%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP203-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:41 AM UTC 2026
% Result : Unsatisfiable 0.31s 0.86s
% Output : CNFRefutation 4.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 4
% Syntax : Number of clauses : 263 ( 263 unt; 0 nHn; 3 RR)
% Number of literals : 263 ( 262 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 512 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang2) ).
cnf(c2,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X3,X2) = multiply(X3,multiply(identity,X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(left_inverse(X3),multiply(X3,X2)) = multiply(left_inverse(X3),multiply(X3,multiply(identity,X2))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
multiply(left_inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c7,plain,
identity = multiply(left_inverse(X2),X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(left_inverse(left_inverse(X2)),identity) = multiply(left_inverse(left_inverse(X2)),multiply(left_inverse(X2),X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(left_inverse(X2),multiply(left_inverse(left_inverse(X2)),identity)) = multiply(left_inverse(X2),multiply(left_inverse(left_inverse(X2)),multiply(left_inverse(X2),X2))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
multiply(multiply(multiply(X,Y),X),Z) = multiply(X,multiply(Y,multiply(X,Z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang3) ).
cnf(c11,plain,
multiply(multiply(multiply(X3,X2),X3),identity) = multiply(X3,multiply(X2,multiply(X3,identity))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(X3,multiply(X2,multiply(X3,identity))) = multiply(multiply(multiply(X3,X2),X3),identity),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(multiply(X3,multiply(X2,multiply(X3,identity))),X4) = multiply(multiply(multiply(multiply(X3,X2),X3),identity),X4),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c15,plain,
multiply(X2,identity) = multiply(multiply(identity,X2),identity),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(multiply(X3,identity),X2) = multiply(multiply(multiply(identity,X3),identity),X2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(multiply(multiply(identity,X3),identity),X2) = multiply(identity,multiply(X3,multiply(identity,X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c18,plain,
multiply(identity,multiply(X3,multiply(identity,X2))) = multiply(X3,multiply(identity,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
multiply(X3,multiply(identity,X2)) = multiply(X3,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c20,plain,
multiply(identity,multiply(X3,multiply(identity,X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c18,c19]) ).
cnf(c21,plain,
multiply(multiply(multiply(identity,X3),identity),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c17,c20]) ).
cnf(c22,plain,
multiply(multiply(X3,identity),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c16,c21]) ).
cnf(c23,plain,
multiply(multiply(multiply(multiply(X4,X3),X4),identity),X2) = multiply(multiply(multiply(X4,X3),X4),X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(multiply(multiply(X4,X3),X4),X2) = multiply(X4,multiply(X3,multiply(X4,X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c25,plain,
multiply(multiply(multiply(multiply(X4,X3),X4),identity),X2) = multiply(X4,multiply(X3,multiply(X4,X2))),
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
multiply(multiply(X4,multiply(X3,multiply(X4,identity))),X2) = multiply(X4,multiply(X3,multiply(X4,X2))),
inference(transitivity,[status(thm)],[c13,c25]) ).
cnf(c27,plain,
multiply(multiply(X3,multiply(left_inverse(X3),multiply(X3,identity))),X2) = multiply(X3,multiply(left_inverse(X3),multiply(X3,X2))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(X3,multiply(left_inverse(X3),multiply(X3,X2))) = multiply(multiply(X3,multiply(left_inverse(X3),multiply(X3,identity))),X2),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
identity = multiply(left_inverse(X2),X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c30,plain,
multiply(X2,identity) = multiply(X2,multiply(left_inverse(X2),X2)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(left_inverse(X2),multiply(X2,identity)) = multiply(left_inverse(X2),multiply(X2,multiply(left_inverse(X2),X2))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(multiply(multiply(left_inverse(X3),X3),left_inverse(X3)),X2) = multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c33,plain,
multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),X2))) = multiply(multiply(multiply(left_inverse(X3),X3),left_inverse(X3)),X2),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(multiply(left_inverse(X2),X2),left_inverse(X2)) = multiply(identity,left_inverse(X2)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c35,plain,
multiply(multiply(multiply(left_inverse(X3),X3),left_inverse(X3)),X2) = multiply(multiply(identity,left_inverse(X3)),X2),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(identity,left_inverse(X2)) = left_inverse(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
multiply(multiply(identity,left_inverse(X3)),X2) = multiply(left_inverse(X3),X2),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(multiply(multiply(left_inverse(X3),X3),left_inverse(X3)),X2) = multiply(left_inverse(X3),X2),
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),X2))) = multiply(left_inverse(X3),X2),
inference(transitivity,[status(thm)],[c33,c38]) ).
cnf(c40,plain,
multiply(left_inverse(X2),multiply(X2,multiply(left_inverse(X2),X2))) = multiply(left_inverse(X2),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(left_inverse(X2),multiply(X2,multiply(left_inverse(X2),X2))) = identity,
inference(transitivity,[status(thm)],[c40,c6]) ).
cnf(c42,plain,
multiply(left_inverse(X2),multiply(X2,identity)) = identity,
inference(transitivity,[status(thm)],[c31,c41]) ).
cnf(c43,plain,
multiply(X2,multiply(left_inverse(X2),multiply(X2,identity))) = multiply(X2,identity),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(multiply(X3,multiply(left_inverse(X3),multiply(X3,identity))),X2) = multiply(multiply(X3,identity),X2),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(multiply(X3,multiply(left_inverse(X3),multiply(X3,identity))),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c44,c22]) ).
cnf(c46,plain,
multiply(X3,multiply(left_inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c28,c45]) ).
cnf(c47,plain,
multiply(left_inverse(X2),multiply(left_inverse(left_inverse(X2)),multiply(left_inverse(X2),X2))) = multiply(left_inverse(X2),X2),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(left_inverse(X2),multiply(left_inverse(left_inverse(X2)),multiply(left_inverse(X2),X2))) = identity,
inference(transitivity,[status(thm)],[c47,c6]) ).
cnf(c49,plain,
multiply(left_inverse(X2),multiply(left_inverse(left_inverse(X2)),identity)) = identity,
inference(transitivity,[status(thm)],[c9,c48]) ).
cnf(c50,plain,
identity = multiply(left_inverse(X2),multiply(left_inverse(left_inverse(X2)),identity)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(identity,X2) = multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(X3,multiply(identity,X2)) = multiply(X3,multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(left_inverse(X3),multiply(X3,multiply(identity,X2))) = multiply(left_inverse(X3),multiply(X3,multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(multiply(X2,identity),X2) = multiply(X2,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c55,plain,
multiply(X2,X2) = multiply(multiply(X2,identity),X2),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(multiply(X3,X3),X2) = multiply(multiply(multiply(X3,identity),X3),X2),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(multiply(multiply(X3,identity),X3),X2) = multiply(X3,multiply(identity,multiply(X3,X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c58,plain,
multiply(identity,multiply(X3,X2)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
multiply(X3,multiply(identity,multiply(X3,X2))) = multiply(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(multiply(multiply(X3,identity),X3),X2) = multiply(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c57,c59]) ).
cnf(c61,plain,
multiply(multiply(X3,X3),X2) = multiply(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c56,c60]) ).
cnf(c62,plain,
multiply(multiply(X2,X2),multiply(X3,identity)) = multiply(X2,multiply(X2,multiply(X3,identity))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(X2,multiply(X2,multiply(X3,identity))) = multiply(multiply(X2,X2),multiply(X3,identity)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(X3,multiply(X2,multiply(X2,multiply(X3,identity)))) = multiply(X3,multiply(multiply(X2,X2),multiply(X3,identity))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(multiply(X4,multiply(X3,multiply(X3,multiply(X4,identity)))),X2) = multiply(multiply(X4,multiply(multiply(X3,X3),multiply(X4,identity))),X2),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(multiply(X4,multiply(multiply(X3,X3),multiply(X4,identity))),X2) = multiply(X4,multiply(multiply(X3,X3),multiply(X4,X2))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c67,plain,
multiply(multiply(X3,X3),multiply(X4,X2)) = multiply(X3,multiply(X3,multiply(X4,X2))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c68,plain,
multiply(X4,multiply(multiply(X3,X3),multiply(X4,X2))) = multiply(X4,multiply(X3,multiply(X3,multiply(X4,X2)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(multiply(X4,multiply(multiply(X3,X3),multiply(X4,identity))),X2) = multiply(X4,multiply(X3,multiply(X3,multiply(X4,X2)))),
inference(transitivity,[status(thm)],[c66,c68]) ).
cnf(c70,plain,
multiply(multiply(X4,multiply(X3,multiply(X3,multiply(X4,identity)))),X2) = multiply(X4,multiply(X3,multiply(X3,multiply(X4,X2)))),
inference(transitivity,[status(thm)],[c65,c69]) ).
cnf(c71,plain,
multiply(multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,identity)))),X2) = multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2)))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2)))) = multiply(multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,identity)))),X2),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,identity))) = multiply(left_inverse(X2),identity),
inference(congruence,[status(thm)],[c42]) ).
cnf(c74,plain,
multiply(X2,multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,identity)))) = multiply(X2,multiply(left_inverse(X2),identity)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,identity)))),X2) = multiply(multiply(X3,multiply(left_inverse(X3),identity)),X2),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2)))) = multiply(multiply(X3,multiply(left_inverse(X3),identity)),X2),
inference(transitivity,[status(thm)],[c72,c75]) ).
cnf(c77,plain,
multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))) = multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2) = multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(X3,multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2)) = multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2))))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(left_inverse(X3),multiply(X3,multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2))) = multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))))) = multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c82,plain,
multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))) = multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2),
inference(substitution,[status(thm)],[c76]) ).
cnf(c83,plain,
multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c84,plain,
multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2) = X2,
inference(transitivity,[status(thm)],[c83,c2]) ).
cnf(c85,plain,
multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))) = X2,
inference(transitivity,[status(thm)],[c82,c84]) ).
cnf(c86,plain,
multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))))) = X2,
inference(transitivity,[status(thm)],[c81,c85]) ).
cnf(c87,plain,
multiply(left_inverse(X3),multiply(X3,multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2))) = X2,
inference(transitivity,[status(thm)],[c80,c86]) ).
cnf(c88,plain,
multiply(left_inverse(X3),multiply(X3,multiply(identity,X2))) = X2,
inference(transitivity,[status(thm)],[c53,c87]) ).
cnf(c89,plain,
multiply(left_inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c5,c88]) ).
cnf(c90,plain,
multiply(left_inverse(X2),multiply(X2,X3)) = X3,
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
X3 = multiply(left_inverse(X2),multiply(X2,X3)),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
multiply(X4,X3) = multiply(X4,multiply(left_inverse(X2),multiply(X2,X3))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(multiply(X4,X3),X2) = multiply(multiply(X4,multiply(left_inverse(X2),multiply(X2,X3))),X2),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
multiply(multiply(multiply(X4,X3),X2),X3) = multiply(multiply(multiply(X4,multiply(left_inverse(X2),multiply(X2,X3))),X2),X3),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(multiply(multiply(X4,multiply(left_inverse(X4),X3)),X4),X2) = multiply(X4,multiply(multiply(left_inverse(X4),X3),multiply(X4,X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c96,plain,
multiply(X4,multiply(multiply(left_inverse(X4),X3),multiply(X4,X2))) = multiply(multiply(multiply(X4,multiply(left_inverse(X4),X3)),X4),X2),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
multiply(identity,multiply(X3,multiply(left_inverse(X3),X2))) = multiply(X3,multiply(left_inverse(X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c98,plain,
multiply(X3,multiply(left_inverse(X3),X2)) = multiply(identity,multiply(X3,multiply(left_inverse(X3),X2))),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
identity = multiply(left_inverse(X2),multiply(left_inverse(left_inverse(X2)),identity)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c100,plain,
multiply(identity,multiply(X3,multiply(left_inverse(X3),X2))) = multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),multiply(X3,multiply(left_inverse(X3),X2))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),X2)))))) = multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),multiply(X3,multiply(left_inverse(X3),X2))),
inference(substitution,[status(thm)],[c76]) ).
cnf(c102,plain,
multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),multiply(X3,multiply(left_inverse(X3),X2))) = multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),X2)))))),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),X2)))) = multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c104,plain,
multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),X2))))) = multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),X2)))))) = multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))) = multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2),
inference(substitution,[status(thm)],[c76]) ).
cnf(c107,plain,
multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c108,plain,
multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),X2) = X2,
inference(transitivity,[status(thm)],[c107,c2]) ).
cnf(c109,plain,
multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),X2)))) = X2,
inference(transitivity,[status(thm)],[c106,c108]) ).
cnf(c110,plain,
multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(left_inverse(X3)),multiply(left_inverse(X3),multiply(X3,multiply(left_inverse(X3),X2)))))) = X2,
inference(transitivity,[status(thm)],[c105,c109]) ).
cnf(c111,plain,
multiply(multiply(left_inverse(X3),multiply(left_inverse(left_inverse(X3)),identity)),multiply(X3,multiply(left_inverse(X3),X2))) = X2,
inference(transitivity,[status(thm)],[c102,c110]) ).
cnf(c112,plain,
multiply(identity,multiply(X3,multiply(left_inverse(X3),X2))) = X2,
inference(transitivity,[status(thm)],[c100,c111]) ).
cnf(c113,plain,
multiply(X3,multiply(left_inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c98,c112]) ).
cnf(c114,plain,
multiply(multiply(X3,multiply(left_inverse(X3),X2)),X3) = multiply(X2,X3),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
multiply(multiply(multiply(X4,multiply(left_inverse(X4),X3)),X4),X2) = multiply(multiply(X3,X4),X2),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(X4,multiply(multiply(left_inverse(X4),X3),multiply(X4,X2))) = multiply(multiply(X3,X4),X2),
inference(transitivity,[status(thm)],[c96,c115]) ).
cnf(c117,plain,
multiply(X2,multiply(multiply(left_inverse(X2),multiply(X4,multiply(left_inverse(X2),multiply(X2,X3)))),multiply(X2,X3))) = multiply(multiply(multiply(X4,multiply(left_inverse(X2),multiply(X2,X3))),X2),X3),
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(multiply(multiply(X4,multiply(left_inverse(X2),multiply(X2,X3))),X2),X3) = multiply(X2,multiply(multiply(left_inverse(X2),multiply(X4,multiply(left_inverse(X2),multiply(X2,X3)))),multiply(X2,X3))),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
multiply(multiply(multiply(X4,X3),X4),X2) = multiply(X4,multiply(X3,multiply(X4,X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c120,plain,
multiply(X4,multiply(X3,multiply(X4,X2))) = multiply(multiply(multiply(X4,X3),X4),X2),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(multiply(X4,multiply(X3,multiply(X4,X2))),X2) = multiply(multiply(multiply(multiply(X4,X3),X4),X2),X2),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
multiply(identity,multiply(multiply(X3,X2),X2)) = multiply(multiply(X3,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c123,plain,
multiply(multiply(X3,X2),X2) = multiply(identity,multiply(multiply(X3,X2),X2)),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(X2,multiply(left_inverse(X2),identity)) = identity,
inference(substitution,[status(thm)],[c113]) ).
cnf(c125,plain,
identity = multiply(X2,multiply(left_inverse(X2),identity)),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(identity,multiply(multiply(X3,X2),X2)) = multiply(multiply(X2,multiply(left_inverse(X2),identity)),multiply(multiply(X3,X2),X2)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(X2,multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,multiply(multiply(X3,X2),X2))))) = multiply(multiply(X2,multiply(left_inverse(X2),identity)),multiply(multiply(X3,X2),X2)),
inference(substitution,[status(thm)],[c76]) ).
cnf(c128,plain,
multiply(multiply(X2,multiply(left_inverse(X2),identity)),multiply(multiply(X3,X2),X2)) = multiply(X2,multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,multiply(multiply(X3,X2),X2))))),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
identity = multiply(left_inverse(X2),X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c130,plain,
multiply(X2,identity) = multiply(X2,multiply(left_inverse(X2),X2)),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(X2,multiply(left_inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c113]) ).
cnf(c132,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c130,c131]) ).
cnf(c133,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
multiply(X2,X3) = multiply(X2,multiply(X3,identity)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
multiply(multiply(X2,X3),X3) = multiply(multiply(X2,multiply(X3,identity)),X3),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
multiply(X3,multiply(multiply(X2,X3),X3)) = multiply(X3,multiply(multiply(X2,multiply(X3,identity)),X3)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c138,plain,
multiply(multiply(X2,multiply(X3,identity)),X3) = multiply(multiply(X2,multiply(X3,identity)),multiply(X3,identity)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(X3,multiply(multiply(X2,multiply(X3,identity)),X3)) = multiply(X3,multiply(multiply(X2,multiply(X3,identity)),multiply(X3,identity))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
multiply(multiply(multiply(X4,multiply(X3,multiply(X4,identity))),X4),X2) = multiply(X4,multiply(multiply(X3,multiply(X4,identity)),multiply(X4,X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c141,plain,
multiply(X4,multiply(multiply(X3,multiply(X4,identity)),multiply(X4,X2))) = multiply(multiply(multiply(X4,multiply(X3,multiply(X4,identity))),X4),X2),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(multiply(X3,multiply(X2,multiply(X3,identity))),X3) = multiply(X3,multiply(X2,multiply(X3,X3))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c143,plain,
multiply(multiply(multiply(X4,multiply(X3,multiply(X4,identity))),X4),X2) = multiply(multiply(X4,multiply(X3,multiply(X4,X4))),X2),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
multiply(X4,multiply(multiply(X3,multiply(X4,identity)),multiply(X4,X2))) = multiply(multiply(X4,multiply(X3,multiply(X4,X4))),X2),
inference(transitivity,[status(thm)],[c141,c143]) ).
cnf(c145,plain,
multiply(X3,multiply(multiply(X2,multiply(X3,identity)),multiply(X3,identity))) = multiply(multiply(X3,multiply(X2,multiply(X3,X3))),identity),
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
multiply(multiply(X3,multiply(X2,multiply(X3,X3))),identity) = multiply(X3,multiply(X2,multiply(X3,X3))),
inference(substitution,[status(thm)],[c132]) ).
cnf(c147,plain,
multiply(X3,multiply(multiply(X2,multiply(X3,identity)),multiply(X3,identity))) = multiply(X3,multiply(X2,multiply(X3,X3))),
inference(transitivity,[status(thm)],[c145,c146]) ).
cnf(c148,plain,
multiply(X3,multiply(multiply(X2,multiply(X3,identity)),X3)) = multiply(X3,multiply(X2,multiply(X3,X3))),
inference(transitivity,[status(thm)],[c139,c147]) ).
cnf(c149,plain,
multiply(X3,multiply(multiply(X2,X3),X3)) = multiply(X3,multiply(X2,multiply(X3,X3))),
inference(transitivity,[status(thm)],[c136,c148]) ).
cnf(c150,plain,
multiply(X2,multiply(multiply(X3,X2),X2)) = multiply(X2,multiply(X3,multiply(X2,X2))),
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
multiply(left_inverse(X2),multiply(X2,multiply(multiply(X3,X2),X2))) = multiply(left_inverse(X2),multiply(X2,multiply(X3,multiply(X2,X2)))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,multiply(multiply(X3,X2),X2)))) = multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,multiply(X3,multiply(X2,X2))))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
multiply(X2,multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,multiply(multiply(X3,X2),X2))))) = multiply(X2,multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,multiply(X3,multiply(X2,X2)))))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
multiply(X2,multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,multiply(X3,multiply(X2,X2)))))) = multiply(multiply(X2,multiply(left_inverse(X2),identity)),multiply(X3,multiply(X2,X2))),
inference(substitution,[status(thm)],[c76]) ).
cnf(c155,plain,
multiply(X2,multiply(left_inverse(X2),identity)) = identity,
inference(substitution,[status(thm)],[c113]) ).
cnf(c156,plain,
multiply(multiply(X2,multiply(left_inverse(X2),identity)),multiply(X3,multiply(X2,X2))) = multiply(identity,multiply(X3,multiply(X2,X2))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
multiply(identity,multiply(X3,multiply(X2,X2))) = multiply(X3,multiply(X2,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c158,plain,
multiply(multiply(X2,multiply(left_inverse(X2),identity)),multiply(X3,multiply(X2,X2))) = multiply(X3,multiply(X2,X2)),
inference(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
multiply(X2,multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,multiply(X3,multiply(X2,X2)))))) = multiply(X3,multiply(X2,X2)),
inference(transitivity,[status(thm)],[c154,c158]) ).
cnf(c160,plain,
multiply(X2,multiply(left_inverse(X2),multiply(left_inverse(X2),multiply(X2,multiply(multiply(X3,X2),X2))))) = multiply(X3,multiply(X2,X2)),
inference(transitivity,[status(thm)],[c153,c159]) ).
cnf(c161,plain,
multiply(multiply(X2,multiply(left_inverse(X2),identity)),multiply(multiply(X3,X2),X2)) = multiply(X3,multiply(X2,X2)),
inference(transitivity,[status(thm)],[c128,c160]) ).
cnf(c162,plain,
multiply(identity,multiply(multiply(X3,X2),X2)) = multiply(X3,multiply(X2,X2)),
inference(transitivity,[status(thm)],[c126,c161]) ).
cnf(c163,plain,
multiply(multiply(X3,X2),X2) = multiply(X3,multiply(X2,X2)),
inference(transitivity,[status(thm)],[c123,c162]) ).
cnf(c164,plain,
multiply(multiply(multiply(multiply(X4,X3),X4),X2),X2) = multiply(multiply(multiply(X4,X3),X4),multiply(X2,X2)),
inference(substitution,[status(thm)],[c163]) ).
cnf(c165,plain,
multiply(multiply(multiply(X4,X3),X4),multiply(X2,X2)) = multiply(X4,multiply(X3,multiply(X4,multiply(X2,X2)))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c166,plain,
multiply(multiply(multiply(multiply(X4,X3),X4),X2),X2) = multiply(X4,multiply(X3,multiply(X4,multiply(X2,X2)))),
inference(transitivity,[status(thm)],[c164,c165]) ).
cnf(c167,plain,
multiply(multiply(X4,multiply(X3,multiply(X4,X2))),X2) = multiply(X4,multiply(X3,multiply(X4,multiply(X2,X2)))),
inference(transitivity,[status(thm)],[c121,c166]) ).
cnf(c168,plain,
multiply(multiply(left_inverse(X2),multiply(X4,multiply(left_inverse(X2),multiply(X2,X3)))),multiply(X2,X3)) = multiply(left_inverse(X2),multiply(X4,multiply(left_inverse(X2),multiply(multiply(X2,X3),multiply(X2,X3))))),
inference(substitution,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(X2,multiply(multiply(left_inverse(X2),multiply(X4,multiply(left_inverse(X2),multiply(X2,X3)))),multiply(X2,X3))) = multiply(X2,multiply(left_inverse(X2),multiply(X4,multiply(left_inverse(X2),multiply(multiply(X2,X3),multiply(X2,X3)))))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(X2,multiply(left_inverse(X2),multiply(X4,multiply(left_inverse(X2),multiply(multiply(X2,X3),multiply(X2,X3)))))) = multiply(X4,multiply(left_inverse(X2),multiply(multiply(X2,X3),multiply(X2,X3)))),
inference(substitution,[status(thm)],[c113]) ).
cnf(c171,plain,
multiply(left_inverse(left_inverse(X2)),identity) = left_inverse(left_inverse(X2)),
inference(substitution,[status(thm)],[c132]) ).
cnf(c172,plain,
left_inverse(left_inverse(X2)) = multiply(left_inverse(left_inverse(X2)),identity),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
identity = multiply(left_inverse(X2),X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c174,plain,
multiply(left_inverse(left_inverse(X2)),identity) = multiply(left_inverse(left_inverse(X2)),multiply(left_inverse(X2),X2)),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
multiply(left_inverse(left_inverse(X2)),multiply(left_inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c89]) ).
cnf(c176,plain,
multiply(left_inverse(left_inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c174,c175]) ).
cnf(c177,plain,
left_inverse(left_inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c172,c176]) ).
cnf(c178,plain,
X2 = left_inverse(left_inverse(X2)),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
multiply(X3,X2) = multiply(X3,left_inverse(left_inverse(X2))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
multiply(multiply(X3,X2),multiply(X3,X2)) = multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(X3,X2)),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
X2 = left_inverse(left_inverse(X2)),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c182,plain,
multiply(X3,X2) = multiply(X3,left_inverse(left_inverse(X2))),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(X3,X2)) = multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(X3,left_inverse(left_inverse(X2)))),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
multiply(left_inverse(X2),identity) = left_inverse(X2),
inference(substitution,[status(thm)],[c132]) ).
cnf(c185,plain,
left_inverse(X2) = multiply(left_inverse(X2),identity),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
multiply(X3,left_inverse(X2)) = multiply(X3,multiply(left_inverse(X2),identity)),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
multiply(X3,multiply(X3,left_inverse(X2))) = multiply(X3,multiply(X3,multiply(left_inverse(X2),identity))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
multiply(multiply(X3,multiply(X3,left_inverse(X2))),X2) = multiply(multiply(X3,multiply(X3,multiply(left_inverse(X2),identity))),X2),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
X2 = multiply(left_inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c190,plain,
multiply(left_inverse(X3),X2) = multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
multiply(multiply(left_inverse(X3),X2),X3) = multiply(multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2))),X3),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
multiply(X3,multiply(multiply(left_inverse(X3),X2),X3)) = multiply(X3,multiply(multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2))),X3)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(multiply(multiply(X3,X2),X3),identity) = multiply(multiply(X3,X2),X3),
inference(substitution,[status(thm)],[c132]) ).
cnf(c194,plain,
multiply(multiply(X3,X2),X3) = multiply(multiply(multiply(X3,X2),X3),identity),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
multiply(multiply(multiply(X3,X2),X3),identity) = multiply(X3,multiply(X2,multiply(X3,identity))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c196,plain,
multiply(X2,multiply(X3,identity)) = multiply(X2,X3),
inference(congruence,[status(thm)],[c132]) ).
cnf(c197,plain,
multiply(X3,multiply(X2,multiply(X3,identity))) = multiply(X3,multiply(X2,X3)),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
multiply(multiply(multiply(X3,X2),X3),identity) = multiply(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c195,c197]) ).
cnf(c199,plain,
multiply(multiply(X3,X2),X3) = multiply(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c194,c198]) ).
cnf(c200,plain,
multiply(multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2)))),X3) = multiply(X3,multiply(multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2))),X3)),
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
multiply(X3,multiply(multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2))),X3)) = multiply(multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2)))),X3),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
multiply(multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2)))),X3) = multiply(multiply(multiply(X3,multiply(left_inverse(X3),identity)),X2),X3),
inference(congruence,[status(thm)],[c76]) ).
cnf(c203,plain,
multiply(X2,multiply(left_inverse(X2),identity)) = identity,
inference(substitution,[status(thm)],[c113]) ).
cnf(c204,plain,
multiply(multiply(X3,multiply(left_inverse(X3),identity)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
multiply(multiply(multiply(X3,multiply(left_inverse(X3),identity)),X2),X3) = multiply(multiply(identity,X2),X3),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(multiply(identity,X2),X3) = multiply(X2,X3),
inference(congruence,[status(thm)],[c2]) ).
cnf(c207,plain,
multiply(multiply(multiply(X3,multiply(left_inverse(X3),identity)),X2),X3) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c205,c206]) ).
cnf(c208,plain,
multiply(multiply(X3,multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2)))),X3) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c202,c207]) ).
cnf(c209,plain,
multiply(X3,multiply(multiply(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2))),X3)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c201,c208]) ).
cnf(c210,plain,
multiply(X3,multiply(multiply(left_inverse(X3),X2),X3)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c192,c209]) ).
cnf(c211,plain,
multiply(X2,multiply(multiply(left_inverse(X2),multiply(X3,multiply(X3,multiply(left_inverse(X2),identity)))),X2)) = multiply(multiply(X3,multiply(X3,multiply(left_inverse(X2),identity))),X2),
inference(substitution,[status(thm)],[c210]) ).
cnf(c212,plain,
multiply(multiply(X3,multiply(X3,multiply(left_inverse(X2),identity))),X2) = multiply(X2,multiply(multiply(left_inverse(X2),multiply(X3,multiply(X3,multiply(left_inverse(X2),identity)))),X2)),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
multiply(multiply(left_inverse(X2),multiply(X3,multiply(X3,multiply(left_inverse(X2),identity)))),X2) = multiply(left_inverse(X2),multiply(X3,multiply(X3,multiply(left_inverse(X2),X2)))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c214,plain,
multiply(X2,multiply(multiply(left_inverse(X2),multiply(X3,multiply(X3,multiply(left_inverse(X2),identity)))),X2)) = multiply(X2,multiply(left_inverse(X2),multiply(X3,multiply(X3,multiply(left_inverse(X2),X2))))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
multiply(X2,multiply(left_inverse(X2),multiply(X3,multiply(X3,multiply(left_inverse(X2),X2))))) = multiply(X3,multiply(X3,multiply(left_inverse(X2),X2))),
inference(substitution,[status(thm)],[c113]) ).
cnf(c216,plain,
multiply(X3,multiply(left_inverse(X2),X2)) = multiply(X3,identity),
inference(congruence,[status(thm)],[c6]) ).
cnf(c217,plain,
multiply(X3,multiply(X3,multiply(left_inverse(X2),X2))) = multiply(X3,multiply(X3,identity)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
multiply(X2,multiply(X2,identity)) = multiply(X2,X2),
inference(congruence,[status(thm)],[c132]) ).
cnf(c219,plain,
multiply(X3,multiply(X3,multiply(left_inverse(X2),X2))) = multiply(X3,X3),
inference(transitivity,[status(thm)],[c217,c218]) ).
cnf(c220,plain,
multiply(X2,multiply(left_inverse(X2),multiply(X3,multiply(X3,multiply(left_inverse(X2),X2))))) = multiply(X3,X3),
inference(transitivity,[status(thm)],[c215,c219]) ).
cnf(c221,plain,
multiply(X2,multiply(multiply(left_inverse(X2),multiply(X3,multiply(X3,multiply(left_inverse(X2),identity)))),X2)) = multiply(X3,X3),
inference(transitivity,[status(thm)],[c214,c220]) ).
cnf(c222,plain,
multiply(multiply(X3,multiply(X3,multiply(left_inverse(X2),identity))),X2) = multiply(X3,X3),
inference(transitivity,[status(thm)],[c212,c221]) ).
cnf(c223,plain,
multiply(multiply(X3,multiply(X3,left_inverse(X2))),X2) = multiply(X3,X3),
inference(transitivity,[status(thm)],[c188,c222]) ).
cnf(c224,plain,
multiply(multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(multiply(X3,left_inverse(left_inverse(X2))),left_inverse(X2))),X2) = multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(X3,left_inverse(left_inverse(X2)))),
inference(substitution,[status(thm)],[c223]) ).
cnf(c225,plain,
multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(X3,left_inverse(left_inverse(X2)))) = multiply(multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(multiply(X3,left_inverse(left_inverse(X2))),left_inverse(X2))),X2),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
multiply(left_inverse(X2),identity) = left_inverse(X2),
inference(substitution,[status(thm)],[c132]) ).
cnf(c227,plain,
left_inverse(X2) = multiply(left_inverse(X2),identity),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
multiply(X3,left_inverse(X2)) = multiply(X3,multiply(left_inverse(X2),identity)),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
multiply(multiply(X3,left_inverse(X2)),X2) = multiply(multiply(X3,multiply(left_inverse(X2),identity)),X2),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
multiply(X2,multiply(multiply(left_inverse(X2),multiply(X3,multiply(left_inverse(X2),identity))),X2)) = multiply(multiply(X3,multiply(left_inverse(X2),identity)),X2),
inference(substitution,[status(thm)],[c210]) ).
cnf(c231,plain,
multiply(multiply(X3,multiply(left_inverse(X2),identity)),X2) = multiply(X2,multiply(multiply(left_inverse(X2),multiply(X3,multiply(left_inverse(X2),identity))),X2)),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
multiply(multiply(left_inverse(X2),multiply(X3,multiply(left_inverse(X2),identity))),X2) = multiply(left_inverse(X2),multiply(X3,multiply(left_inverse(X2),X2))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c233,plain,
multiply(X2,multiply(multiply(left_inverse(X2),multiply(X3,multiply(left_inverse(X2),identity))),X2)) = multiply(X2,multiply(left_inverse(X2),multiply(X3,multiply(left_inverse(X2),X2)))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
multiply(X2,multiply(left_inverse(X2),multiply(X3,multiply(left_inverse(X2),X2)))) = multiply(X3,multiply(left_inverse(X2),X2)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c235,plain,
multiply(X3,multiply(left_inverse(X2),X2)) = multiply(X3,identity),
inference(congruence,[status(thm)],[c6]) ).
cnf(c236,plain,
multiply(X3,multiply(left_inverse(X2),X2)) = X3,
inference(transitivity,[status(thm)],[c235,c132]) ).
cnf(c237,plain,
multiply(X2,multiply(left_inverse(X2),multiply(X3,multiply(left_inverse(X2),X2)))) = X3,
inference(transitivity,[status(thm)],[c234,c236]) ).
cnf(c238,plain,
multiply(X2,multiply(multiply(left_inverse(X2),multiply(X3,multiply(left_inverse(X2),identity))),X2)) = X3,
inference(transitivity,[status(thm)],[c233,c237]) ).
cnf(c239,plain,
multiply(multiply(X3,multiply(left_inverse(X2),identity)),X2) = X3,
inference(transitivity,[status(thm)],[c231,c238]) ).
cnf(c240,plain,
multiply(multiply(X3,left_inverse(X2)),X2) = X3,
inference(transitivity,[status(thm)],[c229,c239]) ).
cnf(c241,plain,
multiply(multiply(X3,left_inverse(left_inverse(X2))),left_inverse(X2)) = X3,
inference(substitution,[status(thm)],[c240]) ).
cnf(c242,plain,
multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(multiply(X3,left_inverse(left_inverse(X2))),left_inverse(X2))) = multiply(multiply(X3,left_inverse(left_inverse(X2))),X3),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
multiply(multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(multiply(X3,left_inverse(left_inverse(X2))),left_inverse(X2))),X2) = multiply(multiply(multiply(X3,left_inverse(left_inverse(X2))),X3),X2),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
multiply(multiply(multiply(X3,left_inverse(left_inverse(X2))),X3),X2) = multiply(X3,multiply(left_inverse(left_inverse(X2)),multiply(X3,X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c245,plain,
multiply(left_inverse(left_inverse(X2)),multiply(X3,X2)) = multiply(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c246,plain,
multiply(X3,multiply(left_inverse(left_inverse(X2)),multiply(X3,X2))) = multiply(X3,multiply(X2,multiply(X3,X2))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
multiply(multiply(multiply(X3,left_inverse(left_inverse(X2))),X3),X2) = multiply(X3,multiply(X2,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c244,c246]) ).
cnf(c248,plain,
multiply(multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(multiply(X3,left_inverse(left_inverse(X2))),left_inverse(X2))),X2) = multiply(X3,multiply(X2,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c243,c247]) ).
cnf(c249,plain,
multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(X3,left_inverse(left_inverse(X2)))) = multiply(X3,multiply(X2,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c225,c248]) ).
cnf(c250,plain,
multiply(multiply(X3,left_inverse(left_inverse(X2))),multiply(X3,X2)) = multiply(X3,multiply(X2,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c183,c249]) ).
cnf(c251,plain,
multiply(multiply(X3,X2),multiply(X3,X2)) = multiply(X3,multiply(X2,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c180,c250]) ).
cnf(c252,plain,
multiply(multiply(X2,X3),multiply(X2,X3)) = multiply(X2,multiply(X3,multiply(X2,X3))),
inference(substitution,[status(thm)],[c251]) ).
cnf(c253,plain,
multiply(left_inverse(X2),multiply(multiply(X2,X3),multiply(X2,X3))) = multiply(left_inverse(X2),multiply(X2,multiply(X3,multiply(X2,X3)))),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
multiply(X4,multiply(left_inverse(X2),multiply(multiply(X2,X3),multiply(X2,X3)))) = multiply(X4,multiply(left_inverse(X2),multiply(X2,multiply(X3,multiply(X2,X3))))),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
multiply(left_inverse(X2),multiply(X2,multiply(X3,multiply(X2,X3)))) = multiply(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c89]) ).
cnf(c256,plain,
multiply(X4,multiply(left_inverse(X2),multiply(X2,multiply(X3,multiply(X2,X3))))) = multiply(X4,multiply(X3,multiply(X2,X3))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
multiply(X4,multiply(left_inverse(X2),multiply(multiply(X2,X3),multiply(X2,X3)))) = multiply(X4,multiply(X3,multiply(X2,X3))),
inference(transitivity,[status(thm)],[c254,c256]) ).
cnf(c258,plain,
multiply(X2,multiply(left_inverse(X2),multiply(X4,multiply(left_inverse(X2),multiply(multiply(X2,X3),multiply(X2,X3)))))) = multiply(X4,multiply(X3,multiply(X2,X3))),
inference(transitivity,[status(thm)],[c170,c257]) ).
cnf(c259,plain,
multiply(X2,multiply(multiply(left_inverse(X2),multiply(X4,multiply(left_inverse(X2),multiply(X2,X3)))),multiply(X2,X3))) = multiply(X4,multiply(X3,multiply(X2,X3))),
inference(transitivity,[status(thm)],[c169,c258]) ).
cnf(c260,plain,
multiply(multiply(multiply(X4,multiply(left_inverse(X2),multiply(X2,X3))),X2),X3) = multiply(X4,multiply(X3,multiply(X2,X3))),
inference(transitivity,[status(thm)],[c118,c259]) ).
cnf(c261,plain,
multiply(multiply(multiply(X4,X3),X2),X3) = multiply(X4,multiply(X3,multiply(X2,X3))),
inference(transitivity,[status(thm)],[c94,c260]) ).
cnf(c262,plain,
multiply(multiply(multiply(a,b),c),b) = multiply(a,multiply(b,multiply(c,b))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c263,plain,
$false,
inference(resolution,[status(thm)],[c1,c262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP203-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n016.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 27 09:42:16 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.86 Command-line arguments: --no-flatten-goal
% 0.31/0.86
% 0.31/0.86 % SZS status Unsatisfiable
% 0.31/0.86
% 0.31/0.88 % SZS output start CNFRefutation
% See solution above
% 4.46/1.12
% 4.46/1.12 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------