%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP181-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:35 AM UTC 2026
% Result : Unsatisfiable 192.33s 24.68s
% Output : CNFRefutation 195.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 20
% Syntax : Number of clauses : 608 ( 608 unt; 0 nHn; 43 RR)
% Number of literals : 608 ( 607 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 1015 ( 39 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p12) ).
cnf(c2,axiom,
inverse(inverse(X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(inverse(X2),identity) = multiply(inverse(X2),inverse(identity)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,hypothesis,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_3) ).
cnf(c9,plain,
inverse(multiply(identity,X2)) = multiply(inverse(X2),inverse(identity)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(inverse(X2),inverse(identity)) = inverse(multiply(identity,X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
inverse(multiply(identity,X2)) = inverse(X2),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(inverse(X2),inverse(identity)) = inverse(X2),
inference(transitivity,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(transitivity,[status(thm)],[c7,c13]) ).
cnf(c15,plain,
multiply(inverse(inverse(X2)),identity) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c15,c2]) ).
cnf(c17,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c4,c16]) ).
cnf(c18,plain,
multiply(b,identity) = b,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
b = multiply(b,identity),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c21,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(c23,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
multiply(greatest_lower_bound(inverse(c),inverse(a)),inverse(greatest_lower_bound(inverse(c),inverse(a)))) = identity,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
identity = multiply(greatest_lower_bound(inverse(c),inverse(a)),inverse(greatest_lower_bound(inverse(c),inverse(a)))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(b,identity) = multiply(b,multiply(greatest_lower_bound(inverse(c),inverse(a)),inverse(greatest_lower_bound(inverse(c),inverse(a))))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c29,plain,
least_upper_bound(X3,X2) = least_upper_bound(X3,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
inverse(least_upper_bound(X3,X2)) = inverse(least_upper_bound(X3,inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
inverse(X2) = multiply(inverse(X2),identity),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c32,plain,
greatest_lower_bound(X3,inverse(X2)) = greatest_lower_bound(X3,multiply(inverse(X2),identity)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
inverse(greatest_lower_bound(X3,inverse(X2))) = inverse(greatest_lower_bound(X3,multiply(inverse(X2),identity))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c35,plain,
greatest_lower_bound(X4,multiply(X3,X2)) = greatest_lower_bound(multiply(X3,X2),X4),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
greatest_lower_bound(multiply(X4,X3),X2) = greatest_lower_bound(X2,multiply(X4,X3)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(greatest_lower_bound(multiply(X4,X3),X2)) = inverse(greatest_lower_bound(X2,multiply(X4,X3))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(inverse(greatest_lower_bound(multiply(X4,X3),X2)),X4) = multiply(inverse(greatest_lower_bound(X2,multiply(X4,X3))),X4),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c40,plain,
multiply(inverse(greatest_lower_bound(X4,multiply(X3,X2))),X3) = multiply(inverse(greatest_lower_bound(X4,multiply(X3,X2))),inverse(inverse(X3))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
inverse(multiply(inverse(X3),greatest_lower_bound(X4,multiply(X3,X2)))) = multiply(inverse(greatest_lower_bound(X4,multiply(X3,X2))),inverse(inverse(X3))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c42,plain,
multiply(inverse(greatest_lower_bound(X4,multiply(X3,X2))),inverse(inverse(X3))) = inverse(multiply(inverse(X3),greatest_lower_bound(X4,multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
greatest_lower_bound(multiply(X4,X2),X3) = greatest_lower_bound(X3,multiply(X4,X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c44,plain,
greatest_lower_bound(X3,multiply(X4,X2)) = greatest_lower_bound(multiply(X4,X2),X3),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(X4),greatest_lower_bound(X3,multiply(X4,X2))) = multiply(inverse(X4),greatest_lower_bound(multiply(X4,X2),X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
multiply(X2,greatest_lower_bound(Y2,Z)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c47,plain,
multiply(inverse(X4),greatest_lower_bound(multiply(X4,X2),X3)) = greatest_lower_bound(multiply(inverse(X4),multiply(X4,X2)),multiply(inverse(X4),X3)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c49,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c52,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c51,c11]) ).
cnf(c53,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
greatest_lower_bound(multiply(inverse(X4),multiply(X4,X2)),multiply(inverse(X4),X3)) = greatest_lower_bound(X2,multiply(inverse(X4),X3)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(inverse(X4),greatest_lower_bound(multiply(X4,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c47,c54]) ).
cnf(c56,plain,
multiply(inverse(X4),greatest_lower_bound(X3,multiply(X4,X2))) = greatest_lower_bound(X2,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c45,c55]) ).
cnf(c57,plain,
multiply(inverse(X3),greatest_lower_bound(X4,multiply(X3,X2))) = greatest_lower_bound(X2,multiply(inverse(X3),X4)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
inverse(multiply(inverse(X3),greatest_lower_bound(X4,multiply(X3,X2)))) = inverse(greatest_lower_bound(X2,multiply(inverse(X3),X4))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(inverse(greatest_lower_bound(X4,multiply(X3,X2))),inverse(inverse(X3))) = inverse(greatest_lower_bound(X2,multiply(inverse(X3),X4))),
inference(transitivity,[status(thm)],[c42,c58]) ).
cnf(c60,plain,
multiply(inverse(greatest_lower_bound(X4,multiply(X3,X2))),X3) = inverse(greatest_lower_bound(X2,multiply(inverse(X3),X4))),
inference(transitivity,[status(thm)],[c40,c59]) ).
cnf(c61,plain,
multiply(inverse(greatest_lower_bound(X2,multiply(X4,X3))),X4) = inverse(greatest_lower_bound(X3,multiply(inverse(X4),X2))),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(inverse(greatest_lower_bound(multiply(X4,X3),X2)),X4) = inverse(greatest_lower_bound(X3,multiply(inverse(X4),X2))),
inference(transitivity,[status(thm)],[c38,c61]) ).
cnf(c63,plain,
multiply(inverse(greatest_lower_bound(multiply(X2,X3),identity)),X2) = inverse(greatest_lower_bound(X3,multiply(inverse(X2),identity))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
inverse(greatest_lower_bound(X3,multiply(inverse(X2),identity))) = multiply(inverse(greatest_lower_bound(multiply(X2,X3),identity)),X2),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),identity) = inverse(greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c66,plain,
inverse(greatest_lower_bound(X2,identity)) = multiply(inverse(greatest_lower_bound(X2,identity)),identity),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c68,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c34]) ).
cnf(c72,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(identity,X2)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
least_upper_bound(inverse(X2),identity) = least_upper_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c75,plain,
least_upper_bound(identity,inverse(X2)) = least_upper_bound(inverse(X2),identity),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(identity,X2)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c78,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(identity,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
least_upper_bound(inverse(X2),identity) = least_upper_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c81,plain,
least_upper_bound(identity,inverse(X2)) = least_upper_bound(inverse(X2),identity),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
least_upper_bound(inverse(X2),identity) = least_upper_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c84,plain,
least_upper_bound(identity,inverse(X2)) = least_upper_bound(inverse(X2),identity),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(least_upper_bound(identity,inverse(X3)),multiply(X3,X2)) = multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c87,plain,
least_upper_bound(X3,multiply(X2,X3)) = least_upper_bound(multiply(identity,X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c89,plain,
multiply(least_upper_bound(identity,X2),X3) = least_upper_bound(multiply(identity,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
least_upper_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(least_upper_bound(identity,X2),X3),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c67]) ).
cnf(c92,plain,
multiply(least_upper_bound(identity,X2),X3) = multiply(least_upper_bound(X2,identity),X3),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
least_upper_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(least_upper_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c90,c92]) ).
cnf(c94,plain,
least_upper_bound(X3,multiply(X2,X3)) = multiply(least_upper_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c87,c93]) ).
cnf(c95,plain,
least_upper_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))) = multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2)) = least_upper_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
least_upper_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))) = least_upper_bound(multiply(X3,X2),X2),
inference(congruence,[status(thm)],[c53]) ).
cnf(c98,plain,
least_upper_bound(multiply(X3,X2),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c99,plain,
least_upper_bound(X2,multiply(X3,X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(substitution,[status(thm)],[c94]) ).
cnf(c100,plain,
least_upper_bound(multiply(X3,X2),X2) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
least_upper_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c97,c100]) ).
cnf(c102,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c96,c101]) ).
cnf(c103,plain,
multiply(least_upper_bound(identity,inverse(X3)),multiply(X3,X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c85,c102]) ).
cnf(c104,plain,
multiply(least_upper_bound(identity,inverse(inverse(X2))),multiply(inverse(X2),greatest_lower_bound(X2,identity))) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(identity,inverse(inverse(X2))),multiply(inverse(X2),greatest_lower_bound(X2,identity))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c107,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c109,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c107,c109]) ).
cnf(c111,plain,
greatest_lower_bound(identity,multiply(inverse(X2),identity)) = multiply(inverse(X2),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
multiply(inverse(X2),greatest_lower_bound(X2,identity)) = greatest_lower_bound(identity,multiply(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
greatest_lower_bound(identity,multiply(inverse(X2),identity)) = greatest_lower_bound(identity,inverse(X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c114,plain,
multiply(inverse(X2),greatest_lower_bound(X2,identity)) = greatest_lower_bound(identity,inverse(X2)),
inference(transitivity,[status(thm)],[c112,c113]) ).
cnf(c115,plain,
multiply(least_upper_bound(identity,inverse(inverse(X2))),multiply(inverse(X2),greatest_lower_bound(X2,identity))) = multiply(least_upper_bound(identity,inverse(inverse(X2))),greatest_lower_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
least_upper_bound(identity,inverse(inverse(X2))) = least_upper_bound(identity,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c117,plain,
multiply(least_upper_bound(identity,inverse(inverse(X2))),greatest_lower_bound(identity,inverse(X2))) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c67]) ).
cnf(c119,plain,
multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(least_upper_bound(identity,inverse(inverse(X2))),greatest_lower_bound(identity,inverse(X2))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c117,c119]) ).
cnf(c121,plain,
multiply(least_upper_bound(identity,inverse(inverse(X2))),multiply(inverse(X2),greatest_lower_bound(X2,identity))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c115,c120]) ).
cnf(c122,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c105,c121]) ).
cnf(c123,plain,
multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c82,c122]) ).
cnf(c124,plain,
multiply(least_upper_bound(identity,inverse(inverse(X2))),greatest_lower_bound(inverse(X2),identity)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,inverse(inverse(X2)))),
inference(substitution,[status(thm)],[c123]) ).
cnf(c125,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,inverse(inverse(X2)))) = multiply(least_upper_bound(identity,inverse(inverse(X2))),greatest_lower_bound(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
least_upper_bound(identity,inverse(inverse(X2))) = least_upper_bound(identity,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c127,plain,
multiply(least_upper_bound(identity,inverse(inverse(X2))),greatest_lower_bound(inverse(X2),identity)) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(inverse(X2),identity)),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
greatest_lower_bound(inverse(X2),identity) = greatest_lower_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c129,plain,
multiply(least_upper_bound(identity,X2),greatest_lower_bound(inverse(X2),identity)) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(least_upper_bound(identity,inverse(inverse(X2))),greatest_lower_bound(inverse(X2),identity)) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c127,c129]) ).
cnf(c131,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,inverse(inverse(X2)))) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c125,c130]) ).
cnf(c132,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(identity,X2)) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c79,c131]) ).
cnf(c133,plain,
multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(identity,X2)) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c76,c132]) ).
cnf(c134,plain,
multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c73,c133]) ).
cnf(c135,plain,
multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))) = multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
greatest_lower_bound(identity,inverse(X2)) = multiply(inverse(X2),greatest_lower_bound(X2,identity)),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c137,plain,
least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = least_upper_bound(greatest_lower_bound(X2,identity),multiply(inverse(X2),greatest_lower_bound(X2,identity))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
least_upper_bound(greatest_lower_bound(X2,identity),multiply(inverse(X2),greatest_lower_bound(X2,identity))) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c94]) ).
cnf(c139,plain,
least_upper_bound(inverse(X2),identity) = least_upper_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c140,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
least_upper_bound(greatest_lower_bound(X2,identity),multiply(inverse(X2),greatest_lower_bound(X2,identity))) = multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c138,c140]) ).
cnf(c142,plain,
least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c137,c141]) ).
cnf(c143,plain,
multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)) = least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)) = least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c145,plain,
least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,axiom,
greatest_lower_bound(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_gld) ).
cnf(c147,plain,
greatest_lower_bound(identity,identity) = identity,
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
identity = greatest_lower_bound(identity,identity),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(X2,greatest_lower_bound(identity,identity)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(X2,greatest_lower_bound(identity,identity))),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c152,plain,
greatest_lower_bound(identity,identity) = greatest_lower_bound(identity,inverse(identity)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
greatest_lower_bound(X2,greatest_lower_bound(identity,identity)) = greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(X2,greatest_lower_bound(identity,identity))) = least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity)))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(identity,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity)))) = greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity))),
inference(substitution,[status(thm)],[c11]) ).
cnf(c156,plain,
greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity))) = multiply(identity,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity)))),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity)))) = least_upper_bound(greatest_lower_bound(identity,inverse(X2)),multiply(identity,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity))))),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c159,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,axiom,
multiply(greatest_lower_bound(Y2,Z2),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c161,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c160]) ).
cnf(c162,plain,
greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(greatest_lower_bound(inverse(X2),X3),X2),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
greatest_lower_bound(inverse(X2),X3) = greatest_lower_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c164,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c162,c164]) ).
cnf(c166,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c159,c165]) ).
cnf(c167,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
identity = multiply(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c169,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = greatest_lower_bound(multiply(X3,inverse(X3)),multiply(X3,X2)),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(X3,greatest_lower_bound(inverse(X3),X2)) = greatest_lower_bound(multiply(X3,inverse(X3)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c171,plain,
greatest_lower_bound(multiply(X3,inverse(X3)),multiply(X3,X2)) = multiply(X3,greatest_lower_bound(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
greatest_lower_bound(inverse(X3),X2) = greatest_lower_bound(X2,inverse(X3)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c173,plain,
multiply(X3,greatest_lower_bound(inverse(X3),X2)) = multiply(X3,greatest_lower_bound(X2,inverse(X3))),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
greatest_lower_bound(multiply(X3,inverse(X3)),multiply(X3,X2)) = multiply(X3,greatest_lower_bound(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c171,c173]) ).
cnf(c175,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = multiply(X3,greatest_lower_bound(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c169,c174]) ).
cnf(c176,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),X2) = multiply(X3,greatest_lower_bound(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c167,c175]) ).
cnf(c177,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,inverse(X2)),X2)) = greatest_lower_bound(X3,multiply(X3,greatest_lower_bound(X2,inverse(X3)))),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c179,plain,
greatest_lower_bound(X3,multiply(X3,X2)) = greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c181,plain,
greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,greatest_lower_bound(identity,X2)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c34]) ).
cnf(c183,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c181,c183]) ).
cnf(c185,plain,
greatest_lower_bound(X3,multiply(X3,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c179,c184]) ).
cnf(c186,plain,
greatest_lower_bound(X3,multiply(X3,greatest_lower_bound(X2,inverse(X3)))) = multiply(X3,greatest_lower_bound(greatest_lower_bound(X2,inverse(X3)),identity)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c188,plain,
greatest_lower_bound(X2,greatest_lower_bound(inverse(X3),identity)) = greatest_lower_bound(greatest_lower_bound(X2,inverse(X3)),identity),
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
greatest_lower_bound(greatest_lower_bound(X2,inverse(X3)),identity) = greatest_lower_bound(X2,greatest_lower_bound(inverse(X3),identity)),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
multiply(X3,greatest_lower_bound(greatest_lower_bound(X2,inverse(X3)),identity)) = multiply(X3,greatest_lower_bound(X2,greatest_lower_bound(inverse(X3),identity))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
greatest_lower_bound(inverse(X2),identity) = greatest_lower_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c192,plain,
greatest_lower_bound(X2,greatest_lower_bound(inverse(X3),identity)) = greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(X3))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(X3,greatest_lower_bound(X2,greatest_lower_bound(inverse(X3),identity))) = multiply(X3,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(X3)))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
multiply(X3,greatest_lower_bound(greatest_lower_bound(X2,inverse(X3)),identity)) = multiply(X3,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(X3)))),
inference(transitivity,[status(thm)],[c190,c193]) ).
cnf(c195,plain,
greatest_lower_bound(X3,multiply(X3,greatest_lower_bound(X2,inverse(X3)))) = multiply(X3,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(X3)))),
inference(transitivity,[status(thm)],[c186,c194]) ).
cnf(c196,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,inverse(X2)),X2)) = multiply(X3,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(X3)))),
inference(transitivity,[status(thm)],[c177,c195]) ).
cnf(c197,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X2)),X2)) = multiply(identity,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity)))),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
multiply(identity,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X2)),X2)),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),multiply(identity,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity))))) = least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X2)),X2))),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
least_upper_bound(X3,greatest_lower_bound(identity,multiply(X3,X2))) = least_upper_bound(X3,multiply(X3,greatest_lower_bound(X2,inverse(X3)))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c201,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c202,plain,
least_upper_bound(X3,multiply(X3,X2)) = least_upper_bound(multiply(X3,identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c204,plain,
multiply(X3,least_upper_bound(identity,X2)) = least_upper_bound(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c203]) ).
cnf(c205,plain,
least_upper_bound(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,least_upper_bound(identity,X2)),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c67]) ).
cnf(c207,plain,
multiply(X3,least_upper_bound(identity,X2)) = multiply(X3,least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
least_upper_bound(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c205,c207]) ).
cnf(c209,plain,
least_upper_bound(X3,multiply(X3,X2)) = multiply(X3,least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c202,c208]) ).
cnf(c210,plain,
least_upper_bound(X3,multiply(X3,greatest_lower_bound(X2,inverse(X3)))) = multiply(X3,least_upper_bound(greatest_lower_bound(X2,inverse(X3)),identity)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
least_upper_bound(greatest_lower_bound(X2,inverse(X3)),identity) = least_upper_bound(identity,greatest_lower_bound(X2,inverse(X3))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c212,plain,
multiply(X3,least_upper_bound(greatest_lower_bound(X2,inverse(X3)),identity)) = multiply(X3,least_upper_bound(identity,greatest_lower_bound(X2,inverse(X3)))),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
least_upper_bound(X3,multiply(X3,greatest_lower_bound(X2,inverse(X3)))) = multiply(X3,least_upper_bound(identity,greatest_lower_bound(X2,inverse(X3)))),
inference(transitivity,[status(thm)],[c210,c212]) ).
cnf(c214,plain,
least_upper_bound(X3,greatest_lower_bound(identity,multiply(X3,X2))) = multiply(X3,least_upper_bound(identity,greatest_lower_bound(X2,inverse(X3)))),
inference(transitivity,[status(thm)],[c200,c213]) ).
cnf(c215,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X2)),X2))) = multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(identity,greatest_lower_bound(X2,inverse(greatest_lower_bound(identity,inverse(X2)))))),
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
greatest_lower_bound(inverse(X3),X2) = greatest_lower_bound(X2,inverse(X3)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c217,plain,
greatest_lower_bound(X2,inverse(X3)) = greatest_lower_bound(inverse(X3),X2),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
inverse(greatest_lower_bound(X2,inverse(X3))) = inverse(greatest_lower_bound(inverse(X3),X2)),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
greatest_lower_bound(X3,inverse(greatest_lower_bound(X2,inverse(X3)))) = greatest_lower_bound(X3,inverse(greatest_lower_bound(inverse(X3),X2))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c221,plain,
greatest_lower_bound(X3,inverse(greatest_lower_bound(inverse(X3),X2))) = greatest_lower_bound(inverse(inverse(X3)),inverse(greatest_lower_bound(inverse(X3),X2))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X3,X2)),inverse(X3)) = greatest_lower_bound(inverse(X3),inverse(greatest_lower_bound(X3,X2))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c223,plain,
greatest_lower_bound(inverse(X3),inverse(greatest_lower_bound(X3,X2))) = greatest_lower_bound(inverse(greatest_lower_bound(X3,X2)),inverse(X3)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c225,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c224]) ).
cnf(c226,plain,
X3 = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c225]) ).
cnf(c227,plain,
inverse(X3) = inverse(least_upper_bound(X3,greatest_lower_bound(X3,X2))),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X3,X2)),inverse(X3)) = greatest_lower_bound(inverse(greatest_lower_bound(X3,X2)),inverse(least_upper_bound(X3,greatest_lower_bound(X3,X2)))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c230,plain,
least_upper_bound(X2,X3) = least_upper_bound(X2,inverse(inverse(X3))),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
inverse(least_upper_bound(X2,X3)) = inverse(least_upper_bound(X2,inverse(inverse(X3)))),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X2,X3))) = greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X2,inverse(inverse(X3))))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
multiply(inverse(least_upper_bound(X2,inverse(X3))),identity) = inverse(least_upper_bound(X2,inverse(X3))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c234,plain,
inverse(least_upper_bound(X2,inverse(X3))) = multiply(inverse(least_upper_bound(X2,inverse(X3))),identity),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
greatest_lower_bound(X3,inverse(least_upper_bound(X2,inverse(X3)))) = greatest_lower_bound(X3,multiply(inverse(least_upper_bound(X2,inverse(X3))),identity)),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
multiply(inverse(least_upper_bound(X2,inverse(X3))),greatest_lower_bound(identity,multiply(least_upper_bound(X2,inverse(X3)),X3))) = greatest_lower_bound(X3,multiply(inverse(least_upper_bound(X2,inverse(X3))),identity)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c237,plain,
greatest_lower_bound(X3,multiply(inverse(least_upper_bound(X2,inverse(X3))),identity)) = multiply(inverse(least_upper_bound(X2,inverse(X3))),greatest_lower_bound(identity,multiply(least_upper_bound(X2,inverse(X3)),X3))),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c239,plain,
least_upper_bound(identity,multiply(X3,X2)) = least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
multiply(least_upper_bound(inverse(X2),X3),X2) = least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c241,plain,
least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(least_upper_bound(inverse(X2),X3),X2),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
least_upper_bound(inverse(X2),X3) = least_upper_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c243,plain,
multiply(least_upper_bound(inverse(X2),X3),X2) = multiply(least_upper_bound(X3,inverse(X2)),X2),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(least_upper_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c241,c243]) ).
cnf(c245,plain,
least_upper_bound(identity,multiply(X3,X2)) = multiply(least_upper_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c239,c244]) ).
cnf(c246,plain,
multiply(least_upper_bound(X3,inverse(X2)),X2) = least_upper_bound(identity,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X3,inverse(X2)),X2)) = greatest_lower_bound(identity,least_upper_bound(identity,multiply(X3,X2))),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c249,plain,
greatest_lower_bound(identity,least_upper_bound(identity,multiply(X3,X2))) = identity,
inference(substitution,[status(thm)],[c248]) ).
cnf(c250,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X3,inverse(X2)),X2)) = identity,
inference(transitivity,[status(thm)],[c247,c249]) ).
cnf(c251,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X2,inverse(X3)),X3)) = identity,
inference(substitution,[status(thm)],[c250]) ).
cnf(c252,plain,
multiply(inverse(least_upper_bound(X2,inverse(X3))),greatest_lower_bound(identity,multiply(least_upper_bound(X2,inverse(X3)),X3))) = multiply(inverse(least_upper_bound(X2,inverse(X3))),identity),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
multiply(inverse(least_upper_bound(X2,inverse(X3))),identity) = inverse(least_upper_bound(X2,inverse(X3))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c254,plain,
multiply(inverse(least_upper_bound(X2,inverse(X3))),greatest_lower_bound(identity,multiply(least_upper_bound(X2,inverse(X3)),X3))) = inverse(least_upper_bound(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c252,c253]) ).
cnf(c255,plain,
greatest_lower_bound(X3,multiply(inverse(least_upper_bound(X2,inverse(X3))),identity)) = inverse(least_upper_bound(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c237,c254]) ).
cnf(c256,plain,
greatest_lower_bound(X3,inverse(least_upper_bound(X2,inverse(X3)))) = inverse(least_upper_bound(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c235,c255]) ).
cnf(c257,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X2,inverse(inverse(X3))))) = inverse(least_upper_bound(X2,inverse(inverse(X3)))),
inference(substitution,[status(thm)],[c256]) ).
cnf(c258,plain,
least_upper_bound(X2,inverse(inverse(X3))) = least_upper_bound(X2,X3),
inference(congruence,[status(thm)],[c2]) ).
cnf(c259,plain,
inverse(least_upper_bound(X2,inverse(inverse(X3)))) = inverse(least_upper_bound(X2,X3)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c67]) ).
cnf(c261,plain,
inverse(least_upper_bound(X2,X3)) = inverse(least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
inverse(least_upper_bound(X2,inverse(inverse(X3)))) = inverse(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c259,c261]) ).
cnf(c263,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X2,inverse(inverse(X3))))) = inverse(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c257,c262]) ).
cnf(c264,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X2,X3))) = inverse(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c232,c263]) ).
cnf(c265,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X3,X2)),inverse(least_upper_bound(X3,greatest_lower_bound(X3,X2)))) = inverse(least_upper_bound(greatest_lower_bound(X3,X2),X3)),
inference(substitution,[status(thm)],[c264]) ).
cnf(c266,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c267,plain,
inverse(least_upper_bound(greatest_lower_bound(X3,X2),X3)) = inverse(least_upper_bound(X3,greatest_lower_bound(X3,X2))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c224]) ).
cnf(c269,plain,
inverse(least_upper_bound(X3,greatest_lower_bound(X3,X2))) = inverse(X3),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
inverse(least_upper_bound(greatest_lower_bound(X3,X2),X3)) = inverse(X3),
inference(transitivity,[status(thm)],[c267,c269]) ).
cnf(c271,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X3,X2)),inverse(least_upper_bound(X3,greatest_lower_bound(X3,X2)))) = inverse(X3),
inference(transitivity,[status(thm)],[c265,c270]) ).
cnf(c272,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X3,X2)),inverse(X3)) = inverse(X3),
inference(transitivity,[status(thm)],[c228,c271]) ).
cnf(c273,plain,
greatest_lower_bound(inverse(X3),inverse(greatest_lower_bound(X3,X2))) = inverse(X3),
inference(transitivity,[status(thm)],[c223,c272]) ).
cnf(c274,plain,
greatest_lower_bound(inverse(inverse(X3)),inverse(greatest_lower_bound(inverse(X3),X2))) = inverse(inverse(X3)),
inference(substitution,[status(thm)],[c273]) ).
cnf(c275,plain,
greatest_lower_bound(inverse(inverse(X3)),inverse(greatest_lower_bound(inverse(X3),X2))) = X3,
inference(transitivity,[status(thm)],[c274,c2]) ).
cnf(c276,plain,
greatest_lower_bound(X3,inverse(greatest_lower_bound(inverse(X3),X2))) = X3,
inference(transitivity,[status(thm)],[c221,c275]) ).
cnf(c277,plain,
greatest_lower_bound(X3,inverse(greatest_lower_bound(X2,inverse(X3)))) = X3,
inference(transitivity,[status(thm)],[c219,c276]) ).
cnf(c278,plain,
greatest_lower_bound(X2,inverse(greatest_lower_bound(identity,inverse(X2)))) = X2,
inference(substitution,[status(thm)],[c277]) ).
cnf(c279,plain,
least_upper_bound(identity,greatest_lower_bound(X2,inverse(greatest_lower_bound(identity,inverse(X2))))) = least_upper_bound(identity,X2),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(identity,greatest_lower_bound(X2,inverse(greatest_lower_bound(identity,inverse(X2)))))) = multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(identity,X2)),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c67]) ).
cnf(c282,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(identity,X2)) = multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c67]) ).
cnf(c284,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(X2,identity)) = multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(identity,X2)),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
greatest_lower_bound(inverse(X2),identity) = greatest_lower_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c287,plain,
greatest_lower_bound(identity,inverse(X2)) = greatest_lower_bound(inverse(X2),identity),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(identity,X2)) = multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(identity,X2)),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c290,plain,
least_upper_bound(identity,X2) = least_upper_bound(identity,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(identity,X2)) = multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(identity,inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
greatest_lower_bound(inverse(X2),identity) = greatest_lower_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c293,plain,
greatest_lower_bound(identity,inverse(X2)) = greatest_lower_bound(inverse(X2),identity),
inference(symmetry,[status(thm)],[c292]) ).
cnf(c294,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(X2,identity)) = multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
greatest_lower_bound(inverse(X2),identity) = greatest_lower_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c296,plain,
greatest_lower_bound(identity,inverse(X2)) = greatest_lower_bound(inverse(X2),identity),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
multiply(greatest_lower_bound(identity,inverse(X3)),multiply(X3,X2)) = multiply(greatest_lower_bound(inverse(X3),identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c299,plain,
greatest_lower_bound(X3,multiply(X2,X3)) = greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
multiply(greatest_lower_bound(identity,X2),X3) = greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c160]) ).
cnf(c301,plain,
greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(identity,X2),X3),
inference(symmetry,[status(thm)],[c300]) ).
cnf(c302,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c34]) ).
cnf(c303,plain,
multiply(greatest_lower_bound(identity,X2),X3) = multiply(greatest_lower_bound(X2,identity),X3),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c301,c303]) ).
cnf(c305,plain,
greatest_lower_bound(X3,multiply(X2,X3)) = multiply(greatest_lower_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c299,c304]) ).
cnf(c306,plain,
greatest_lower_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))) = multiply(greatest_lower_bound(inverse(X3),identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c305]) ).
cnf(c307,plain,
multiply(greatest_lower_bound(inverse(X3),identity),multiply(X3,X2)) = greatest_lower_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c306]) ).
cnf(c308,plain,
greatest_lower_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))) = greatest_lower_bound(multiply(X3,X2),X2),
inference(congruence,[status(thm)],[c53]) ).
cnf(c309,plain,
greatest_lower_bound(multiply(X3,X2),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c310,plain,
greatest_lower_bound(X2,multiply(X3,X2)) = multiply(greatest_lower_bound(X3,identity),X2),
inference(substitution,[status(thm)],[c305]) ).
cnf(c311,plain,
greatest_lower_bound(multiply(X3,X2),X2) = multiply(greatest_lower_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c309,c310]) ).
cnf(c312,plain,
greatest_lower_bound(multiply(X3,X2),multiply(inverse(X3),multiply(X3,X2))) = multiply(greatest_lower_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c308,c311]) ).
cnf(c313,plain,
multiply(greatest_lower_bound(inverse(X3),identity),multiply(X3,X2)) = multiply(greatest_lower_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c307,c312]) ).
cnf(c314,plain,
multiply(greatest_lower_bound(identity,inverse(X3)),multiply(X3,X2)) = multiply(greatest_lower_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c297,c313]) ).
cnf(c315,plain,
multiply(greatest_lower_bound(identity,inverse(inverse(X2))),multiply(inverse(X2),least_upper_bound(X2,identity))) = multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c314]) ).
cnf(c316,plain,
multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(X2,identity)) = multiply(greatest_lower_bound(identity,inverse(inverse(X2))),multiply(inverse(X2),least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c318,plain,
least_upper_bound(identity,multiply(inverse(X3),X2)) = least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c203]) ).
cnf(c320,plain,
least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c319]) ).
cnf(c321,plain,
least_upper_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c318,c320]) ).
cnf(c322,plain,
least_upper_bound(identity,multiply(inverse(X2),identity)) = multiply(inverse(X2),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c321]) ).
cnf(c323,plain,
multiply(inverse(X2),least_upper_bound(X2,identity)) = least_upper_bound(identity,multiply(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c324,plain,
least_upper_bound(identity,multiply(inverse(X2),identity)) = least_upper_bound(identity,inverse(X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c325,plain,
multiply(inverse(X2),least_upper_bound(X2,identity)) = least_upper_bound(identity,inverse(X2)),
inference(transitivity,[status(thm)],[c323,c324]) ).
cnf(c326,plain,
multiply(greatest_lower_bound(identity,inverse(inverse(X2))),multiply(inverse(X2),least_upper_bound(X2,identity))) = multiply(greatest_lower_bound(identity,inverse(inverse(X2))),least_upper_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
greatest_lower_bound(identity,inverse(inverse(X2))) = greatest_lower_bound(identity,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c328,plain,
multiply(greatest_lower_bound(identity,inverse(inverse(X2))),least_upper_bound(identity,inverse(X2))) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c34]) ).
cnf(c330,plain,
multiply(greatest_lower_bound(identity,X2),least_upper_bound(identity,inverse(X2))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
multiply(greatest_lower_bound(identity,inverse(inverse(X2))),least_upper_bound(identity,inverse(X2))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c328,c330]) ).
cnf(c332,plain,
multiply(greatest_lower_bound(identity,inverse(inverse(X2))),multiply(inverse(X2),least_upper_bound(X2,identity))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c326,c331]) ).
cnf(c333,plain,
multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(X2,identity)) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c316,c332]) ).
cnf(c334,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(X2,identity)) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c294,c333]) ).
cnf(c335,plain,
multiply(greatest_lower_bound(identity,inverse(inverse(X2))),least_upper_bound(inverse(X2),identity)) = multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(identity,inverse(inverse(X2)))),
inference(substitution,[status(thm)],[c334]) ).
cnf(c336,plain,
multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(identity,inverse(inverse(X2)))) = multiply(greatest_lower_bound(identity,inverse(inverse(X2))),least_upper_bound(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c335]) ).
cnf(c337,plain,
greatest_lower_bound(identity,inverse(inverse(X2))) = greatest_lower_bound(identity,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c338,plain,
multiply(greatest_lower_bound(identity,inverse(inverse(X2))),least_upper_bound(inverse(X2),identity)) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(inverse(X2),identity)),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
least_upper_bound(inverse(X2),identity) = least_upper_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c340,plain,
multiply(greatest_lower_bound(identity,X2),least_upper_bound(inverse(X2),identity)) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
multiply(greatest_lower_bound(identity,inverse(inverse(X2))),least_upper_bound(inverse(X2),identity)) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c338,c340]) ).
cnf(c342,plain,
multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(identity,inverse(inverse(X2)))) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c336,c341]) ).
cnf(c343,plain,
multiply(greatest_lower_bound(inverse(X2),identity),least_upper_bound(identity,X2)) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c291,c342]) ).
cnf(c344,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(identity,X2)) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c288,c343]) ).
cnf(c345,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(X2,identity)) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c285,c344]) ).
cnf(c346,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c34]) ).
cnf(c347,plain,
multiply(greatest_lower_bound(identity,X2),least_upper_bound(identity,inverse(X2))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(X2,identity)) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c345,c347]) ).
cnf(c349,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(identity,X2)) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c282,c348]) ).
cnf(c350,plain,
multiply(greatest_lower_bound(identity,inverse(X2)),least_upper_bound(identity,greatest_lower_bound(X2,inverse(greatest_lower_bound(identity,inverse(X2)))))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c280,c349]) ).
cnf(c351,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X2)),X2))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c215,c350]) ).
cnf(c352,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),multiply(identity,greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity))))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c199,c351]) ).
cnf(c353,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(X2,greatest_lower_bound(identity,inverse(identity)))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c157,c352]) ).
cnf(c354,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(X2,greatest_lower_bound(identity,identity))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c154,c353]) ).
cnf(c355,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c150,c354]) ).
cnf(c356,plain,
least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c145,c355]) ).
cnf(c357,plain,
multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c143,c356]) ).
cnf(c358,plain,
multiply(least_upper_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c135,c357]) ).
cnf(c359,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c70,c358]) ).
cnf(c360,plain,
multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(symmetry,[status(thm)],[c359]) ).
cnf(c361,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c34]) ).
cnf(c362,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(symmetry,[status(thm)],[c361]) ).
cnf(c363,plain,
least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))) = least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
greatest_lower_bound(identity,inverse(X2)) = multiply(inverse(X2),greatest_lower_bound(X2,identity)),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c365,plain,
least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = least_upper_bound(greatest_lower_bound(X2,identity),multiply(inverse(X2),greatest_lower_bound(X2,identity))),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
least_upper_bound(greatest_lower_bound(X2,identity),multiply(inverse(X2),greatest_lower_bound(X2,identity))) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c94]) ).
cnf(c367,plain,
least_upper_bound(inverse(X2),identity) = least_upper_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c368,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(identity,inverse(X2)),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c368,c123]) ).
cnf(c370,plain,
least_upper_bound(greatest_lower_bound(X2,identity),multiply(inverse(X2),greatest_lower_bound(X2,identity))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c366,c369]) ).
cnf(c371,plain,
least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c365,c370]) ).
cnf(c372,plain,
least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c363,c371]) ).
cnf(c373,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))),
inference(symmetry,[status(thm)],[c372]) ).
cnf(c374,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c67]) ).
cnf(c375,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(symmetry,[status(thm)],[c374]) ).
cnf(c376,plain,
greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X3,greatest_lower_bound(X4,X2))) = greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X3,greatest_lower_bound(X4,X2))),
inference(congruence,[status(thm)],[c375]) ).
cnf(c377,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c67]) ).
cnf(c378,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(symmetry,[status(thm)],[c377]) ).
cnf(c379,plain,
greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X4,greatest_lower_bound(X3,X2))) = greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X4,greatest_lower_bound(X3,X2))),
inference(congruence,[status(thm)],[c378]) ).
cnf(c380,plain,
greatest_lower_bound(least_upper_bound(X4,greatest_lower_bound(X3,X2)),least_upper_bound(X3,X4)) = greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X4,greatest_lower_bound(X3,X2))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c381,plain,
greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X4,greatest_lower_bound(X3,X2))) = greatest_lower_bound(least_upper_bound(X4,greatest_lower_bound(X3,X2)),least_upper_bound(X3,X4)),
inference(symmetry,[status(thm)],[c380]) ).
cnf(c382,plain,
least_upper_bound(greatest_lower_bound(X4,X2),X3) = least_upper_bound(X3,greatest_lower_bound(X4,X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c383,plain,
least_upper_bound(X3,greatest_lower_bound(X4,X2)) = least_upper_bound(greatest_lower_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c382]) ).
cnf(c384,plain,
least_upper_bound(X4,least_upper_bound(X3,greatest_lower_bound(X4,X2))) = least_upper_bound(X4,least_upper_bound(greatest_lower_bound(X4,X2),X3)),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,axiom,
least_upper_bound(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(least_upper_bound(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
cnf(c386,plain,
least_upper_bound(X4,least_upper_bound(greatest_lower_bound(X4,X2),X3)) = least_upper_bound(least_upper_bound(X4,greatest_lower_bound(X4,X2)),X3),
inference(substitution,[status(thm)],[c385]) ).
cnf(c387,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c224]) ).
cnf(c388,plain,
least_upper_bound(least_upper_bound(X4,greatest_lower_bound(X4,X2)),X3) = least_upper_bound(X4,X3),
inference(congruence,[status(thm)],[c387]) ).
cnf(c389,plain,
least_upper_bound(X4,least_upper_bound(greatest_lower_bound(X4,X2),X3)) = least_upper_bound(X4,X3),
inference(transitivity,[status(thm)],[c386,c388]) ).
cnf(c390,plain,
least_upper_bound(X4,least_upper_bound(X3,greatest_lower_bound(X4,X2))) = least_upper_bound(X4,X3),
inference(transitivity,[status(thm)],[c384,c389]) ).
cnf(c391,plain,
least_upper_bound(X3,least_upper_bound(X4,greatest_lower_bound(X3,X2))) = least_upper_bound(X3,X4),
inference(substitution,[status(thm)],[c390]) ).
cnf(c392,plain,
least_upper_bound(X3,X4) = least_upper_bound(X3,least_upper_bound(X4,greatest_lower_bound(X3,X2))),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
greatest_lower_bound(least_upper_bound(X4,greatest_lower_bound(X3,X2)),least_upper_bound(X3,X4)) = greatest_lower_bound(least_upper_bound(X4,greatest_lower_bound(X3,X2)),least_upper_bound(X3,least_upper_bound(X4,greatest_lower_bound(X3,X2)))),
inference(congruence,[status(thm)],[c392]) ).
cnf(c394,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c67]) ).
cnf(c395,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c394]) ).
cnf(c396,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c248]) ).
cnf(c398,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c396,c397]) ).
cnf(c399,plain,
greatest_lower_bound(least_upper_bound(X4,greatest_lower_bound(X3,X2)),least_upper_bound(X3,least_upper_bound(X4,greatest_lower_bound(X3,X2)))) = least_upper_bound(X4,greatest_lower_bound(X3,X2)),
inference(substitution,[status(thm)],[c398]) ).
cnf(c400,plain,
greatest_lower_bound(least_upper_bound(X4,greatest_lower_bound(X3,X2)),least_upper_bound(X3,X4)) = least_upper_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c393,c399]) ).
cnf(c401,plain,
greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X4,greatest_lower_bound(X3,X2))) = least_upper_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c381,c400]) ).
cnf(c402,plain,
greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X4,greatest_lower_bound(X3,X2))) = least_upper_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c379,c401]) ).
cnf(c403,plain,
greatest_lower_bound(least_upper_bound(X3,X4),least_upper_bound(X3,greatest_lower_bound(X4,X2))) = least_upper_bound(X3,greatest_lower_bound(X4,X2)),
inference(substitution,[status(thm)],[c402]) ).
cnf(c404,plain,
greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X3,greatest_lower_bound(X4,X2))) = least_upper_bound(X3,greatest_lower_bound(X4,X2)),
inference(transitivity,[status(thm)],[c376,c403]) ).
cnf(c405,plain,
greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X2)),least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2)))) = least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))),
inference(substitution,[status(thm)],[c404]) ).
cnf(c406,plain,
least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X2)),least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2)))),
inference(symmetry,[status(thm)],[c405]) ).
cnf(c407,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c34]) ).
cnf(c408,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(symmetry,[status(thm)],[c407]) ).
cnf(c409,plain,
least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))) = least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
least_upper_bound(greatest_lower_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c371,c359]) ).
cnf(c411,plain,
least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(transitivity,[status(thm)],[c409,c410]) ).
cnf(c412,plain,
greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X2)),least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2)))) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X2)),multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2)))),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X2)) = identity,
inference(substitution,[status(thm)],[c224]) ).
cnf(c414,plain,
greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X2)),multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2)))),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
greatest_lower_bound(least_upper_bound(X4,X2),multiply(X3,least_upper_bound(X4,X2))) = multiply(greatest_lower_bound(X3,identity),least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c305]) ).
cnf(c416,plain,
multiply(greatest_lower_bound(X3,identity),least_upper_bound(X4,X2)) = greatest_lower_bound(least_upper_bound(X4,X2),multiply(X3,least_upper_bound(X4,X2))),
inference(symmetry,[status(thm)],[c415]) ).
cnf(c417,plain,
greatest_lower_bound(X4,multiply(greatest_lower_bound(X3,identity),least_upper_bound(X4,X2))) = greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X2),multiply(X3,least_upper_bound(X4,X2)))),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
greatest_lower_bound(X2,least_upper_bound(X4,X3)) = greatest_lower_bound(least_upper_bound(X4,X3),X2),
inference(substitution,[status(thm)],[c34]) ).
cnf(c419,plain,
greatest_lower_bound(least_upper_bound(X4,X3),X2) = greatest_lower_bound(X2,least_upper_bound(X4,X3)),
inference(symmetry,[status(thm)],[c418]) ).
cnf(c420,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),X2)) = greatest_lower_bound(X4,greatest_lower_bound(X2,least_upper_bound(X4,X3))),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,plain,
greatest_lower_bound(least_upper_bound(X4,X2),X3) = greatest_lower_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c422,plain,
greatest_lower_bound(X3,least_upper_bound(X4,X2)) = greatest_lower_bound(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c421]) ).
cnf(c423,plain,
greatest_lower_bound(X4,greatest_lower_bound(X3,least_upper_bound(X4,X2))) = greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X2),X3)),
inference(congruence,[status(thm)],[c422]) ).
cnf(c424,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X2),X3)) = greatest_lower_bound(greatest_lower_bound(X4,least_upper_bound(X4,X2)),X3),
inference(substitution,[status(thm)],[c187]) ).
cnf(c425,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c248]) ).
cnf(c426,plain,
greatest_lower_bound(greatest_lower_bound(X4,least_upper_bound(X4,X2)),X3) = greatest_lower_bound(X4,X3),
inference(congruence,[status(thm)],[c425]) ).
cnf(c427,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X2),X3)) = greatest_lower_bound(X4,X3),
inference(transitivity,[status(thm)],[c424,c426]) ).
cnf(c428,plain,
greatest_lower_bound(X4,greatest_lower_bound(X3,least_upper_bound(X4,X2))) = greatest_lower_bound(X4,X3),
inference(transitivity,[status(thm)],[c423,c427]) ).
cnf(c429,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,least_upper_bound(X4,X3))) = greatest_lower_bound(X4,X2),
inference(substitution,[status(thm)],[c428]) ).
cnf(c430,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),X2)) = greatest_lower_bound(X4,X2),
inference(transitivity,[status(thm)],[c420,c429]) ).
cnf(c431,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X2),multiply(X3,least_upper_bound(X4,X2)))) = greatest_lower_bound(X4,multiply(X3,least_upper_bound(X4,X2))),
inference(substitution,[status(thm)],[c430]) ).
cnf(c432,plain,
greatest_lower_bound(X4,multiply(greatest_lower_bound(X3,identity),least_upper_bound(X4,X2))) = greatest_lower_bound(X4,multiply(X3,least_upper_bound(X4,X2))),
inference(transitivity,[status(thm)],[c417,c431]) ).
cnf(c433,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2)))) = greatest_lower_bound(identity,multiply(X2,least_upper_bound(identity,inverse(X2)))),
inference(substitution,[status(thm)],[c432]) ).
cnf(c434,plain,
identity = multiply(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c435,plain,
least_upper_bound(identity,multiply(X3,X2)) = least_upper_bound(multiply(X3,inverse(X3)),multiply(X3,X2)),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
multiply(X3,least_upper_bound(inverse(X3),X2)) = least_upper_bound(multiply(X3,inverse(X3)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c203]) ).
cnf(c437,plain,
least_upper_bound(multiply(X3,inverse(X3)),multiply(X3,X2)) = multiply(X3,least_upper_bound(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c436]) ).
cnf(c438,plain,
least_upper_bound(inverse(X3),X2) = least_upper_bound(X2,inverse(X3)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c439,plain,
multiply(X3,least_upper_bound(inverse(X3),X2)) = multiply(X3,least_upper_bound(X2,inverse(X3))),
inference(congruence,[status(thm)],[c438]) ).
cnf(c440,plain,
least_upper_bound(multiply(X3,inverse(X3)),multiply(X3,X2)) = multiply(X3,least_upper_bound(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c437,c439]) ).
cnf(c441,plain,
least_upper_bound(identity,multiply(X3,X2)) = multiply(X3,least_upper_bound(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c435,c440]) ).
cnf(c442,plain,
multiply(X3,least_upper_bound(X2,inverse(X3))) = least_upper_bound(identity,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c441]) ).
cnf(c443,plain,
greatest_lower_bound(identity,multiply(X3,least_upper_bound(X2,inverse(X3)))) = greatest_lower_bound(identity,least_upper_bound(identity,multiply(X3,X2))),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
greatest_lower_bound(identity,least_upper_bound(identity,multiply(X3,X2))) = identity,
inference(substitution,[status(thm)],[c248]) ).
cnf(c445,plain,
greatest_lower_bound(identity,multiply(X3,least_upper_bound(X2,inverse(X3)))) = identity,
inference(transitivity,[status(thm)],[c443,c444]) ).
cnf(c446,plain,
greatest_lower_bound(identity,multiply(X2,least_upper_bound(identity,inverse(X2)))) = identity,
inference(substitution,[status(thm)],[c445]) ).
cnf(c447,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2)))) = identity,
inference(transitivity,[status(thm)],[c433,c446]) ).
cnf(c448,plain,
greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X2)),multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2)))) = identity,
inference(transitivity,[status(thm)],[c414,c447]) ).
cnf(c449,plain,
greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X2)),least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2)))) = identity,
inference(transitivity,[status(thm)],[c412,c448]) ).
cnf(c450,plain,
least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c406,c449]) ).
cnf(c451,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(identity,inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c373,c450]) ).
cnf(c452,plain,
multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c360,c451]) ).
cnf(c453,plain,
identity = multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2))),
inference(symmetry,[status(thm)],[c452]) ).
cnf(c454,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),identity) = multiply(inverse(greatest_lower_bound(X2,identity)),multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2)))),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),multiply(greatest_lower_bound(X2,identity),least_upper_bound(identity,inverse(X2)))) = least_upper_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c456,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),identity) = least_upper_bound(identity,inverse(X2)),
inference(transitivity,[status(thm)],[c454,c455]) ).
cnf(c457,plain,
inverse(greatest_lower_bound(X2,identity)) = least_upper_bound(identity,inverse(X2)),
inference(transitivity,[status(thm)],[c66,c456]) ).
cnf(c458,plain,
inverse(greatest_lower_bound(multiply(X2,X3),identity)) = least_upper_bound(identity,inverse(multiply(X2,X3))),
inference(substitution,[status(thm)],[c457]) ).
cnf(c459,plain,
multiply(inverse(greatest_lower_bound(multiply(X2,X3),identity)),X2) = multiply(least_upper_bound(identity,inverse(multiply(X2,X3))),X2),
inference(congruence,[status(thm)],[c458]) ).
cnf(c460,plain,
inverse(multiply(X2,X3)) = multiply(inverse(X3),inverse(X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c461,plain,
least_upper_bound(identity,inverse(multiply(X2,X3))) = least_upper_bound(identity,multiply(inverse(X3),inverse(X2))),
inference(congruence,[status(thm)],[c460]) ).
cnf(c462,plain,
multiply(least_upper_bound(identity,inverse(multiply(X2,X3))),X2) = multiply(least_upper_bound(identity,multiply(inverse(X3),inverse(X2))),X2),
inference(congruence,[status(thm)],[c461]) ).
cnf(c463,plain,
multiply(multiply(X3,X2),X4) = multiply(X3,multiply(X2,X4)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c464,plain,
multiply(X3,multiply(X2,X4)) = multiply(multiply(X3,X2),X4),
inference(symmetry,[status(thm)],[c463]) ).
cnf(c465,plain,
least_upper_bound(X4,multiply(X3,multiply(X2,X4))) = least_upper_bound(X4,multiply(multiply(X3,X2),X4)),
inference(congruence,[status(thm)],[c464]) ).
cnf(c466,plain,
least_upper_bound(X4,multiply(multiply(X3,X2),X4)) = multiply(least_upper_bound(multiply(X3,X2),identity),X4),
inference(substitution,[status(thm)],[c94]) ).
cnf(c467,plain,
least_upper_bound(multiply(X3,X2),identity) = least_upper_bound(identity,multiply(X3,X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c468,plain,
multiply(least_upper_bound(multiply(X3,X2),identity),X4) = multiply(least_upper_bound(identity,multiply(X3,X2)),X4),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
least_upper_bound(X4,multiply(multiply(X3,X2),X4)) = multiply(least_upper_bound(identity,multiply(X3,X2)),X4),
inference(transitivity,[status(thm)],[c466,c468]) ).
cnf(c470,plain,
least_upper_bound(X4,multiply(X3,multiply(X2,X4))) = multiply(least_upper_bound(identity,multiply(X3,X2)),X4),
inference(transitivity,[status(thm)],[c465,c469]) ).
cnf(c471,plain,
least_upper_bound(X2,multiply(X3,multiply(inverse(X2),X2))) = multiply(least_upper_bound(identity,multiply(X3,inverse(X2))),X2),
inference(substitution,[status(thm)],[c470]) ).
cnf(c472,plain,
multiply(least_upper_bound(identity,multiply(X3,inverse(X2))),X2) = least_upper_bound(X2,multiply(X3,multiply(inverse(X2),X2))),
inference(symmetry,[status(thm)],[c471]) ).
cnf(c473,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c474,plain,
least_upper_bound(X2,multiply(X4,multiply(X3,X2))) = least_upper_bound(multiply(inverse(X3),multiply(X3,X2)),multiply(X4,multiply(X3,X2))),
inference(congruence,[status(thm)],[c473]) ).
cnf(c475,plain,
multiply(least_upper_bound(inverse(X3),X4),multiply(X3,X2)) = least_upper_bound(multiply(inverse(X3),multiply(X3,X2)),multiply(X4,multiply(X3,X2))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c476,plain,
least_upper_bound(multiply(inverse(X3),multiply(X3,X2)),multiply(X4,multiply(X3,X2))) = multiply(least_upper_bound(inverse(X3),X4),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c475]) ).
cnf(c477,plain,
least_upper_bound(inverse(X2),X3) = least_upper_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c478,plain,
multiply(least_upper_bound(inverse(X3),X4),multiply(X3,X2)) = multiply(least_upper_bound(X4,inverse(X3)),multiply(X3,X2)),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
least_upper_bound(multiply(inverse(X3),multiply(X3,X2)),multiply(X4,multiply(X3,X2))) = multiply(least_upper_bound(X4,inverse(X3)),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c476,c478]) ).
cnf(c480,plain,
least_upper_bound(X2,multiply(X4,multiply(X3,X2))) = multiply(least_upper_bound(X4,inverse(X3)),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c474,c479]) ).
cnf(c481,plain,
least_upper_bound(X2,multiply(X3,multiply(inverse(X2),X2))) = multiply(least_upper_bound(X3,inverse(inverse(X2))),multiply(inverse(X2),X2)),
inference(substitution,[status(thm)],[c480]) ).
cnf(c482,plain,
multiply(least_upper_bound(X3,inverse(inverse(X2))),multiply(inverse(X2),X2)) = multiply(least_upper_bound(X3,inverse(inverse(X2))),identity),
inference(congruence,[status(thm)],[c22]) ).
cnf(c483,plain,
multiply(least_upper_bound(X3,inverse(inverse(X2))),identity) = least_upper_bound(X3,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c484,plain,
least_upper_bound(X3,inverse(inverse(X2))) = least_upper_bound(X3,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c485,plain,
multiply(least_upper_bound(X3,inverse(inverse(X2))),identity) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c483,c484]) ).
cnf(c486,plain,
multiply(least_upper_bound(X3,inverse(inverse(X2))),multiply(inverse(X2),X2)) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c482,c485]) ).
cnf(c487,plain,
least_upper_bound(X2,multiply(X3,multiply(inverse(X2),X2))) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c481,c486]) ).
cnf(c488,plain,
multiply(least_upper_bound(identity,multiply(X3,inverse(X2))),X2) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c472,c487]) ).
cnf(c489,plain,
multiply(least_upper_bound(identity,multiply(inverse(X3),inverse(X2))),X2) = least_upper_bound(inverse(X3),X2),
inference(substitution,[status(thm)],[c488]) ).
cnf(c490,plain,
least_upper_bound(inverse(X3),X2) = least_upper_bound(X2,inverse(X3)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c491,plain,
multiply(least_upper_bound(identity,multiply(inverse(X3),inverse(X2))),X2) = least_upper_bound(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c489,c490]) ).
cnf(c492,plain,
multiply(least_upper_bound(identity,inverse(multiply(X2,X3))),X2) = least_upper_bound(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c462,c491]) ).
cnf(c493,plain,
multiply(inverse(greatest_lower_bound(multiply(X2,X3),identity)),X2) = least_upper_bound(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c459,c492]) ).
cnf(c494,plain,
inverse(greatest_lower_bound(X3,multiply(inverse(X2),identity))) = least_upper_bound(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c64,c493]) ).
cnf(c495,plain,
inverse(greatest_lower_bound(X3,inverse(X2))) = least_upper_bound(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c33,c494]) ).
cnf(c496,plain,
inverse(greatest_lower_bound(X2,inverse(X3))) = least_upper_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c495]) ).
cnf(c497,plain,
least_upper_bound(X3,inverse(X2)) = inverse(greatest_lower_bound(X2,inverse(X3))),
inference(symmetry,[status(thm)],[c496]) ).
cnf(c498,plain,
inverse(least_upper_bound(X3,inverse(X2))) = inverse(inverse(greatest_lower_bound(X2,inverse(X3)))),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,plain,
inverse(inverse(greatest_lower_bound(X2,inverse(X3)))) = greatest_lower_bound(X2,inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c500,plain,
inverse(least_upper_bound(X3,inverse(X2))) = greatest_lower_bound(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c498,c499]) ).
cnf(c501,plain,
inverse(least_upper_bound(X3,inverse(inverse(X2)))) = greatest_lower_bound(inverse(X2),inverse(X3)),
inference(substitution,[status(thm)],[c500]) ).
cnf(c502,plain,
greatest_lower_bound(inverse(X2),inverse(X3)) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c503,plain,
inverse(least_upper_bound(X3,inverse(inverse(X2)))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c501,c502]) ).
cnf(c504,plain,
inverse(least_upper_bound(X3,X2)) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c30,c503]) ).
cnf(c505,plain,
inverse(least_upper_bound(c,b)) = greatest_lower_bound(inverse(c),inverse(b)),
inference(substitution,[status(thm)],[c504]) ).
cnf(c506,plain,
greatest_lower_bound(inverse(c),inverse(b)) = inverse(least_upper_bound(c,b)),
inference(symmetry,[status(thm)],[c505]) ).
cnf(c507,plain,
least_upper_bound(b,c) = least_upper_bound(c,b),
inference(substitution,[status(thm)],[c67]) ).
cnf(c508,plain,
least_upper_bound(c,b) = least_upper_bound(b,c),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c509,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c510,plain,
least_upper_bound(b,c) = least_upper_bound(a,c),
inference(symmetry,[status(thm)],[c509]) ).
cnf(c511,plain,
least_upper_bound(a,c) = least_upper_bound(c,a),
inference(substitution,[status(thm)],[c67]) ).
cnf(c512,plain,
least_upper_bound(b,c) = least_upper_bound(c,a),
inference(transitivity,[status(thm)],[c510,c511]) ).
cnf(c513,plain,
least_upper_bound(c,b) = least_upper_bound(c,a),
inference(transitivity,[status(thm)],[c508,c512]) ).
cnf(c514,plain,
inverse(least_upper_bound(c,b)) = inverse(least_upper_bound(c,a)),
inference(congruence,[status(thm)],[c513]) ).
cnf(c515,plain,
inverse(least_upper_bound(c,a)) = greatest_lower_bound(inverse(c),inverse(a)),
inference(substitution,[status(thm)],[c504]) ).
cnf(c516,plain,
inverse(least_upper_bound(c,b)) = greatest_lower_bound(inverse(c),inverse(a)),
inference(transitivity,[status(thm)],[c514,c515]) ).
cnf(c517,plain,
greatest_lower_bound(inverse(c),inverse(b)) = greatest_lower_bound(inverse(c),inverse(a)),
inference(transitivity,[status(thm)],[c506,c516]) ).
cnf(c518,plain,
greatest_lower_bound(inverse(c),inverse(a)) = greatest_lower_bound(inverse(c),inverse(b)),
inference(symmetry,[status(thm)],[c517]) ).
cnf(c519,plain,
multiply(greatest_lower_bound(inverse(c),inverse(a)),X2) = multiply(greatest_lower_bound(inverse(c),inverse(b)),X2),
inference(congruence,[status(thm)],[c518]) ).
cnf(c520,plain,
multiply(b,multiply(greatest_lower_bound(inverse(c),inverse(a)),X2)) = multiply(b,multiply(greatest_lower_bound(inverse(c),inverse(b)),X2)),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c34]) ).
cnf(c522,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(symmetry,[status(thm)],[c521]) ).
cnf(c523,plain,
multiply(greatest_lower_bound(X4,X3),multiply(inverse(X4),X2)) = multiply(greatest_lower_bound(X3,X4),multiply(inverse(X4),X2)),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c34]) ).
cnf(c525,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c524]) ).
cnf(c526,plain,
inverse(greatest_lower_bound(X2,X3)) = inverse(greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c525]) ).
cnf(c527,plain,
greatest_lower_bound(inverse(X3),inverse(greatest_lower_bound(X2,X3))) = greatest_lower_bound(inverse(X3),inverse(greatest_lower_bound(X3,X2))),
inference(congruence,[status(thm)],[c526]) ).
cnf(c528,plain,
greatest_lower_bound(inverse(X3),inverse(greatest_lower_bound(X2,X3))) = inverse(X3),
inference(transitivity,[status(thm)],[c527,c273]) ).
cnf(c529,plain,
inverse(X3) = greatest_lower_bound(inverse(X3),inverse(greatest_lower_bound(X2,X3))),
inference(symmetry,[status(thm)],[c528]) ).
cnf(c530,plain,
multiply(inverse(X4),X2) = multiply(greatest_lower_bound(inverse(X4),inverse(greatest_lower_bound(X3,X4))),X2),
inference(congruence,[status(thm)],[c529]) ).
cnf(c531,plain,
multiply(greatest_lower_bound(X3,X4),multiply(inverse(X4),X2)) = multiply(greatest_lower_bound(X3,X4),multiply(greatest_lower_bound(inverse(X4),inverse(greatest_lower_bound(X3,X4))),X2)),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
multiply(greatest_lower_bound(identity,multiply(X4,X3)),X2) = multiply(multiply(X4,greatest_lower_bound(X3,inverse(X4))),X2),
inference(congruence,[status(thm)],[c175]) ).
cnf(c533,plain,
multiply(multiply(X4,greatest_lower_bound(X3,inverse(X4))),X2) = multiply(X4,multiply(greatest_lower_bound(X3,inverse(X4)),X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c534,plain,
multiply(greatest_lower_bound(identity,multiply(X4,X3)),X2) = multiply(X4,multiply(greatest_lower_bound(X3,inverse(X4)),X2)),
inference(transitivity,[status(thm)],[c532,c533]) ).
cnf(c535,plain,
multiply(greatest_lower_bound(identity,multiply(greatest_lower_bound(X3,X4),inverse(X4))),X2) = multiply(greatest_lower_bound(X3,X4),multiply(greatest_lower_bound(inverse(X4),inverse(greatest_lower_bound(X3,X4))),X2)),
inference(substitution,[status(thm)],[c534]) ).
cnf(c536,plain,
multiply(greatest_lower_bound(X3,X4),multiply(greatest_lower_bound(inverse(X4),inverse(greatest_lower_bound(X3,X4))),X2)) = multiply(greatest_lower_bound(identity,multiply(greatest_lower_bound(X3,X4),inverse(X4))),X2),
inference(symmetry,[status(thm)],[c535]) ).
cnf(c537,plain,
identity = multiply(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c538,plain,
greatest_lower_bound(identity,multiply(X3,inverse(X2))) = greatest_lower_bound(multiply(X2,inverse(X2)),multiply(X3,inverse(X2))),
inference(congruence,[status(thm)],[c537]) ).
cnf(c539,plain,
multiply(greatest_lower_bound(X2,X3),inverse(X2)) = greatest_lower_bound(multiply(X2,inverse(X2)),multiply(X3,inverse(X2))),
inference(substitution,[status(thm)],[c160]) ).
cnf(c540,plain,
greatest_lower_bound(multiply(X2,inverse(X2)),multiply(X3,inverse(X2))) = multiply(greatest_lower_bound(X2,X3),inverse(X2)),
inference(symmetry,[status(thm)],[c539]) ).
cnf(c541,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c34]) ).
cnf(c542,plain,
multiply(greatest_lower_bound(X2,X3),inverse(X2)) = multiply(greatest_lower_bound(X3,X2),inverse(X2)),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
greatest_lower_bound(multiply(X2,inverse(X2)),multiply(X3,inverse(X2))) = multiply(greatest_lower_bound(X3,X2),inverse(X2)),
inference(transitivity,[status(thm)],[c540,c542]) ).
cnf(c544,plain,
greatest_lower_bound(identity,multiply(X3,inverse(X2))) = multiply(greatest_lower_bound(X3,X2),inverse(X2)),
inference(transitivity,[status(thm)],[c538,c543]) ).
cnf(c545,plain,
multiply(greatest_lower_bound(X3,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X3,inverse(X2))),
inference(symmetry,[status(thm)],[c544]) ).
cnf(c546,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c547,plain,
multiply(X3,X2) = multiply(inverse(inverse(X3)),X2),
inference(congruence,[status(thm)],[c546]) ).
cnf(c548,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = greatest_lower_bound(identity,multiply(inverse(inverse(X3)),X2)),
inference(congruence,[status(thm)],[c547]) ).
cnf(c549,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(X3)),X2)) = multiply(inverse(inverse(X3)),greatest_lower_bound(inverse(X3),X2)),
inference(substitution,[status(thm)],[c110]) ).
cnf(c550,plain,
multiply(inverse(inverse(X3)),greatest_lower_bound(inverse(X3),X2)) = multiply(X3,greatest_lower_bound(inverse(X3),X2)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c551,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(X3)),X2)) = multiply(X3,greatest_lower_bound(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c549,c550]) ).
cnf(c552,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = multiply(X3,greatest_lower_bound(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c548,c551]) ).
cnf(c553,plain,
greatest_lower_bound(identity,multiply(X3,inverse(X2))) = multiply(X3,greatest_lower_bound(inverse(X3),inverse(X2))),
inference(substitution,[status(thm)],[c552]) ).
cnf(c554,plain,
multiply(greatest_lower_bound(X3,X2),inverse(X2)) = multiply(X3,greatest_lower_bound(inverse(X3),inverse(X2))),
inference(transitivity,[status(thm)],[c545,c553]) ).
cnf(c555,plain,
multiply(greatest_lower_bound(X2,X3),inverse(X3)) = multiply(X2,greatest_lower_bound(inverse(X2),inverse(X3))),
inference(substitution,[status(thm)],[c554]) ).
cnf(c556,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X2,X3),inverse(X3))) = greatest_lower_bound(identity,multiply(X2,greatest_lower_bound(inverse(X2),inverse(X3)))),
inference(congruence,[status(thm)],[c555]) ).
cnf(c557,plain,
multiply(greatest_lower_bound(identity,multiply(greatest_lower_bound(X3,X4),inverse(X4))),X2) = multiply(greatest_lower_bound(identity,multiply(X3,greatest_lower_bound(inverse(X3),inverse(X4)))),X2),
inference(congruence,[status(thm)],[c556]) ).
cnf(c558,plain,
greatest_lower_bound(identity,multiply(X4,greatest_lower_bound(X3,X2))) = multiply(X4,greatest_lower_bound(greatest_lower_bound(X3,X2),inverse(X4))),
inference(substitution,[status(thm)],[c175]) ).
cnf(c559,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,inverse(X4))) = greatest_lower_bound(greatest_lower_bound(X3,X2),inverse(X4)),
inference(substitution,[status(thm)],[c187]) ).
cnf(c560,plain,
greatest_lower_bound(greatest_lower_bound(X3,X2),inverse(X4)) = greatest_lower_bound(X3,greatest_lower_bound(X2,inverse(X4))),
inference(symmetry,[status(thm)],[c559]) ).
cnf(c561,plain,
multiply(X4,greatest_lower_bound(greatest_lower_bound(X3,X2),inverse(X4))) = multiply(X4,greatest_lower_bound(X3,greatest_lower_bound(X2,inverse(X4)))),
inference(congruence,[status(thm)],[c560]) ).
cnf(c562,plain,
greatest_lower_bound(identity,multiply(X4,greatest_lower_bound(X3,X2))) = multiply(X4,greatest_lower_bound(X3,greatest_lower_bound(X2,inverse(X4)))),
inference(transitivity,[status(thm)],[c558,c561]) ).
cnf(c563,plain,
greatest_lower_bound(identity,multiply(X3,greatest_lower_bound(inverse(X3),X2))) = multiply(X3,greatest_lower_bound(inverse(X3),greatest_lower_bound(X2,inverse(X3)))),
inference(substitution,[status(thm)],[c562]) ).
cnf(c564,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c34]) ).
cnf(c565,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c564]) ).
cnf(c566,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c565]) ).
cnf(c567,plain,
greatest_lower_bound(X3,greatest_lower_bound(X3,X2)) = greatest_lower_bound(greatest_lower_bound(X3,X3),X2),
inference(substitution,[status(thm)],[c187]) ).
cnf(c568,plain,
greatest_lower_bound(greatest_lower_bound(X3,X3),X2) = greatest_lower_bound(X3,X2),
inference(congruence,[status(thm)],[c146]) ).
cnf(c569,plain,
greatest_lower_bound(X3,greatest_lower_bound(X3,X2)) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c567,c568]) ).
cnf(c570,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c566,c569]) ).
cnf(c571,plain,
greatest_lower_bound(inverse(X3),greatest_lower_bound(X2,inverse(X3))) = greatest_lower_bound(inverse(X3),X2),
inference(substitution,[status(thm)],[c570]) ).
cnf(c572,plain,
multiply(X3,greatest_lower_bound(inverse(X3),greatest_lower_bound(X2,inverse(X3)))) = multiply(X3,greatest_lower_bound(inverse(X3),X2)),
inference(congruence,[status(thm)],[c571]) ).
cnf(c573,plain,
greatest_lower_bound(inverse(X3),X2) = greatest_lower_bound(X2,inverse(X3)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c574,plain,
multiply(X3,greatest_lower_bound(inverse(X3),X2)) = multiply(X3,greatest_lower_bound(X2,inverse(X3))),
inference(congruence,[status(thm)],[c573]) ).
cnf(c575,plain,
multiply(X3,greatest_lower_bound(inverse(X3),greatest_lower_bound(X2,inverse(X3)))) = multiply(X3,greatest_lower_bound(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c572,c574]) ).
cnf(c576,plain,
greatest_lower_bound(identity,multiply(X3,greatest_lower_bound(inverse(X3),X2))) = multiply(X3,greatest_lower_bound(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c563,c575]) ).
cnf(c577,plain,
greatest_lower_bound(identity,multiply(X2,greatest_lower_bound(inverse(X2),inverse(X3)))) = multiply(X2,greatest_lower_bound(inverse(X3),inverse(X2))),
inference(substitution,[status(thm)],[c576]) ).
cnf(c578,plain,
multiply(greatest_lower_bound(identity,multiply(X3,greatest_lower_bound(inverse(X3),inverse(X4)))),X2) = multiply(multiply(X3,greatest_lower_bound(inverse(X4),inverse(X3))),X2),
inference(congruence,[status(thm)],[c577]) ).
cnf(c579,plain,
multiply(multiply(X3,greatest_lower_bound(inverse(X4),inverse(X3))),X2) = multiply(X3,multiply(greatest_lower_bound(inverse(X4),inverse(X3)),X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c580,plain,
multiply(greatest_lower_bound(identity,multiply(X3,greatest_lower_bound(inverse(X3),inverse(X4)))),X2) = multiply(X3,multiply(greatest_lower_bound(inverse(X4),inverse(X3)),X2)),
inference(transitivity,[status(thm)],[c578,c579]) ).
cnf(c581,plain,
multiply(greatest_lower_bound(identity,multiply(greatest_lower_bound(X3,X4),inverse(X4))),X2) = multiply(X3,multiply(greatest_lower_bound(inverse(X4),inverse(X3)),X2)),
inference(transitivity,[status(thm)],[c557,c580]) ).
cnf(c582,plain,
multiply(greatest_lower_bound(X3,X4),multiply(greatest_lower_bound(inverse(X4),inverse(greatest_lower_bound(X3,X4))),X2)) = multiply(X3,multiply(greatest_lower_bound(inverse(X4),inverse(X3)),X2)),
inference(transitivity,[status(thm)],[c536,c581]) ).
cnf(c583,plain,
multiply(greatest_lower_bound(X3,X4),multiply(inverse(X4),X2)) = multiply(X3,multiply(greatest_lower_bound(inverse(X4),inverse(X3)),X2)),
inference(transitivity,[status(thm)],[c531,c582]) ).
cnf(c584,plain,
multiply(greatest_lower_bound(X4,X3),multiply(inverse(X4),X2)) = multiply(X3,multiply(greatest_lower_bound(inverse(X4),inverse(X3)),X2)),
inference(transitivity,[status(thm)],[c523,c583]) ).
cnf(c585,plain,
multiply(greatest_lower_bound(c,b),multiply(inverse(c),X2)) = multiply(b,multiply(greatest_lower_bound(inverse(c),inverse(b)),X2)),
inference(substitution,[status(thm)],[c584]) ).
cnf(c586,plain,
multiply(b,multiply(greatest_lower_bound(inverse(c),inverse(b)),X2)) = multiply(greatest_lower_bound(c,b),multiply(inverse(c),X2)),
inference(symmetry,[status(thm)],[c585]) ).
cnf(c587,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(c,b),
inference(substitution,[status(thm)],[c34]) ).
cnf(c588,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(b,c),
inference(symmetry,[status(thm)],[c587]) ).
cnf(c589,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c590,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
inference(symmetry,[status(thm)],[c589]) ).
cnf(c591,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(c,a),
inference(substitution,[status(thm)],[c34]) ).
cnf(c592,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(c,a),
inference(transitivity,[status(thm)],[c590,c591]) ).
cnf(c593,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(c,a),
inference(transitivity,[status(thm)],[c588,c592]) ).
cnf(c594,plain,
multiply(greatest_lower_bound(c,b),multiply(inverse(c),X2)) = multiply(greatest_lower_bound(c,a),multiply(inverse(c),X2)),
inference(congruence,[status(thm)],[c593]) ).
cnf(c595,plain,
multiply(greatest_lower_bound(c,a),multiply(inverse(c),X2)) = multiply(a,multiply(greatest_lower_bound(inverse(c),inverse(a)),X2)),
inference(substitution,[status(thm)],[c584]) ).
cnf(c596,plain,
multiply(greatest_lower_bound(c,b),multiply(inverse(c),X2)) = multiply(a,multiply(greatest_lower_bound(inverse(c),inverse(a)),X2)),
inference(transitivity,[status(thm)],[c594,c595]) ).
cnf(c597,plain,
multiply(b,multiply(greatest_lower_bound(inverse(c),inverse(b)),X2)) = multiply(a,multiply(greatest_lower_bound(inverse(c),inverse(a)),X2)),
inference(transitivity,[status(thm)],[c586,c596]) ).
cnf(c598,plain,
multiply(b,multiply(greatest_lower_bound(inverse(c),inverse(a)),X2)) = multiply(a,multiply(greatest_lower_bound(inverse(c),inverse(a)),X2)),
inference(transitivity,[status(thm)],[c520,c597]) ).
cnf(c599,plain,
multiply(b,multiply(greatest_lower_bound(inverse(c),inverse(a)),inverse(greatest_lower_bound(inverse(c),inverse(a))))) = multiply(a,multiply(greatest_lower_bound(inverse(c),inverse(a)),inverse(greatest_lower_bound(inverse(c),inverse(a))))),
inference(substitution,[status(thm)],[c598]) ).
cnf(c600,plain,
multiply(greatest_lower_bound(inverse(c),inverse(a)),inverse(greatest_lower_bound(inverse(c),inverse(a)))) = identity,
inference(substitution,[status(thm)],[c24]) ).
cnf(c601,plain,
multiply(a,multiply(greatest_lower_bound(inverse(c),inverse(a)),inverse(greatest_lower_bound(inverse(c),inverse(a))))) = multiply(a,identity),
inference(congruence,[status(thm)],[c600]) ).
cnf(c602,plain,
multiply(a,identity) = a,
inference(substitution,[status(thm)],[c17]) ).
cnf(c603,plain,
multiply(a,multiply(greatest_lower_bound(inverse(c),inverse(a)),inverse(greatest_lower_bound(inverse(c),inverse(a))))) = a,
inference(transitivity,[status(thm)],[c601,c602]) ).
cnf(c604,plain,
multiply(b,multiply(greatest_lower_bound(inverse(c),inverse(a)),inverse(greatest_lower_bound(inverse(c),inverse(a))))) = a,
inference(transitivity,[status(thm)],[c599,c603]) ).
cnf(c605,plain,
multiply(b,identity) = a,
inference(transitivity,[status(thm)],[c27,c604]) ).
cnf(c606,plain,
b = a,
inference(transitivity,[status(thm)],[c19,c605]) ).
cnf(c607,plain,
a = b,
inference(symmetry,[status(thm)],[c606]) ).
cnf(c608,plain,
$false,
inference(resolution,[status(thm)],[c1,c607]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP181-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n016.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 09:41:01 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 192.33/24.68 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 192.33/24.68
% 192.33/24.68 % SZS status Unsatisfiable
% 192.33/24.68
% 192.66/24.72 % SZS output start CNFRefutation
% See solution above
% 195.02/25.01
% 195.02/25.01 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------