%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO073-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 09:35:43 AM UTC 2026
% Result : Unsatisfiable 8.82s 1.34s
% Output : CNFRefutation 11.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 154
% Number of leaves : 2
% Syntax : Number of clauses : 779 ( 779 unt; 0 nHn; 9 RR)
% Number of literals : 779 ( 778 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 1793 ( 177 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
add(add(a,b),c) != add(a,add(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',huntinton_2) ).
cnf(c2,axiom,
inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D)))))))) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dn1) ).
cnf(c3,plain,
inverse(add(inverse(add(inverse(add(inverse(inverse(X3)),X2)),X3)),inverse(add(inverse(inverse(X3)),inverse(add(inverse(X3),inverse(add(X3,X)))))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X3 = inverse(add(inverse(add(inverse(add(inverse(inverse(X3)),X2)),X3)),inverse(add(inverse(inverse(X3)),inverse(add(inverse(X3),inverse(add(X3,X)))))))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
add(X3,inverse(X3)) = add(inverse(add(inverse(add(inverse(add(inverse(inverse(X3)),X2)),X3)),inverse(add(inverse(inverse(X3)),inverse(add(inverse(X3),inverse(add(X3,X)))))))),inverse(X3)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
inverse(add(X3,inverse(X3))) = inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X3)),X2)),X3)),inverse(add(inverse(inverse(X3)),inverse(add(inverse(X3),inverse(add(X3,X)))))))),inverse(X3))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
add(inverse(add(X3,inverse(X3))),X3) = add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X3)),X2)),X3)),inverse(add(inverse(inverse(X3)),inverse(add(inverse(X3),inverse(add(X3,X)))))))),inverse(X3))),X3),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
inverse(add(inverse(add(X3,inverse(X3))),X3)) = inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X3)),X2)),X3)),inverse(add(inverse(inverse(X3)),inverse(add(inverse(X3),inverse(add(X3,X)))))))),inverse(X3))),X3)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
inverse(add(inverse(add(inverse(add(inverse(inverse(X2)),X)),X2)),inverse(add(inverse(inverse(X2)),inverse(add(inverse(X2),inverse(add(X2,X3)))))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
X3 = inverse(add(inverse(add(inverse(add(inverse(inverse(X3)),X2)),X3)),inverse(add(inverse(inverse(X3)),inverse(add(inverse(X3),inverse(add(X3,X)))))))),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X4)),X3)),X4)),X2)),inverse(X4))),X4) = add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X4)),X3)),X4)),X2)),inverse(X4))),inverse(add(inverse(add(inverse(add(inverse(inverse(X4)),X3)),X4)),inverse(add(inverse(inverse(X4)),inverse(add(inverse(X4),inverse(add(X4,X))))))))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X4)),X3)),X4)),X2)),inverse(X4))),X4)) = inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X4)),X3)),X4)),X2)),inverse(X4))),inverse(add(inverse(add(inverse(add(inverse(inverse(X4)),X3)),X4)),inverse(add(inverse(inverse(X4)),inverse(add(inverse(X4),inverse(add(X4,X)))))))))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X4)),X3)),X4)),X2)),inverse(X4))),inverse(add(inverse(add(inverse(add(inverse(inverse(X4)),X3)),X4)),inverse(add(inverse(inverse(X4)),inverse(add(inverse(X4),inverse(add(X4,X)))))))))) = inverse(X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X3)),X2)),X3)),X)),inverse(X3))),X3)) = inverse(X3),
inference(transitivity,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X3)),X2)),X3)),inverse(add(inverse(inverse(X3)),inverse(add(inverse(X3),inverse(add(X3,X)))))))),inverse(X3))),X3)) = inverse(X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(add(inverse(add(X,inverse(X))),X)) = inverse(X),
inference(transitivity,[status(thm)],[c8,c15]) ).
cnf(c17,plain,
inverse(X) = inverse(add(inverse(add(X,inverse(X))),X)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))) = add(inverse(add(inverse(add(X2,inverse(X2))),X2)),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))) = inverse(add(inverse(add(inverse(add(X2,inverse(X2))),X2)),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
inverse(add(inverse(add(inverse(add(X2,inverse(X2))),X2)),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))) = X2,
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
inverse(add(inverse(add(X,X)),inverse(add(add(X,X),inverse(add(inverse(add(X,X)),inverse(add(add(X,X),X)))))))) = add(X,X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
add(X,X) = inverse(add(inverse(add(X,X)),inverse(add(add(X,X),inverse(add(inverse(add(X,X)),inverse(add(add(X,X),X)))))))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
X2 = inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c25,plain,
add(X2,X2) = add(X2,inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
inverse(add(X2,X2)) = inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
add(inverse(X2),inverse(add(X2,X2))) = add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
inverse(add(inverse(X2),inverse(add(X2,X2)))) = inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))))))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))))))) = X2,
inference(substitution,[status(thm)],[c21]) ).
cnf(c30,plain,
inverse(add(inverse(X),inverse(add(X,X)))) = X,
inference(transitivity,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
X = inverse(add(inverse(X),inverse(add(X,X)))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
add(inverse(add(X,inverse(add(X,X)))),X) = add(inverse(add(X,inverse(add(X,X)))),inverse(add(inverse(X),inverse(add(X,X))))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
inverse(add(inverse(add(X,inverse(add(X,X)))),X)) = inverse(add(inverse(add(X,inverse(add(X,X)))),inverse(add(inverse(X),inverse(add(X,X)))))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
X2 = inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c35,plain,
add(X3,X2) = add(inverse(add(inverse(X3),inverse(add(X3,inverse(add(inverse(X3),inverse(add(X3,X)))))))),X2),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
inverse(add(X3,X2)) = inverse(add(inverse(add(inverse(X3),inverse(add(X3,inverse(add(inverse(X3),inverse(add(X3,X)))))))),X2)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
add(inverse(add(X3,X2)),inverse(add(inverse(X3),X2))) = add(inverse(add(inverse(add(inverse(X3),inverse(add(X3,inverse(add(inverse(X3),inverse(add(X3,X)))))))),X2)),inverse(add(inverse(X3),X2))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
inverse(add(inverse(add(X3,X2)),inverse(add(inverse(X3),X2)))) = inverse(add(inverse(add(inverse(add(inverse(X3),inverse(add(X3,inverse(add(inverse(X3),inverse(add(X3,X)))))))),X2)),inverse(add(inverse(X3),X2)))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
X2 = inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c40,plain,
add(X3,X2) = add(X3,inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
inverse(add(X3,X2)) = inverse(add(X3,inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
add(inverse(add(inverse(add(X4,X3)),X2)),inverse(add(X4,X2))) = add(inverse(add(inverse(add(X4,X3)),X2)),inverse(add(X4,inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
inverse(add(inverse(add(inverse(add(X4,X3)),X2)),inverse(add(X4,X2)))) = inverse(add(inverse(add(inverse(add(X4,X3)),X2)),inverse(add(X4,inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))))))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
inverse(add(inverse(add(inverse(add(X4,X3)),X2)),inverse(add(X4,inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
inverse(add(inverse(add(inverse(add(X3,X2)),X)),inverse(add(X3,X)))) = X,
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
inverse(add(inverse(add(inverse(add(inverse(X3),inverse(add(X3,inverse(add(inverse(X3),inverse(add(X3,X)))))))),X2)),inverse(add(inverse(X3),X2)))) = X2,
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
inverse(add(inverse(add(X2,X)),inverse(add(inverse(X2),X)))) = X,
inference(transitivity,[status(thm)],[c38,c46]) ).
cnf(c48,plain,
inverse(add(inverse(add(X,inverse(add(X,X)))),inverse(add(inverse(X),inverse(add(X,X)))))) = inverse(add(X,X)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
inverse(add(inverse(add(X,inverse(add(X,X)))),X)) = inverse(add(X,X)),
inference(transitivity,[status(thm)],[c33,c48]) ).
cnf(c50,plain,
inverse(add(X,X)) = inverse(add(inverse(add(X,inverse(add(X,X)))),X)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
add(inverse(add(X,X)),inverse(add(X,X))) = add(inverse(add(inverse(add(X,inverse(add(X,X)))),X)),inverse(add(X,X))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
inverse(add(inverse(add(X,X)),inverse(add(X,X)))) = inverse(add(inverse(add(inverse(add(X,inverse(add(X,X)))),X)),inverse(add(X,X)))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
inverse(add(inverse(add(inverse(add(X,inverse(add(X,X)))),X)),inverse(add(X,X)))) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c54,plain,
inverse(add(inverse(add(X,X)),inverse(add(X,X)))) = X,
inference(transitivity,[status(thm)],[c52,c53]) ).
cnf(c55,plain,
X = inverse(add(inverse(add(X,X)),inverse(add(X,X)))),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
add(inverse(add(add(X,X),inverse(add(X,X)))),X) = add(inverse(add(add(X,X),inverse(add(X,X)))),inverse(add(inverse(add(X,X)),inverse(add(X,X))))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
inverse(add(inverse(add(add(X,X),inverse(add(X,X)))),X)) = inverse(add(inverse(add(add(X,X),inverse(add(X,X)))),inverse(add(inverse(add(X,X)),inverse(add(X,X)))))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
inverse(add(inverse(add(add(X,X),inverse(add(X,X)))),inverse(add(inverse(add(X,X)),inverse(add(X,X)))))) = inverse(add(X,X)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c59,plain,
inverse(add(inverse(add(add(X,X),inverse(add(X,X)))),X)) = inverse(add(X,X)),
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
inverse(add(X,X)) = inverse(add(inverse(add(add(X,X),inverse(add(X,X)))),X)),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
add(inverse(add(X,X)),inverse(add(add(X,X),X))) = add(inverse(add(inverse(add(add(X,X),inverse(add(X,X)))),X)),inverse(add(add(X,X),X))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
inverse(add(inverse(add(X,X)),inverse(add(add(X,X),X)))) = inverse(add(inverse(add(inverse(add(add(X,X),inverse(add(X,X)))),X)),inverse(add(add(X,X),X)))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
inverse(add(inverse(add(inverse(add(add(X,X),inverse(add(X,X)))),X)),inverse(add(add(X,X),X)))) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c64,plain,
inverse(add(inverse(add(X,X)),inverse(add(add(X,X),X)))) = X,
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
add(add(X,X),inverse(add(inverse(add(X,X)),inverse(add(add(X,X),X))))) = add(add(X,X),X),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
inverse(add(add(X,X),inverse(add(inverse(add(X,X)),inverse(add(add(X,X),X)))))) = inverse(add(add(X,X),X)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
add(inverse(add(X,X)),inverse(add(add(X,X),inverse(add(inverse(add(X,X)),inverse(add(add(X,X),X))))))) = add(inverse(add(X,X)),inverse(add(add(X,X),X))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
inverse(add(inverse(add(X,X)),inverse(add(add(X,X),inverse(add(inverse(add(X,X)),inverse(add(add(X,X),X)))))))) = inverse(add(inverse(add(X,X)),inverse(add(add(X,X),X)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
inverse(add(inverse(add(X,X)),inverse(add(add(X,X),inverse(add(inverse(add(X,X)),inverse(add(add(X,X),X)))))))) = X,
inference(transitivity,[status(thm)],[c68,c64]) ).
cnf(c70,plain,
add(X,X) = X,
inference(transitivity,[status(thm)],[c23,c69]) ).
cnf(c71,plain,
add(inverse(X),inverse(X)) = inverse(X),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
inverse(X) = add(inverse(X),inverse(X)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
add(inverse(X),inverse(add(X,X2))) = add(add(inverse(X),inverse(X)),inverse(add(X,X2))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
inverse(add(inverse(X),inverse(add(X,X2)))) = inverse(add(add(inverse(X),inverse(X)),inverse(add(X,X2)))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
add(X2,inverse(add(inverse(X),inverse(add(X,X2))))) = add(X2,inverse(add(add(inverse(X),inverse(X)),inverse(add(X,X2))))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
X = add(X,X),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c77,plain,
inverse(X) = inverse(add(X,X)),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
add(inverse(X),inverse(X)) = add(inverse(X),inverse(add(X,X))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
add(add(inverse(X),inverse(X)),inverse(add(X,X2))) = add(add(inverse(X),inverse(add(X,X))),inverse(add(X,X2))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
inverse(add(add(inverse(X),inverse(X)),inverse(add(X,X2)))) = inverse(add(add(inverse(X),inverse(add(X,X))),inverse(add(X,X2)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
add(X2,inverse(add(add(inverse(X),inverse(X)),inverse(add(X,X2))))) = add(X2,inverse(add(add(inverse(X),inverse(add(X,X))),inverse(add(X,X2))))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
X = inverse(add(inverse(X),inverse(add(X,X)))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c83,plain,
add(X,X2) = add(inverse(add(inverse(X),inverse(add(X,X)))),X2),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
inverse(add(X,X2)) = inverse(add(inverse(add(inverse(X),inverse(add(X,X)))),X2)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
add(add(inverse(X),inverse(add(X,X))),inverse(add(X,X2))) = add(add(inverse(X),inverse(add(X,X))),inverse(add(inverse(add(inverse(X),inverse(add(X,X)))),X2))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
inverse(add(add(inverse(X),inverse(add(X,X))),inverse(add(X,X2)))) = inverse(add(add(inverse(X),inverse(add(X,X))),inverse(add(inverse(add(inverse(X),inverse(add(X,X)))),X2)))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
add(X2,inverse(add(add(inverse(X),inverse(add(X,X))),inverse(add(X,X2))))) = add(X2,inverse(add(add(inverse(X),inverse(add(X,X))),inverse(add(inverse(add(inverse(X),inverse(add(X,X)))),X2))))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
inverse(add(inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))),inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))))) = add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c89,plain,
add(X2,inverse(add(X,inverse(add(inverse(X),X2))))) = inverse(add(inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))),inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))) = X2,
inference(substitution,[status(thm)],[c47]) ).
cnf(c91,plain,
X2 = inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
add(X2,inverse(add(X,inverse(add(inverse(X),X2))))) = add(inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),inverse(add(X,inverse(add(inverse(X),X2))))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))) = inverse(add(inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),inverse(add(X,inverse(add(inverse(X),X2)))))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
inverse(add(inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),inverse(add(X,inverse(add(inverse(X),X2)))))) = inverse(add(inverse(X),X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c95,plain,
inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))) = inverse(add(inverse(X),X2)),
inference(transitivity,[status(thm)],[c93,c94]) ).
cnf(c96,plain,
add(inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))),inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))))) = add(inverse(add(inverse(X),X2)),inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
inverse(add(inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))),inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))))) = inverse(add(inverse(add(inverse(X),X2)),inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))) = add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c99,plain,
inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))) = inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
add(inverse(add(inverse(X),X2)),inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))))) = add(inverse(add(inverse(X),X2)),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
inverse(add(inverse(add(inverse(X),X2)),inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))))) = inverse(add(inverse(add(inverse(X),X2)),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))))),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
add(inverse(add(inverse(X),X2)),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))) = add(inverse(add(inverse(X),X2)),inverse(add(inverse(X),X2))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c103,plain,
inverse(add(inverse(add(inverse(X),X2)),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))))) = inverse(add(inverse(add(inverse(X),X2)),inverse(add(inverse(X),X2)))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
add(inverse(add(inverse(X),X2)),inverse(add(inverse(X),X2))) = inverse(add(inverse(X),X2)),
inference(substitution,[status(thm)],[c70]) ).
cnf(c105,plain,
inverse(add(inverse(add(inverse(X),X2)),inverse(add(inverse(X),X2)))) = inverse(inverse(add(inverse(X),X2))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
add(inverse(X),inverse(X)) = inverse(X),
inference(substitution,[status(thm)],[c70]) ).
cnf(c107,plain,
inverse(X) = add(inverse(X),inverse(X)),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
inverse(inverse(X)) = inverse(add(inverse(X),inverse(X))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
X = add(X,X),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c110,plain,
inverse(X) = inverse(add(X,X)),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
add(inverse(X),inverse(X)) = add(inverse(X),inverse(add(X,X))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
inverse(add(inverse(X),inverse(X))) = inverse(add(inverse(X),inverse(add(X,X)))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
inverse(add(inverse(X),inverse(X))) = X,
inference(transitivity,[status(thm)],[c112,c30]) ).
cnf(c114,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c108,c113]) ).
cnf(c115,plain,
inverse(inverse(add(inverse(X),X2))) = add(inverse(X),X2),
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
inverse(add(inverse(add(inverse(X),X2)),inverse(add(inverse(X),X2)))) = add(inverse(X),X2),
inference(transitivity,[status(thm)],[c105,c115]) ).
cnf(c117,plain,
inverse(add(inverse(add(inverse(X),X2)),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))))) = add(inverse(X),X2),
inference(transitivity,[status(thm)],[c103,c116]) ).
cnf(c118,plain,
inverse(add(inverse(add(inverse(X),X2)),inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))))) = add(inverse(X),X2),
inference(transitivity,[status(thm)],[c101,c117]) ).
cnf(c119,plain,
inverse(add(inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))),inverse(add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))))) = add(inverse(X),X2),
inference(transitivity,[status(thm)],[c97,c118]) ).
cnf(c120,plain,
add(X2,inverse(add(X,inverse(add(inverse(X),X2))))) = add(inverse(X),X2),
inference(transitivity,[status(thm)],[c89,c119]) ).
cnf(c121,plain,
add(X2,inverse(add(add(inverse(X),inverse(add(X,X))),inverse(add(inverse(add(inverse(X),inverse(add(X,X)))),X2))))) = add(inverse(add(inverse(X),inverse(add(X,X)))),X2),
inference(substitution,[status(thm)],[c120]) ).
cnf(c122,plain,
add(inverse(add(inverse(X),inverse(add(X,X)))),X2) = add(X,X2),
inference(congruence,[status(thm)],[c30]) ).
cnf(c123,plain,
add(X2,inverse(add(add(inverse(X),inverse(add(X,X))),inverse(add(inverse(add(inverse(X),inverse(add(X,X)))),X2))))) = add(X,X2),
inference(transitivity,[status(thm)],[c121,c122]) ).
cnf(c124,plain,
add(X2,inverse(add(add(inverse(X),inverse(add(X,X))),inverse(add(X,X2))))) = add(X,X2),
inference(transitivity,[status(thm)],[c87,c123]) ).
cnf(c125,plain,
add(X2,inverse(add(add(inverse(X),inverse(X)),inverse(add(X,X2))))) = add(X,X2),
inference(transitivity,[status(thm)],[c81,c124]) ).
cnf(c126,plain,
add(X2,inverse(add(inverse(X),inverse(add(X,X2))))) = add(X,X2),
inference(transitivity,[status(thm)],[c75,c125]) ).
cnf(c127,plain,
add(X,inverse(add(inverse(X2),inverse(add(X2,X))))) = add(X2,X),
inference(substitution,[status(thm)],[c126]) ).
cnf(c128,plain,
add(X2,X) = add(X,inverse(add(inverse(X2),inverse(add(X2,X))))),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
inverse(inverse(add(X2,add(X2,X)))) = add(X2,add(X2,X)),
inference(substitution,[status(thm)],[c114]) ).
cnf(c130,plain,
add(X2,add(X2,X)) = inverse(inverse(add(X2,add(X2,X)))),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
add(inverse(add(X2,add(X2,X))),inverse(add(X2,add(X2,X)))) = inverse(add(X2,add(X2,X))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c132,plain,
inverse(add(X2,add(X2,X))) = add(inverse(add(X2,add(X2,X))),inverse(add(X2,add(X2,X)))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
inverse(inverse(add(X2,add(X2,X)))) = inverse(add(inverse(add(X2,add(X2,X))),inverse(add(X2,add(X2,X))))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,X3)))) = X3,
inference(substitution,[status(thm)],[c45]) ).
cnf(c135,plain,
X3 = inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,X3)))),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))) = add(inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,X3)))),inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))) = inverse(add(inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,X3)))),inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
inverse(add(inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,X3)))),inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))) = inverse(add(X2,X3)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c139,plain,
inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))) = inverse(add(X2,X3)),
inference(transitivity,[status(thm)],[c137,c138]) ).
cnf(c140,plain,
inverse(add(add(X2,X),inverse(add(inverse(add(X2,X)),inverse(add(X2,add(X2,X))))))) = inverse(add(X2,add(X2,X))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
inverse(add(X2,add(X2,X))) = inverse(add(add(X2,X),inverse(add(inverse(add(X2,X)),inverse(add(X2,add(X2,X))))))),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
add(inverse(add(X2,add(X2,X))),inverse(add(X2,add(X2,X)))) = add(inverse(add(X2,add(X2,X))),inverse(add(add(X2,X),inverse(add(inverse(add(X2,X)),inverse(add(X2,add(X2,X)))))))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
inverse(add(inverse(add(X2,add(X2,X))),inverse(add(X2,add(X2,X))))) = inverse(add(inverse(add(X2,add(X2,X))),inverse(add(add(X2,X),inverse(add(inverse(add(X2,X)),inverse(add(X2,add(X2,X))))))))),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
inverse(add(inverse(add(X2,add(X2,X))),inverse(add(add(X2,X),inverse(add(inverse(add(X2,X)),inverse(add(X2,add(X2,X))))))))) = inverse(add(inverse(add(X2,X)),inverse(add(X2,add(X2,X))))),
inference(substitution,[status(thm)],[c95]) ).
cnf(c145,plain,
add(inverse(X),inverse(X)) = inverse(X),
inference(substitution,[status(thm)],[c70]) ).
cnf(c146,plain,
inverse(X) = add(inverse(X),inverse(X)),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
add(inverse(X2),inverse(add(X,X2))) = add(add(inverse(X2),inverse(X2)),inverse(add(X,X2))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
X = add(X,X),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c149,plain,
inverse(X) = inverse(add(X,X)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
add(inverse(X),inverse(X)) = add(inverse(X),inverse(add(X,X))),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
add(add(inverse(X2),inverse(X2)),inverse(add(X,X2))) = add(add(inverse(X2),inverse(add(X2,X2))),inverse(add(X,X2))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
X = inverse(add(inverse(X),inverse(add(X,X)))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c153,plain,
add(X,X2) = add(X,inverse(add(inverse(X2),inverse(add(X2,X2))))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
inverse(add(X,X2)) = inverse(add(X,inverse(add(inverse(X2),inverse(add(X2,X2)))))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
add(add(inverse(X2),inverse(add(X2,X2))),inverse(add(X,X2))) = add(add(inverse(X2),inverse(add(X2,X2))),inverse(add(X,inverse(add(inverse(X2),inverse(add(X2,X2))))))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
inverse(add(inverse(add(X2,inverse(add(X,inverse(X2))))),inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2)))))))) = add(X2,inverse(add(X,inverse(X2)))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c157,plain,
add(X2,inverse(add(X,inverse(X2)))) = inverse(add(inverse(add(X2,inverse(add(X,inverse(X2))))),inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2)))))))),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
X = add(X,X),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c159,plain,
inverse(X) = inverse(add(X,X)),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
add(inverse(add(X2,X)),inverse(X)) = add(inverse(add(X2,X)),inverse(add(X,X))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
inverse(add(inverse(add(X2,X)),inverse(X))) = inverse(add(inverse(add(X2,X)),inverse(add(X,X)))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,X3)))) = X3,
inference(substitution,[status(thm)],[c45]) ).
cnf(c163,plain,
X3 = inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,X3)))),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
add(inverse(add(X3,inverse(add(X2,X3)))),X3) = add(inverse(add(X3,inverse(add(X2,X3)))),inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,X3))))),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
inverse(add(inverse(add(X3,inverse(add(X2,X3)))),X3)) = inverse(add(inverse(add(X3,inverse(add(X2,X3)))),inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,X3)))))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))) = X2,
inference(substitution,[status(thm)],[c47]) ).
cnf(c167,plain,
X2 = inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
add(X3,X2) = add(inverse(add(inverse(add(X,X3)),inverse(add(inverse(X),X3)))),X2),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
inverse(add(X3,X2)) = inverse(add(inverse(add(inverse(add(X,X3)),inverse(add(inverse(X),X3)))),X2)),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))) = add(inverse(add(inverse(add(inverse(add(X,X3)),inverse(add(inverse(X),X3)))),X2)),inverse(add(inverse(add(X,X3)),X2))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))) = inverse(add(inverse(add(inverse(add(inverse(add(X,X3)),inverse(add(inverse(X),X3)))),X2)),inverse(add(inverse(add(X,X3)),X2)))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
inverse(add(inverse(add(inverse(add(inverse(add(X,X3)),inverse(add(inverse(X),X3)))),X2)),inverse(add(inverse(add(X,X3)),X2)))) = X2,
inference(substitution,[status(thm)],[c45]) ).
cnf(c173,plain,
inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))) = X2,
inference(transitivity,[status(thm)],[c171,c172]) ).
cnf(c174,plain,
inverse(add(inverse(add(X3,inverse(add(X2,X3)))),inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,X3)))))) = inverse(add(X2,X3)),
inference(substitution,[status(thm)],[c173]) ).
cnf(c175,plain,
inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2)) = inverse(add(X,X2)),
inference(transitivity,[status(thm)],[c165,c174]) ).
cnf(c176,plain,
inverse(add(inverse(add(X,inverse(add(X2,X)))),X)) = inverse(add(X2,X)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
inverse(add(X2,X)) = inverse(add(inverse(add(X,inverse(add(X2,X)))),X)),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
add(inverse(add(X2,X)),inverse(add(X,X))) = add(inverse(add(inverse(add(X,inverse(add(X2,X)))),X)),inverse(add(X,X))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
inverse(add(inverse(add(X2,X)),inverse(add(X,X)))) = inverse(add(inverse(add(inverse(add(X,inverse(add(X2,X)))),X)),inverse(add(X,X)))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
inverse(add(inverse(add(inverse(add(X,inverse(add(X2,X)))),X)),inverse(add(X,X)))) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c181,plain,
inverse(add(inverse(add(X2,X)),inverse(add(X,X)))) = X,
inference(transitivity,[status(thm)],[c179,c180]) ).
cnf(c182,plain,
inverse(add(inverse(add(X2,X)),inverse(X))) = X,
inference(transitivity,[status(thm)],[c161,c181]) ).
cnf(c183,plain,
inverse(add(inverse(add(X,X2)),inverse(X2))) = X2,
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
X2 = inverse(add(inverse(add(X,X2)),inverse(X2))),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
add(X2,inverse(add(X,inverse(X2)))) = add(inverse(add(inverse(add(X,X2)),inverse(X2))),inverse(add(X,inverse(X2)))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
inverse(add(X2,inverse(add(X,inverse(X2))))) = inverse(add(inverse(add(inverse(add(X,X2)),inverse(X2))),inverse(add(X,inverse(X2))))),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
inverse(add(inverse(add(inverse(add(X,X2)),inverse(X2))),inverse(add(X,inverse(X2))))) = inverse(X2),
inference(substitution,[status(thm)],[c45]) ).
cnf(c188,plain,
inverse(add(X2,inverse(add(X,inverse(X2))))) = inverse(X2),
inference(transitivity,[status(thm)],[c186,c187]) ).
cnf(c189,plain,
add(inverse(add(X2,inverse(add(X,inverse(X2))))),inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2))))))) = add(inverse(X2),inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2))))))),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
inverse(add(inverse(add(X2,inverse(add(X,inverse(X2))))),inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2)))))))) = inverse(add(inverse(X2),inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2)))))))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2))))) = add(X2,inverse(add(X,inverse(X2)))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c192,plain,
inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2)))))) = inverse(add(X2,inverse(add(X,inverse(X2))))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
add(inverse(X2),inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2))))))) = add(inverse(X2),inverse(add(X2,inverse(add(X,inverse(X2)))))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
inverse(add(inverse(X2),inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2)))))))) = inverse(add(inverse(X2),inverse(add(X2,inverse(add(X,inverse(X2))))))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
add(inverse(X2),inverse(add(X2,inverse(add(X,inverse(X2)))))) = add(inverse(X2),inverse(X2)),
inference(congruence,[status(thm)],[c188]) ).
cnf(c196,plain,
inverse(add(inverse(X2),inverse(add(X2,inverse(add(X,inverse(X2))))))) = inverse(add(inverse(X2),inverse(X2))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
add(inverse(X),inverse(X)) = inverse(X),
inference(substitution,[status(thm)],[c70]) ).
cnf(c198,plain,
inverse(add(inverse(X),inverse(X))) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
inverse(add(inverse(X),inverse(X))) = X,
inference(transitivity,[status(thm)],[c198,c114]) ).
cnf(c200,plain,
inverse(add(inverse(X2),inverse(add(X2,inverse(add(X,inverse(X2))))))) = X2,
inference(transitivity,[status(thm)],[c196,c199]) ).
cnf(c201,plain,
inverse(add(inverse(X2),inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2)))))))) = X2,
inference(transitivity,[status(thm)],[c194,c200]) ).
cnf(c202,plain,
inverse(add(inverse(add(X2,inverse(add(X,inverse(X2))))),inverse(add(add(X2,inverse(add(X,inverse(X2)))),add(X2,inverse(add(X,inverse(X2)))))))) = X2,
inference(transitivity,[status(thm)],[c190,c201]) ).
cnf(c203,plain,
add(X2,inverse(add(X,inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c157,c202]) ).
cnf(c204,plain,
add(add(inverse(X2),inverse(add(X2,X2))),inverse(add(X,inverse(add(inverse(X2),inverse(add(X2,X2))))))) = add(inverse(X2),inverse(add(X2,X2))),
inference(substitution,[status(thm)],[c203]) ).
cnf(c205,plain,
inverse(add(X,X)) = inverse(X),
inference(congruence,[status(thm)],[c70]) ).
cnf(c206,plain,
add(inverse(X),inverse(add(X,X))) = add(inverse(X),inverse(X)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
add(inverse(X),inverse(X)) = inverse(X),
inference(substitution,[status(thm)],[c70]) ).
cnf(c208,plain,
add(inverse(X),inverse(add(X,X))) = inverse(X),
inference(transitivity,[status(thm)],[c206,c207]) ).
cnf(c209,plain,
add(add(inverse(X2),inverse(add(X2,X2))),inverse(add(X,inverse(add(inverse(X2),inverse(add(X2,X2))))))) = inverse(X2),
inference(transitivity,[status(thm)],[c204,c208]) ).
cnf(c210,plain,
add(add(inverse(X2),inverse(add(X2,X2))),inverse(add(X,X2))) = inverse(X2),
inference(transitivity,[status(thm)],[c155,c209]) ).
cnf(c211,plain,
add(add(inverse(X2),inverse(X2)),inverse(add(X,X2))) = inverse(X2),
inference(transitivity,[status(thm)],[c151,c210]) ).
cnf(c212,plain,
add(inverse(X2),inverse(add(X,X2))) = inverse(X2),
inference(transitivity,[status(thm)],[c147,c211]) ).
cnf(c213,plain,
add(inverse(add(X2,X)),inverse(add(X2,add(X2,X)))) = inverse(add(X2,X)),
inference(substitution,[status(thm)],[c212]) ).
cnf(c214,plain,
inverse(add(inverse(add(X2,X)),inverse(add(X2,add(X2,X))))) = inverse(inverse(add(X2,X))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
inverse(inverse(add(X2,X))) = add(X2,X),
inference(substitution,[status(thm)],[c114]) ).
cnf(c216,plain,
inverse(add(inverse(add(X2,X)),inverse(add(X2,add(X2,X))))) = add(X2,X),
inference(transitivity,[status(thm)],[c214,c215]) ).
cnf(c217,plain,
inverse(add(inverse(add(X2,add(X2,X))),inverse(add(add(X2,X),inverse(add(inverse(add(X2,X)),inverse(add(X2,add(X2,X))))))))) = add(X2,X),
inference(transitivity,[status(thm)],[c144,c216]) ).
cnf(c218,plain,
inverse(add(inverse(add(X2,add(X2,X))),inverse(add(X2,add(X2,X))))) = add(X2,X),
inference(transitivity,[status(thm)],[c143,c217]) ).
cnf(c219,plain,
inverse(inverse(add(X2,add(X2,X)))) = add(X2,X),
inference(transitivity,[status(thm)],[c133,c218]) ).
cnf(c220,plain,
add(X2,add(X2,X)) = add(X2,X),
inference(transitivity,[status(thm)],[c130,c219]) ).
cnf(c221,plain,
add(inverse(X2),add(inverse(X2),inverse(add(X2,X)))) = add(inverse(X2),inverse(add(X2,X))),
inference(substitution,[status(thm)],[c220]) ).
cnf(c222,plain,
add(inverse(X2),inverse(add(X2,X))) = add(inverse(X2),add(inverse(X2),inverse(add(X2,X)))),
inference(symmetry,[status(thm)],[c221]) ).
cnf(c223,plain,
inverse(add(inverse(X2),inverse(add(X2,X)))) = inverse(add(inverse(X2),add(inverse(X2),inverse(add(X2,X))))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
inverse(inverse(add(inverse(X2),inverse(add(X2,X))))) = add(inverse(X2),inverse(add(X2,X))),
inference(substitution,[status(thm)],[c114]) ).
cnf(c225,plain,
add(inverse(X2),inverse(add(X2,X))) = inverse(inverse(add(inverse(X2),inverse(add(X2,X))))),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
add(inverse(X2),add(inverse(X2),inverse(add(X2,X)))) = add(inverse(X2),inverse(inverse(add(inverse(X2),inverse(add(X2,X)))))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
inverse(add(inverse(X2),add(inverse(X2),inverse(add(X2,X))))) = inverse(add(inverse(X2),inverse(inverse(add(inverse(X2),inverse(add(X2,X))))))),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
inverse(add(inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))))))) = add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c229,plain,
add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))) = inverse(add(inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))))))),
inference(symmetry,[status(thm)],[c228]) ).
cnf(c230,plain,
add(inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))))) = add(inverse(add(X2,X3)),inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))))),
inference(congruence,[status(thm)],[c139]) ).
cnf(c231,plain,
inverse(add(inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))))))) = inverse(add(inverse(add(X2,X3)),inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))))))),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))) = add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c233,plain,
inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))))) = inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
add(inverse(add(X2,X3)),inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))))) = add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))))),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
inverse(add(inverse(add(X2,X3)),inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))))))) = inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))))),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))))) = add(inverse(add(X2,X3)),inverse(add(X2,X3))),
inference(congruence,[status(thm)],[c139]) ).
cnf(c237,plain,
inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))))) = inverse(add(inverse(add(X2,X3)),inverse(add(X2,X3)))),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
add(inverse(add(X,X2)),inverse(add(X,X2))) = inverse(add(X,X2)),
inference(substitution,[status(thm)],[c70]) ).
cnf(c239,plain,
inverse(add(inverse(add(X,X2)),inverse(add(X,X2)))) = inverse(inverse(add(X,X2))),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
inverse(inverse(add(X,X2))) = add(X,X2),
inference(substitution,[status(thm)],[c114]) ).
cnf(c241,plain,
inverse(add(inverse(add(X,X2)),inverse(add(X,X2)))) = add(X,X2),
inference(transitivity,[status(thm)],[c239,c240]) ).
cnf(c242,plain,
inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))))) = add(X2,X3),
inference(transitivity,[status(thm)],[c237,c241]) ).
cnf(c243,plain,
inverse(add(inverse(add(X2,X3)),inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))))))) = add(X2,X3),
inference(transitivity,[status(thm)],[c235,c242]) ).
cnf(c244,plain,
inverse(add(inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),inverse(add(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))),add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))))))) = add(X2,X3),
inference(transitivity,[status(thm)],[c231,c243]) ).
cnf(c245,plain,
add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3))))) = add(X2,X3),
inference(transitivity,[status(thm)],[c229,c244]) ).
cnf(c246,plain,
add(inverse(add(inverse(X2),inverse(add(X2,X)))),inverse(add(inverse(add(X2,X)),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))) = add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))),
inference(substitution,[status(thm)],[c245]) ).
cnf(c247,plain,
add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))) = add(inverse(add(inverse(X2),inverse(add(X2,X)))),inverse(add(inverse(add(X2,X)),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
inverse(add(inverse(add(X2,X)),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))) = inverse(add(inverse(X2),inverse(add(X2,X)))),
inference(substitution,[status(thm)],[c95]) ).
cnf(c249,plain,
add(inverse(add(inverse(X2),inverse(add(X2,X)))),inverse(add(inverse(add(X2,X)),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))) = add(inverse(add(inverse(X2),inverse(add(X2,X)))),inverse(add(inverse(X2),inverse(add(X2,X))))),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
add(inverse(add(inverse(X2),inverse(add(X2,X)))),inverse(add(inverse(X2),inverse(add(X2,X))))) = inverse(add(inverse(X2),inverse(add(X2,X)))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c251,plain,
add(inverse(add(inverse(X2),inverse(add(X2,X)))),inverse(add(inverse(add(X2,X)),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))) = inverse(add(inverse(X2),inverse(add(X2,X)))),
inference(transitivity,[status(thm)],[c249,c250]) ).
cnf(c252,plain,
add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))) = inverse(add(inverse(X2),inverse(add(X2,X)))),
inference(transitivity,[status(thm)],[c247,c251]) ).
cnf(c253,plain,
inverse(add(inverse(X2),inverse(add(X2,X)))) = add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
inverse(inverse(add(inverse(X2),inverse(add(X2,X))))) = inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
add(inverse(X2),inverse(inverse(add(inverse(X2),inverse(add(X2,X)))))) = add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
inverse(add(inverse(X2),inverse(inverse(add(inverse(X2),inverse(add(X2,X))))))) = inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
inverse(add(inverse(X2),inverse(inverse(add(inverse(X2),inverse(add(X2,X))))))) = X2,
inference(transitivity,[status(thm)],[c256,c21]) ).
cnf(c258,plain,
inverse(add(inverse(X2),add(inverse(X2),inverse(add(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c227,c257]) ).
cnf(c259,plain,
inverse(add(inverse(X2),inverse(add(X2,X)))) = X2,
inference(transitivity,[status(thm)],[c223,c258]) ).
cnf(c260,plain,
add(X,inverse(add(inverse(X2),inverse(add(X2,X))))) = add(X,X2),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
add(X2,X) = add(X,X2),
inference(transitivity,[status(thm)],[c128,c260]) ).
cnf(c262,plain,
add(add(a,b),c) = add(c,add(a,b)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c263,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c264,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
add(X2,add(X3,X)) = add(X2,add(X,X3)),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
add(add(X3,X),add(X3,X2)) = add(add(X3,X2),add(X3,X)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c267,plain,
add(add(X3,X2),add(X3,X)) = add(add(X3,X),add(X3,X2)),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c269,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
add(add(X3,X2),add(X3,X)) = add(add(X3,X2),add(X,X3)),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c272,plain,
add(X,X2) = add(X,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
add(add(X3,X2),add(X,X3)) = add(add(X3,X2),add(X,inverse(inverse(X3)))),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
add(X,add(X3,X2)) = add(add(X3,X2),X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c275,plain,
add(add(X3,X2),X) = add(X,add(X3,X2)),
inference(symmetry,[status(thm)],[c274]) ).
cnf(c276,plain,
inverse(add(add(X3,X2),X)) = inverse(add(X,add(X3,X2))),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
add(inverse(X3),inverse(add(add(X3,X2),X))) = add(inverse(X3),inverse(add(X,add(X3,X2)))),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))))))) = add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c279,plain,
add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))) = inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))))))),
inference(symmetry,[status(thm)],[c278]) ).
cnf(c280,plain,
add(inverse(X),X2) = add(X2,inverse(X)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c281,plain,
add(X2,inverse(X)) = add(inverse(X),X2),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,plain,
inverse(add(X2,inverse(X))) = inverse(add(inverse(X),X2)),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
add(add(X2,X),inverse(add(X2,inverse(X)))) = add(add(X2,X),inverse(add(inverse(X),X2))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
inverse(add(add(X2,X),inverse(add(X2,inverse(X))))) = inverse(add(add(X2,X),inverse(add(inverse(X),X2)))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
add(X2,inverse(add(add(X2,X),inverse(add(X2,inverse(X)))))) = add(X2,inverse(add(add(X2,X),inverse(add(inverse(X),X2))))),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
inverse(add(X2,inverse(add(add(X2,X),inverse(add(X2,inverse(X))))))) = inverse(add(X2,inverse(add(add(X2,X),inverse(add(inverse(X),X2)))))),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c288,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c287]) ).
cnf(c289,plain,
add(add(X2,X),inverse(add(inverse(X),X2))) = add(add(X,X2),inverse(add(inverse(X),X2))),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
inverse(add(add(X2,X),inverse(add(inverse(X),X2)))) = inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
add(X2,inverse(add(add(X2,X),inverse(add(inverse(X),X2))))) = add(X2,inverse(add(add(X,X2),inverse(add(inverse(X),X2))))),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
inverse(add(X2,inverse(add(add(X2,X),inverse(add(inverse(X),X2)))))) = inverse(add(X2,inverse(add(add(X,X2),inverse(add(inverse(X),X2)))))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
add(inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),X2) = add(X2,inverse(add(add(X,X2),inverse(add(inverse(X),X2))))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c294,plain,
add(X2,inverse(add(add(X,X2),inverse(add(inverse(X),X2))))) = add(inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),X2),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
inverse(add(X2,inverse(add(add(X,X2),inverse(add(inverse(X),X2)))))) = inverse(add(inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),X2)),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))) = X2,
inference(substitution,[status(thm)],[c47]) ).
cnf(c297,plain,
X2 = inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
add(inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),X2) = add(inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2))))),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
inverse(add(inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),X2)) = inverse(add(inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
inverse(add(inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))))) = inverse(add(inverse(X),X2)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c301,plain,
add(inverse(X),X2) = add(X2,inverse(X)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c302,plain,
inverse(add(inverse(X),X2)) = inverse(add(X2,inverse(X))),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
inverse(add(inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))))) = inverse(add(X2,inverse(X))),
inference(transitivity,[status(thm)],[c300,c302]) ).
cnf(c304,plain,
inverse(add(inverse(add(add(X,X2),inverse(add(inverse(X),X2)))),X2)) = inverse(add(X2,inverse(X))),
inference(transitivity,[status(thm)],[c299,c303]) ).
cnf(c305,plain,
inverse(add(X2,inverse(add(add(X,X2),inverse(add(inverse(X),X2)))))) = inverse(add(X2,inverse(X))),
inference(transitivity,[status(thm)],[c295,c304]) ).
cnf(c306,plain,
inverse(add(X2,inverse(add(add(X2,X),inverse(add(inverse(X),X2)))))) = inverse(add(X2,inverse(X))),
inference(transitivity,[status(thm)],[c292,c305]) ).
cnf(c307,plain,
inverse(add(X2,inverse(add(add(X2,X),inverse(add(X2,inverse(X))))))) = inverse(add(X2,inverse(X))),
inference(transitivity,[status(thm)],[c286,c306]) ).
cnf(c308,plain,
add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))))) = add(inverse(add(X3,inverse(X2))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))))),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))))))) = inverse(add(inverse(add(X3,inverse(X2))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))))))),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))) = inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))),
inference(substitution,[status(thm)],[c252]) ).
cnf(c311,plain,
inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))))) = inverse(inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
add(inverse(add(X3,inverse(X2))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))))) = add(inverse(add(X3,inverse(X2))),inverse(inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))))),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
inverse(add(inverse(add(X3,inverse(X2))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))))))) = inverse(add(inverse(add(X3,inverse(X2))),inverse(inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))))),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
inverse(inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))) = add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))),
inference(substitution,[status(thm)],[c114]) ).
cnf(c315,plain,
add(inverse(add(X3,inverse(X2))),inverse(inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))))) = add(inverse(add(X3,inverse(X2))),add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
inverse(add(inverse(add(X3,inverse(X2))),inverse(inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))))) = inverse(add(inverse(add(X3,inverse(X2))),add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c318,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c317]) ).
cnf(c319,plain,
inverse(add(X2,X)) = inverse(add(X,X2)),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
add(inverse(X2),inverse(add(X2,X))) = add(inverse(X2),inverse(add(X,X2))),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
add(inverse(X2),inverse(add(X2,X))) = inverse(X2),
inference(transitivity,[status(thm)],[c320,c212]) ).
cnf(c322,plain,
add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))) = inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),
inference(substitution,[status(thm)],[c321]) ).
cnf(c323,plain,
add(inverse(add(X3,inverse(X2))),add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))) = add(inverse(add(X3,inverse(X2))),inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))))),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
inverse(add(inverse(add(X3,inverse(X2))),add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))) = inverse(add(inverse(add(X3,inverse(X2))),inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))))),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
add(inverse(add(X2,inverse(X))),inverse(add(X2,inverse(add(add(X2,X),inverse(add(X2,inverse(X)))))))) = add(inverse(add(X2,inverse(X))),inverse(add(X2,inverse(X)))),
inference(congruence,[status(thm)],[c307]) ).
cnf(c326,plain,
inverse(add(inverse(add(X2,inverse(X))),inverse(add(X2,inverse(add(add(X2,X),inverse(add(X2,inverse(X))))))))) = inverse(add(inverse(add(X2,inverse(X))),inverse(add(X2,inverse(X))))),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
add(inverse(add(X2,inverse(X))),inverse(add(X2,inverse(X)))) = inverse(add(X2,inverse(X))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c328,plain,
inverse(add(inverse(add(X2,inverse(X))),inverse(add(X2,inverse(X))))) = inverse(inverse(add(X2,inverse(X)))),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
inverse(inverse(add(X2,inverse(X)))) = add(X2,inverse(X)),
inference(substitution,[status(thm)],[c114]) ).
cnf(c330,plain,
inverse(add(inverse(add(X2,inverse(X))),inverse(add(X2,inverse(X))))) = add(X2,inverse(X)),
inference(transitivity,[status(thm)],[c328,c329]) ).
cnf(c331,plain,
inverse(add(inverse(add(X2,inverse(X))),inverse(add(X2,inverse(add(add(X2,X),inverse(add(X2,inverse(X))))))))) = add(X2,inverse(X)),
inference(transitivity,[status(thm)],[c326,c330]) ).
cnf(c332,plain,
inverse(add(inverse(add(X3,inverse(X2))),add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))) = add(X3,inverse(X2)),
inference(transitivity,[status(thm)],[c324,c331]) ).
cnf(c333,plain,
inverse(add(inverse(add(X3,inverse(X2))),inverse(inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X))))))) = add(X3,inverse(X2)),
inference(transitivity,[status(thm)],[c316,c332]) ).
cnf(c334,plain,
inverse(add(inverse(add(X3,inverse(X2))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))))))) = add(X3,inverse(X2)),
inference(transitivity,[status(thm)],[c313,c333]) ).
cnf(c335,plain,
inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),inverse(add(inverse(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2))))))),inverse(add(add(X3,inverse(add(add(X3,X2),inverse(add(X3,inverse(X2)))))),X)))))))) = add(X3,inverse(X2)),
inference(transitivity,[status(thm)],[c309,c334]) ).
cnf(c336,plain,
add(X2,inverse(add(add(X2,X),inverse(add(X2,inverse(X)))))) = add(X2,inverse(X)),
inference(transitivity,[status(thm)],[c279,c335]) ).
cnf(c337,plain,
add(inverse(X3),inverse(add(add(inverse(X3),add(X2,add(X3,X))),inverse(add(inverse(X3),inverse(add(X2,add(X3,X)))))))) = add(inverse(X3),inverse(add(X2,add(X3,X)))),
inference(substitution,[status(thm)],[c336]) ).
cnf(c338,plain,
add(inverse(X3),inverse(add(X2,add(X3,X)))) = add(inverse(X3),inverse(add(add(inverse(X3),add(X2,add(X3,X))),inverse(add(inverse(X3),inverse(add(X2,add(X3,X)))))))),
inference(symmetry,[status(thm)],[c337]) ).
cnf(c339,plain,
inverse(inverse(add(X2,add(X3,X)))) = add(X2,add(X3,X)),
inference(substitution,[status(thm)],[c114]) ).
cnf(c340,plain,
add(X2,add(X3,X)) = inverse(inverse(add(X2,add(X3,X)))),
inference(symmetry,[status(thm)],[c339]) ).
cnf(c341,plain,
add(inverse(X3),add(X2,add(X3,X))) = add(inverse(X3),inverse(inverse(add(X2,add(X3,X))))),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c343,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c342]) ).
cnf(c344,plain,
inverse(add(X2,X)) = inverse(add(X,X2)),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
add(X2,inverse(add(X2,X))) = add(X2,inverse(add(X,X2))),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c347,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c346]) ).
cnf(c348,plain,
inverse(add(X2,X)) = inverse(add(X,X2)),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
add(X3,inverse(add(X2,X))) = add(X3,inverse(add(X,X2))),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
inverse(add(X3,inverse(add(X2,X)))) = inverse(add(X3,inverse(add(X,X2)))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
add(X2,inverse(add(X3,inverse(add(X2,X))))) = add(X2,inverse(add(X3,inverse(add(X,X2))))),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
inverse(add(X2,inverse(add(X3,inverse(add(X2,X)))))) = inverse(add(X2,inverse(add(X3,inverse(add(X,X2)))))),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
add(X3,inverse(add(X2,inverse(add(X3,inverse(add(X2,X))))))) = add(X3,inverse(add(X2,inverse(add(X3,inverse(add(X,X2))))))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
add(inverse(add(X,X2)),X3) = add(X3,inverse(add(X,X2))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c355,plain,
add(X3,inverse(add(X,X2))) = add(inverse(add(X,X2)),X3),
inference(symmetry,[status(thm)],[c354]) ).
cnf(c356,plain,
inverse(add(X3,inverse(add(X,X2)))) = inverse(add(inverse(add(X,X2)),X3)),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
add(X2,inverse(add(X3,inverse(add(X,X2))))) = add(X2,inverse(add(inverse(add(X,X2)),X3))),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
inverse(add(X2,inverse(add(X3,inverse(add(X,X2)))))) = inverse(add(X2,inverse(add(inverse(add(X,X2)),X3)))),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
add(X3,inverse(add(X2,inverse(add(X3,inverse(add(X,X2))))))) = add(X3,inverse(add(X2,inverse(add(inverse(add(X,X2)),X3))))),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))) = X2,
inference(substitution,[status(thm)],[c47]) ).
cnf(c361,plain,
X2 = inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),
inference(symmetry,[status(thm)],[c360]) ).
cnf(c362,plain,
add(X2,inverse(add(inverse(add(X,X2)),X3))) = add(inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),inverse(add(inverse(add(X,X2)),X3))),
inference(congruence,[status(thm)],[c361]) ).
cnf(c363,plain,
inverse(add(X2,inverse(add(inverse(add(X,X2)),X3)))) = inverse(add(inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),inverse(add(inverse(add(X,X2)),X3)))),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
add(X3,inverse(add(X2,inverse(add(inverse(add(X,X2)),X3))))) = add(X3,inverse(add(inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),inverse(add(inverse(add(X,X2)),X3))))),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
add(X3,inverse(add(inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),inverse(add(inverse(add(X,X2)),X3))))) = add(inverse(add(X,X2)),X3),
inference(substitution,[status(thm)],[c245]) ).
cnf(c366,plain,
add(inverse(add(X,X2)),X3) = add(X3,inverse(add(X,X2))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c367,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c368,plain,
inverse(add(X,X2)) = inverse(add(X2,X)),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
add(X3,inverse(add(X,X2))) = add(X3,inverse(add(X2,X))),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
add(inverse(add(X,X2)),X3) = add(X3,inverse(add(X2,X))),
inference(transitivity,[status(thm)],[c366,c369]) ).
cnf(c371,plain,
add(X3,inverse(add(inverse(add(inverse(add(X,X2)),inverse(add(inverse(X),X2)))),inverse(add(inverse(add(X,X2)),X3))))) = add(X3,inverse(add(X2,X))),
inference(transitivity,[status(thm)],[c365,c370]) ).
cnf(c372,plain,
add(X3,inverse(add(X2,inverse(add(inverse(add(X,X2)),X3))))) = add(X3,inverse(add(X2,X))),
inference(transitivity,[status(thm)],[c364,c371]) ).
cnf(c373,plain,
add(X3,inverse(add(X2,inverse(add(X3,inverse(add(X,X2))))))) = add(X3,inverse(add(X2,X))),
inference(transitivity,[status(thm)],[c359,c372]) ).
cnf(c374,plain,
add(X3,inverse(add(X2,inverse(add(X3,inverse(add(X2,X))))))) = add(X3,inverse(add(X2,X))),
inference(transitivity,[status(thm)],[c353,c373]) ).
cnf(c375,plain,
add(X2,inverse(add(X,inverse(add(X2,inverse(add(X,X2))))))) = add(X2,inverse(add(X,X2))),
inference(substitution,[status(thm)],[c374]) ).
cnf(c376,plain,
add(X2,inverse(add(X,X2))) = add(X2,inverse(add(X,inverse(add(X2,inverse(add(X,X2))))))),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c378,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c377]) ).
cnf(c379,plain,
inverse(add(X2,X)) = inverse(add(X,X2)),
inference(congruence,[status(thm)],[c378]) ).
cnf(c380,plain,
add(X,inverse(add(X2,X))) = add(X,inverse(add(X,X2))),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
inverse(add(X,inverse(add(X2,X)))) = inverse(add(X,inverse(add(X,X2)))),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
add(X2,inverse(add(X,inverse(add(X2,X))))) = add(X2,inverse(add(X,inverse(add(X,X2))))),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
add(inverse(add(X,X2)),X) = add(X,inverse(add(X,X2))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c384,plain,
add(X,inverse(add(X,X2))) = add(inverse(add(X,X2)),X),
inference(symmetry,[status(thm)],[c383]) ).
cnf(c385,plain,
inverse(add(X,inverse(add(X,X2)))) = inverse(add(inverse(add(X,X2)),X)),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
add(X2,inverse(add(X,inverse(add(X,X2))))) = add(X2,inverse(add(inverse(add(X,X2)),X))),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
add(X2,inverse(add(inverse(add(X,X2)),inverse(add(X2,inverse(add(inverse(add(X,X2)),X))))))) = add(X2,inverse(add(inverse(add(X,X2)),X))),
inference(substitution,[status(thm)],[c374]) ).
cnf(c388,plain,
add(X2,inverse(add(inverse(add(X,X2)),X))) = add(X2,inverse(add(inverse(add(X,X2)),inverse(add(X2,inverse(add(inverse(add(X,X2)),X))))))),
inference(symmetry,[status(thm)],[c387]) ).
cnf(c389,plain,
add(inverse(add(X,X3)),X2) = add(X2,inverse(add(X,X3))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c390,plain,
add(X2,inverse(add(X,X3))) = add(inverse(add(X,X3)),X2),
inference(symmetry,[status(thm)],[c389]) ).
cnf(c391,plain,
inverse(add(X2,inverse(add(X,X3)))) = inverse(add(inverse(add(X,X3)),X2)),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
add(inverse(add(X3,X2)),inverse(add(X2,inverse(add(X,X3))))) = add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),
inference(congruence,[status(thm)],[c391]) ).
cnf(c393,plain,
inverse(add(inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))),inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))))))) = add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c394,plain,
add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))) = inverse(add(inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))),inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))))))),
inference(symmetry,[status(thm)],[c393]) ).
cnf(c395,plain,
add(inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))),inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))))) = add(X2,inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c396,plain,
inverse(add(inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))),inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))))))) = inverse(add(X2,inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))))))),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))) = add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c398,plain,
inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))))) = inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))),
inference(congruence,[status(thm)],[c397]) ).
cnf(c399,plain,
add(X2,inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))))) = add(X2,inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))))),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
inverse(add(X2,inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))))))) = inverse(add(X2,inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))))),
inference(congruence,[status(thm)],[c399]) ).
cnf(c401,plain,
add(X2,inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))))) = add(X2,X2),
inference(congruence,[status(thm)],[c173]) ).
cnf(c402,plain,
inverse(add(X2,inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))))) = inverse(add(X2,X2)),
inference(congruence,[status(thm)],[c401]) ).
cnf(c403,plain,
inverse(add(X,X)) = inverse(X),
inference(congruence,[status(thm)],[c70]) ).
cnf(c404,plain,
inverse(add(X2,inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))))) = inverse(X2),
inference(transitivity,[status(thm)],[c402,c403]) ).
cnf(c405,plain,
inverse(add(X2,inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))))))) = inverse(X2),
inference(transitivity,[status(thm)],[c400,c404]) ).
cnf(c406,plain,
inverse(add(inverse(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2)))),inverse(add(add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))),add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))))))) = inverse(X2),
inference(transitivity,[status(thm)],[c396,c405]) ).
cnf(c407,plain,
add(inverse(add(X3,X2)),inverse(add(inverse(add(X,X3)),X2))) = inverse(X2),
inference(transitivity,[status(thm)],[c394,c406]) ).
cnf(c408,plain,
add(inverse(add(X3,X2)),inverse(add(X2,inverse(add(X,X3))))) = inverse(X2),
inference(transitivity,[status(thm)],[c392,c407]) ).
cnf(c409,plain,
add(inverse(add(X,X2)),inverse(add(X2,inverse(add(inverse(add(X,X2)),X))))) = inverse(X2),
inference(substitution,[status(thm)],[c408]) ).
cnf(c410,plain,
inverse(add(inverse(add(X,X2)),inverse(add(X2,inverse(add(inverse(add(X,X2)),X)))))) = inverse(inverse(X2)),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
add(X2,inverse(add(inverse(add(X,X2)),inverse(add(X2,inverse(add(inverse(add(X,X2)),X))))))) = add(X2,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c410]) ).
cnf(c412,plain,
add(X,inverse(inverse(X))) = add(X,X),
inference(congruence,[status(thm)],[c114]) ).
cnf(c413,plain,
add(X,inverse(inverse(X))) = X,
inference(transitivity,[status(thm)],[c412,c70]) ).
cnf(c414,plain,
add(X2,inverse(add(inverse(add(X,X2)),inverse(add(X2,inverse(add(inverse(add(X,X2)),X))))))) = X2,
inference(transitivity,[status(thm)],[c411,c413]) ).
cnf(c415,plain,
add(X2,inverse(add(inverse(add(X,X2)),X))) = X2,
inference(transitivity,[status(thm)],[c388,c414]) ).
cnf(c416,plain,
add(X2,inverse(add(X,inverse(add(X,X2))))) = X2,
inference(transitivity,[status(thm)],[c386,c415]) ).
cnf(c417,plain,
add(X2,inverse(add(X,inverse(add(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c382,c416]) ).
cnf(c418,plain,
add(X,inverse(add(X2,inverse(add(X,X2))))) = X,
inference(substitution,[status(thm)],[c417]) ).
cnf(c419,plain,
inverse(add(X,inverse(add(X2,inverse(add(X,X2)))))) = inverse(X),
inference(congruence,[status(thm)],[c418]) ).
cnf(c420,plain,
add(X2,inverse(add(X,inverse(add(X2,inverse(add(X,X2))))))) = add(X2,inverse(X)),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,plain,
add(X2,inverse(add(X,X2))) = add(X2,inverse(X)),
inference(transitivity,[status(thm)],[c376,c420]) ).
cnf(c422,plain,
add(X2,inverse(add(X2,X))) = add(X2,inverse(X)),
inference(transitivity,[status(thm)],[c345,c421]) ).
cnf(c423,plain,
add(inverse(X3),inverse(add(inverse(X3),inverse(add(X2,add(X3,X)))))) = add(inverse(X3),inverse(inverse(add(X2,add(X3,X))))),
inference(substitution,[status(thm)],[c422]) ).
cnf(c424,plain,
add(inverse(X3),inverse(inverse(add(X2,add(X3,X))))) = add(inverse(X3),inverse(add(inverse(X3),inverse(add(X2,add(X3,X)))))),
inference(symmetry,[status(thm)],[c423]) ).
cnf(c425,plain,
add(X,inverse(add(X2,inverse(X2)))) = add(inverse(add(X2,inverse(X2))),X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c426,plain,
add(inverse(add(X2,inverse(X2))),X) = add(X,inverse(add(X2,inverse(X2)))),
inference(symmetry,[status(thm)],[c425]) ).
cnf(c427,plain,
inverse(add(inverse(add(inverse(add(X2,X)),X3)),inverse(add(X2,inverse(add(inverse(X3),inverse(add(X3,X4)))))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c428,plain,
X4 = inverse(add(inverse(add(inverse(add(X3,X2)),X4)),inverse(add(X3,inverse(add(inverse(X4),inverse(add(X4,X)))))))),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
add(X5,inverse(add(X4,inverse(X4)))) = add(inverse(add(inverse(add(inverse(add(X3,X2)),X5)),inverse(add(X3,inverse(add(inverse(X5),inverse(add(X5,X)))))))),inverse(add(X4,inverse(X4)))),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
add(inverse(add(X,inverse(X))),inverse(X2)) = add(inverse(X2),inverse(add(X,inverse(X)))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c431,plain,
add(inverse(X2),inverse(add(X,inverse(X)))) = add(inverse(add(X,inverse(X))),inverse(X2)),
inference(symmetry,[status(thm)],[c430]) ).
cnf(c432,plain,
add(inverse(add(X2,X)),add(X2,X)) = add(add(X2,X),inverse(add(X2,X))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c433,plain,
add(add(X2,X),inverse(add(X2,X))) = add(inverse(add(X2,X)),add(X2,X)),
inference(symmetry,[status(thm)],[c432]) ).
cnf(c434,plain,
add(X2,X) = add(X2,add(X2,X)),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c435,plain,
inverse(add(X2,X)) = inverse(add(X2,add(X2,X))),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
add(inverse(add(X2,X)),add(X2,X)) = add(inverse(add(X2,add(X2,X))),add(X2,X)),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
add(X,add(X3,X2)) = add(add(X3,X2),X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c438,plain,
add(add(X3,X2),X) = add(X,add(X3,X2)),
inference(symmetry,[status(thm)],[c437]) ).
cnf(c439,plain,
inverse(add(add(X3,X2),X)) = inverse(add(X,add(X3,X2))),
inference(congruence,[status(thm)],[c438]) ).
cnf(c440,plain,
add(X3,inverse(add(add(X3,X2),X))) = add(X3,inverse(add(X,add(X3,X2)))),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
inverse(add(X3,inverse(add(add(X3,X2),X)))) = inverse(add(X3,inverse(add(X,add(X3,X2))))),
inference(congruence,[status(thm)],[c440]) ).
cnf(c442,plain,
add(add(X3,X2),inverse(add(X3,inverse(add(add(X3,X2),X))))) = add(add(X3,X2),inverse(add(X3,inverse(add(X,add(X3,X2)))))),
inference(congruence,[status(thm)],[c441]) ).
cnf(c443,plain,
add(add(X3,X2),X) = add(X,add(X3,X2)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c444,plain,
add(X,add(X3,X2)) = add(add(X3,X2),X),
inference(symmetry,[status(thm)],[c443]) ).
cnf(c445,plain,
inverse(add(X,add(X3,X2))) = inverse(add(add(X3,X2),X)),
inference(congruence,[status(thm)],[c444]) ).
cnf(c446,plain,
add(X3,inverse(add(X,add(X3,X2)))) = add(X3,inverse(add(add(X3,X2),X))),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
inverse(add(X3,inverse(add(X,add(X3,X2))))) = inverse(add(X3,inverse(add(add(X3,X2),X)))),
inference(congruence,[status(thm)],[c446]) ).
cnf(c448,plain,
add(add(X3,X2),inverse(add(X3,inverse(add(X,add(X3,X2)))))) = add(add(X3,X2),inverse(add(X3,inverse(add(add(X3,X2),X))))),
inference(congruence,[status(thm)],[c447]) ).
cnf(c449,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c450,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c449]) ).
cnf(c451,plain,
add(add(X3,X2),inverse(add(X3,inverse(add(add(X3,X2),X))))) = add(add(X2,X3),inverse(add(X3,inverse(add(add(X3,X2),X))))),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c453,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c452]) ).
cnf(c454,plain,
add(add(X3,X2),X) = add(add(X2,X3),X),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
inverse(add(add(X3,X2),X)) = inverse(add(add(X2,X3),X)),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
add(X3,inverse(add(add(X3,X2),X))) = add(X3,inverse(add(add(X2,X3),X))),
inference(congruence,[status(thm)],[c455]) ).
cnf(c457,plain,
inverse(add(X3,inverse(add(add(X3,X2),X)))) = inverse(add(X3,inverse(add(add(X2,X3),X)))),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
add(add(X2,X3),inverse(add(X3,inverse(add(add(X3,X2),X))))) = add(add(X2,X3),inverse(add(X3,inverse(add(add(X2,X3),X))))),
inference(congruence,[status(thm)],[c457]) ).
cnf(c459,plain,
add(inverse(add(X3,inverse(add(add(X2,X3),X)))),add(X2,X3)) = add(add(X2,X3),inverse(add(X3,inverse(add(add(X2,X3),X))))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c460,plain,
add(add(X2,X3),inverse(add(X3,inverse(add(add(X2,X3),X))))) = add(inverse(add(X3,inverse(add(add(X2,X3),X)))),add(X2,X3)),
inference(symmetry,[status(thm)],[c459]) ).
cnf(c461,plain,
inverse(add(inverse(add(X2,X3)),inverse(add(add(X2,X3),X)))) = add(X2,X3),
inference(substitution,[status(thm)],[c259]) ).
cnf(c462,plain,
add(X2,X3) = inverse(add(inverse(add(X2,X3)),inverse(add(add(X2,X3),X)))),
inference(symmetry,[status(thm)],[c461]) ).
cnf(c463,plain,
add(inverse(add(X3,inverse(add(add(X2,X3),X)))),add(X2,X3)) = add(inverse(add(X3,inverse(add(add(X2,X3),X)))),inverse(add(inverse(add(X2,X3)),inverse(add(add(X2,X3),X))))),
inference(congruence,[status(thm)],[c462]) ).
cnf(c464,plain,
add(inverse(add(X3,inverse(add(add(X2,X3),X)))),inverse(add(inverse(add(X2,X3)),inverse(add(add(X2,X3),X))))) = inverse(inverse(add(add(X2,X3),X))),
inference(substitution,[status(thm)],[c407]) ).
cnf(c465,plain,
inverse(inverse(add(add(X2,X3),X))) = add(add(X2,X3),X),
inference(substitution,[status(thm)],[c114]) ).
cnf(c466,plain,
add(add(X2,X3),X) = add(X,add(X2,X3)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c467,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c468,plain,
add(X,add(X2,X3)) = add(X,add(X3,X2)),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
add(add(X2,X3),X) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c466,c468]) ).
cnf(c470,plain,
inverse(inverse(add(add(X2,X3),X))) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c465,c469]) ).
cnf(c471,plain,
add(inverse(add(X3,inverse(add(add(X2,X3),X)))),inverse(add(inverse(add(X2,X3)),inverse(add(add(X2,X3),X))))) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c464,c470]) ).
cnf(c472,plain,
add(inverse(add(X3,inverse(add(add(X2,X3),X)))),add(X2,X3)) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c463,c471]) ).
cnf(c473,plain,
add(add(X2,X3),inverse(add(X3,inverse(add(add(X2,X3),X))))) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c460,c472]) ).
cnf(c474,plain,
add(add(X2,X3),inverse(add(X3,inverse(add(add(X3,X2),X))))) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c458,c473]) ).
cnf(c475,plain,
add(add(X3,X2),inverse(add(X3,inverse(add(add(X3,X2),X))))) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c451,c474]) ).
cnf(c476,plain,
add(add(X3,X2),inverse(add(X3,inverse(add(X,add(X3,X2)))))) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c448,c475]) ).
cnf(c477,plain,
add(add(X3,X2),inverse(add(X3,inverse(add(add(X3,X2),X))))) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c442,c476]) ).
cnf(c478,plain,
add(add(X2,X),inverse(add(X2,inverse(add(add(X2,X),inverse(add(X2,add(X2,X)))))))) = add(inverse(add(X2,add(X2,X))),add(X2,X)),
inference(substitution,[status(thm)],[c477]) ).
cnf(c479,plain,
add(inverse(add(X2,add(X2,X))),add(X2,X)) = add(add(X2,X),inverse(add(X2,inverse(add(add(X2,X),inverse(add(X2,add(X2,X)))))))),
inference(symmetry,[status(thm)],[c478]) ).
cnf(c480,plain,
add(X2,inverse(add(add(X2,X),inverse(add(X2,add(X2,X)))))) = X2,
inference(substitution,[status(thm)],[c417]) ).
cnf(c481,plain,
inverse(add(X2,inverse(add(add(X2,X),inverse(add(X2,add(X2,X))))))) = inverse(X2),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
add(add(X2,X),inverse(add(X2,inverse(add(add(X2,X),inverse(add(X2,add(X2,X)))))))) = add(add(X2,X),inverse(X2)),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
add(add(X2,X),inverse(X2)) = add(inverse(X2),add(X2,X)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c484,plain,
inverse(inverse(add(X2,X))) = add(X2,X),
inference(substitution,[status(thm)],[c114]) ).
cnf(c485,plain,
add(X2,X) = inverse(inverse(add(X2,X))),
inference(symmetry,[status(thm)],[c484]) ).
cnf(c486,plain,
add(inverse(X2),add(X2,X)) = add(inverse(X2),inverse(inverse(add(X2,X)))),
inference(congruence,[status(thm)],[c485]) ).
cnf(c487,plain,
add(inverse(X2),inverse(add(inverse(X2),inverse(add(X2,X))))) = add(inverse(X2),inverse(inverse(add(X2,X)))),
inference(substitution,[status(thm)],[c422]) ).
cnf(c488,plain,
add(inverse(X2),inverse(inverse(add(X2,X)))) = add(inverse(X2),inverse(add(inverse(X2),inverse(add(X2,X))))),
inference(symmetry,[status(thm)],[c487]) ).
cnf(c489,plain,
inverse(add(inverse(X2),inverse(add(X2,X)))) = add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c490,plain,
add(inverse(X2),inverse(add(inverse(X2),inverse(add(X2,X))))) = add(inverse(X2),add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))),
inference(congruence,[status(thm)],[c489]) ).
cnf(c491,plain,
inverse(inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))) = add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))),
inference(substitution,[status(thm)],[c114]) ).
cnf(c492,plain,
add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))) = inverse(inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))),
inference(symmetry,[status(thm)],[c491]) ).
cnf(c493,plain,
add(inverse(X2),add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))) = add(inverse(X2),inverse(inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
add(inverse(X2),inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))) = add(inverse(X2),inverse(inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))),
inference(substitution,[status(thm)],[c422]) ).
cnf(c495,plain,
add(inverse(X2),inverse(inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))) = add(inverse(X2),inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))),
inference(symmetry,[status(thm)],[c494]) ).
cnf(c496,plain,
add(inverse(X2),inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))) = add(inverse(X2),X2),
inference(congruence,[status(thm)],[c21]) ).
cnf(c497,plain,
add(inverse(X),X) = add(X,inverse(X)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c498,plain,
add(inverse(X2),inverse(add(inverse(X2),inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X))))))))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c496,c497]) ).
cnf(c499,plain,
add(inverse(X2),inverse(inverse(add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c495,c498]) ).
cnf(c500,plain,
add(inverse(X2),add(X2,inverse(add(inverse(X2),inverse(add(X2,X)))))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c493,c499]) ).
cnf(c501,plain,
add(inverse(X2),inverse(add(inverse(X2),inverse(add(X2,X))))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c490,c500]) ).
cnf(c502,plain,
add(inverse(X2),inverse(inverse(add(X2,X)))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c488,c501]) ).
cnf(c503,plain,
add(inverse(X2),add(X2,X)) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c486,c502]) ).
cnf(c504,plain,
add(add(X2,X),inverse(X2)) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c483,c503]) ).
cnf(c505,plain,
add(add(X2,X),inverse(add(X2,inverse(add(add(X2,X),inverse(add(X2,add(X2,X)))))))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c482,c504]) ).
cnf(c506,plain,
add(inverse(add(X2,add(X2,X))),add(X2,X)) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c479,c505]) ).
cnf(c507,plain,
add(inverse(add(X2,X)),add(X2,X)) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c436,c506]) ).
cnf(c508,plain,
add(add(X2,X),inverse(add(X2,X))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c433,c507]) ).
cnf(c509,plain,
add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))) = add(X2,inverse(X2)),
inference(substitution,[status(thm)],[c508]) ).
cnf(c510,plain,
add(X2,inverse(X2)) = add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))),
inference(symmetry,[status(thm)],[c509]) ).
cnf(c511,plain,
add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))) = add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(inverse(X),X2))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c512,plain,
add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(inverse(X),X2))) = add(add(inverse(X),X2),inverse(add(inverse(X),X2))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c513,plain,
add(add(inverse(X),X2),inverse(add(inverse(X),X2))) = add(inverse(X),inverse(inverse(X))),
inference(substitution,[status(thm)],[c508]) ).
cnf(c514,plain,
add(add(inverse(X),X2),inverse(add(inverse(X),X2))) = add(inverse(X),inverse(inverse(X))),
inference(substitution,[status(thm)],[c508]) ).
cnf(c515,plain,
add(inverse(X),inverse(inverse(X))) = add(add(inverse(X),X2),inverse(add(inverse(X),X2))),
inference(symmetry,[status(thm)],[c514]) ).
cnf(c516,plain,
add(inverse(X),X2) = add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c517,plain,
add(add(inverse(X),X2),inverse(add(inverse(X),X2))) = add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(inverse(X),X2))),
inference(congruence,[status(thm)],[c516]) ).
cnf(c518,plain,
inverse(add(inverse(X),X2)) = inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2)))))),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c519,plain,
add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(inverse(X),X2))) = add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))),
inference(congruence,[status(thm)],[c518]) ).
cnf(c520,plain,
add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))) = add(X2,inverse(X2)),
inference(substitution,[status(thm)],[c508]) ).
cnf(c521,plain,
add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(inverse(X),X2))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c519,c520]) ).
cnf(c522,plain,
add(add(inverse(X),X2),inverse(add(inverse(X),X2))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c517,c521]) ).
cnf(c523,plain,
add(inverse(X),inverse(inverse(X))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c515,c522]) ).
cnf(c524,plain,
add(add(inverse(X),X2),inverse(add(inverse(X),X2))) = add(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c513,c523]) ).
cnf(c525,plain,
add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(inverse(X),X2))) = add(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c512,c524]) ).
cnf(c526,plain,
add(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))),inverse(add(X2,inverse(add(X,inverse(add(inverse(X),X2))))))) = add(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c511,c525]) ).
cnf(c527,plain,
add(X,inverse(X)) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c510,c526]) ).
cnf(c528,plain,
inverse(add(X,inverse(X))) = inverse(add(X2,inverse(X2))),
inference(congruence,[status(thm)],[c527]) ).
cnf(c529,plain,
add(inverse(add(X,inverse(X))),inverse(X2)) = add(inverse(add(X2,inverse(X2))),inverse(X2)),
inference(congruence,[status(thm)],[c528]) ).
cnf(c530,plain,
add(X,inverse(add(inverse(X),inverse(add(X,inverse(X)))))) = X,
inference(substitution,[status(thm)],[c417]) ).
cnf(c531,plain,
X = add(X,inverse(add(inverse(X),inverse(add(X,inverse(X)))))),
inference(symmetry,[status(thm)],[c530]) ).
cnf(c532,plain,
inverse(X) = inverse(add(X,inverse(add(inverse(X),inverse(add(X,inverse(X))))))),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
add(inverse(add(X,inverse(X))),inverse(X)) = add(inverse(add(X,inverse(X))),inverse(add(X,inverse(add(inverse(X),inverse(add(X,inverse(X)))))))),
inference(congruence,[status(thm)],[c532]) ).
cnf(c534,plain,
add(inverse(add(X,inverse(X))),inverse(add(X,inverse(add(inverse(X),inverse(add(X,inverse(X)))))))) = add(inverse(X),inverse(add(X,inverse(X)))),
inference(substitution,[status(thm)],[c120]) ).
cnf(c535,plain,
add(inverse(X),inverse(add(X,inverse(X)))) = inverse(X),
inference(substitution,[status(thm)],[c321]) ).
cnf(c536,plain,
add(inverse(add(X,inverse(X))),inverse(add(X,inverse(add(inverse(X),inverse(add(X,inverse(X)))))))) = inverse(X),
inference(transitivity,[status(thm)],[c534,c535]) ).
cnf(c537,plain,
add(inverse(add(X,inverse(X))),inverse(X)) = inverse(X),
inference(transitivity,[status(thm)],[c533,c536]) ).
cnf(c538,plain,
add(inverse(add(X,inverse(X))),inverse(X2)) = inverse(X2),
inference(transitivity,[status(thm)],[c529,c537]) ).
cnf(c539,plain,
add(inverse(X2),inverse(add(X,inverse(X)))) = inverse(X2),
inference(transitivity,[status(thm)],[c431,c538]) ).
cnf(c540,plain,
add(inverse(add(inverse(add(inverse(add(X3,X2)),X5)),inverse(add(X3,inverse(add(inverse(X5),inverse(add(X5,X)))))))),inverse(add(X4,inverse(X4)))) = inverse(add(inverse(add(inverse(add(X3,X2)),X5)),inverse(add(X3,inverse(add(inverse(X5),inverse(add(X5,X)))))))),
inference(substitution,[status(thm)],[c539]) ).
cnf(c541,plain,
inverse(add(inverse(add(inverse(add(X3,X2)),X4)),inverse(add(X3,inverse(add(inverse(X4),inverse(add(X4,X)))))))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c542,plain,
add(inverse(add(inverse(add(inverse(add(X3,X2)),X5)),inverse(add(X3,inverse(add(inverse(X5),inverse(add(X5,X)))))))),inverse(add(X4,inverse(X4)))) = X5,
inference(transitivity,[status(thm)],[c540,c541]) ).
cnf(c543,plain,
add(X2,inverse(add(X,inverse(X)))) = X2,
inference(transitivity,[status(thm)],[c429,c542]) ).
cnf(c544,plain,
add(X,inverse(add(X2,inverse(X2)))) = X,
inference(substitution,[status(thm)],[c543]) ).
cnf(c545,plain,
add(inverse(add(X2,inverse(X2))),X) = X,
inference(transitivity,[status(thm)],[c426,c544]) ).
cnf(c546,plain,
add(inverse(add(X3,inverse(X3))),add(inverse(X3),inverse(add(X2,add(X3,X))))) = add(inverse(X3),inverse(add(X2,add(X3,X)))),
inference(substitution,[status(thm)],[c545]) ).
cnf(c547,plain,
add(inverse(X3),inverse(add(X2,add(X3,X)))) = add(inverse(add(X3,inverse(X3))),add(inverse(X3),inverse(add(X2,add(X3,X))))),
inference(symmetry,[status(thm)],[c546]) ).
cnf(c548,plain,
inverse(add(inverse(X3),inverse(add(X2,add(X3,X))))) = inverse(add(inverse(add(X3,inverse(X3))),add(inverse(X3),inverse(add(X2,add(X3,X)))))),
inference(congruence,[status(thm)],[c547]) ).
cnf(c549,plain,
add(inverse(X3),inverse(add(inverse(X3),inverse(add(X2,add(X3,X)))))) = add(inverse(X3),inverse(add(inverse(add(X3,inverse(X3))),add(inverse(X3),inverse(add(X2,add(X3,X))))))),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
add(X2,inverse(X2)) = add(inverse(X2),add(X2,X)),
inference(symmetry,[status(thm)],[c503]) ).
cnf(c551,plain,
inverse(add(X2,inverse(X2))) = inverse(add(inverse(X2),add(X2,X))),
inference(congruence,[status(thm)],[c550]) ).
cnf(c552,plain,
add(inverse(add(X3,inverse(X3))),add(inverse(X3),inverse(add(X2,add(X3,X))))) = add(inverse(add(inverse(X3),add(X3,X))),add(inverse(X3),inverse(add(X2,add(X3,X))))),
inference(congruence,[status(thm)],[c551]) ).
cnf(c553,plain,
inverse(add(inverse(add(X3,inverse(X3))),add(inverse(X3),inverse(add(X2,add(X3,X)))))) = inverse(add(inverse(add(inverse(X3),add(X3,X))),add(inverse(X3),inverse(add(X2,add(X3,X)))))),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
add(inverse(X3),inverse(add(inverse(add(X3,inverse(X3))),add(inverse(X3),inverse(add(X2,add(X3,X))))))) = add(inverse(X3),inverse(add(inverse(add(inverse(X3),add(X3,X))),add(inverse(X3),inverse(add(X2,add(X3,X))))))),
inference(congruence,[status(thm)],[c553]) ).
cnf(c555,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c556,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c555]) ).
cnf(c557,plain,
inverse(add(X2,X)) = inverse(add(X,X2)),
inference(congruence,[status(thm)],[c556]) ).
cnf(c558,plain,
add(inverse(add(X3,X2)),add(X3,inverse(add(X,X2)))) = add(inverse(add(X2,X3)),add(X3,inverse(add(X,X2)))),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
inverse(add(inverse(add(X3,X2)),add(X3,inverse(add(X,X2))))) = inverse(add(inverse(add(X2,X3)),add(X3,inverse(add(X,X2))))),
inference(congruence,[status(thm)],[c558]) ).
cnf(c560,plain,
add(X3,inverse(add(inverse(add(X3,X2)),add(X3,inverse(add(X,X2)))))) = add(X3,inverse(add(inverse(add(X2,X3)),add(X3,inverse(add(X,X2)))))),
inference(congruence,[status(thm)],[c559]) ).
cnf(c561,plain,
inverse(inverse(add(X3,inverse(add(X,X2))))) = add(X3,inverse(add(X,X2))),
inference(substitution,[status(thm)],[c114]) ).
cnf(c562,plain,
add(X3,inverse(add(X,X2))) = inverse(inverse(add(X3,inverse(add(X,X2))))),
inference(symmetry,[status(thm)],[c561]) ).
cnf(c563,plain,
add(inverse(add(X2,X3)),add(X3,inverse(add(X,X2)))) = add(inverse(add(X2,X3)),inverse(inverse(add(X3,inverse(add(X,X2)))))),
inference(congruence,[status(thm)],[c562]) ).
cnf(c564,plain,
inverse(add(inverse(add(X2,X3)),add(X3,inverse(add(X,X2))))) = inverse(add(inverse(add(X2,X3)),inverse(inverse(add(X3,inverse(add(X,X2))))))),
inference(congruence,[status(thm)],[c563]) ).
cnf(c565,plain,
add(X3,inverse(add(inverse(add(X2,X3)),add(X3,inverse(add(X,X2)))))) = add(X3,inverse(add(inverse(add(X2,X3)),inverse(inverse(add(X3,inverse(add(X,X2)))))))),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))) = add(inverse(add(X2,X3)),inverse(inverse(add(X3,inverse(add(X,X2)))))),
inference(substitution,[status(thm)],[c422]) ).
cnf(c567,plain,
add(inverse(add(X2,X3)),inverse(inverse(add(X3,inverse(add(X,X2)))))) = add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))),
inference(symmetry,[status(thm)],[c566]) ).
cnf(c568,plain,
inverse(add(inverse(add(X2,X3)),inverse(inverse(add(X3,inverse(add(X,X2))))))) = inverse(add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2)))))))),
inference(congruence,[status(thm)],[c567]) ).
cnf(c569,plain,
add(X3,inverse(add(inverse(add(X2,X3)),inverse(inverse(add(X3,inverse(add(X,X2)))))))) = add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))))),
inference(congruence,[status(thm)],[c568]) ).
cnf(c570,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c571,plain,
add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))))) = add(inverse(inverse(X3)),inverse(add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))))),
inference(congruence,[status(thm)],[c570]) ).
cnf(c572,plain,
add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))) = inverse(X3),
inference(substitution,[status(thm)],[c408]) ).
cnf(c573,plain,
inverse(X3) = add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))),
inference(symmetry,[status(thm)],[c572]) ).
cnf(c574,plain,
inverse(inverse(X3)) = inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2)))))),
inference(congruence,[status(thm)],[c573]) ).
cnf(c575,plain,
add(inverse(inverse(X3)),inverse(add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))))) = add(inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2)))))),inverse(add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))))),
inference(congruence,[status(thm)],[c574]) ).
cnf(c576,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c577,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c576]) ).
cnf(c578,plain,
inverse(add(X2,X)) = inverse(add(X,X2)),
inference(congruence,[status(thm)],[c577]) ).
cnf(c579,plain,
add(inverse(add(X2,X)),inverse(add(X2,inverse(add(X2,X))))) = add(inverse(add(X,X2)),inverse(add(X2,inverse(add(X2,X))))),
inference(congruence,[status(thm)],[c578]) ).
cnf(c580,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c581,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c580]) ).
cnf(c582,plain,
inverse(add(X2,X)) = inverse(add(X,X2)),
inference(congruence,[status(thm)],[c581]) ).
cnf(c583,plain,
add(X2,inverse(add(X2,X))) = add(X2,inverse(add(X,X2))),
inference(congruence,[status(thm)],[c582]) ).
cnf(c584,plain,
inverse(add(X2,inverse(add(X2,X)))) = inverse(add(X2,inverse(add(X,X2)))),
inference(congruence,[status(thm)],[c583]) ).
cnf(c585,plain,
add(inverse(add(X,X2)),inverse(add(X2,inverse(add(X2,X))))) = add(inverse(add(X,X2)),inverse(add(X2,inverse(add(X,X2))))),
inference(congruence,[status(thm)],[c584]) ).
cnf(c586,plain,
add(inverse(add(X2,inverse(add(X,X2)))),inverse(add(X,X2))) = add(inverse(add(X,X2)),inverse(add(X2,inverse(add(X,X2))))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c587,plain,
add(inverse(add(X,X2)),inverse(add(X2,inverse(add(X,X2))))) = add(inverse(add(X2,inverse(add(X,X2)))),inverse(add(X,X2))),
inference(symmetry,[status(thm)],[c586]) ).
cnf(c588,plain,
add(inverse(add(X,X2)),X2) = add(X2,inverse(add(X,X2))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c589,plain,
add(X2,inverse(add(X,X2))) = add(inverse(add(X,X2)),X2),
inference(symmetry,[status(thm)],[c588]) ).
cnf(c590,plain,
inverse(add(X2,inverse(add(X,X2)))) = inverse(add(inverse(add(X,X2)),X2)),
inference(congruence,[status(thm)],[c589]) ).
cnf(c591,plain,
add(inverse(add(X2,inverse(add(X,X2)))),inverse(add(X,X2))) = add(inverse(add(inverse(add(X,X2)),X2)),inverse(add(X,X2))),
inference(congruence,[status(thm)],[c590]) ).
cnf(c592,plain,
inverse(X2) = inverse(add(X2,inverse(add(X,inverse(X2))))),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c593,plain,
add(inverse(X3),X2) = add(inverse(add(X3,inverse(add(X,inverse(X3))))),X2),
inference(congruence,[status(thm)],[c592]) ).
cnf(c594,plain,
inverse(add(inverse(X3),X2)) = inverse(add(inverse(add(X3,inverse(add(X,inverse(X3))))),X2)),
inference(congruence,[status(thm)],[c593]) ).
cnf(c595,plain,
add(inverse(add(inverse(X3),X2)),inverse(add(X3,X2))) = add(inverse(add(inverse(add(X3,inverse(add(X,inverse(X3))))),X2)),inverse(add(X3,X2))),
inference(congruence,[status(thm)],[c594]) ).
cnf(c596,plain,
inverse(add(inverse(add(inverse(X3),X2)),inverse(add(X3,X2)))) = inverse(add(inverse(add(inverse(add(X3,inverse(add(X,inverse(X3))))),X2)),inverse(add(X3,X2)))),
inference(congruence,[status(thm)],[c595]) ).
cnf(c597,plain,
inverse(add(inverse(add(inverse(add(X3,inverse(add(X,inverse(X3))))),X2)),inverse(add(X3,X2)))) = X2,
inference(substitution,[status(thm)],[c45]) ).
cnf(c598,plain,
inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))) = X,
inference(transitivity,[status(thm)],[c596,c597]) ).
cnf(c599,plain,
X = inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))),
inference(symmetry,[status(thm)],[c598]) ).
cnf(c600,plain,
add(inverse(add(X2,X)),X) = add(inverse(add(X2,X)),inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))),
inference(congruence,[status(thm)],[c599]) ).
cnf(c601,plain,
inverse(add(inverse(add(X2,X)),X)) = inverse(add(inverse(add(X2,X)),inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))))),
inference(congruence,[status(thm)],[c600]) ).
cnf(c602,plain,
add(inverse(add(inverse(add(X2,X)),X)),inverse(add(X2,X))) = add(inverse(add(inverse(add(X2,X)),inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))))),inverse(add(X2,X))),
inference(congruence,[status(thm)],[c601]) ).
cnf(c603,plain,
inverse(add(inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2)),inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2))))) = add(inverse(add(X2,inverse(add(X,X2)))),X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c604,plain,
add(inverse(add(X2,inverse(add(X,X2)))),X2) = inverse(add(inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2)),inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2))))),
inference(symmetry,[status(thm)],[c603]) ).
cnf(c605,plain,
add(inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2)),inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2)))) = add(inverse(add(X,X2)),inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2)))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c606,plain,
inverse(add(inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2)),inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2))))) = inverse(add(inverse(add(X,X2)),inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2))))),
inference(congruence,[status(thm)],[c605]) ).
cnf(c607,plain,
add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2)) = add(inverse(add(X2,inverse(add(X,X2)))),X2),
inference(substitution,[status(thm)],[c70]) ).
cnf(c608,plain,
inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2))) = inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2)),
inference(congruence,[status(thm)],[c607]) ).
cnf(c609,plain,
add(inverse(add(X,X2)),inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2)))) = add(inverse(add(X,X2)),inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2))),
inference(congruence,[status(thm)],[c608]) ).
cnf(c610,plain,
inverse(add(inverse(add(X,X2)),inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2))))) = inverse(add(inverse(add(X,X2)),inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2)))),
inference(congruence,[status(thm)],[c609]) ).
cnf(c611,plain,
add(inverse(add(X,X2)),inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2))) = add(inverse(add(X,X2)),inverse(add(X,X2))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c612,plain,
inverse(add(inverse(add(X,X2)),inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2)))) = inverse(add(inverse(add(X,X2)),inverse(add(X,X2)))),
inference(congruence,[status(thm)],[c611]) ).
cnf(c613,plain,
add(inverse(add(X,X2)),inverse(add(X,X2))) = inverse(add(X,X2)),
inference(substitution,[status(thm)],[c70]) ).
cnf(c614,plain,
inverse(add(inverse(add(X,X2)),inverse(add(X,X2)))) = inverse(inverse(add(X,X2))),
inference(congruence,[status(thm)],[c613]) ).
cnf(c615,plain,
inverse(inverse(add(X,X2))) = add(X,X2),
inference(substitution,[status(thm)],[c114]) ).
cnf(c616,plain,
inverse(add(inverse(add(X,X2)),inverse(add(X,X2)))) = add(X,X2),
inference(transitivity,[status(thm)],[c614,c615]) ).
cnf(c617,plain,
inverse(add(inverse(add(X,X2)),inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2)))) = add(X,X2),
inference(transitivity,[status(thm)],[c612,c616]) ).
cnf(c618,plain,
inverse(add(inverse(add(X,X2)),inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2))))) = add(X,X2),
inference(transitivity,[status(thm)],[c610,c617]) ).
cnf(c619,plain,
inverse(add(inverse(add(inverse(add(X2,inverse(add(X,X2)))),X2)),inverse(add(add(inverse(add(X2,inverse(add(X,X2)))),X2),add(inverse(add(X2,inverse(add(X,X2)))),X2))))) = add(X,X2),
inference(transitivity,[status(thm)],[c606,c618]) ).
cnf(c620,plain,
add(inverse(add(X2,inverse(add(X,X2)))),X2) = add(X,X2),
inference(transitivity,[status(thm)],[c604,c619]) ).
cnf(c621,plain,
add(inverse(add(inverse(add(X2,X)),inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))))),inverse(add(X2,X))) = add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),
inference(substitution,[status(thm)],[c620]) ).
cnf(c622,plain,
inverse(add(inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))),inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))))) = add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c623,plain,
add(inverse(add(inverse(X2),X)),inverse(add(X2,X))) = inverse(add(inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))),inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))))),
inference(symmetry,[status(thm)],[c622]) ).
cnf(c624,plain,
add(inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))),inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))))) = add(X,inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))))),
inference(congruence,[status(thm)],[c598]) ).
cnf(c625,plain,
inverse(add(inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))),inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))))) = inverse(add(X,inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))))),
inference(congruence,[status(thm)],[c624]) ).
cnf(c626,plain,
add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))) = add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c627,plain,
inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))) = inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))),
inference(congruence,[status(thm)],[c626]) ).
cnf(c628,plain,
add(X,inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))))) = add(X,inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))),
inference(congruence,[status(thm)],[c627]) ).
cnf(c629,plain,
inverse(add(X,inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))))) = inverse(add(X,inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))))),
inference(congruence,[status(thm)],[c628]) ).
cnf(c630,plain,
add(X,inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))) = add(X,X),
inference(congruence,[status(thm)],[c598]) ).
cnf(c631,plain,
inverse(add(X,inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))))) = inverse(add(X,X)),
inference(congruence,[status(thm)],[c630]) ).
cnf(c632,plain,
inverse(add(X,X)) = inverse(X),
inference(congruence,[status(thm)],[c70]) ).
cnf(c633,plain,
inverse(add(X,inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))))) = inverse(X),
inference(transitivity,[status(thm)],[c631,c632]) ).
cnf(c634,plain,
inverse(add(X,inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))))) = inverse(X),
inference(transitivity,[status(thm)],[c629,c633]) ).
cnf(c635,plain,
inverse(add(inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))),inverse(add(add(inverse(add(inverse(X2),X)),inverse(add(X2,X))),add(inverse(add(inverse(X2),X)),inverse(add(X2,X))))))) = inverse(X),
inference(transitivity,[status(thm)],[c625,c634]) ).
cnf(c636,plain,
add(inverse(add(inverse(X2),X)),inverse(add(X2,X))) = inverse(X),
inference(transitivity,[status(thm)],[c623,c635]) ).
cnf(c637,plain,
add(inverse(add(inverse(add(X2,X)),inverse(add(inverse(add(inverse(X2),X)),inverse(add(X2,X)))))),inverse(add(X2,X))) = inverse(X),
inference(transitivity,[status(thm)],[c621,c636]) ).
cnf(c638,plain,
add(inverse(add(inverse(add(X2,X)),X)),inverse(add(X2,X))) = inverse(X),
inference(transitivity,[status(thm)],[c602,c637]) ).
cnf(c639,plain,
add(inverse(add(inverse(add(X,X2)),X2)),inverse(add(X,X2))) = inverse(X2),
inference(substitution,[status(thm)],[c638]) ).
cnf(c640,plain,
add(inverse(add(X2,inverse(add(X,X2)))),inverse(add(X,X2))) = inverse(X2),
inference(transitivity,[status(thm)],[c591,c639]) ).
cnf(c641,plain,
add(inverse(add(X,X2)),inverse(add(X2,inverse(add(X,X2))))) = inverse(X2),
inference(transitivity,[status(thm)],[c587,c640]) ).
cnf(c642,plain,
add(inverse(add(X,X2)),inverse(add(X2,inverse(add(X2,X))))) = inverse(X2),
inference(transitivity,[status(thm)],[c585,c641]) ).
cnf(c643,plain,
add(inverse(add(X2,X)),inverse(add(X2,inverse(add(X2,X))))) = inverse(X2),
inference(transitivity,[status(thm)],[c579,c642]) ).
cnf(c644,plain,
add(inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2)))))),inverse(add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))))) = inverse(inverse(add(X2,X3))),
inference(substitution,[status(thm)],[c643]) ).
cnf(c645,plain,
inverse(inverse(add(X,X2))) = add(X,X2),
inference(substitution,[status(thm)],[c114]) ).
cnf(c646,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c647,plain,
inverse(inverse(add(X,X2))) = add(X2,X),
inference(transitivity,[status(thm)],[c645,c646]) ).
cnf(c648,plain,
add(inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2)))))),inverse(add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c644,c647]) ).
cnf(c649,plain,
add(inverse(inverse(X3)),inverse(add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c575,c648]) ).
cnf(c650,plain,
add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(inverse(add(X2,X3)),inverse(add(X3,inverse(add(X,X2))))))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c571,c649]) ).
cnf(c651,plain,
add(X3,inverse(add(inverse(add(X2,X3)),inverse(inverse(add(X3,inverse(add(X,X2)))))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c569,c650]) ).
cnf(c652,plain,
add(X3,inverse(add(inverse(add(X2,X3)),add(X3,inverse(add(X,X2)))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c565,c651]) ).
cnf(c653,plain,
add(X3,inverse(add(inverse(add(X3,X2)),add(X3,inverse(add(X,X2)))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c560,c652]) ).
cnf(c654,plain,
add(inverse(X3),inverse(add(inverse(add(inverse(X3),add(X3,X))),add(inverse(X3),inverse(add(X2,add(X3,X))))))) = add(inverse(X3),add(X3,X)),
inference(substitution,[status(thm)],[c653]) ).
cnf(c655,plain,
add(X2,inverse(X2)) = add(X,inverse(X)),
inference(symmetry,[status(thm)],[c527]) ).
cnf(c656,plain,
add(inverse(X3),add(X3,X2)) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c503,c655]) ).
cnf(c657,plain,
add(inverse(X4),inverse(add(inverse(add(inverse(X4),add(X4,X2))),add(inverse(X4),inverse(add(X3,add(X4,X2))))))) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c654,c656]) ).
cnf(c658,plain,
add(inverse(X4),inverse(add(inverse(add(X4,inverse(X4))),add(inverse(X4),inverse(add(X3,add(X4,X2))))))) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c554,c657]) ).
cnf(c659,plain,
add(inverse(X4),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2)))))) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c549,c658]) ).
cnf(c660,plain,
add(inverse(X4),inverse(inverse(add(X3,add(X4,X2))))) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c424,c659]) ).
cnf(c661,plain,
add(inverse(X4),add(X3,add(X4,X2))) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c341,c660]) ).
cnf(c662,plain,
add(add(inverse(X4),add(X3,add(X4,X2))),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2)))))) = add(add(X,inverse(X)),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2)))))),
inference(congruence,[status(thm)],[c661]) ).
cnf(c663,plain,
inverse(add(add(inverse(X4),add(X3,add(X4,X2))),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2))))))) = inverse(add(add(X,inverse(X)),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2))))))),
inference(congruence,[status(thm)],[c662]) ).
cnf(c664,plain,
add(inverse(X4),inverse(add(add(inverse(X4),add(X3,add(X4,X2))),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2)))))))) = add(inverse(X4),inverse(add(add(X,inverse(X)),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2)))))))),
inference(congruence,[status(thm)],[c663]) ).
cnf(c665,plain,
add(X,add(X2,inverse(X2))) = add(add(X2,inverse(X2)),X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c666,plain,
add(add(X2,inverse(X2)),X) = add(X,add(X2,inverse(X2))),
inference(symmetry,[status(thm)],[c665]) ).
cnf(c667,plain,
inverse(inverse(add(X,inverse(X)))) = add(X,inverse(X)),
inference(substitution,[status(thm)],[c114]) ).
cnf(c668,plain,
add(X,inverse(X)) = inverse(inverse(add(X,inverse(X)))),
inference(symmetry,[status(thm)],[c667]) ).
cnf(c669,plain,
add(X2,add(X,inverse(X))) = add(X2,inverse(inverse(add(X,inverse(X))))),
inference(congruence,[status(thm)],[c668]) ).
cnf(c670,plain,
add(X2,inverse(add(X2,inverse(add(X,inverse(X)))))) = add(X2,inverse(inverse(add(X,inverse(X))))),
inference(substitution,[status(thm)],[c422]) ).
cnf(c671,plain,
add(X2,inverse(inverse(add(X,inverse(X))))) = add(X2,inverse(add(X2,inverse(add(X,inverse(X)))))),
inference(symmetry,[status(thm)],[c670]) ).
cnf(c672,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c673,plain,
add(X2,inverse(add(X2,inverse(add(X,inverse(X)))))) = add(inverse(inverse(X2)),inverse(add(X2,inverse(add(X,inverse(X)))))),
inference(congruence,[status(thm)],[c672]) ).
cnf(c674,plain,
inverse(X2) = add(inverse(X2),inverse(add(X,inverse(X)))),
inference(symmetry,[status(thm)],[c539]) ).
cnf(c675,plain,
inverse(inverse(X2)) = inverse(add(inverse(X2),inverse(add(X,inverse(X))))),
inference(congruence,[status(thm)],[c674]) ).
cnf(c676,plain,
add(inverse(inverse(X2)),inverse(add(X2,inverse(add(X,inverse(X)))))) = add(inverse(add(inverse(X2),inverse(add(X,inverse(X))))),inverse(add(X2,inverse(add(X,inverse(X)))))),
inference(congruence,[status(thm)],[c675]) ).
cnf(c677,plain,
add(inverse(add(inverse(X2),inverse(add(X,inverse(X))))),inverse(add(X2,inverse(add(X,inverse(X)))))) = inverse(inverse(add(X,inverse(X)))),
inference(substitution,[status(thm)],[c636]) ).
cnf(c678,plain,
inverse(inverse(add(X,inverse(X)))) = add(X,inverse(X)),
inference(substitution,[status(thm)],[c114]) ).
cnf(c679,plain,
add(inverse(add(inverse(X2),inverse(add(X,inverse(X))))),inverse(add(X2,inverse(add(X,inverse(X)))))) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c677,c678]) ).
cnf(c680,plain,
add(inverse(inverse(X2)),inverse(add(X2,inverse(add(X,inverse(X)))))) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c676,c679]) ).
cnf(c681,plain,
add(X2,inverse(add(X2,inverse(add(X,inverse(X)))))) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c673,c680]) ).
cnf(c682,plain,
add(X2,inverse(inverse(add(X,inverse(X))))) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c671,c681]) ).
cnf(c683,plain,
add(X2,add(X,inverse(X))) = add(X,inverse(X)),
inference(transitivity,[status(thm)],[c669,c682]) ).
cnf(c684,plain,
add(X,add(X2,inverse(X2))) = add(X2,inverse(X2)),
inference(substitution,[status(thm)],[c683]) ).
cnf(c685,plain,
add(add(X2,inverse(X2)),X) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c666,c684]) ).
cnf(c686,plain,
add(add(X,inverse(X)),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2)))))) = add(X,inverse(X)),
inference(substitution,[status(thm)],[c685]) ).
cnf(c687,plain,
inverse(add(add(X,inverse(X)),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2))))))) = inverse(add(X,inverse(X))),
inference(congruence,[status(thm)],[c686]) ).
cnf(c688,plain,
add(inverse(X4),inverse(add(add(X,inverse(X)),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2)))))))) = add(inverse(X4),inverse(add(X,inverse(X)))),
inference(congruence,[status(thm)],[c687]) ).
cnf(c689,plain,
add(inverse(X4),inverse(add(add(X,inverse(X)),inverse(add(inverse(X4),inverse(add(X3,add(X4,X2)))))))) = inverse(X4),
inference(transitivity,[status(thm)],[c688,c539]) ).
cnf(c690,plain,
add(inverse(X3),inverse(add(add(inverse(X3),add(X2,add(X3,X))),inverse(add(inverse(X3),inverse(add(X2,add(X3,X)))))))) = inverse(X3),
inference(transitivity,[status(thm)],[c664,c689]) ).
cnf(c691,plain,
add(inverse(X3),inverse(add(X2,add(X3,X)))) = inverse(X3),
inference(transitivity,[status(thm)],[c338,c690]) ).
cnf(c692,plain,
add(inverse(X3),inverse(add(X,add(X3,X2)))) = inverse(X3),
inference(substitution,[status(thm)],[c691]) ).
cnf(c693,plain,
add(inverse(X3),inverse(add(add(X3,X2),X))) = inverse(X3),
inference(transitivity,[status(thm)],[c277,c692]) ).
cnf(c694,plain,
inverse(X3) = add(inverse(X3),inverse(add(add(X3,X2),X))),
inference(symmetry,[status(thm)],[c693]) ).
cnf(c695,plain,
inverse(inverse(X3)) = inverse(add(inverse(X3),inverse(add(add(X3,X2),X)))),
inference(congruence,[status(thm)],[c694]) ).
cnf(c696,plain,
add(X,inverse(inverse(X3))) = add(X,inverse(add(inverse(X3),inverse(add(add(X3,X2),X))))),
inference(congruence,[status(thm)],[c695]) ).
cnf(c697,plain,
add(add(X3,X2),add(X,inverse(inverse(X3)))) = add(add(X3,X2),add(X,inverse(add(inverse(X3),inverse(add(add(X3,X2),X)))))),
inference(congruence,[status(thm)],[c696]) ).
cnf(c698,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c699,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c698]) ).
cnf(c700,plain,
inverse(add(X2,X)) = inverse(add(X,X2)),
inference(congruence,[status(thm)],[c699]) ).
cnf(c701,plain,
add(X,inverse(add(X3,X2))) = add(X,inverse(add(X2,X3))),
inference(congruence,[status(thm)],[c700]) ).
cnf(c702,plain,
inverse(add(X,inverse(add(X3,X2)))) = inverse(add(X,inverse(add(X2,X3)))),
inference(congruence,[status(thm)],[c701]) ).
cnf(c703,plain,
add(X2,inverse(add(X,inverse(add(X3,X2))))) = add(X2,inverse(add(X,inverse(add(X2,X3))))),
inference(congruence,[status(thm)],[c702]) ).
cnf(c704,plain,
add(X3,add(X2,inverse(add(X,inverse(add(X3,X2)))))) = add(X3,add(X2,inverse(add(X,inverse(add(X2,X3)))))),
inference(congruence,[status(thm)],[c703]) ).
cnf(c705,plain,
inverse(inverse(add(X2,inverse(add(X,inverse(add(X2,X3))))))) = add(X2,inverse(add(X,inverse(add(X2,X3))))),
inference(substitution,[status(thm)],[c114]) ).
cnf(c706,plain,
add(X2,inverse(add(X,inverse(add(X2,X3))))) = inverse(inverse(add(X2,inverse(add(X,inverse(add(X2,X3))))))),
inference(symmetry,[status(thm)],[c705]) ).
cnf(c707,plain,
add(X3,add(X2,inverse(add(X,inverse(add(X2,X3)))))) = add(X3,inverse(inverse(add(X2,inverse(add(X,inverse(add(X2,X3)))))))),
inference(congruence,[status(thm)],[c706]) ).
cnf(c708,plain,
add(inverse(add(X3,X2)),X) = add(X,inverse(add(X3,X2))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c709,plain,
add(X,inverse(add(X3,X2))) = add(inverse(add(X3,X2)),X),
inference(symmetry,[status(thm)],[c708]) ).
cnf(c710,plain,
inverse(add(X,inverse(add(X3,X2)))) = inverse(add(inverse(add(X3,X2)),X)),
inference(congruence,[status(thm)],[c709]) ).
cnf(c711,plain,
add(X3,inverse(add(X,inverse(add(X3,X2))))) = add(X3,inverse(add(inverse(add(X3,X2)),X))),
inference(congruence,[status(thm)],[c710]) ).
cnf(c712,plain,
inverse(add(X3,inverse(add(X,inverse(add(X3,X2)))))) = inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))),
inference(congruence,[status(thm)],[c711]) ).
cnf(c713,plain,
add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(X,inverse(add(X3,X2))))))) = add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))),
inference(congruence,[status(thm)],[c712]) ).
cnf(c714,plain,
add(inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))),inverse(add(inverse(add(inverse(add(X3,X2)),X)),inverse(add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))))))) = add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))),
inference(substitution,[status(thm)],[c245]) ).
cnf(c715,plain,
add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))) = add(inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))),inverse(add(inverse(add(inverse(add(X3,X2)),X)),inverse(add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))))))),
inference(symmetry,[status(thm)],[c714]) ).
cnf(c716,plain,
inverse(add(inverse(add(inverse(add(X3,X2)),X)),inverse(add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))))))) = inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c717,plain,
add(inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))),inverse(add(inverse(add(inverse(add(X3,X2)),X)),inverse(add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))))))) = add(inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))),
inference(congruence,[status(thm)],[c716]) ).
cnf(c718,plain,
add(inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))) = inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c719,plain,
add(inverse(add(X3,X2)),X) = add(X,inverse(add(X3,X2))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c720,plain,
inverse(add(inverse(add(X3,X2)),X)) = inverse(add(X,inverse(add(X3,X2)))),
inference(congruence,[status(thm)],[c719]) ).
cnf(c721,plain,
add(X3,inverse(add(inverse(add(X3,X2)),X))) = add(X3,inverse(add(X,inverse(add(X3,X2))))),
inference(congruence,[status(thm)],[c720]) ).
cnf(c722,plain,
inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))) = inverse(add(X3,inverse(add(X,inverse(add(X3,X2)))))),
inference(congruence,[status(thm)],[c721]) ).
cnf(c723,plain,
add(inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))) = inverse(add(X3,inverse(add(X,inverse(add(X3,X2)))))),
inference(transitivity,[status(thm)],[c718,c722]) ).
cnf(c724,plain,
add(inverse(add(X3,inverse(add(inverse(add(X3,X2)),X)))),inverse(add(inverse(add(inverse(add(X3,X2)),X)),inverse(add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))))))) = inverse(add(X3,inverse(add(X,inverse(add(X3,X2)))))),
inference(transitivity,[status(thm)],[c717,c723]) ).
cnf(c725,plain,
add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(inverse(add(X3,X2)),X))))) = inverse(add(X3,inverse(add(X,inverse(add(X3,X2)))))),
inference(transitivity,[status(thm)],[c715,c724]) ).
cnf(c726,plain,
add(inverse(add(X3,X2)),inverse(add(X3,inverse(add(X,inverse(add(X3,X2))))))) = inverse(add(X3,inverse(add(X,inverse(add(X3,X2)))))),
inference(transitivity,[status(thm)],[c713,c725]) ).
cnf(c727,plain,
add(inverse(add(X2,X3)),inverse(add(X2,inverse(add(X,inverse(add(X2,X3))))))) = inverse(add(X2,inverse(add(X,inverse(add(X2,X3)))))),
inference(substitution,[status(thm)],[c726]) ).
cnf(c728,plain,
inverse(add(X2,inverse(add(X,inverse(add(X2,X3)))))) = add(inverse(add(X2,X3)),inverse(add(X2,inverse(add(X,inverse(add(X2,X3))))))),
inference(symmetry,[status(thm)],[c727]) ).
cnf(c729,plain,
inverse(inverse(add(X2,inverse(add(X,inverse(add(X2,X3))))))) = inverse(add(inverse(add(X2,X3)),inverse(add(X2,inverse(add(X,inverse(add(X2,X3)))))))),
inference(congruence,[status(thm)],[c728]) ).
cnf(c730,plain,
add(X3,inverse(inverse(add(X2,inverse(add(X,inverse(add(X2,X3)))))))) = add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(X2,inverse(add(X,inverse(add(X2,X3))))))))),
inference(congruence,[status(thm)],[c729]) ).
cnf(c731,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c732,plain,
add(X2,X) = add(X,X2),
inference(symmetry,[status(thm)],[c731]) ).
cnf(c733,plain,
inverse(add(X2,X)) = inverse(add(X,X2)),
inference(congruence,[status(thm)],[c732]) ).
cnf(c734,plain,
add(inverse(add(X2,X3)),inverse(add(X2,X))) = add(inverse(add(X2,X3)),inverse(add(X,X2))),
inference(congruence,[status(thm)],[c733]) ).
cnf(c735,plain,
inverse(add(inverse(add(X2,X3)),inverse(add(X2,X)))) = inverse(add(inverse(add(X2,X3)),inverse(add(X,X2)))),
inference(congruence,[status(thm)],[c734]) ).
cnf(c736,plain,
add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(X2,X))))) = add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(X,X2))))),
inference(congruence,[status(thm)],[c735]) ).
cnf(c737,plain,
add(inverse(add(X,X2)),inverse(add(X2,X3))) = add(inverse(add(X2,X3)),inverse(add(X,X2))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c738,plain,
add(inverse(add(X2,X3)),inverse(add(X,X2))) = add(inverse(add(X,X2)),inverse(add(X2,X3))),
inference(symmetry,[status(thm)],[c737]) ).
cnf(c739,plain,
inverse(add(inverse(add(X2,X3)),inverse(add(X,X2)))) = inverse(add(inverse(add(X,X2)),inverse(add(X2,X3)))),
inference(congruence,[status(thm)],[c738]) ).
cnf(c740,plain,
add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(X,X2))))) = add(X3,inverse(add(inverse(add(X,X2)),inverse(add(X2,X3))))),
inference(congruence,[status(thm)],[c739]) ).
cnf(c741,plain,
inverse(add(X2,X3)) = inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c742,plain,
add(inverse(add(X2,X3)),inverse(add(X3,X4))) = add(inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),inverse(add(X3,X4))),
inference(congruence,[status(thm)],[c741]) ).
cnf(c743,plain,
inverse(add(inverse(add(X2,X3)),inverse(add(X3,X4)))) = inverse(add(inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),inverse(add(X3,X4)))),
inference(congruence,[status(thm)],[c742]) ).
cnf(c744,plain,
add(X4,inverse(add(inverse(add(X2,X3)),inverse(add(X3,X4))))) = add(X4,inverse(add(inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),inverse(add(X3,X4))))),
inference(congruence,[status(thm)],[c743]) ).
cnf(c745,plain,
add(X4,inverse(add(inverse(add(X3,inverse(add(inverse(add(X2,X)),inverse(add(X2,X3)))))),inverse(add(X3,X4))))) = add(X3,X4),
inference(substitution,[status(thm)],[c245]) ).
cnf(c746,plain,
add(X3,inverse(add(inverse(add(X,X2)),inverse(add(X2,X3))))) = add(X2,X3),
inference(transitivity,[status(thm)],[c744,c745]) ).
cnf(c747,plain,
add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(X,X2))))) = add(X2,X3),
inference(transitivity,[status(thm)],[c740,c746]) ).
cnf(c748,plain,
add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(X2,X))))) = add(X2,X3),
inference(transitivity,[status(thm)],[c736,c747]) ).
cnf(c749,plain,
add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(X2,inverse(add(X,inverse(add(X2,X3))))))))) = add(X2,X3),
inference(substitution,[status(thm)],[c748]) ).
cnf(c750,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c751,plain,
add(X3,inverse(add(inverse(add(X2,X3)),inverse(add(X2,inverse(add(X,inverse(add(X2,X3))))))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c749,c750]) ).
cnf(c752,plain,
add(X3,inverse(inverse(add(X2,inverse(add(X,inverse(add(X2,X3)))))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c730,c751]) ).
cnf(c753,plain,
add(X3,add(X2,inverse(add(X,inverse(add(X2,X3)))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c707,c752]) ).
cnf(c754,plain,
add(X3,add(X2,inverse(add(X,inverse(add(X3,X2)))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c704,c753]) ).
cnf(c755,plain,
add(add(X3,X2),add(X,inverse(add(inverse(X3),inverse(add(add(X3,X2),X)))))) = add(add(X3,X2),X),
inference(substitution,[status(thm)],[c754]) ).
cnf(c756,plain,
add(add(X3,X2),X) = add(X,add(X3,X2)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c757,plain,
add(add(X3,X2),add(X,inverse(add(inverse(X3),inverse(add(add(X3,X2),X)))))) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c755,c756]) ).
cnf(c758,plain,
add(add(X3,X2),add(X,inverse(inverse(X3)))) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c697,c757]) ).
cnf(c759,plain,
add(add(X3,X2),add(X,X3)) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c273,c758]) ).
cnf(c760,plain,
add(add(X3,X2),add(X3,X)) = add(X,add(X3,X2)),
inference(transitivity,[status(thm)],[c270,c759]) ).
cnf(c761,plain,
add(add(X3,X),add(X3,X2)) = add(X2,add(X3,X)),
inference(substitution,[status(thm)],[c760]) ).
cnf(c762,plain,
add(add(X3,X2),add(X3,X)) = add(X2,add(X3,X)),
inference(transitivity,[status(thm)],[c267,c761]) ).
cnf(c763,plain,
add(add(X,X2),add(X,X3)) = add(X2,add(X,X3)),
inference(substitution,[status(thm)],[c762]) ).
cnf(c764,plain,
add(X2,add(X,X3)) = add(add(X,X2),add(X,X3)),
inference(symmetry,[status(thm)],[c763]) ).
cnf(c765,plain,
add(add(X,X2),add(X,X3)) = add(add(X,X3),add(X,X2)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c766,plain,
add(add(X,X3),add(X,X2)) = add(X3,add(X,X2)),
inference(substitution,[status(thm)],[c762]) ).
cnf(c767,plain,
add(X,X2) = add(X2,X),
inference(substitution,[status(thm)],[c261]) ).
cnf(c768,plain,
add(X3,add(X,X2)) = add(X3,add(X2,X)),
inference(congruence,[status(thm)],[c767]) ).
cnf(c769,plain,
add(add(X,X3),add(X,X2)) = add(X3,add(X2,X)),
inference(transitivity,[status(thm)],[c766,c768]) ).
cnf(c770,plain,
add(add(X,X2),add(X,X3)) = add(X3,add(X2,X)),
inference(transitivity,[status(thm)],[c765,c769]) ).
cnf(c771,plain,
add(X2,add(X,X3)) = add(X3,add(X2,X)),
inference(transitivity,[status(thm)],[c764,c770]) ).
cnf(c772,plain,
add(X2,add(X3,X)) = add(X3,add(X2,X)),
inference(transitivity,[status(thm)],[c265,c771]) ).
cnf(c773,plain,
add(a,add(c,b)) = add(c,add(a,b)),
inference(substitution,[status(thm)],[c772]) ).
cnf(c774,plain,
add(c,add(a,b)) = add(a,add(c,b)),
inference(symmetry,[status(thm)],[c773]) ).
cnf(c775,plain,
add(c,b) = add(b,c),
inference(substitution,[status(thm)],[c261]) ).
cnf(c776,plain,
add(a,add(c,b)) = add(a,add(b,c)),
inference(congruence,[status(thm)],[c775]) ).
cnf(c777,plain,
add(c,add(a,b)) = add(a,add(b,c)),
inference(transitivity,[status(thm)],[c774,c776]) ).
cnf(c778,plain,
add(add(a,b),c) = add(a,add(b,c)),
inference(transitivity,[status(thm)],[c262,c777]) ).
cnf(c779,plain,
$false,
inference(resolution,[status(thm)],[c1,c778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : BOO073-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 21:07:34 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.82/1.34 Command-line arguments: --no-flatten-goal
% 8.82/1.34
% 8.82/1.34 % SZS status Unsatisfiable
% 8.82/1.34
% 8.82/1.38 % SZS output start CNFRefutation
% See solution above
% 11.11/1.69
% 11.11/1.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------