%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP183-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 10:09:36 AM UTC 2026
% Result : Unsatisfiable 11.71s 2.07s
% Output : CNFRefutation 16.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 14
% Syntax : Number of clauses : 516 ( 516 unt; 0 nHn; 3 RR)
% Number of literals : 516 ( 515 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 902 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_20x) ).
cnf(c2,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c3,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
multiply(inverse(X2),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = multiply(inverse(X2),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(X2,identity)) = multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))) = multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(X2,identity)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c15,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c17,plain,
least_upper_bound(inverse(X2),identity) = least_upper_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(least_upper_bound(inverse(X2),identity),X2) = multiply(least_upper_bound(identity,inverse(X2)),X2),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c20,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(least_upper_bound(identity,X2),X3) = multiply(least_upper_bound(X2,identity),X3),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c16]) ).
cnf(c23,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(least_upper_bound(X3,identity),X2) = multiply(least_upper_bound(identity,X3),X2),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c26,plain,
multiply(least_upper_bound(identity,X3),X2) = least_upper_bound(multiply(identity,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
least_upper_bound(multiply(identity,X2),multiply(X3,X2)) = least_upper_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c28,plain,
multiply(least_upper_bound(identity,X3),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c26,c27]) ).
cnf(c29,plain,
multiply(least_upper_bound(X3,identity),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c24,c28]) ).
cnf(c30,plain,
multiply(least_upper_bound(X2,identity),X3) = least_upper_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(least_upper_bound(identity,X2),X3) = least_upper_bound(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c21,c30]) ).
cnf(c32,plain,
multiply(least_upper_bound(identity,inverse(X2)),X2) = least_upper_bound(X2,multiply(inverse(X2),X2)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
least_upper_bound(X2,multiply(inverse(X2),X2)) = least_upper_bound(X2,identity),
inference(congruence,[status(thm)],[c5]) ).
cnf(c34,plain,
multiply(least_upper_bound(identity,inverse(X2)),X2) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c32,c33]) ).
cnf(c35,plain,
multiply(least_upper_bound(inverse(X2),identity),X2) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c18,c34]) ).
cnf(c36,plain,
least_upper_bound(X2,identity) = multiply(least_upper_bound(inverse(X2),identity),X2),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(least_upper_bound(inverse(X2),identity),X2)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c39,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c41,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c39,c40]) ).
cnf(c42,plain,
multiply(inverse(inverse(X2)),identity) = multiply(X2,identity),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c45,plain,
multiply(inverse(inverse(X2)),identity) = multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c47,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c45,c46]) ).
cnf(c48,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c43,c47]) ).
cnf(c49,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
greatest_lower_bound(X3,multiply(X3,X2)) = greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,axiom,
multiply(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c52,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,greatest_lower_bound(identity,X2)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c14]) ).
cnf(c55,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c53,c55]) ).
cnf(c57,plain,
greatest_lower_bound(X3,multiply(X3,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c50,c56]) ).
cnf(c58,plain,
greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(least_upper_bound(inverse(X2),identity),X2)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c60,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(least_upper_bound(inverse(X2),identity),X2)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2)),
inference(transitivity,[status(thm)],[c58,c60]) ).
cnf(c62,plain,
greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2)),
inference(transitivity,[status(thm)],[c37,c61]) ).
cnf(c63,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2)),
inference(transitivity,[status(thm)],[c15,c62]) ).
cnf(c64,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c66,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(identity,X2),
inference(transitivity,[status(thm)],[c64,c65]) ).
cnf(c67,plain,
multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(X2,identity)) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c69,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(greatest_lower_bound(identity,X2),least_upper_bound(X2,identity)) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c72,plain,
greatest_lower_bound(X3,multiply(X2,X3)) = greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,axiom,
multiply(greatest_lower_bound(Y2,Z2),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c74,plain,
multiply(greatest_lower_bound(identity,X2),X3) = greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(identity,X2),X3),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c14]) ).
cnf(c77,plain,
multiply(greatest_lower_bound(identity,X2),X3) = multiply(greatest_lower_bound(X2,identity),X3),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c75,c77]) ).
cnf(c79,plain,
greatest_lower_bound(X3,multiply(X2,X3)) = multiply(greatest_lower_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c72,c78]) ).
cnf(c80,plain,
greatest_lower_bound(least_upper_bound(X2,identity),multiply(X2,least_upper_bound(X2,identity))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(greatest_lower_bound(X2,identity),least_upper_bound(X2,identity)) = greatest_lower_bound(least_upper_bound(X2,identity),multiply(X2,least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),multiply(least_upper_bound(X2,identity),X2))) = multiply(least_upper_bound(X2,identity),X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c83,plain,
multiply(least_upper_bound(X2,identity),X2) = multiply(inverse(inverse(X2)),multiply(inverse(X2),multiply(least_upper_bound(X2,identity),X2))),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(least_upper_bound(X2,identity),X2) = least_upper_bound(X2,multiply(X2,X2)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c85,plain,
multiply(inverse(X2),multiply(least_upper_bound(X2,identity),X2)) = multiply(inverse(X2),least_upper_bound(X2,multiply(X2,X2))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c87,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = multiply(inverse(X3),least_upper_bound(X2,X3)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c90,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(inverse(X3),least_upper_bound(X2,X3)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c93,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c95,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c93,c94]) ).
cnf(c96,plain,
multiply(inverse(X3),least_upper_bound(X2,X3)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c91,c95]) ).
cnf(c97,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c88,c96]) ).
cnf(c98,plain,
multiply(inverse(X2),least_upper_bound(X2,multiply(X2,X2))) = least_upper_bound(identity,multiply(inverse(X2),multiply(X2,X2))),
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
multiply(inverse(X2),multiply(X2,X2)) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c100,plain,
least_upper_bound(identity,multiply(inverse(X2),multiply(X2,X2))) = least_upper_bound(identity,X2),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c102,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
least_upper_bound(identity,multiply(inverse(X2),multiply(X2,X2))) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c100,c102]) ).
cnf(c104,plain,
multiply(inverse(X2),least_upper_bound(X2,multiply(X2,X2))) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c98,c103]) ).
cnf(c105,plain,
multiply(inverse(X2),multiply(least_upper_bound(X2,identity),X2)) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c85,c104]) ).
cnf(c106,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),multiply(least_upper_bound(X2,identity),X2))) = multiply(inverse(inverse(X2)),least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
multiply(inverse(inverse(X2)),least_upper_bound(X2,identity)) = multiply(X2,least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c108,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),multiply(least_upper_bound(X2,identity),X2))) = multiply(X2,least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c106,c107]) ).
cnf(c109,plain,
multiply(least_upper_bound(X2,identity),X2) = multiply(X2,least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c83,c108]) ).
cnf(c110,plain,
multiply(X2,least_upper_bound(X2,identity)) = multiply(least_upper_bound(X2,identity),X2),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
greatest_lower_bound(least_upper_bound(X2,identity),multiply(X2,least_upper_bound(X2,identity))) = greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(X2,identity),X2)),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(X2,identity),X2)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c113,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c114,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,X2)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
greatest_lower_bound(identity,X2) = multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c116,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,X2)) = multiply(least_upper_bound(X2,identity),multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(inverse(inverse(X3)),multiply(least_upper_bound(inverse(X3),identity),X2)) = multiply(X3,multiply(least_upper_bound(inverse(X3),identity),X2)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c118,plain,
multiply(X3,multiply(least_upper_bound(inverse(X3),identity),X2)) = multiply(inverse(inverse(X3)),multiply(least_upper_bound(inverse(X3),identity),X2)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
multiply(multiply(inverse(X3),least_upper_bound(X3,identity)),X2) = multiply(inverse(X3),multiply(least_upper_bound(X3,identity),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c120,plain,
multiply(inverse(X3),multiply(least_upper_bound(X3,identity),X2)) = multiply(multiply(inverse(X3),least_upper_bound(X3,identity)),X2),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(least_upper_bound(inverse(X2),identity),identity) = least_upper_bound(identity,multiply(inverse(X2),identity)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c122,plain,
multiply(inverse(X2),least_upper_bound(identity,X2)) = least_upper_bound(identity,multiply(inverse(X2),identity)),
inference(substitution,[status(thm)],[c96]) ).
cnf(c123,plain,
least_upper_bound(identity,multiply(inverse(X2),identity)) = multiply(inverse(X2),least_upper_bound(identity,X2)),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c125,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(inverse(X2),least_upper_bound(identity,X2)) = multiply(inverse(X2),least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
least_upper_bound(identity,multiply(inverse(X2),identity)) = multiply(inverse(X2),least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c123,c126]) ).
cnf(c128,plain,
multiply(least_upper_bound(inverse(X2),identity),identity) = multiply(inverse(X2),least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c121,c127]) ).
cnf(c129,plain,
multiply(inverse(X2),least_upper_bound(X2,identity)) = multiply(least_upper_bound(inverse(X2),identity),identity),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(multiply(inverse(X3),least_upper_bound(X3,identity)),X2) = multiply(multiply(least_upper_bound(inverse(X3),identity),identity),X2),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(multiply(least_upper_bound(inverse(X3),identity),identity),X2) = multiply(least_upper_bound(inverse(X3),identity),multiply(identity,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c132,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(identity,X2)) = multiply(least_upper_bound(inverse(X3),identity),X2),
inference(congruence,[status(thm)],[c7]) ).
cnf(c133,plain,
multiply(multiply(least_upper_bound(inverse(X3),identity),identity),X2) = multiply(least_upper_bound(inverse(X3),identity),X2),
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
multiply(multiply(inverse(X3),least_upper_bound(X3,identity)),X2) = multiply(least_upper_bound(inverse(X3),identity),X2),
inference(transitivity,[status(thm)],[c130,c133]) ).
cnf(c135,plain,
multiply(inverse(X3),multiply(least_upper_bound(X3,identity),X2)) = multiply(least_upper_bound(inverse(X3),identity),X2),
inference(transitivity,[status(thm)],[c120,c134]) ).
cnf(c136,plain,
multiply(least_upper_bound(inverse(X3),identity),X2) = multiply(inverse(X3),multiply(least_upper_bound(X3,identity),X2)),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
multiply(inverse(inverse(X3)),multiply(least_upper_bound(inverse(X3),identity),X2)) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(least_upper_bound(X3,identity),X2))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(least_upper_bound(X3,identity),X2))) = multiply(least_upper_bound(X3,identity),X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c139,plain,
multiply(inverse(inverse(X3)),multiply(least_upper_bound(inverse(X3),identity),X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c137,c138]) ).
cnf(c140,plain,
multiply(X3,multiply(least_upper_bound(inverse(X3),identity),X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c118,c139]) ).
cnf(c141,plain,
multiply(X2,multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(inverse(X2),identity)))) = multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(inverse(X2),identity))),
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(inverse(X2),identity))) = multiply(X2,multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(inverse(X2),identity)))),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c144,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c146,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c144,c145]) ).
cnf(c147,plain,
multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(inverse(X2),identity))) = identity,
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
multiply(X2,multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(inverse(X2),identity)))) = multiply(X2,identity),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(X2,multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(inverse(X2),identity)))) = X2,
inference(transitivity,[status(thm)],[c148,c48]) ).
cnf(c150,plain,
multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(inverse(X2),identity))) = X2,
inference(transitivity,[status(thm)],[c142,c149]) ).
cnf(c151,plain,
X2 = multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(inverse(X2),identity))),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
multiply(inverse(least_upper_bound(X2,identity)),X2) = multiply(inverse(least_upper_bound(X2,identity)),multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
multiply(inverse(least_upper_bound(X2,identity)),multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(inverse(X2),identity)))) = inverse(least_upper_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c154,plain,
multiply(inverse(least_upper_bound(X2,identity)),X2) = inverse(least_upper_bound(inverse(X2),identity)),
inference(transitivity,[status(thm)],[c152,c153]) ).
cnf(c155,plain,
inverse(least_upper_bound(inverse(X2),identity)) = multiply(inverse(least_upper_bound(X2,identity)),X2),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(inverse(X2),identity))) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(least_upper_bound(X2,identity)),X2)),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
multiply(multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity))),X2) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(least_upper_bound(X2,identity)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c158,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(least_upper_bound(X2,identity)),X2)) = multiply(multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity))),X2),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c160,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity))) = multiply(greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)),inverse(least_upper_bound(X2,identity))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
multiply(inverse(inverse(X2)),identity) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c162,plain,
inverse(inverse(X2)) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c162,c47]) ).
cnf(c164,plain,
inverse(inverse(least_upper_bound(X2,identity))) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c163]) ).
cnf(c165,plain,
least_upper_bound(X2,identity) = inverse(inverse(least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),inverse(inverse(least_upper_bound(X2,identity)))),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)),inverse(least_upper_bound(X2,identity))) = multiply(greatest_lower_bound(least_upper_bound(inverse(X2),identity),inverse(inverse(least_upper_bound(X2,identity)))),inverse(least_upper_bound(X2,identity))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c169,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c73]) ).
cnf(c171,plain,
greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(greatest_lower_bound(inverse(X2),X3),X2),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
greatest_lower_bound(inverse(X2),X3) = greatest_lower_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c173,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c171,c173]) ).
cnf(c175,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c169,c174]) ).
cnf(c176,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(X2,identity)))) = multiply(greatest_lower_bound(least_upper_bound(inverse(X2),identity),inverse(inverse(least_upper_bound(X2,identity)))),inverse(least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
multiply(greatest_lower_bound(least_upper_bound(inverse(X2),identity),inverse(inverse(least_upper_bound(X2,identity)))),inverse(least_upper_bound(X2,identity))) = greatest_lower_bound(identity,multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(X2,identity)))),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
multiply(inverse(X2),multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(X2,identity)))) = multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c135]) ).
cnf(c179,plain,
multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(X2,identity))) = multiply(inverse(X2),multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(X2,identity)))),
inference(symmetry,[status(thm)],[c178]) ).
cnf(c180,plain,
multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(X2,identity))) = identity,
inference(substitution,[status(thm)],[c146]) ).
cnf(c181,plain,
multiply(inverse(X2),multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(X2,identity)))) = multiply(inverse(X2),identity),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(substitution,[status(thm)],[c48]) ).
cnf(c183,plain,
multiply(inverse(X2),multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(X2,identity)))) = inverse(X2),
inference(transitivity,[status(thm)],[c181,c182]) ).
cnf(c184,plain,
multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(X2,identity))) = inverse(X2),
inference(transitivity,[status(thm)],[c179,c183]) ).
cnf(c185,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(X2,identity)))) = greatest_lower_bound(identity,inverse(X2)),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
multiply(greatest_lower_bound(least_upper_bound(inverse(X2),identity),inverse(inverse(least_upper_bound(X2,identity)))),inverse(least_upper_bound(X2,identity))) = greatest_lower_bound(identity,inverse(X2)),
inference(transitivity,[status(thm)],[c177,c185]) ).
cnf(c187,plain,
multiply(greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)),inverse(least_upper_bound(X2,identity))) = greatest_lower_bound(identity,inverse(X2)),
inference(transitivity,[status(thm)],[c167,c186]) ).
cnf(c188,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity))) = greatest_lower_bound(identity,inverse(X2)),
inference(transitivity,[status(thm)],[c160,c187]) ).
cnf(c189,plain,
multiply(multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity))),X2) = multiply(greatest_lower_bound(identity,inverse(X2)),X2),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
greatest_lower_bound(inverse(X2),identity) = greatest_lower_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c191,plain,
greatest_lower_bound(identity,inverse(X2)) = greatest_lower_bound(inverse(X2),identity),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),X2) = multiply(greatest_lower_bound(inverse(X2),identity),X2),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
greatest_lower_bound(X2,multiply(inverse(X2),X2)) = multiply(greatest_lower_bound(inverse(X2),identity),X2),
inference(substitution,[status(thm)],[c79]) ).
cnf(c194,plain,
multiply(greatest_lower_bound(inverse(X2),identity),X2) = greatest_lower_bound(X2,multiply(inverse(X2),X2)),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
greatest_lower_bound(X2,multiply(inverse(X2),X2)) = greatest_lower_bound(X2,identity),
inference(congruence,[status(thm)],[c5]) ).
cnf(c196,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c197,plain,
greatest_lower_bound(X2,multiply(inverse(X2),X2)) = greatest_lower_bound(identity,X2),
inference(transitivity,[status(thm)],[c195,c196]) ).
cnf(c198,plain,
multiply(greatest_lower_bound(inverse(X2),identity),X2) = greatest_lower_bound(identity,X2),
inference(transitivity,[status(thm)],[c194,c197]) ).
cnf(c199,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),X2) = greatest_lower_bound(identity,X2),
inference(transitivity,[status(thm)],[c192,c198]) ).
cnf(c200,plain,
greatest_lower_bound(identity,X2) = multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c201,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),X2) = multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c199,c200]) ).
cnf(c202,plain,
multiply(multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity))),X2) = multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c189,c201]) ).
cnf(c203,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(least_upper_bound(X2,identity)),X2)) = multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c158,c202]) ).
cnf(c204,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(inverse(X2),identity))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c156,c203]) ).
cnf(c205,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(inverse(X2),identity))),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(least_upper_bound(X2,identity),multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(inverse(X2),identity)))) = multiply(least_upper_bound(X2,identity),multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c208,plain,
multiply(least_upper_bound(X2,identity),multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,X2)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c209,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c210,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,X2)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(X2,identity),X2)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c213,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)) = greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(X2,identity),X2)),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
least_upper_bound(X2,identity) = multiply(least_upper_bound(inverse(X2),identity),X2),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c215,plain,
greatest_lower_bound(least_upper_bound(X3,identity),multiply(X2,X3)) = greatest_lower_bound(multiply(least_upper_bound(inverse(X3),identity),X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
multiply(greatest_lower_bound(least_upper_bound(inverse(X3),identity),X2),X3) = greatest_lower_bound(multiply(least_upper_bound(inverse(X3),identity),X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c73]) ).
cnf(c217,plain,
greatest_lower_bound(multiply(least_upper_bound(inverse(X3),identity),X3),multiply(X2,X3)) = multiply(greatest_lower_bound(least_upper_bound(inverse(X3),identity),X2),X3),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
greatest_lower_bound(least_upper_bound(inverse(X3),identity),X2) = greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c219,plain,
multiply(greatest_lower_bound(least_upper_bound(inverse(X3),identity),X2),X3) = multiply(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),X3),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
greatest_lower_bound(multiply(least_upper_bound(inverse(X3),identity),X3),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),X3),
inference(transitivity,[status(thm)],[c217,c219]) ).
cnf(c221,plain,
greatest_lower_bound(least_upper_bound(X3,identity),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),X3),
inference(transitivity,[status(thm)],[c215,c220]) ).
cnf(c222,plain,
greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(X2,identity),X2)) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2),
inference(substitution,[status(thm)],[c221]) ).
cnf(c223,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2),
inference(transitivity,[status(thm)],[c213,c222]) ).
cnf(c224,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,X2)) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2),
inference(transitivity,[status(thm)],[c211,c223]) ).
cnf(c225,plain,
multiply(least_upper_bound(X2,identity),multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2),
inference(transitivity,[status(thm)],[c208,c224]) ).
cnf(c226,plain,
multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(inverse(X2),identity)))) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2),
inference(transitivity,[status(thm)],[c207,c225]) ).
cnf(c227,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2) = multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(inverse(X2),identity)))),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(inverse(X2),identity)))) = multiply(least_upper_bound(X2,identity),multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c229,plain,
multiply(least_upper_bound(X2,identity),multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,X2)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c230,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c231,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,X2)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
greatest_lower_bound(inverse(X2),identity) = greatest_lower_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c234,plain,
greatest_lower_bound(identity,inverse(X2)) = greatest_lower_bound(inverse(X2),identity),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
multiply(X2,greatest_lower_bound(identity,inverse(X2))) = multiply(X2,greatest_lower_bound(inverse(X2),identity)),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
multiply(inverse(inverse(X2)),greatest_lower_bound(inverse(X2),identity)) = multiply(X2,greatest_lower_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c237,plain,
multiply(X2,greatest_lower_bound(inverse(X2),identity)) = multiply(inverse(inverse(X2)),greatest_lower_bound(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c239,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c241,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c239,c241]) ).
cnf(c243,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(X2)),identity)) = multiply(inverse(inverse(X2)),greatest_lower_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c242]) ).
cnf(c244,plain,
multiply(inverse(inverse(X2)),greatest_lower_bound(inverse(X2),identity)) = greatest_lower_bound(identity,multiply(inverse(inverse(X2)),identity)),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(X2)),identity)) = greatest_lower_bound(identity,X2),
inference(congruence,[status(thm)],[c47]) ).
cnf(c246,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c14]) ).
cnf(c247,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(X2)),identity)) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c245,c246]) ).
cnf(c248,plain,
multiply(inverse(inverse(X2)),greatest_lower_bound(inverse(X2),identity)) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c244,c247]) ).
cnf(c249,plain,
multiply(X2,greatest_lower_bound(inverse(X2),identity)) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c237,c248]) ).
cnf(c250,plain,
multiply(X2,greatest_lower_bound(identity,inverse(X2))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c235,c249]) ).
cnf(c251,plain,
greatest_lower_bound(X2,identity) = multiply(X2,greatest_lower_bound(identity,inverse(X2))),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(X2,identity),multiply(X2,greatest_lower_bound(identity,inverse(X2)))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
multiply(least_upper_bound(X3,identity),multiply(X3,X2)) = least_upper_bound(multiply(X3,X2),multiply(X3,multiply(X3,X2))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c254,plain,
multiply(X3,least_upper_bound(X2,multiply(X3,X2))) = least_upper_bound(multiply(X3,X2),multiply(X3,multiply(X3,X2))),
inference(substitution,[status(thm)],[c92]) ).
cnf(c255,plain,
least_upper_bound(multiply(X3,X2),multiply(X3,multiply(X3,X2))) = multiply(X3,least_upper_bound(X2,multiply(X3,X2))),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
least_upper_bound(X2,multiply(X3,X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c257,plain,
multiply(X3,least_upper_bound(X2,multiply(X3,X2))) = multiply(X3,multiply(least_upper_bound(X3,identity),X2)),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
least_upper_bound(multiply(X3,X2),multiply(X3,multiply(X3,X2))) = multiply(X3,multiply(least_upper_bound(X3,identity),X2)),
inference(transitivity,[status(thm)],[c255,c257]) ).
cnf(c259,plain,
multiply(least_upper_bound(X3,identity),multiply(X3,X2)) = multiply(X3,multiply(least_upper_bound(X3,identity),X2)),
inference(transitivity,[status(thm)],[c253,c258]) ).
cnf(c260,plain,
multiply(least_upper_bound(X2,identity),multiply(X2,greatest_lower_bound(identity,inverse(X2)))) = multiply(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2)))),
inference(substitution,[status(thm)],[c259]) ).
cnf(c261,plain,
greatest_lower_bound(identity,inverse(X2)) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c262,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity)))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
multiply(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2)))) = multiply(X2,multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity))))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity)))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c188]) ).
cnf(c265,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c266,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c268,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c269,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c270,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(transitivity,[status(thm)],[c268,c270]) ).
cnf(c272,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(transitivity,[status(thm)],[c266,c271]) ).
cnf(c273,plain,
greatest_lower_bound(identity,multiply(inverse(X2),identity)) = multiply(inverse(X2),greatest_lower_bound(identity,X2)),
inference(substitution,[status(thm)],[c272]) ).
cnf(c274,plain,
multiply(inverse(X2),greatest_lower_bound(identity,X2)) = greatest_lower_bound(identity,multiply(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
greatest_lower_bound(identity,multiply(inverse(X2),identity)) = multiply(greatest_lower_bound(inverse(X2),identity),identity),
inference(substitution,[status(thm)],[c79]) ).
cnf(c276,plain,
multiply(greatest_lower_bound(inverse(X2),identity),identity) = greatest_lower_bound(inverse(X2),identity),
inference(substitution,[status(thm)],[c48]) ).
cnf(c277,plain,
greatest_lower_bound(inverse(X2),identity) = greatest_lower_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c278,plain,
multiply(greatest_lower_bound(inverse(X2),identity),identity) = greatest_lower_bound(identity,inverse(X2)),
inference(transitivity,[status(thm)],[c276,c277]) ).
cnf(c279,plain,
greatest_lower_bound(identity,multiply(inverse(X2),identity)) = greatest_lower_bound(identity,inverse(X2)),
inference(transitivity,[status(thm)],[c275,c278]) ).
cnf(c280,plain,
multiply(inverse(X2),greatest_lower_bound(identity,X2)) = greatest_lower_bound(identity,inverse(X2)),
inference(transitivity,[status(thm)],[c274,c279]) ).
cnf(c281,plain,
greatest_lower_bound(identity,inverse(X2)) = multiply(inverse(X2),greatest_lower_bound(identity,X2)),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = multiply(least_upper_bound(X2,identity),multiply(inverse(X2),greatest_lower_bound(identity,X2))),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
least_upper_bound(inverse(X2),identity) = least_upper_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c284,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2)) = multiply(least_upper_bound(identity,inverse(X3)),multiply(X3,X2)),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
multiply(least_upper_bound(identity,inverse(X3)),multiply(X3,X2)) = least_upper_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c286,plain,
least_upper_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))) = least_upper_bound(multiply(X3,X2),X2),
inference(congruence,[status(thm)],[c9]) ).
cnf(c287,plain,
least_upper_bound(multiply(X3,X2),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c288,plain,
least_upper_bound(X2,multiply(X3,X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c289,plain,
least_upper_bound(multiply(X3,X2),X2) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c287,c288]) ).
cnf(c290,plain,
least_upper_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c286,c289]) ).
cnf(c291,plain,
multiply(least_upper_bound(identity,inverse(X3)),multiply(X3,X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c285,c290]) ).
cnf(c292,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c284,c291]) ).
cnf(c293,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(X3,multiply(inverse(X3),X2))) = multiply(least_upper_bound(X3,identity),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c292]) ).
cnf(c294,plain,
multiply(least_upper_bound(X3,identity),multiply(inverse(X3),X2)) = multiply(least_upper_bound(inverse(X3),identity),multiply(X3,multiply(inverse(X3),X2))),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)) = multiply(X3,multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c296,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c298,plain,
multiply(X3,multiply(inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c296,c297]) ).
cnf(c299,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(X3,multiply(inverse(X3),X2))) = multiply(least_upper_bound(inverse(X3),identity),X2),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
multiply(least_upper_bound(X3,identity),multiply(inverse(X3),X2)) = multiply(least_upper_bound(inverse(X3),identity),X2),
inference(transitivity,[status(thm)],[c294,c299]) ).
cnf(c301,plain,
multiply(least_upper_bound(X2,identity),multiply(inverse(X2),greatest_lower_bound(identity,X2))) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2)),
inference(substitution,[status(thm)],[c300]) ).
cnf(c302,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2)) = greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c303,plain,
multiply(least_upper_bound(X2,identity),multiply(inverse(X2),greatest_lower_bound(identity,X2))) = greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),
inference(transitivity,[status(thm)],[c301,c302]) ).
cnf(c304,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),
inference(transitivity,[status(thm)],[c282,c303]) ).
cnf(c305,plain,
multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity)))) = greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),
inference(transitivity,[status(thm)],[c264,c304]) ).
cnf(c306,plain,
multiply(X2,multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(X2,identity))))) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
multiply(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2)))) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c263,c306]) ).
cnf(c308,plain,
multiply(least_upper_bound(X2,identity),multiply(X2,greatest_lower_bound(identity,inverse(X2)))) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c260,c307]) ).
cnf(c309,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c252,c308]) ).
cnf(c310,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,X2)) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c232,c309]) ).
cnf(c311,plain,
multiply(least_upper_bound(X2,identity),multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c229,c310]) ).
cnf(c312,plain,
multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(inverse(X2),identity)))) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c228,c311]) ).
cnf(c313,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c227,c312]) ).
cnf(c314,plain,
multiply(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(least_upper_bound(inverse(X2),identity)))) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c226,c313]) ).
cnf(c315,plain,
multiply(least_upper_bound(X2,identity),multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c206,c314]) ).
cnf(c316,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,X2)) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c116,c315]) ).
cnf(c317,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c114,c316]) ).
cnf(c318,plain,
greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(X2,identity),X2)) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c112,c317]) ).
cnf(c319,plain,
greatest_lower_bound(least_upper_bound(X2,identity),multiply(X2,least_upper_bound(X2,identity))) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c111,c318]) ).
cnf(c320,plain,
multiply(greatest_lower_bound(X2,identity),least_upper_bound(X2,identity)) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c81,c319]) ).
cnf(c321,plain,
multiply(greatest_lower_bound(identity,X2),least_upper_bound(X2,identity)) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c70,c320]) ).
cnf(c322,plain,
multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(X2,identity)) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c67,c321]) ).
cnf(c323,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))) = multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c13,c322]) ).
cnf(c324,plain,
multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c323]) ).
cnf(c325,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(X4,identity))),X3) = least_upper_bound(X3,multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(X4,identity)),X3)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c326,plain,
least_upper_bound(X4,multiply(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),X4)) = multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity))),X4),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)),X4) = least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c328,plain,
least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)),X4),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c329,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(X3,greatest_lower_bound(X2,X4)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c330,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X4)) = greatest_lower_bound(greatest_lower_bound(X2,X4),X3),
inference(symmetry,[status(thm)],[c329]) ).
cnf(c331,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c332,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c334,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c333]) ).
cnf(c335,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c334]) ).
cnf(c336,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c337,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c335,c337]) ).
cnf(c339,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c332,c338]) ).
cnf(c340,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c330,c339]) ).
cnf(c341,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4))) = greatest_lower_bound(least_upper_bound(X2,X4),greatest_lower_bound(X4,least_upper_bound(X3,X4))),
inference(substitution,[status(thm)],[c340]) ).
cnf(c342,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c343,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c345,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c344]) ).
cnf(c346,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c343,c345]) ).
cnf(c347,plain,
greatest_lower_bound(least_upper_bound(X2,X4),greatest_lower_bound(X4,least_upper_bound(X3,X4))) = greatest_lower_bound(least_upper_bound(X2,X4),X4),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
greatest_lower_bound(least_upper_bound(X2,X3),X3) = greatest_lower_bound(X3,least_upper_bound(X2,X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c349,plain,
greatest_lower_bound(least_upper_bound(X2,X3),X3) = X3,
inference(transitivity,[status(thm)],[c348,c346]) ).
cnf(c350,plain,
greatest_lower_bound(least_upper_bound(X2,X4),greatest_lower_bound(X4,least_upper_bound(X3,X4))) = X4,
inference(transitivity,[status(thm)],[c347,c349]) ).
cnf(c351,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4))) = X4,
inference(transitivity,[status(thm)],[c341,c350]) ).
cnf(c352,plain,
X4 = greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4))),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)),X4) = least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)),greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c355,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c354]) ).
cnf(c356,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c358,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c357]) ).
cnf(c359,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c356,c358]) ).
cnf(c360,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)),greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)))) = greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)),
inference(substitution,[status(thm)],[c359]) ).
cnf(c361,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)),X4) = greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)),
inference(transitivity,[status(thm)],[c353,c360]) ).
cnf(c362,plain,
least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4))) = greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X2,X4)),
inference(transitivity,[status(thm)],[c328,c361]) ).
cnf(c363,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity))) = greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c362]) ).
cnf(c364,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity))),X4) = multiply(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),X4),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
least_upper_bound(X4,multiply(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),X4)) = multiply(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),X4),
inference(transitivity,[status(thm)],[c326,c364]) ).
cnf(c366,plain,
least_upper_bound(least_upper_bound(X4,X5),multiply(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),least_upper_bound(X4,X5))) = multiply(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),least_upper_bound(X4,X5)),
inference(substitution,[status(thm)],[c365]) ).
cnf(c367,plain,
multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)) = least_upper_bound(least_upper_bound(X5,X2),multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2))),
inference(symmetry,[status(thm)],[c366]) ).
cnf(c368,plain,
least_upper_bound(X5,multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2))) = least_upper_bound(X5,least_upper_bound(least_upper_bound(X5,X2),multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)))),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
least_upper_bound(X2,least_upper_bound(X4,X3)) = least_upper_bound(least_upper_bound(X4,X3),X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c370,plain,
least_upper_bound(least_upper_bound(X4,X3),X2) = least_upper_bound(X2,least_upper_bound(X4,X3)),
inference(symmetry,[status(thm)],[c369]) ).
cnf(c371,plain,
least_upper_bound(X4,least_upper_bound(least_upper_bound(X4,X3),X2)) = least_upper_bound(X4,least_upper_bound(X2,least_upper_bound(X4,X3))),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c373,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c372]) ).
cnf(c374,plain,
least_upper_bound(X4,least_upper_bound(X3,least_upper_bound(X4,X2))) = least_upper_bound(X4,least_upper_bound(least_upper_bound(X4,X2),X3)),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,axiom,
least_upper_bound(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(least_upper_bound(X2,Y2),Z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
cnf(c376,plain,
least_upper_bound(X4,least_upper_bound(least_upper_bound(X4,X2),X3)) = least_upper_bound(least_upper_bound(X4,least_upper_bound(X4,X2)),X3),
inference(substitution,[status(thm)],[c375]) ).
cnf(c377,plain,
least_upper_bound(least_upper_bound(X3,X2),X3) = least_upper_bound(X3,least_upper_bound(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c378,plain,
least_upper_bound(X3,least_upper_bound(X3,X2)) = least_upper_bound(least_upper_bound(X3,X2),X3),
inference(symmetry,[status(thm)],[c377]) ).
cnf(c379,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c344]) ).
cnf(c380,plain,
X3 = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c379]) ).
cnf(c381,plain,
least_upper_bound(least_upper_bound(X3,X2),X3) = least_upper_bound(least_upper_bound(X3,X2),greatest_lower_bound(X3,least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
least_upper_bound(least_upper_bound(X3,X2),greatest_lower_bound(X3,least_upper_bound(X3,X2))) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c359]) ).
cnf(c383,plain,
least_upper_bound(least_upper_bound(X3,X2),X3) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c381,c382]) ).
cnf(c384,plain,
least_upper_bound(X3,least_upper_bound(X3,X2)) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c378,c383]) ).
cnf(c385,plain,
least_upper_bound(least_upper_bound(X4,least_upper_bound(X4,X2)),X3) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c387,plain,
least_upper_bound(least_upper_bound(X4,least_upper_bound(X4,X2)),X3) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(transitivity,[status(thm)],[c385,c386]) ).
cnf(c388,plain,
least_upper_bound(X4,least_upper_bound(least_upper_bound(X4,X2),X3)) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(transitivity,[status(thm)],[c376,c387]) ).
cnf(c389,plain,
least_upper_bound(X4,least_upper_bound(X3,least_upper_bound(X4,X2))) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(transitivity,[status(thm)],[c374,c388]) ).
cnf(c390,plain,
least_upper_bound(X4,least_upper_bound(X2,least_upper_bound(X4,X3))) = least_upper_bound(X2,least_upper_bound(X4,X3)),
inference(substitution,[status(thm)],[c389]) ).
cnf(c391,plain,
least_upper_bound(X4,least_upper_bound(least_upper_bound(X4,X3),X2)) = least_upper_bound(X2,least_upper_bound(X4,X3)),
inference(transitivity,[status(thm)],[c371,c390]) ).
cnf(c392,plain,
least_upper_bound(X5,least_upper_bound(least_upper_bound(X5,X2),multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)))) = least_upper_bound(multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)),least_upper_bound(X5,X2)),
inference(substitution,[status(thm)],[c391]) ).
cnf(c393,plain,
least_upper_bound(multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)),least_upper_bound(X5,X2)) = least_upper_bound(least_upper_bound(X5,X2),multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c394,plain,
least_upper_bound(least_upper_bound(X5,X2),multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2))) = multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)),
inference(substitution,[status(thm)],[c365]) ).
cnf(c395,plain,
least_upper_bound(multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)),least_upper_bound(X5,X2)) = multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)),
inference(transitivity,[status(thm)],[c393,c394]) ).
cnf(c396,plain,
least_upper_bound(X5,least_upper_bound(least_upper_bound(X5,X2),multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)))) = multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)),
inference(transitivity,[status(thm)],[c392,c395]) ).
cnf(c397,plain,
least_upper_bound(X5,multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2))) = multiply(greatest_lower_bound(least_upper_bound(X4,identity),least_upper_bound(X3,identity)),least_upper_bound(X5,X2)),
inference(transitivity,[status(thm)],[c368,c396]) ).
cnf(c398,plain,
least_upper_bound(X2,multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c397]) ).
cnf(c399,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)) = least_upper_bound(X2,multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c398]) ).
cnf(c400,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c401,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(identity,X2)),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c403,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(symmetry,[status(thm)],[c402]) ).
cnf(c404,plain,
multiply(X3,least_upper_bound(identity,X2)) = multiply(X3,least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c16]) ).
cnf(c406,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c405]) ).
cnf(c407,plain,
multiply(X3,least_upper_bound(X2,identity)) = multiply(X3,least_upper_bound(identity,X2)),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
multiply(X3,least_upper_bound(identity,X2)) = least_upper_bound(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c409,plain,
least_upper_bound(multiply(X3,identity),multiply(X3,X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c410,plain,
multiply(X3,least_upper_bound(identity,X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c408,c409]) ).
cnf(c411,plain,
multiply(X3,least_upper_bound(X2,identity)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c407,c410]) ).
cnf(c412,plain,
multiply(X3,least_upper_bound(identity,X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c404,c411]) ).
cnf(c413,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(identity,X2)) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2)),
inference(substitution,[status(thm)],[c412]) ).
cnf(c414,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2)) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c313]) ).
cnf(c415,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c416,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(symmetry,[status(thm)],[c415]) ).
cnf(c417,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c414,c416]) ).
cnf(c418,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(identity,X2)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c413,c417]) ).
cnf(c419,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c401,c418]) ).
cnf(c420,plain,
least_upper_bound(X2,multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))) = least_upper_bound(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c422,plain,
least_upper_bound(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = least_upper_bound(X2,least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))))),
inference(congruence,[status(thm)],[c421]) ).
cnf(c423,plain,
least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c424,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),X2) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4))),
inference(symmetry,[status(thm)],[c423]) ).
cnf(c425,plain,
least_upper_bound(X5,least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),X2)) = least_upper_bound(X5,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)))),
inference(congruence,[status(thm)],[c424]) ).
cnf(c426,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3)),X4) = least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c427,plain,
least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3)),X4),
inference(symmetry,[status(thm)],[c426]) ).
cnf(c428,plain,
least_upper_bound(X5,least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3)))) = least_upper_bound(X5,least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3)),X4)),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
least_upper_bound(X5,least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3)),X4)) = least_upper_bound(least_upper_bound(X5,greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3))),X4),
inference(substitution,[status(thm)],[c375]) ).
cnf(c430,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5)),X4) = least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c431,plain,
least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5)),X4),
inference(symmetry,[status(thm)],[c430]) ).
cnf(c432,plain,
least_upper_bound(X5,least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5)))) = least_upper_bound(X5,least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5)),X4)),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
least_upper_bound(X5,least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5)),X4)) = least_upper_bound(least_upper_bound(X5,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5))),X4),
inference(substitution,[status(thm)],[c375]) ).
cnf(c434,plain,
least_upper_bound(least_upper_bound(X5,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5))),X4) = least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5)),X4),
inference(congruence,[status(thm)],[c362]) ).
cnf(c435,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5)),X4) = least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c436,plain,
least_upper_bound(least_upper_bound(X5,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5))),X4) = least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5))),
inference(transitivity,[status(thm)],[c434,c435]) ).
cnf(c437,plain,
least_upper_bound(X5,least_upper_bound(greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5)),X4)) = least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5))),
inference(transitivity,[status(thm)],[c433,c436]) ).
cnf(c438,plain,
least_upper_bound(X5,least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5)))) = least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X3,X5),least_upper_bound(X2,X5))),
inference(transitivity,[status(thm)],[c432,c437]) ).
cnf(c439,plain,
least_upper_bound(X3,least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)))) = least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))),
inference(substitution,[status(thm)],[c438]) ).
cnf(c440,plain,
least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))) = least_upper_bound(X3,least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)))),
inference(symmetry,[status(thm)],[c439]) ).
cnf(c441,plain,
least_upper_bound(least_upper_bound(X2,X4),X3) = least_upper_bound(X3,least_upper_bound(X2,X4)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c442,plain,
least_upper_bound(X3,least_upper_bound(X2,X4)) = least_upper_bound(least_upper_bound(X2,X4),X3),
inference(symmetry,[status(thm)],[c441]) ).
cnf(c443,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c444,plain,
least_upper_bound(least_upper_bound(X2,X4),X3) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c375]) ).
cnf(c446,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c445]) ).
cnf(c447,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c448,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c447]) ).
cnf(c449,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c446,c448]) ).
cnf(c450,plain,
least_upper_bound(least_upper_bound(X2,X4),X3) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c444,c449]) ).
cnf(c451,plain,
least_upper_bound(X3,least_upper_bound(X2,X4)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c442,c450]) ).
cnf(c452,plain,
least_upper_bound(X2,least_upper_bound(X3,X4)) = least_upper_bound(X4,least_upper_bound(X2,X3)),
inference(substitution,[status(thm)],[c451]) ).
cnf(c453,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c454,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
least_upper_bound(X2,least_upper_bound(X3,X4)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c452,c454]) ).
cnf(c456,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),least_upper_bound(X4,X3)) = least_upper_bound(X3,least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)))),
inference(substitution,[status(thm)],[c455]) ).
cnf(c457,plain,
least_upper_bound(X3,least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),least_upper_bound(X4,X3)),
inference(symmetry,[status(thm)],[c456]) ).
cnf(c458,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(X3,X2),X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c459,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c458]) ).
cnf(c460,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c461,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = least_upper_bound(X3,greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c460]) ).
cnf(c462,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c461,c359]) ).
cnf(c463,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c459,c462]) ).
cnf(c464,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),least_upper_bound(X4,X3)) = least_upper_bound(X4,X3),
inference(substitution,[status(thm)],[c463]) ).
cnf(c465,plain,
least_upper_bound(X3,least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)))) = least_upper_bound(X4,X3),
inference(transitivity,[status(thm)],[c457,c464]) ).
cnf(c466,plain,
least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))) = least_upper_bound(X4,X3),
inference(transitivity,[status(thm)],[c440,c465]) ).
cnf(c467,plain,
least_upper_bound(least_upper_bound(X5,greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3))),X4) = least_upper_bound(least_upper_bound(X5,X3),X4),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c469,plain,
least_upper_bound(least_upper_bound(X5,greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3))),X4) = least_upper_bound(X4,least_upper_bound(X5,X3)),
inference(transitivity,[status(thm)],[c467,c468]) ).
cnf(c470,plain,
least_upper_bound(X5,least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3)),X4)) = least_upper_bound(X4,least_upper_bound(X5,X3)),
inference(transitivity,[status(thm)],[c429,c469]) ).
cnf(c471,plain,
least_upper_bound(X5,least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X5,X3),least_upper_bound(X2,X3)))) = least_upper_bound(X4,least_upper_bound(X5,X3)),
inference(transitivity,[status(thm)],[c428,c470]) ).
cnf(c472,plain,
least_upper_bound(X5,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)))) = least_upper_bound(X2,least_upper_bound(X5,X4)),
inference(substitution,[status(thm)],[c471]) ).
cnf(c473,plain,
least_upper_bound(X5,least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),X2)) = least_upper_bound(X2,least_upper_bound(X5,X4)),
inference(transitivity,[status(thm)],[c425,c472]) ).
cnf(c474,plain,
least_upper_bound(X2,least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))))) = least_upper_bound(multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c473]) ).
cnf(c475,plain,
least_upper_bound(multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(X2,identity)) = least_upper_bound(least_upper_bound(X2,identity),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c476,plain,
multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c477,plain,
least_upper_bound(least_upper_bound(X2,identity),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = least_upper_bound(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2)),
inference(congruence,[status(thm)],[c476]) ).
cnf(c478,plain,
least_upper_bound(least_upper_bound(inverse(X2),identity),X3) = least_upper_bound(X3,least_upper_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c479,plain,
least_upper_bound(X3,least_upper_bound(inverse(X2),identity)) = least_upper_bound(least_upper_bound(inverse(X2),identity),X3),
inference(symmetry,[status(thm)],[c478]) ).
cnf(c480,plain,
multiply(least_upper_bound(X3,least_upper_bound(inverse(X2),identity)),X2) = multiply(least_upper_bound(least_upper_bound(inverse(X2),identity),X3),X2),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X2),identity),X3),X2) = least_upper_bound(multiply(least_upper_bound(inverse(X2),identity),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c482,plain,
least_upper_bound(multiply(least_upper_bound(inverse(X2),identity),X2),multiply(X3,X2)) = least_upper_bound(least_upper_bound(X2,identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c483,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X2),identity),X3),X2) = least_upper_bound(least_upper_bound(X2,identity),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c481,c482]) ).
cnf(c484,plain,
multiply(least_upper_bound(X3,least_upper_bound(inverse(X2),identity)),X2) = least_upper_bound(least_upper_bound(X2,identity),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c480,c483]) ).
cnf(c485,plain,
multiply(least_upper_bound(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),least_upper_bound(inverse(X3),identity)),X3) = least_upper_bound(least_upper_bound(X3,identity),multiply(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),X3)),
inference(substitution,[status(thm)],[c484]) ).
cnf(c486,plain,
least_upper_bound(least_upper_bound(X3,identity),multiply(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),X3)) = multiply(least_upper_bound(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),least_upper_bound(inverse(X3),identity)),X3),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(X3,X2),X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c488,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X2) = least_upper_bound(X2,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c487]) ).
cnf(c489,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c490,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c489]) ).
cnf(c491,plain,
least_upper_bound(X2,greatest_lower_bound(X2,X3)) = X2,
inference(substitution,[status(thm)],[c357]) ).
cnf(c492,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c490,c491]) ).
cnf(c493,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c488,c492]) ).
cnf(c494,plain,
least_upper_bound(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),least_upper_bound(inverse(X3),identity)) = least_upper_bound(inverse(X3),identity),
inference(substitution,[status(thm)],[c493]) ).
cnf(c495,plain,
multiply(least_upper_bound(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),least_upper_bound(inverse(X3),identity)),X3) = multiply(least_upper_bound(inverse(X3),identity),X3),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
multiply(least_upper_bound(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),least_upper_bound(inverse(X3),identity)),X3) = least_upper_bound(X3,identity),
inference(transitivity,[status(thm)],[c495,c35]) ).
cnf(c497,plain,
least_upper_bound(least_upper_bound(X3,identity),multiply(greatest_lower_bound(X2,least_upper_bound(inverse(X3),identity)),X3)) = least_upper_bound(X3,identity),
inference(transitivity,[status(thm)],[c486,c496]) ).
cnf(c498,plain,
least_upper_bound(least_upper_bound(X2,identity),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),X2)) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c497]) ).
cnf(c499,plain,
least_upper_bound(least_upper_bound(X2,identity),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c477,c498]) ).
cnf(c500,plain,
least_upper_bound(multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(X2,identity)) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c475,c499]) ).
cnf(c501,plain,
least_upper_bound(X2,least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))))) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c474,c500]) ).
cnf(c502,plain,
least_upper_bound(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c422,c501]) ).
cnf(c503,plain,
least_upper_bound(X2,multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c420,c502]) ).
cnf(c504,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c399,c503]) ).
cnf(c505,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
least_upper_bound(X2,identity) = multiply(least_upper_bound(inverse(X2),identity),X2),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c507,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)) = multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(least_upper_bound(inverse(X2),identity),X2)),
inference(congruence,[status(thm)],[c506]) ).
cnf(c508,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(least_upper_bound(inverse(X2),identity),X2)) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c509,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)) = X2,
inference(transitivity,[status(thm)],[c507,c508]) ).
cnf(c510,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))) = X2,
inference(transitivity,[status(thm)],[c505,c509]) ).
cnf(c511,plain,
multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = X2,
inference(transitivity,[status(thm)],[c324,c510]) ).
cnf(c512,plain,
multiply(inverse(X2),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(inverse(X2),X2),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
multiply(inverse(X2),multiply(X2,greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = identity,
inference(transitivity,[status(thm)],[c512,c5]) ).
cnf(c514,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = identity,
inference(transitivity,[status(thm)],[c11,c513]) ).
cnf(c515,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = identity,
inference(substitution,[status(thm)],[c514]) ).
cnf(c516,plain,
$false,
inference(resolution,[status(thm)],[c1,c515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP183-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:36:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.71/2.07 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 11.71/2.07
% 11.71/2.07 % SZS status Unsatisfiable
% 11.71/2.07
% 13.10/2.16 % SZS output start CNFRefutation
% See solution above
% 16.91/2.63
% 16.91/2.63 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------