%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO015-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 09:35:25 AM UTC 2026
% Result : Unsatisfiable 4.64s 0.96s
% Output : CNFRefutation 6.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 9
% Syntax : Number of clauses : 369 ( 369 unt; 0 nHn; 3 RR)
% Number of literals : 369 ( 368 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 692 ( 53 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
inverse(multiply(a,b)) != add(inverse(a),inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
cnf(c2,axiom,
add(X,additive_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id1) ).
cnf(c3,plain,
add(inverse(inverse(X2)),additive_identity) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(inverse(X2)) = add(inverse(inverse(X2)),additive_identity),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
add(X2,Y) = add(Y,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c6,plain,
add(inverse(X2),X3) = add(X3,inverse(X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
add(X2,inverse(X3)) = add(inverse(X3),X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,add(inverse(X3),X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
multiply(X2,add(Y2,Z)) = add(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
cnf(c10,plain,
multiply(X3,add(inverse(X3),X2)) = add(multiply(X3,inverse(X3)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(X2,inverse(X2)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
add(multiply(X3,inverse(X3)),multiply(X3,X2)) = add(additive_identity,multiply(X3,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
add(X2,additive_identity) = add(additive_identity,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c14,plain,
add(additive_identity,X2) = add(X2,additive_identity),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
add(additive_identity,X2) = X2,
inference(transitivity,[status(thm)],[c14,c2]) ).
cnf(c16,plain,
add(additive_identity,multiply(X3,X2)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,axiom,
multiply(X2,Y2) = multiply(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c18,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
add(additive_identity,multiply(X3,X2)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c16,c18]) ).
cnf(c20,plain,
add(multiply(X3,inverse(X3)),multiply(X3,X2)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c12,c19]) ).
cnf(c21,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c10,c20]) ).
cnf(c22,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c8,c21]) ).
cnf(c23,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(additive_identity,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(additive_identity,X2) = multiply(X2,add(additive_identity,inverse(X2))),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
add(additive_identity,inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c26,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(X2,inverse(X2)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(X2,add(additive_identity,inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c26,c11]) ).
cnf(c28,plain,
multiply(additive_identity,X2) = additive_identity,
inference(transitivity,[status(thm)],[c24,c27]) ).
cnf(c29,plain,
additive_identity = multiply(additive_identity,X2),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
add(inverse(inverse(X2)),additive_identity) = add(inverse(inverse(X2)),multiply(additive_identity,X2)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(X2,additive_identity) = multiply(additive_identity,X2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c32,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
add(X3,multiply(additive_identity,X2)) = add(X3,multiply(X2,additive_identity)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c17]) ).
cnf(c35,plain,
multiply(X2,additive_identity) = multiply(additive_identity,X2),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
add(X3,multiply(X2,additive_identity)) = add(X3,multiply(additive_identity,X2)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,axiom,
add(X2,multiply(Y2,Z2)) = multiply(add(X2,Y2),add(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(c38,plain,
add(X3,multiply(additive_identity,X2)) = multiply(add(X3,additive_identity),add(X3,X2)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(add(X3,additive_identity),add(X3,X2)) = multiply(X3,add(X3,X2)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c40,plain,
add(X3,multiply(additive_identity,X2)) = multiply(X3,add(X3,X2)),
inference(transitivity,[status(thm)],[c38,c39]) ).
cnf(c41,plain,
add(X3,multiply(X2,additive_identity)) = multiply(X3,add(X3,X2)),
inference(transitivity,[status(thm)],[c36,c40]) ).
cnf(c42,plain,
add(X3,multiply(additive_identity,X2)) = multiply(X3,add(X3,X2)),
inference(transitivity,[status(thm)],[c33,c41]) ).
cnf(c43,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c44,plain,
multiply(X3,add(X3,X2)) = multiply(X3,add(X2,X3)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
add(X3,multiply(additive_identity,X2)) = multiply(X3,add(X2,X3)),
inference(transitivity,[status(thm)],[c42,c44]) ).
cnf(c46,plain,
add(inverse(inverse(X2)),multiply(additive_identity,X2)) = multiply(inverse(inverse(X2)),add(X2,inverse(inverse(X2)))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
add(inverse(inverse(X2)),X2) = add(X2,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c48,plain,
add(X2,inverse(inverse(X2))) = add(inverse(inverse(X2)),X2),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(X2,inverse(X3)) = multiply(inverse(X3),X2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c50,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
add(X3,multiply(inverse(X3),X2)) = add(X3,multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c53,plain,
multiply(X2,inverse(X3)) = multiply(inverse(X3),X2),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
add(X3,multiply(X2,inverse(X3))) = add(X3,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
add(X3,multiply(inverse(X3),X2)) = multiply(add(X3,inverse(X3)),add(X3,X2)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c56,axiom,
add(X2,inverse(X2)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c57,plain,
multiply(add(X3,inverse(X3)),add(X3,X2)) = multiply(multiplicative_identity,add(X3,X2)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(X2,multiplicative_identity) = multiply(multiplicative_identity,X2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c59,plain,
multiply(multiplicative_identity,X2) = multiply(X2,multiplicative_identity),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,axiom,
multiply(X2,multiplicative_identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c61,plain,
multiply(multiplicative_identity,X2) = X2,
inference(transitivity,[status(thm)],[c59,c60]) ).
cnf(c62,plain,
multiply(multiplicative_identity,add(X3,X2)) = add(X3,X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c64,plain,
multiply(multiplicative_identity,add(X3,X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
multiply(add(X3,inverse(X3)),add(X3,X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c57,c64]) ).
cnf(c66,plain,
add(X3,multiply(inverse(X3),X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c55,c65]) ).
cnf(c67,plain,
add(X3,multiply(X2,inverse(X3))) = add(X2,X3),
inference(transitivity,[status(thm)],[c54,c66]) ).
cnf(c68,plain,
add(X3,multiply(inverse(X3),X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c51,c67]) ).
cnf(c69,plain,
add(X2,multiply(inverse(X2),inverse(inverse(X2)))) = add(inverse(inverse(X2)),X2),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
add(inverse(inverse(X2)),X2) = add(X2,multiply(inverse(X2),inverse(inverse(X2)))),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(inverse(X2),inverse(inverse(X2))) = additive_identity,
inference(substitution,[status(thm)],[c11]) ).
cnf(c72,plain,
add(X2,multiply(inverse(X2),inverse(inverse(X2)))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
add(X2,multiply(inverse(X2),inverse(inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c72,c2]) ).
cnf(c74,plain,
add(inverse(inverse(X2)),X2) = X2,
inference(transitivity,[status(thm)],[c70,c73]) ).
cnf(c75,plain,
add(X2,inverse(inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c48,c74]) ).
cnf(c76,plain,
multiply(inverse(inverse(X2)),add(X2,inverse(inverse(X2)))) = multiply(inverse(inverse(X2)),X2),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(inverse(inverse(X2)),X2) = multiply(X2,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c78,plain,
multiply(inverse(inverse(X2)),X2) = multiply(X2,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c79,plain,
multiply(X2,inverse(inverse(X2))) = multiply(inverse(inverse(X2)),X2),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
add(X2,inverse(X3)) = add(inverse(X3),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c81,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X3,add(X2,inverse(X3))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c82,c22]) ).
cnf(c84,plain,
multiply(X2,add(inverse(X2),inverse(inverse(X2)))) = multiply(inverse(inverse(X2)),X2),
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(inverse(inverse(X2)),X2) = multiply(X2,add(inverse(X2),inverse(inverse(X2)))),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
add(inverse(X2),inverse(inverse(X2))) = multiplicative_identity,
inference(substitution,[status(thm)],[c56]) ).
cnf(c87,plain,
multiply(X2,add(inverse(X2),inverse(inverse(X2)))) = multiply(X2,multiplicative_identity),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(X2,add(inverse(X2),inverse(inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c87,c60]) ).
cnf(c89,plain,
multiply(inverse(inverse(X2)),X2) = X2,
inference(transitivity,[status(thm)],[c85,c88]) ).
cnf(c90,plain,
multiply(X2,inverse(inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c79,c89]) ).
cnf(c91,plain,
multiply(inverse(inverse(X2)),X2) = X2,
inference(transitivity,[status(thm)],[c77,c90]) ).
cnf(c92,plain,
multiply(inverse(inverse(X2)),add(X2,inverse(inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c76,c91]) ).
cnf(c93,plain,
add(inverse(inverse(X2)),multiply(additive_identity,X2)) = X2,
inference(transitivity,[status(thm)],[c46,c92]) ).
cnf(c94,plain,
add(inverse(inverse(X2)),additive_identity) = X2,
inference(transitivity,[status(thm)],[c30,c93]) ).
cnf(c95,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c4,c94]) ).
cnf(c96,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
multiply(X2,X3) = multiply(X2,inverse(inverse(X3))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
add(inverse(X3),multiply(X2,X3)) = add(inverse(X3),multiply(X2,inverse(inverse(X3)))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
add(X3,multiply(X2,inverse(X3))) = multiply(add(X3,X2),add(X3,inverse(X3))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c100,plain,
multiply(add(X3,X2),add(X3,inverse(X3))) = multiply(add(X3,X2),multiplicative_identity),
inference(congruence,[status(thm)],[c56]) ).
cnf(c101,plain,
multiply(add(X3,X2),multiplicative_identity) = add(X3,X2),
inference(substitution,[status(thm)],[c60]) ).
cnf(c102,plain,
multiply(add(X3,X2),add(X3,inverse(X3))) = add(X3,X2),
inference(transitivity,[status(thm)],[c100,c101]) ).
cnf(c103,plain,
add(X3,multiply(X2,inverse(X3))) = add(X3,X2),
inference(transitivity,[status(thm)],[c99,c102]) ).
cnf(c104,plain,
add(inverse(X3),multiply(X2,inverse(inverse(X3)))) = add(inverse(X3),X2),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c106,plain,
add(inverse(X3),multiply(X2,inverse(inverse(X3)))) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c104,c105]) ).
cnf(c107,plain,
add(inverse(X3),multiply(X2,X3)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c98,c106]) ).
cnf(c108,plain,
add(inverse(multiply(X3,X2)),multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2))) = add(add(inverse(X3),inverse(X2)),inverse(multiply(X3,X2))),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
add(add(inverse(X3),inverse(X2)),inverse(multiply(X3,X2))) = add(inverse(multiply(X3,X2)),multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
multiply(multiply(X3,X2),add(inverse(X3),inverse(X2))) = multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c111,plain,
multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2)) = multiply(multiply(X3,X2),add(inverse(X3),inverse(X2))),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
add(inverse(X2),X3) = add(X3,inverse(X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c113,plain,
add(X2,inverse(X3)) = add(inverse(X3),X2),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(multiply(X4,X3),add(X2,inverse(X3))) = multiply(multiply(X4,X3),add(inverse(X3),X2)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
multiply(multiply(X4,X3),add(inverse(X3),X2)) = add(multiply(multiply(X4,X3),inverse(X3)),multiply(multiply(X4,X3),X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c116,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c117,plain,
add(X3,X2) = add(inverse(inverse(X3)),X2),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(inverse(X3),add(X3,X2)) = multiply(inverse(X3),add(inverse(inverse(X3)),X2)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
add(X2,inverse(X3)) = add(inverse(X3),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c120,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X3,add(X2,inverse(X3))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
multiply(X3,add(X2,inverse(X3))) = add(multiply(X3,X2),multiply(X3,inverse(X3))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c123,plain,
add(multiply(X3,X2),multiply(X3,inverse(X3))) = add(multiply(X3,X2),additive_identity),
inference(congruence,[status(thm)],[c11]) ).
cnf(c124,plain,
add(multiply(X3,X2),additive_identity) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c125,plain,
add(multiply(X3,X2),multiply(X3,inverse(X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c122,c125]) ).
cnf(c127,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c121,c126]) ).
cnf(c128,plain,
multiply(inverse(X3),add(inverse(inverse(X3)),X2)) = multiply(inverse(X3),X2),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c130,plain,
multiply(inverse(X3),add(inverse(inverse(X3)),X2)) = multiply(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c128,c129]) ).
cnf(c131,plain,
multiply(inverse(X3),add(X3,X2)) = multiply(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c118,c130]) ).
cnf(c132,plain,
multiply(inverse(X2),add(X2,multiply(X3,X2))) = multiply(multiply(X3,X2),inverse(X2)),
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(multiply(X3,X2),inverse(X2)) = multiply(inverse(X2),add(X2,multiply(X3,X2))),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c135,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
add(X3,multiply(X2,X3)) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
X2 = multiply(X2,multiplicative_identity),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c138,plain,
add(X3,multiply(X3,X2)) = add(multiply(X3,multiplicative_identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(X3,add(multiplicative_identity,X2)) = add(multiply(X3,multiplicative_identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c140,plain,
add(multiply(X3,multiplicative_identity),multiply(X3,X2)) = multiply(X3,add(multiplicative_identity,X2)),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
add(multiplicative_identity,X2) = add(X2,multiplicative_identity),
inference(substitution,[status(thm)],[c5]) ).
cnf(c142,plain,
multiply(X3,add(multiplicative_identity,X2)) = multiply(X3,add(X2,multiplicative_identity)),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
add(multiply(X3,multiplicative_identity),multiply(X3,X2)) = multiply(X3,add(X2,multiplicative_identity)),
inference(transitivity,[status(thm)],[c140,c142]) ).
cnf(c144,plain,
add(X3,multiply(X3,X2)) = multiply(X3,add(X2,multiplicative_identity)),
inference(transitivity,[status(thm)],[c138,c143]) ).
cnf(c145,plain,
add(X3,multiply(X2,X3)) = multiply(X3,add(X2,multiplicative_identity)),
inference(transitivity,[status(thm)],[c136,c144]) ).
cnf(c146,plain,
add(multiplicative_identity,X2) = add(X2,multiplicative_identity),
inference(substitution,[status(thm)],[c5]) ).
cnf(c147,plain,
add(X2,multiplicative_identity) = add(multiplicative_identity,X2),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
add(X2,multiply(multiplicative_identity,inverse(X2))) = add(multiplicative_identity,X2),
inference(substitution,[status(thm)],[c67]) ).
cnf(c149,plain,
add(multiplicative_identity,X2) = add(X2,multiply(multiplicative_identity,inverse(X2))),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
multiply(multiplicative_identity,inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c151,plain,
add(X2,multiply(multiplicative_identity,inverse(X2))) = add(X2,inverse(X2)),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
add(X2,multiply(multiplicative_identity,inverse(X2))) = multiplicative_identity,
inference(transitivity,[status(thm)],[c151,c56]) ).
cnf(c153,plain,
add(multiplicative_identity,X2) = multiplicative_identity,
inference(transitivity,[status(thm)],[c149,c152]) ).
cnf(c154,plain,
add(X2,multiplicative_identity) = multiplicative_identity,
inference(transitivity,[status(thm)],[c147,c153]) ).
cnf(c155,plain,
multiply(X3,add(X2,multiplicative_identity)) = multiply(X3,multiplicative_identity),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(X3,add(X2,multiplicative_identity)) = X3,
inference(transitivity,[status(thm)],[c155,c60]) ).
cnf(c157,plain,
add(X3,multiply(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c145,c156]) ).
cnf(c158,plain,
add(X2,multiply(X3,X2)) = X2,
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
multiply(inverse(X2),add(X2,multiply(X3,X2))) = multiply(inverse(X2),X2),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
multiply(inverse(X2),X2) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c161,plain,
multiply(inverse(X2),X2) = additive_identity,
inference(transitivity,[status(thm)],[c160,c11]) ).
cnf(c162,plain,
multiply(inverse(X2),add(X2,multiply(X3,X2))) = additive_identity,
inference(transitivity,[status(thm)],[c159,c161]) ).
cnf(c163,plain,
multiply(multiply(X3,X2),inverse(X2)) = additive_identity,
inference(transitivity,[status(thm)],[c133,c162]) ).
cnf(c164,plain,
add(multiply(multiply(X4,X3),inverse(X3)),multiply(multiply(X4,X3),X2)) = add(additive_identity,multiply(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
add(additive_identity,multiply(multiply(X4,X3),X2)) = multiply(multiply(X4,X3),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c166,plain,
multiply(multiply(X4,X3),X2) = multiply(X2,multiply(X4,X3)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c167,plain,
add(additive_identity,multiply(multiply(X4,X3),X2)) = multiply(X2,multiply(X4,X3)),
inference(transitivity,[status(thm)],[c165,c166]) ).
cnf(c168,plain,
add(multiply(multiply(X4,X3),inverse(X3)),multiply(multiply(X4,X3),X2)) = multiply(X2,multiply(X4,X3)),
inference(transitivity,[status(thm)],[c164,c167]) ).
cnf(c169,plain,
multiply(multiply(X4,X3),add(inverse(X3),X2)) = multiply(X2,multiply(X4,X3)),
inference(transitivity,[status(thm)],[c115,c168]) ).
cnf(c170,plain,
multiply(multiply(X4,X3),add(X2,inverse(X3))) = multiply(X2,multiply(X4,X3)),
inference(transitivity,[status(thm)],[c114,c169]) ).
cnf(c171,plain,
multiply(multiply(X3,X2),add(inverse(X3),inverse(X2))) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c170]) ).
cnf(c172,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(X3,X2),inverse(X3)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c173,plain,
multiply(inverse(X3),add(X3,multiply(X3,X2))) = multiply(multiply(X3,X2),inverse(X3)),
inference(substitution,[status(thm)],[c131]) ).
cnf(c174,plain,
multiply(multiply(X3,X2),inverse(X3)) = multiply(inverse(X3),add(X3,multiply(X3,X2))),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
multiply(X3,add(X2,multiplicative_identity)) = multiply(X3,multiplicative_identity),
inference(congruence,[status(thm)],[c154]) ).
cnf(c176,plain,
multiply(X3,add(X2,multiplicative_identity)) = X3,
inference(transitivity,[status(thm)],[c175,c60]) ).
cnf(c177,plain,
add(X3,multiply(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c144,c176]) ).
cnf(c178,plain,
multiply(inverse(X3),add(X3,multiply(X3,X2))) = multiply(inverse(X3),X3),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
multiply(inverse(X2),X2) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c180,plain,
multiply(inverse(X2),X2) = additive_identity,
inference(transitivity,[status(thm)],[c179,c11]) ).
cnf(c181,plain,
multiply(inverse(X3),add(X3,multiply(X3,X2))) = additive_identity,
inference(transitivity,[status(thm)],[c178,c180]) ).
cnf(c182,plain,
multiply(multiply(X3,X2),inverse(X3)) = additive_identity,
inference(transitivity,[status(thm)],[c174,c181]) ).
cnf(c183,plain,
multiply(inverse(X3),multiply(X3,X2)) = additive_identity,
inference(transitivity,[status(thm)],[c172,c182]) ).
cnf(c184,plain,
multiply(multiply(X3,X2),add(inverse(X3),inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c171,c183]) ).
cnf(c185,plain,
multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2)) = additive_identity,
inference(transitivity,[status(thm)],[c111,c184]) ).
cnf(c186,plain,
add(inverse(multiply(X3,X2)),multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2))) = add(inverse(multiply(X3,X2)),additive_identity),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
add(inverse(multiply(X3,X2)),additive_identity) = inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c188,plain,
add(inverse(multiply(X3,X2)),multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2))) = inverse(multiply(X3,X2)),
inference(transitivity,[status(thm)],[c186,c187]) ).
cnf(c189,plain,
add(add(inverse(X3),inverse(X2)),inverse(multiply(X3,X2))) = inverse(multiply(X3,X2)),
inference(transitivity,[status(thm)],[c109,c188]) ).
cnf(c190,plain,
inverse(multiply(X3,X2)) = add(add(inverse(X3),inverse(X2)),inverse(multiply(X3,X2))),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
multiply(inverse(add(inverse(X3),inverse(X2))),X3) = multiply(X3,inverse(add(inverse(X3),inverse(X2)))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c192,plain,
multiply(X3,inverse(add(inverse(X3),inverse(X2)))) = multiply(inverse(add(inverse(X3),inverse(X2))),X3),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
add(inverse(add(inverse(X3),inverse(X2))),X3) = add(X3,inverse(add(inverse(X3),inverse(X2)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c194,plain,
add(X3,inverse(add(inverse(X3),inverse(X2)))) = add(inverse(add(inverse(X3),inverse(X2))),X3),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
add(X3,multiply(inverse(X3),inverse(add(inverse(X3),inverse(X2))))) = add(inverse(add(inverse(X3),inverse(X2))),X3),
inference(substitution,[status(thm)],[c68]) ).
cnf(c196,plain,
add(inverse(add(inverse(X3),inverse(X2))),X3) = add(X3,multiply(inverse(X3),inverse(add(inverse(X3),inverse(X2))))),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
multiply(inverse(add(X3,inverse(X2))),X3) = multiply(X3,inverse(add(X3,inverse(X2)))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c198,plain,
multiply(X3,inverse(add(X3,inverse(X2)))) = multiply(inverse(add(X3,inverse(X2))),X3),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c200,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
multiply(add(X4,X2),add(X3,X4)) = multiply(add(X4,X2),add(X4,X3)),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
add(X4,multiply(X2,X3)) = multiply(add(X4,X2),add(X4,X3)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c203,plain,
multiply(add(X4,X2),add(X4,X3)) = add(X4,multiply(X2,X3)),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c205,plain,
add(X4,multiply(X2,X3)) = add(X4,multiply(X3,X2)),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(add(X4,X2),add(X4,X3)) = add(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c203,c205]) ).
cnf(c207,plain,
multiply(add(X4,X2),add(X3,X4)) = add(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c201,c206]) ).
cnf(c208,plain,
multiply(add(X3,inverse(X2)),add(X2,X3)) = add(X3,multiply(X2,inverse(X2))),
inference(substitution,[status(thm)],[c207]) ).
cnf(c209,plain,
add(X3,multiply(X2,inverse(X2))) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c11]) ).
cnf(c210,plain,
add(X3,multiply(X2,inverse(X2))) = X3,
inference(transitivity,[status(thm)],[c209,c2]) ).
cnf(c211,plain,
multiply(add(X3,inverse(X2)),add(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c208,c210]) ).
cnf(c212,plain,
X3 = multiply(add(X3,inverse(X2)),add(X2,X3)),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
multiply(inverse(add(X3,inverse(X2))),X3) = multiply(inverse(add(X3,inverse(X2))),multiply(add(X3,inverse(X2)),add(X2,X3))),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c215,plain,
multiply(X3,X2) = multiply(inverse(inverse(X3)),X2),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(inverse(X3),multiply(inverse(inverse(X3)),X2)),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
multiply(X2,inverse(X3)) = multiply(inverse(X3),X2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c218,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(X3,multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c221,plain,
multiply(X2,inverse(X3)) = multiply(inverse(X3),X2),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
multiply(X3,multiply(X2,inverse(X3))) = multiply(X3,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
multiply(X3,add(inverse(X3),multiply(inverse(X3),X2))) = multiply(X3,multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c127]) ).
cnf(c224,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(X3,add(inverse(X3),multiply(inverse(X3),X2))),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
add(inverse(X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),add(X2,multiplicative_identity)),
inference(substitution,[status(thm)],[c144]) ).
cnf(c226,plain,
multiply(X3,add(inverse(X3),multiply(inverse(X3),X2))) = multiply(X3,multiply(inverse(X3),add(X2,multiplicative_identity))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
multiply(inverse(X3),add(X2,multiplicative_identity)) = multiply(inverse(X3),multiplicative_identity),
inference(congruence,[status(thm)],[c154]) ).
cnf(c228,plain,
multiply(X3,multiply(inverse(X3),add(X2,multiplicative_identity))) = multiply(X3,multiply(inverse(X3),multiplicative_identity)),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
multiply(inverse(X2),multiplicative_identity) = inverse(X2),
inference(substitution,[status(thm)],[c60]) ).
cnf(c230,plain,
multiply(X2,multiply(inverse(X2),multiplicative_identity)) = multiply(X2,inverse(X2)),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
multiply(X2,multiply(inverse(X2),multiplicative_identity)) = additive_identity,
inference(transitivity,[status(thm)],[c230,c11]) ).
cnf(c232,plain,
multiply(X3,multiply(inverse(X3),add(X2,multiplicative_identity))) = additive_identity,
inference(transitivity,[status(thm)],[c228,c231]) ).
cnf(c233,plain,
multiply(X3,add(inverse(X3),multiply(inverse(X3),X2))) = additive_identity,
inference(transitivity,[status(thm)],[c226,c232]) ).
cnf(c234,plain,
multiply(X3,multiply(inverse(X3),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c224,c233]) ).
cnf(c235,plain,
multiply(X3,multiply(X2,inverse(X3))) = additive_identity,
inference(transitivity,[status(thm)],[c222,c234]) ).
cnf(c236,plain,
multiply(X3,multiply(inverse(X3),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c219,c235]) ).
cnf(c237,plain,
multiply(inverse(X3),multiply(inverse(inverse(X3)),X2)) = additive_identity,
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,plain,
multiply(inverse(X3),multiply(X3,X2)) = additive_identity,
inference(transitivity,[status(thm)],[c216,c237]) ).
cnf(c239,plain,
multiply(inverse(add(X3,inverse(X2))),multiply(add(X3,inverse(X2)),add(X2,X3))) = additive_identity,
inference(substitution,[status(thm)],[c238]) ).
cnf(c240,plain,
multiply(inverse(add(X3,inverse(X2))),X3) = additive_identity,
inference(transitivity,[status(thm)],[c213,c239]) ).
cnf(c241,plain,
multiply(X3,inverse(add(X3,inverse(X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c198,c240]) ).
cnf(c242,plain,
multiply(inverse(X3),inverse(add(inverse(X3),inverse(X2)))) = additive_identity,
inference(substitution,[status(thm)],[c241]) ).
cnf(c243,plain,
add(X3,multiply(inverse(X3),inverse(add(inverse(X3),inverse(X2))))) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
add(X3,multiply(inverse(X3),inverse(add(inverse(X3),inverse(X2))))) = X3,
inference(transitivity,[status(thm)],[c243,c2]) ).
cnf(c245,plain,
add(inverse(add(inverse(X3),inverse(X2))),X3) = X3,
inference(transitivity,[status(thm)],[c196,c244]) ).
cnf(c246,plain,
add(X3,inverse(add(inverse(X3),inverse(X2)))) = X3,
inference(transitivity,[status(thm)],[c194,c245]) ).
cnf(c247,plain,
X3 = add(X3,inverse(add(inverse(X3),inverse(X2)))),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
multiply(inverse(add(inverse(X3),inverse(X2))),X3) = multiply(inverse(add(inverse(X3),inverse(X2))),add(X3,inverse(add(inverse(X3),inverse(X2))))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c250,plain,
multiply(X3,add(X3,X2)) = multiply(X3,add(X2,X3)),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
add(X3,multiply(X2,additive_identity)) = multiply(X3,add(X2,X3)),
inference(transitivity,[status(thm)],[c41,c250]) ).
cnf(c252,plain,
add(inverse(add(inverse(X3),inverse(X2))),multiply(X3,additive_identity)) = multiply(inverse(add(inverse(X3),inverse(X2))),add(X3,inverse(add(inverse(X3),inverse(X2))))),
inference(substitution,[status(thm)],[c251]) ).
cnf(c253,plain,
multiply(inverse(add(inverse(X3),inverse(X2))),add(X3,inverse(add(inverse(X3),inverse(X2))))) = add(inverse(add(inverse(X3),inverse(X2))),multiply(X3,additive_identity)),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c17]) ).
cnf(c255,plain,
multiply(X2,additive_identity) = multiply(additive_identity,X2),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(additive_identity,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c257,plain,
multiply(additive_identity,X2) = multiply(X2,add(additive_identity,inverse(X2))),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
add(additive_identity,inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c259,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(X2,inverse(X2)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
multiply(X2,add(additive_identity,inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c259,c11]) ).
cnf(c261,plain,
multiply(additive_identity,X2) = additive_identity,
inference(transitivity,[status(thm)],[c257,c260]) ).
cnf(c262,plain,
multiply(X2,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c255,c261]) ).
cnf(c263,plain,
add(inverse(add(inverse(X3),inverse(X2))),multiply(X3,additive_identity)) = add(inverse(add(inverse(X3),inverse(X2))),additive_identity),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
add(inverse(add(inverse(X3),inverse(X2))),additive_identity) = inverse(add(inverse(X3),inverse(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c265,plain,
add(inverse(add(inverse(X3),inverse(X2))),multiply(X3,additive_identity)) = inverse(add(inverse(X3),inverse(X2))),
inference(transitivity,[status(thm)],[c263,c264]) ).
cnf(c266,plain,
multiply(inverse(add(inverse(X3),inverse(X2))),add(X3,inverse(add(inverse(X3),inverse(X2))))) = inverse(add(inverse(X3),inverse(X2))),
inference(transitivity,[status(thm)],[c253,c265]) ).
cnf(c267,plain,
multiply(inverse(add(inverse(X3),inverse(X2))),X3) = inverse(add(inverse(X3),inverse(X2))),
inference(transitivity,[status(thm)],[c248,c266]) ).
cnf(c268,plain,
multiply(X3,inverse(add(inverse(X3),inverse(X2)))) = inverse(add(inverse(X3),inverse(X2))),
inference(transitivity,[status(thm)],[c192,c267]) ).
cnf(c269,plain,
inverse(add(inverse(X3),inverse(X2))) = multiply(X3,inverse(add(inverse(X3),inverse(X2)))),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c271,plain,
multiply(X3,X2) = multiply(inverse(inverse(X3)),X2),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
add(inverse(X3),multiply(X3,X2)) = add(inverse(X3),multiply(inverse(inverse(X3)),X2)),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
multiply(X2,inverse(X3)) = multiply(inverse(X3),X2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c274,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
add(X3,multiply(inverse(X3),X2)) = add(X3,multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
add(X3,multiply(inverse(X3),X2)) = add(X3,X2),
inference(transitivity,[status(thm)],[c275,c103]) ).
cnf(c277,plain,
add(inverse(X3),multiply(inverse(inverse(X3)),X2)) = add(inverse(X3),X2),
inference(substitution,[status(thm)],[c276]) ).
cnf(c278,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c279,plain,
add(inverse(X3),multiply(inverse(inverse(X3)),X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c277,c278]) ).
cnf(c280,plain,
add(inverse(X3),multiply(X3,X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c272,c279]) ).
cnf(c281,plain,
add(inverse(add(inverse(X3),inverse(X2))),multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2))) = add(multiply(X3,X2),inverse(add(inverse(X3),inverse(X2)))),
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
add(multiply(X3,X2),inverse(add(inverse(X3),inverse(X2)))) = add(inverse(add(inverse(X3),inverse(X2))),multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
add(inverse(add(inverse(X3),inverse(X2))),multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2))) = add(inverse(add(inverse(X3),inverse(X2))),additive_identity),
inference(congruence,[status(thm)],[c185]) ).
cnf(c284,plain,
add(inverse(add(inverse(X3),inverse(X2))),additive_identity) = inverse(add(inverse(X3),inverse(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c285,plain,
add(inverse(add(inverse(X3),inverse(X2))),multiply(add(inverse(X3),inverse(X2)),multiply(X3,X2))) = inverse(add(inverse(X3),inverse(X2))),
inference(transitivity,[status(thm)],[c283,c284]) ).
cnf(c286,plain,
add(multiply(X3,X2),inverse(add(inverse(X3),inverse(X2)))) = inverse(add(inverse(X3),inverse(X2))),
inference(transitivity,[status(thm)],[c282,c285]) ).
cnf(c287,plain,
inverse(add(inverse(X3),inverse(X2))) = add(multiply(X3,X2),inverse(add(inverse(X3),inverse(X2)))),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
multiply(X3,inverse(add(inverse(X3),inverse(X2)))) = multiply(X3,add(multiply(X3,X2),inverse(add(inverse(X3),inverse(X2))))),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
add(X3,multiply(X4,X2)) = add(multiply(X4,X2),X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c290,plain,
add(multiply(X4,X2),X3) = add(X3,multiply(X4,X2)),
inference(symmetry,[status(thm)],[c289]) ).
cnf(c291,plain,
multiply(X4,add(multiply(X4,X2),X3)) = multiply(X4,add(X3,multiply(X4,X2))),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
add(multiply(X4,X2),X3) = add(X3,multiply(X4,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c293,plain,
add(X3,multiply(X4,X2)) = add(multiply(X4,X2),X3),
inference(symmetry,[status(thm)],[c292]) ).
cnf(c294,plain,
multiply(X4,add(X3,multiply(X4,X2))) = multiply(X4,add(multiply(X4,X2),X3)),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
multiply(X4,add(multiply(X4,X2),X3)) = add(multiply(X4,multiply(X4,X2)),multiply(X4,X3)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c296,plain,
multiply(multiply(X3,X2),X3) = multiply(X3,multiply(X3,X2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c297,plain,
multiply(X3,multiply(X3,X2)) = multiply(multiply(X3,X2),X3),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
X3 = add(X3,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c299,plain,
multiply(multiply(X3,X2),X3) = multiply(multiply(X3,X2),add(X3,multiply(X3,X2))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
add(multiply(X3,X2),multiply(X3,additive_identity)) = multiply(multiply(X3,X2),add(X3,multiply(X3,X2))),
inference(substitution,[status(thm)],[c251]) ).
cnf(c301,plain,
multiply(multiply(X3,X2),add(X3,multiply(X3,X2))) = add(multiply(X3,X2),multiply(X3,additive_identity)),
inference(symmetry,[status(thm)],[c300]) ).
cnf(c302,plain,
add(multiply(X3,X2),multiply(X3,additive_identity)) = add(multiply(X3,X2),additive_identity),
inference(congruence,[status(thm)],[c262]) ).
cnf(c303,plain,
add(multiply(X3,X2),additive_identity) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c304,plain,
add(multiply(X3,X2),multiply(X3,additive_identity)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c302,c303]) ).
cnf(c305,plain,
multiply(multiply(X3,X2),add(X3,multiply(X3,X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c301,c304]) ).
cnf(c306,plain,
multiply(multiply(X3,X2),X3) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c299,c305]) ).
cnf(c307,plain,
multiply(X3,multiply(X3,X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c297,c306]) ).
cnf(c308,plain,
add(multiply(X4,multiply(X4,X2)),multiply(X4,X3)) = add(multiply(X4,X2),multiply(X4,X3)),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c310,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c309]) ).
cnf(c311,plain,
add(multiply(X4,X3),multiply(X4,X2)) = add(multiply(X4,X3),multiply(X2,X4)),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c313,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c312]) ).
cnf(c314,plain,
add(multiply(X4,X3),multiply(X2,X4)) = add(multiply(X4,X3),multiply(X4,X2)),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
multiply(X4,add(X3,X2)) = add(multiply(X4,X3),multiply(X4,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c316,plain,
add(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,add(X3,X2)),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c318,plain,
multiply(X4,add(X3,X2)) = multiply(X4,add(X2,X3)),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
add(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,add(X2,X3)),
inference(transitivity,[status(thm)],[c316,c318]) ).
cnf(c320,plain,
add(multiply(X4,X3),multiply(X2,X4)) = multiply(X4,add(X2,X3)),
inference(transitivity,[status(thm)],[c314,c319]) ).
cnf(c321,plain,
add(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,add(X2,X3)),
inference(transitivity,[status(thm)],[c311,c320]) ).
cnf(c322,plain,
add(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,add(X3,X2)),
inference(substitution,[status(thm)],[c321]) ).
cnf(c323,plain,
add(multiply(X4,multiply(X4,X2)),multiply(X4,X3)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c308,c322]) ).
cnf(c324,plain,
multiply(X4,add(multiply(X4,X2),X3)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c295,c323]) ).
cnf(c325,plain,
multiply(X4,add(X3,multiply(X4,X2))) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c294,c324]) ).
cnf(c326,plain,
multiply(X4,add(multiply(X4,X2),X3)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c291,c325]) ).
cnf(c327,plain,
multiply(X4,add(multiply(X4,X3),X2)) = multiply(X4,add(X2,X3)),
inference(substitution,[status(thm)],[c326]) ).
cnf(c328,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c329,plain,
multiply(X4,add(X2,X3)) = multiply(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
multiply(X4,add(multiply(X4,X3),X2)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c327,c329]) ).
cnf(c331,plain,
multiply(X3,add(multiply(X3,X2),inverse(add(inverse(X3),inverse(X2))))) = multiply(X3,add(X2,inverse(add(inverse(X3),inverse(X2))))),
inference(substitution,[status(thm)],[c330]) ).
cnf(c332,plain,
add(inverse(add(X2,inverse(X3))),X3) = add(X3,inverse(add(X2,inverse(X3)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c333,plain,
add(X3,inverse(add(X2,inverse(X3)))) = add(inverse(add(X2,inverse(X3))),X3),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
add(X3,multiply(inverse(X3),inverse(add(X2,inverse(X3))))) = add(inverse(add(X2,inverse(X3))),X3),
inference(substitution,[status(thm)],[c68]) ).
cnf(c335,plain,
add(inverse(add(X2,inverse(X3))),X3) = add(X3,multiply(inverse(X3),inverse(add(X2,inverse(X3))))),
inference(symmetry,[status(thm)],[c334]) ).
cnf(c336,plain,
multiply(inverse(add(X2,X3)),X3) = multiply(X3,inverse(add(X2,X3))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c337,plain,
multiply(X3,inverse(add(X2,X3))) = multiply(inverse(add(X2,X3)),X3),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
multiply(X2,add(X3,X2)) = multiply(add(X3,X2),X2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c339,plain,
multiply(add(X3,X2),X2) = multiply(X2,add(X3,X2)),
inference(symmetry,[status(thm)],[c338]) ).
cnf(c340,plain,
multiply(X3,add(X2,X3)) = add(X3,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c251]) ).
cnf(c341,plain,
add(X3,multiply(X2,additive_identity)) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c262]) ).
cnf(c342,plain,
add(X3,multiply(X2,additive_identity)) = X3,
inference(transitivity,[status(thm)],[c341,c2]) ).
cnf(c343,plain,
multiply(X3,add(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c340,c342]) ).
cnf(c344,plain,
multiply(X2,add(X3,X2)) = X2,
inference(substitution,[status(thm)],[c343]) ).
cnf(c345,plain,
multiply(add(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c339,c344]) ).
cnf(c346,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c345]) ).
cnf(c347,plain,
X3 = multiply(add(X2,X3),X3),
inference(symmetry,[status(thm)],[c346]) ).
cnf(c348,plain,
multiply(inverse(add(X2,X3)),X3) = multiply(inverse(add(X2,X3)),multiply(add(X2,X3),X3)),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
multiply(inverse(add(X2,X3)),multiply(add(X2,X3),X3)) = additive_identity,
inference(substitution,[status(thm)],[c238]) ).
cnf(c350,plain,
multiply(inverse(add(X2,X3)),X3) = additive_identity,
inference(transitivity,[status(thm)],[c348,c349]) ).
cnf(c351,plain,
multiply(X3,inverse(add(X2,X3))) = additive_identity,
inference(transitivity,[status(thm)],[c337,c350]) ).
cnf(c352,plain,
multiply(inverse(X3),inverse(add(X2,inverse(X3)))) = additive_identity,
inference(substitution,[status(thm)],[c351]) ).
cnf(c353,plain,
add(X3,multiply(inverse(X3),inverse(add(X2,inverse(X3))))) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
add(X3,multiply(inverse(X3),inverse(add(X2,inverse(X3))))) = X3,
inference(transitivity,[status(thm)],[c353,c2]) ).
cnf(c355,plain,
add(inverse(add(X2,inverse(X3))),X3) = X3,
inference(transitivity,[status(thm)],[c335,c354]) ).
cnf(c356,plain,
add(X3,inverse(add(X2,inverse(X3)))) = X3,
inference(transitivity,[status(thm)],[c333,c355]) ).
cnf(c357,plain,
add(X2,inverse(add(inverse(X3),inverse(X2)))) = X2,
inference(substitution,[status(thm)],[c356]) ).
cnf(c358,plain,
multiply(X3,add(X2,inverse(add(inverse(X3),inverse(X2))))) = multiply(X3,X2),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
multiply(X3,add(multiply(X3,X2),inverse(add(inverse(X3),inverse(X2))))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c331,c358]) ).
cnf(c360,plain,
multiply(X3,inverse(add(inverse(X3),inverse(X2)))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c288,c359]) ).
cnf(c361,plain,
inverse(add(inverse(X3),inverse(X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c269,c360]) ).
cnf(c362,plain,
multiply(X3,X2) = inverse(add(inverse(X3),inverse(X2))),
inference(symmetry,[status(thm)],[c361]) ).
cnf(c363,plain,
inverse(multiply(X3,X2)) = inverse(inverse(add(inverse(X3),inverse(X2)))),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
add(add(inverse(X3),inverse(X2)),inverse(multiply(X3,X2))) = add(add(inverse(X3),inverse(X2)),inverse(inverse(add(inverse(X3),inverse(X2))))),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
add(add(inverse(X3),inverse(X2)),inverse(inverse(add(inverse(X3),inverse(X2))))) = add(inverse(X3),inverse(X2)),
inference(substitution,[status(thm)],[c75]) ).
cnf(c366,plain,
add(add(inverse(X3),inverse(X2)),inverse(multiply(X3,X2))) = add(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c364,c365]) ).
cnf(c367,plain,
inverse(multiply(X3,X2)) = add(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c190,c366]) ).
cnf(c368,plain,
inverse(multiply(a,b)) = add(inverse(a),inverse(b)),
inference(substitution,[status(thm)],[c367]) ).
cnf(c369,plain,
$false,
inference(resolution,[status(thm)],[c1,c368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO015-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.23 % Computer : n020.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Mon Sep 28 21:05:04 UTC 2026
% 0.08/0.24 % CPUTime :
% 0.08/0.24 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.64/0.96 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 4.64/0.96
% 4.64/0.96 % SZS status Unsatisfiable
% 4.64/0.96
% 5.33/1.01 % SZS output start CNFRefutation
% See solution above
% 6.74/1.30
% 6.74/1.30 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------