],[c382]) ).
cnf(c384,plain,
product(difference(b,c),c) = product(quotient(c,quotient(c,b)),c),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,plain,
X = difference(quotient(X2,X),X2),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c386,plain,
product(X,X2) = product(difference(quotient(X2,X),X2),X2),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
quotient(X2,product(X,X2)) = quotient(X2,product(difference(quotient(X2,X),X2),X2)),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
product(product(product(X2,X),X),product(X,product(X,X2))) = X,
inference(substitution,[status(thm)],[c75]) ).
cnf(c389,plain,
X = product(product(product(X2,X),X),product(X,product(X,X2))),
inference(symmetry,[status(thm)],[c388]) ).
cnf(c390,plain,
difference(product(product(X2,X),X),X) = difference(product(product(X2,X),X),product(product(product(X2,X),X),product(X,product(X,X2)))),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
difference(product(product(X2,X),X),product(product(product(X2,X),X),product(X,product(X,X2)))) = product(X,product(X,X2)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c392,plain,
difference(product(product(X2,X),X),X) = product(X,product(X,X2)),
inference(transitivity,[status(thm)],[c390,c391]) ).
cnf(c393,plain,
difference(product(product(quotient(X,X2),X2),X2),X2) = product(X2,product(X2,quotient(X,X2))),
inference(substitution,[status(thm)],[c392]) ).
cnf(c394,plain,
product(X2,product(X2,quotient(X,X2))) = difference(product(product(quotient(X,X2),X2),X2),X2),
inference(symmetry,[status(thm)],[c393]) ).
cnf(c395,plain,
product(quotient(X,X2),X2) = X,
inference(substitution,[status(thm)],[c165]) ).
cnf(c396,plain,
product(product(quotient(X,X2),X2),X2) = product(X,X2),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
difference(product(product(quotient(X,X2),X2),X2),X2) = difference(product(X,X2),X2),
inference(congruence,[status(thm)],[c396]) ).
cnf(c398,plain,
product(X2,product(X2,quotient(X,X2))) = difference(product(X,X2),X2),
inference(transitivity,[status(thm)],[c394,c397]) ).
cnf(c399,plain,
product(X,product(X,quotient(X2,X))) = difference(product(X2,X),X),
inference(substitution,[status(thm)],[c398]) ).
cnf(c400,plain,
difference(product(X2,X),X) = product(X,product(X,quotient(X2,X))),
inference(symmetry,[status(thm)],[c399]) ).
cnf(c401,plain,
product(difference(product(X2,X),X),X) = product(product(X,product(X,quotient(X2,X))),X),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
product(product(X,product(X,quotient(X2,X))),X) = bigC(X,X,product(X,quotient(X2,X))),
inference(substitution,[status(thm)],[c98]) ).
cnf(c403,plain,
product(X2,product(product(X2,X),X2)) = bigC(X2,X2,product(X2,X)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c404,plain,
bigC(X2,X2,product(X2,X)) = product(X2,product(product(X2,X),X2)),
inference(symmetry,[status(thm)],[c403]) ).
cnf(c405,plain,
product(X2,product(product(X2,X),X2)) = product(X2,bigC(X2,X2,X)),
inference(congruence,[status(thm)],[c98]) ).
cnf(c406,plain,
bigC(X2,X2,product(X2,X)) = product(X2,bigC(X2,X2,X)),
inference(transitivity,[status(thm)],[c404,c405]) ).
cnf(c407,plain,
bigC(X,X,product(X,quotient(X2,X))) = product(X,bigC(X,X,quotient(X2,X))),
inference(substitution,[status(thm)],[c406]) ).
cnf(c408,plain,
bigC(X,X,quotient(X2,X)) = product(product(X,X),X2),
inference(substitution,[status(thm)],[c168]) ).
cnf(c409,plain,
product(X,bigC(X,X,quotient(X2,X))) = product(X,product(product(X,X),X2)),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c411,plain,
product(product(X,X),X2) = product(X,X2),
inference(congruence,[status(thm)],[c410]) ).
cnf(c412,plain,
product(X,product(product(X,X),X2)) = product(X,product(X,X2)),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
product(X,bigC(X,X,quotient(X2,X))) = product(X,product(X,X2)),
inference(transitivity,[status(thm)],[c409,c412]) ).
cnf(c414,plain,
bigC(X,X,product(X,quotient(X2,X))) = product(X,product(X,X2)),
inference(transitivity,[status(thm)],[c407,c413]) ).
cnf(c415,plain,
product(product(X,product(X,quotient(X2,X))),X) = product(X,product(X,X2)),
inference(transitivity,[status(thm)],[c402,c414]) ).
cnf(c416,plain,
product(difference(product(X2,X),X),X) = product(X,product(X,X2)),
inference(transitivity,[status(thm)],[c401,c415]) ).
cnf(c417,plain,
product(difference(product(quotient(X,X2),X2),X2),X2) = product(X2,product(X2,quotient(X,X2))),
inference(substitution,[status(thm)],[c416]) ).
cnf(c418,plain,
product(X2,product(X2,quotient(X,X2))) = product(difference(product(quotient(X,X2),X2),X2),X2),
inference(symmetry,[status(thm)],[c417]) ).
cnf(c419,plain,
product(quotient(X,X2),X2) = X,
inference(substitution,[status(thm)],[c165]) ).
cnf(c420,plain,
difference(product(quotient(X,X2),X2),X2) = difference(X,X2),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,plain,
product(difference(product(quotient(X,X2),X2),X2),X2) = product(difference(X,X2),X2),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
product(X2,product(X2,quotient(X,X2))) = product(difference(X,X2),X2),
inference(transitivity,[status(thm)],[c418,c421]) ).
cnf(c423,plain,
product(difference(X,X2),X2) = product(X2,product(X2,quotient(X,X2))),
inference(symmetry,[status(thm)],[c422]) ).
cnf(c424,plain,
quotient(X2,product(difference(X,X2),X2)) = quotient(X2,product(X2,product(X2,quotient(X,X2)))),
inference(congruence,[status(thm)],[c423]) ).
cnf(c425,plain,
quotient(X2,product(X2,product(X2,quotient(X,X2)))) = product(product(quotient(X,X2),X2),X2),
inference(substitution,[status(thm)],[c80]) ).
cnf(c426,plain,
product(product(quotient(X,X2),X2),X2) = product(X,product(X2,X2)),
inference(substitution,[status(thm)],[c178]) ).
cnf(c427,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c428,plain,
product(X,product(X2,X2)) = product(X,X2),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
product(product(quotient(X,X2),X2),X2) = product(X,X2),
inference(transitivity,[status(thm)],[c426,c428]) ).
cnf(c430,plain,
quotient(X2,product(X2,product(X2,quotient(X,X2)))) = product(X,X2),
inference(transitivity,[status(thm)],[c425,c429]) ).
cnf(c431,plain,
quotient(X2,product(difference(X,X2),X2)) = product(X,X2),
inference(transitivity,[status(thm)],[c424,c430]) ).
cnf(c432,plain,
quotient(X2,product(difference(quotient(X2,X),X2),X2)) = product(quotient(X2,X),X2),
inference(substitution,[status(thm)],[c431]) ).
cnf(c433,plain,
quotient(X2,product(X,X2)) = product(quotient(X2,X),X2),
inference(transitivity,[status(thm)],[c387,c432]) ).
cnf(c434,plain,
quotient(c,product(quotient(c,b),c)) = product(quotient(c,quotient(c,b)),c),
inference(substitution,[status(thm)],[c433]) ).
cnf(c435,plain,
product(quotient(c,quotient(c,b)),c) = quotient(c,product(quotient(c,b),c)),
inference(symmetry,[status(thm)],[c434]) ).
cnf(c436,plain,
quotient(c,product(quotient(c,b),c)) = quotient(c,product(c,a)),
inference(congruence,[status(thm)],[c260]) ).
cnf(c437,plain,
quotient(c,product(c,a)) = product(c,quotient(c,a)),
inference(substitution,[status(thm)],[c283]) ).
cnf(c438,plain,
quotient(c,product(quotient(c,b),c)) = product(c,quotient(c,a)),
inference(transitivity,[status(thm)],[c436,c437]) ).
cnf(c439,plain,
product(quotient(c,quotient(c,b)),c) = product(c,quotient(c,a)),
inference(transitivity,[status(thm)],[c435,c438]) ).
cnf(c440,plain,
product(difference(b,c),c) = product(c,quotient(c,a)),
inference(transitivity,[status(thm)],[c384,c439]) ).
cnf(c441,plain,
product(c,quotient(c,a)) = product(difference(b,c),c),
inference(symmetry,[status(thm)],[c440]) ).
cnf(c442,plain,
product(c,product(c,quotient(b,c))) = product(difference(b,c),c),
inference(substitution,[status(thm)],[c422]) ).
cnf(c443,plain,
product(difference(b,c),c) = product(c,product(c,quotient(b,c))),
inference(symmetry,[status(thm)],[c442]) ).
cnf(c444,plain,
bigC(X2,X,difference(X,X2)) = product(product(X2,X),product(difference(X,X2),X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c445,plain,
product(X,product(X,quotient(X2,X))) = difference(product(X2,X),X),
inference(substitution,[status(thm)],[c398]) ).
cnf(c446,plain,
difference(product(X2,X),X) = product(X,product(X,quotient(X2,X))),
inference(symmetry,[status(thm)],[c445]) ).
cnf(c447,plain,
product(X,product(X,quotient(X2,X))) = product(difference(X2,X),X),
inference(substitution,[status(thm)],[c422]) ).
cnf(c448,plain,
difference(product(X2,X),X) = product(difference(X2,X),X),
inference(transitivity,[status(thm)],[c446,c447]) ).
cnf(c449,plain,
difference(product(X,X2),X2) = product(difference(X,X2),X2),
inference(substitution,[status(thm)],[c448]) ).
cnf(c450,plain,
product(difference(X,X2),X2) = difference(product(X,X2),X2),
inference(symmetry,[status(thm)],[c449]) ).
cnf(c451,plain,
product(product(X2,X),product(difference(X,X2),X2)) = product(product(X2,X),difference(product(X,X2),X2)),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c453,plain,
X = product(X,X),
inference(symmetry,[status(thm)],[c452]) ).
cnf(c454,plain,
product(X2,X) = product(product(X2,X2),X),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
product(product(X2,X),difference(product(X,X2),X2)) = product(product(product(X2,X2),X),difference(product(X,X2),X2)),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
product(product(X2,quotient(X,X2)),X2) = product(product(X2,X2),X),
inference(substitution,[status(thm)],[c369]) ).
cnf(c457,plain,
product(product(X2,X2),X) = product(product(X2,quotient(X,X2)),X2),
inference(symmetry,[status(thm)],[c456]) ).
cnf(c458,plain,
product(product(product(X2,X2),X),difference(product(X,X2),X2)) = product(product(product(X2,quotient(X,X2)),X2),difference(product(X,X2),X2)),
inference(congruence,[status(thm)],[c457]) ).
cnf(c459,plain,
difference(product(X,X2),X2) = product(X2,product(X2,quotient(X,X2))),
inference(symmetry,[status(thm)],[c398]) ).
cnf(c460,plain,
difference(X2,difference(product(X,X2),X2)) = difference(X2,product(X2,product(X2,quotient(X,X2)))),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
difference(X2,product(X2,product(X2,quotient(X,X2)))) = product(X2,quotient(X,X2)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c462,plain,
difference(X2,difference(product(X,X2),X2)) = product(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c460,c461]) ).
cnf(c463,plain,
product(X2,quotient(X,X2)) = difference(X2,difference(product(X,X2),X2)),
inference(symmetry,[status(thm)],[c462]) ).
cnf(c464,plain,
product(product(X2,quotient(X,X2)),X2) = product(difference(X2,difference(product(X,X2),X2)),X2),
inference(congruence,[status(thm)],[c463]) ).
cnf(c465,plain,
product(product(product(X2,quotient(X,X2)),X2),difference(product(X,X2),X2)) = product(product(difference(X2,difference(product(X,X2),X2)),X2),difference(product(X,X2),X2)),
inference(congruence,[status(thm)],[c464]) ).
cnf(c466,plain,
product(product(difference(X2,X),X),product(X2,X)) = product(product(difference(X2,X),X2),X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c467,plain,
product(product(difference(X2,X),X2),X) = product(product(difference(X2,X),X),product(X2,X)),
inference(symmetry,[status(thm)],[c466]) ).
cnf(c468,plain,
product(difference(X2,X),X) = difference(product(X2,X),X),
inference(symmetry,[status(thm)],[c448]) ).
cnf(c469,plain,
product(product(difference(X2,X),X),product(X2,X)) = product(difference(product(X2,X),X),product(X2,X)),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
product(difference(product(X2,X),X),product(X2,X)) = product(X,quotient(product(X2,X),X)),
inference(substitution,[status(thm)],[c313]) ).
cnf(c471,plain,
quotient(product(X2,X),X) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c472,plain,
product(X,quotient(product(X2,X),X)) = product(X,X2),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
product(difference(product(X2,X),X),product(X2,X)) = product(X,X2),
inference(transitivity,[status(thm)],[c470,c472]) ).
cnf(c474,plain,
product(product(difference(X2,X),X),product(X2,X)) = product(X,X2),
inference(transitivity,[status(thm)],[c469,c473]) ).
cnf(c475,plain,
product(product(difference(X2,X),X2),X) = product(X,X2),
inference(transitivity,[status(thm)],[c467,c474]) ).
cnf(c476,plain,
product(product(difference(X2,difference(product(X,X2),X2)),X2),difference(product(X,X2),X2)) = product(difference(product(X,X2),X2),X2),
inference(substitution,[status(thm)],[c475]) ).
cnf(c477,plain,
product(difference(product(X,X2),X2),X2) = product(X2,product(X2,X)),
inference(substitution,[status(thm)],[c416]) ).
cnf(c478,plain,
product(product(difference(X2,difference(product(X,X2),X2)),X2),difference(product(X,X2),X2)) = product(X2,product(X2,X)),
inference(transitivity,[status(thm)],[c476,c477]) ).
cnf(c479,plain,
product(product(product(X2,quotient(X,X2)),X2),difference(product(X,X2),X2)) = product(X2,product(X2,X)),
inference(transitivity,[status(thm)],[c465,c478]) ).
cnf(c480,plain,
product(product(product(X2,X2),X),difference(product(X,X2),X2)) = product(X2,product(X2,X)),
inference(transitivity,[status(thm)],[c458,c479]) ).
cnf(c481,plain,
product(product(X2,X),difference(product(X,X2),X2)) = product(X2,product(X2,X)),
inference(transitivity,[status(thm)],[c455,c480]) ).
cnf(c482,plain,
product(product(X2,X),product(difference(X,X2),X2)) = product(X2,product(X2,X)),
inference(transitivity,[status(thm)],[c451,c481]) ).
cnf(c483,plain,
bigC(X2,X,difference(X,X2)) = product(X2,product(X2,X)),
inference(transitivity,[status(thm)],[c444,c482]) ).
cnf(c484,plain,
bigC(c,quotient(b,c),difference(quotient(b,c),c)) = product(c,product(c,quotient(b,c))),
inference(substitution,[status(thm)],[c483]) ).
cnf(c485,plain,
product(c,product(c,quotient(b,c))) = bigC(c,quotient(b,c),difference(quotient(b,c),c)),
inference(symmetry,[status(thm)],[c484]) ).
cnf(c486,plain,
quotient(c,quotient(c,quotient(b,c))) = difference(quotient(b,c),c),
inference(substitution,[status(thm)],[c349]) ).
cnf(c487,plain,
difference(quotient(b,c),c) = quotient(c,quotient(c,quotient(b,c))),
inference(symmetry,[status(thm)],[c486]) ).
cnf(c488,plain,
difference(difference(X,X2),X2) = quotient(X2,X),
inference(substitution,[status(thm)],[c340]) ).
cnf(c489,plain,
quotient(X2,X) = difference(difference(X,X2),X2),
inference(symmetry,[status(thm)],[c488]) ).
cnf(c490,plain,
quotient(quotient(X2,X),X2) = quotient(difference(difference(X,X2),X2),X2),
inference(congruence,[status(thm)],[c489]) ).
cnf(c491,plain,
product(X,product(X,quotient(quotient(X2,X),X))) = product(difference(quotient(X2,X),X),X),
inference(substitution,[status(thm)],[c422]) ).
cnf(c492,plain,
product(difference(quotient(X2,X),X),X) = product(X,product(X,quotient(quotient(X2,X),X))),
inference(symmetry,[status(thm)],[c491]) ).
cnf(c493,plain,
quotient(product(X,quotient(X2,X)),X) = product(X,quotient(quotient(X2,X),X)),
inference(substitution,[status(thm)],[c233]) ).
cnf(c494,plain,
product(X,quotient(quotient(X2,X),X)) = quotient(product(X,quotient(X2,X)),X),
inference(symmetry,[status(thm)],[c493]) ).
cnf(c495,plain,
product(X,product(X,quotient(quotient(X2,X),X))) = product(X,quotient(product(X,quotient(X2,X)),X)),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
quotient(product(X,product(X,quotient(X2,X))),X) = product(X,quotient(product(X,quotient(X2,X)),X)),
inference(substitution,[status(thm)],[c233]) ).
cnf(c497,plain,
product(X,quotient(product(X,quotient(X2,X)),X)) = quotient(product(X,product(X,quotient(X2,X))),X),
inference(symmetry,[status(thm)],[c496]) ).
cnf(c498,plain,
product(X,product(X,quotient(X2,X))) = difference(product(X2,X),X),
inference(substitution,[status(thm)],[c398]) ).
cnf(c499,plain,
quotient(product(X,product(X,quotient(X2,X))),X) = quotient(difference(product(X2,X),X),X),
inference(congruence,[status(thm)],[c498]) ).
cnf(c500,plain,
quotient(difference(product(X2,X),X),X) = quotient(product(difference(X2,X),X),X),
inference(congruence,[status(thm)],[c448]) ).
cnf(c501,plain,
quotient(product(difference(X2,X),X),X) = difference(X2,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c502,plain,
quotient(difference(product(X2,X),X),X) = difference(X2,X),
inference(transitivity,[status(thm)],[c500,c501]) ).
cnf(c503,plain,
quotient(product(X,product(X,quotient(X2,X))),X) = difference(X2,X),
inference(transitivity,[status(thm)],[c499,c502]) ).
cnf(c504,plain,
product(X,quotient(product(X,quotient(X2,X)),X)) = difference(X2,X),
inference(transitivity,[status(thm)],[c497,c503]) ).
cnf(c505,plain,
product(X,product(X,quotient(quotient(X2,X),X))) = difference(X2,X),
inference(transitivity,[status(thm)],[c495,c504]) ).
cnf(c506,plain,
product(difference(quotient(X2,X),X),X) = difference(X2,X),
inference(transitivity,[status(thm)],[c492,c505]) ).
cnf(c507,plain,
difference(X2,X) = product(difference(quotient(X2,X),X),X),
inference(symmetry,[status(thm)],[c506]) ).
cnf(c508,plain,
quotient(difference(X2,X),X) = quotient(product(difference(quotient(X2,X),X),X),X),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
quotient(product(difference(quotient(X2,X),X),X),X) = difference(quotient(X2,X),X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c510,plain,
quotient(difference(X2,X),X) = difference(quotient(X2,X),X),
inference(transitivity,[status(thm)],[c508,c509]) ).
cnf(c511,plain,
quotient(difference(difference(X,X2),X2),X2) = difference(quotient(difference(X,X2),X2),X2),
inference(substitution,[status(thm)],[c510]) ).
cnf(c512,plain,
quotient(difference(X,X2),X2) = difference(quotient(X,X2),X2),
inference(substitution,[status(thm)],[c510]) ).
cnf(c513,plain,
difference(quotient(difference(X,X2),X2),X2) = difference(difference(quotient(X,X2),X2),X2),
inference(congruence,[status(thm)],[c512]) ).
cnf(c514,plain,
difference(difference(quotient(X,X2),X2),X2) = quotient(X2,quotient(X,X2)),
inference(substitution,[status(thm)],[c340]) ).
cnf(c515,plain,
difference(quotient(difference(X,X2),X2),X2) = quotient(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c513,c514]) ).
cnf(c516,plain,
quotient(difference(difference(X,X2),X2),X2) = quotient(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c511,c515]) ).
cnf(c517,plain,
quotient(quotient(X2,X),X2) = quotient(X2,quotient(X,X2)),
inference(transitivity,[status(thm)],[c490,c516]) ).
cnf(c518,plain,
quotient(quotient(c,b),c) = quotient(c,quotient(b,c)),
inference(substitution,[status(thm)],[c517]) ).
cnf(c519,plain,
quotient(c,quotient(b,c)) = quotient(quotient(c,b),c),
inference(symmetry,[status(thm)],[c518]) ).
cnf(c520,plain,
quotient(c,quotient(c,quotient(b,c))) = quotient(c,quotient(quotient(c,b),c)),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
quotient(quotient(c,quotient(c,b)),c) = quotient(c,quotient(quotient(c,b),c)),
inference(substitution,[status(thm)],[c517]) ).
cnf(c522,plain,
quotient(c,quotient(quotient(c,b),c)) = quotient(quotient(c,quotient(c,b)),c),
inference(symmetry,[status(thm)],[c521]) ).
cnf(c523,plain,
quotient(c,b) = product(c,quotient(a,c)),
inference(symmetry,[status(thm)],[c265]) ).
cnf(c524,plain,
quotient(c,quotient(c,b)) = quotient(c,product(c,quotient(a,c))),
inference(congruence,[status(thm)],[c523]) ).
cnf(c525,plain,
quotient(quotient(c,quotient(c,b)),c) = quotient(quotient(c,product(c,quotient(a,c))),c),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
quotient(X2,product(X2,X)) = product(product(difference(X2,X),X2),X2),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c527,plain,
quotient(quotient(X2,product(X2,X)),X2) = quotient(product(product(difference(X2,X),X2),X2),X2),
inference(congruence,[status(thm)],[c526]) ).
cnf(c528,plain,
quotient(product(product(difference(X2,X),X2),X2),X2) = product(difference(X2,X),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c529,plain,
quotient(quotient(X2,product(X2,X)),X2) = product(difference(X2,X),X2),
inference(transitivity,[status(thm)],[c527,c528]) ).
cnf(c530,plain,
quotient(quotient(c,product(c,quotient(a,c))),c) = product(difference(c,quotient(a,c)),c),
inference(substitution,[status(thm)],[c529]) ).
cnf(c531,plain,
product(difference(c,quotient(a,c)),c) = difference(c,a),
inference(substitution,[status(thm)],[c331]) ).
cnf(c532,plain,
quotient(quotient(c,product(c,quotient(a,c))),c) = difference(c,a),
inference(transitivity,[status(thm)],[c530,c531]) ).
cnf(c533,plain,
quotient(quotient(c,quotient(c,b)),c) = difference(c,a),
inference(transitivity,[status(thm)],[c525,c532]) ).
cnf(c534,plain,
quotient(c,quotient(quotient(c,b),c)) = difference(c,a),
inference(transitivity,[status(thm)],[c522,c533]) ).
cnf(c535,plain,
quotient(c,quotient(c,quotient(b,c))) = difference(c,a),
inference(transitivity,[status(thm)],[c520,c534]) ).
cnf(c536,plain,
difference(quotient(b,c),c) = difference(c,a),
inference(transitivity,[status(thm)],[c487,c535]) ).
cnf(c537,plain,
bigC(c,quotient(b,c),difference(quotient(b,c),c)) = bigC(c,quotient(b,c),difference(c,a)),
inference(congruence,[status(thm)],[c536]) ).
cnf(c538,plain,
bigC(c,quotient(b,c),difference(c,a)) = product(product(c,difference(c,a)),b),
inference(substitution,[status(thm)],[c170]) ).
cnf(c539,plain,
product(c,difference(c,a)) = a,
inference(substitution,[status(thm)],[c38]) ).
cnf(c540,plain,
product(product(c,difference(c,a)),b) = product(a,b),
inference(congruence,[status(thm)],[c539]) ).
cnf(c541,plain,
bigC(c,quotient(b,c),difference(c,a)) = product(a,b),
inference(transitivity,[status(thm)],[c538,c540]) ).
cnf(c542,plain,
bigC(c,quotient(b,c),difference(quotient(b,c),c)) = product(a,b),
inference(transitivity,[status(thm)],[c537,c541]) ).
cnf(c543,plain,
product(c,product(c,quotient(b,c))) = product(a,b),
inference(transitivity,[status(thm)],[c485,c542]) ).
cnf(c544,plain,
product(difference(b,c),c) = product(a,b),
inference(transitivity,[status(thm)],[c443,c543]) ).
cnf(c545,plain,
product(c,quotient(c,a)) = product(a,b),
inference(transitivity,[status(thm)],[c441,c544]) ).
cnf(c546,plain,
product(X,product(c,quotient(c,a))) = product(X,product(a,b)),
inference(congruence,[status(thm)],[c545]) ).
cnf(c547,plain,
product(product(a,difference(c,X)),c) = product(X,product(a,b)),
inference(transitivity,[status(thm)],[c381,c546]) ).
cnf(c548,plain,
product(product(c,difference(b,X)),c) = product(X,product(a,b)),
inference(transitivity,[status(thm)],[c380,c547]) ).
cnf(c549,plain,
bigC(c,c,difference(b,X)) = product(X,product(a,b)),
inference(transitivity,[status(thm)],[c151,c548]) ).
cnf(c550,plain,
bigC(c,c,difference(b,product(b,X))) = product(product(b,X),product(a,b)),
inference(substitution,[status(thm)],[c549]) ).
cnf(c551,plain,
product(product(b,X),product(a,b)) = bigC(c,c,difference(b,product(b,X))),
inference(symmetry,[status(thm)],[c550]) ).
cnf(c552,plain,
difference(b,product(b,X)) = X,
inference(substitution,[status(thm)],[c66]) ).
cnf(c553,plain,
bigC(c,c,difference(b,product(b,X))) = bigC(c,c,X),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
difference(X2,product(X2,X)) = X,
inference(substitution,[status(thm)],[c66]) ).
cnf(c555,plain,
X = difference(X2,product(X2,X)),
inference(symmetry,[status(thm)],[c554]) ).
cnf(c556,plain,
bigC(X,X2,X2) = bigC(difference(X2,product(X2,X)),X2,X2),
inference(congruence,[status(thm)],[c555]) ).
cnf(c557,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c558,plain,
X = product(X2,difference(X2,X)),
inference(symmetry,[status(thm)],[c557]) ).
cnf(c559,plain,
product(product(difference(X3,X2),X),X2) = product(product(difference(X3,X2),X),product(X3,difference(X3,X2))),
inference(congruence,[status(thm)],[c558]) ).
cnf(c560,plain,
bigC(difference(X3,X2),X,X3) = product(product(difference(X3,X2),X),product(X3,difference(X3,X2))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c561,plain,
product(product(difference(X3,X2),X),product(X3,difference(X3,X2))) = bigC(difference(X3,X2),X,X3),
inference(symmetry,[status(thm)],[c560]) ).
cnf(c562,plain,
bigC(difference(X3,X2),X3,X) = bigC(difference(X3,X2),X,X3),
inference(substitution,[status(thm)],[c12]) ).
cnf(c563,plain,
bigC(difference(X3,X2),X,X3) = bigC(difference(X3,X2),X3,X),
inference(symmetry,[status(thm)],[c562]) ).
cnf(c564,plain,
product(product(difference(X3,X2),X),product(X3,difference(X3,X2))) = bigC(difference(X3,X2),X3,X),
inference(transitivity,[status(thm)],[c561,c563]) ).
cnf(c565,plain,
product(product(difference(X3,X2),X),X2) = bigC(difference(X3,X2),X3,X),
inference(transitivity,[status(thm)],[c559,c564]) ).
cnf(c566,plain,
product(product(difference(X2,X),X2),X) = bigC(difference(X2,X),X2,X2),
inference(substitution,[status(thm)],[c565]) ).
cnf(c567,plain,
bigC(difference(X2,X),X2,X2) = product(product(difference(X2,X),X2),X),
inference(symmetry,[status(thm)],[c566]) ).
cnf(c568,plain,
product(product(difference(X2,X),X2),X) = product(product(X,quotient(X2,X)),X),
inference(congruence,[status(thm)],[c313]) ).
cnf(c569,plain,
product(product(X,quotient(X2,X)),X) = bigC(X,X,quotient(X2,X)),
inference(substitution,[status(thm)],[c98]) ).
cnf(c570,plain,
bigC(X,X,quotient(X2,X)) = product(product(X,X),X2),
inference(substitution,[status(thm)],[c168]) ).
cnf(c571,plain,
product(X,X) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c572,plain,
product(product(X,X),X2) = product(X,X2),
inference(congruence,[status(thm)],[c571]) ).
cnf(c573,plain,
bigC(X,X,quotient(X2,X)) = product(X,X2),
inference(transitivity,[status(thm)],[c570,c572]) ).
cnf(c574,plain,
product(product(X,quotient(X2,X)),X) = product(X,X2),
inference(transitivity,[status(thm)],[c569,c573]) ).
cnf(c575,plain,
product(product(difference(X2,X),X2),X) = product(X,X2),
inference(transitivity,[status(thm)],[c568,c574]) ).
cnf(c576,plain,
bigC(difference(X2,X),X2,X2) = product(X,X2),
inference(transitivity,[status(thm)],[c567,c575]) ).
cnf(c577,plain,
bigC(difference(X2,product(X2,X)),X2,X2) = product(product(X2,X),X2),
inference(substitution,[status(thm)],[c576]) ).
cnf(c578,plain,
bigC(difference(X2,product(X2,X)),X2,X2) = bigC(X2,X2,X),
inference(transitivity,[status(thm)],[c577,c98]) ).
cnf(c579,plain,
bigC(X,X2,X2) = bigC(X2,X2,X),
inference(transitivity,[status(thm)],[c556,c578]) ).
cnf(c580,plain,
bigC(X,c,c) = bigC(c,c,X),
inference(substitution,[status(thm)],[c579]) ).
cnf(c581,plain,
bigC(c,c,X) = bigC(X,c,c),
inference(symmetry,[status(thm)],[c580]) ).
cnf(c582,plain,
bigC(c,c,difference(b,product(b,X))) = bigC(X,c,c),
inference(transitivity,[status(thm)],[c553,c581]) ).
cnf(c583,plain,
product(product(b,X),product(a,b)) = bigC(X,c,c),
inference(transitivity,[status(thm)],[c551,c582]) ).
cnf(c584,plain,
bigC(b,X,a) = bigC(X,c,c),
inference(transitivity,[status(thm)],[c149,c583]) ).
cnf(c585,plain,
bigC(b,a,X) = bigC(X,c,c),
inference(transitivity,[status(thm)],[c148,c584]) ).
cnf(c586,plain,
bigC(X,c,c) = bigC(c,c,X),
inference(substitution,[status(thm)],[c579]) ).
cnf(c587,plain,
bigC(b,a,X) = bigC(c,c,X),
inference(transitivity,[status(thm)],[c585,c586]) ).
cnf(c588,plain,
bigC(a,b,X) = bigC(c,c,X),
inference(transitivity,[status(thm)],[c147,c587]) ).
cnf(c589,plain,
bigC(a,b,x0) = bigC(c,c,x0),
inference(substitution,[status(thm)],[c588]) ).
cnf(c590,plain,
$false,
inference(resolution,[status(thm)],[c3,c589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 10:39:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.86/1.02 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.86/1.02
% 3.86/1.02 % SZS status Theorem
% 3.86/1.02
% 3.86/1.06 % SZS output start CNFRefutation
% See solution above
% 7.01/1.34
% 7.01/1.34 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------