%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO072-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.55s 0.35s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 2
% Syntax : Number of clauses : 264 ( 264 unt; 0 nHn; 4 RR)
% Number of literals : 264 ( 263 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 522 ( 79 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
add(b,a) != add(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',huntinton_1) ).
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(a,b) = add(b,a),
inference(substitution,[status(thm)],[c261]) ).
cnf(c263,plain,
add(b,a) = add(a,b),
inference(symmetry,[status(thm)],[c262]) ).
cnf(c264,plain,
$false,
inference(resolution,[status(thm)],[c1,c263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO072-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n026.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 21:10:56 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.35 Command-line arguments: --no-flatten-goal
% 0.55/0.35
% 0.55/0.35 % SZS status Unsatisfiable
% 0.55/0.35
% 0.55/0.37 % SZS output start CNFRefutation
% See solution above
% 2.19/0.55
% 2.19/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------