%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP167-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:43:37 AM UTC 2025
% Result : Unsatisfiable 47.48s 47.58s
% Output : CNFRefutation 47.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 20
% Syntax : Number of clauses : 141 ( 141 unt; 0 nHn; 4 RR)
% Number of literals : 141 ( 140 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 297 ( 45 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('theBenchmark.p',prove_lat4) ).
cnf(c1,axiom,
least_upper_bound(X,X) = X,
file('GRP004-2.ax',idempotence_of_lub) ).
cnf(c2,axiom,
greatest_lower_bound(X,X) = X,
file('GRP004-2.ax',idempotence_of_gld) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
positive_part(X) = least_upper_bound(X,identity),
file('theBenchmark.p',lat4_1) ).
cnf(c5,axiom,
negative_part(X) = greatest_lower_bound(X,identity),
file('theBenchmark.p',lat4_2) ).
cnf(c6,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c7,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c8,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c9,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c10,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c11,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(equational,[status(thm)],[c7,c10]) ).
cnf(c12,plain,
least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c13,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
file('GRP004-2.ax',associativity_of_glb) ).
cnf(c14,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c13]) ).
cnf(c15,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
file('GRP004-2.ax',associativity_of_lub) ).
cnf(c16,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c15]) ).
cnf(c17,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c18,plain,
least_upper_bound(X,least_upper_bound(X,Y)) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c1,c16]) ).
cnf(c19,plain,
greatest_lower_bound(X,greatest_lower_bound(X,Y)) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c2,c14]) ).
cnf(c20,plain,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(X,Z)),
inference(equational,[status(thm)],[c7,c16]) ).
cnf(c21,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(X,Z)),
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c22,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c8,c17]) ).
cnf(c23,plain,
multiply(inverse(identity),X) = X,
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c24,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c8,c22]) ).
cnf(c25,plain,
least_upper_bound(X,least_upper_bound(Y,X)) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c7,c18]) ).
cnf(c26,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X)) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c6,c19]) ).
cnf(c27,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c22]) ).
cnf(c28,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c24,c27]) ).
cnf(c29,plain,
inverse(identity) = identity,
inference(equational,[status(thm)],[c8,c28]) ).
cnf(c30,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c24,c28]) ).
cnf(c31,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c8,c27]) ).
cnf(c32,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c22,c27]) ).
cnf(c33,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c34,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c35,axiom,
least_upper_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)),
file('theBenchmark.p',lat4_3) ).
cnf(c36,axiom,
greatest_lower_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z)),
file('theBenchmark.p',lat4_4) ).
cnf(c37,plain,
greatest_lower_bound(X,least_upper_bound(greatest_lower_bound(X,Y),Z)) = greatest_lower_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c1,c7,c10,c35,c36]) ).
cnf(c38,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c39,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c41,plain,
greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),Z)) = greatest_lower_bound(X,Z),
inference(equational,[status(thm)],[c10,c14]) ).
cnf(c44,plain,
greatest_lower_bound(X,least_upper_bound(greatest_lower_bound(Y,X),Z)) = greatest_lower_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c6,c37]) ).
cnf(c45,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)) = least_upper_bound(greatest_lower_bound(Y,Z),X),
inference(equational,[status(thm)],[c7,c35]) ).
cnf(c46,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(X,Z))) = greatest_lower_bound(Y,X),
inference(equational,[status(thm)],[c10,c21]) ).
cnf(c47,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(Z,X))) = greatest_lower_bound(Y,X),
inference(equational,[status(thm)],[c11,c21]) ).
cnf(c49,plain,
least_upper_bound(X,Y) = greatest_lower_bound(least_upper_bound(Y,X),least_upper_bound(Y,least_upper_bound(X,Z))),
inference(equational,[status(thm)],[c9,c20,c25,c35]) ).
cnf(c51,plain,
least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X,Z))) = least_upper_bound(Y,least_upper_bound(X,Z)),
inference(equational,[status(thm)],[c18,c20]) ).
cnf(c53,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,Z))) = greatest_lower_bound(Y,greatest_lower_bound(X,Z)),
inference(equational,[status(thm)],[c19,c21]) ).
cnf(c55,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(Y,Z)) = least_upper_bound(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c7,c45]) ).
cnf(c59,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Z,Y))),
inference(equational,[status(thm)],[c21,c26]) ).
cnf(c60,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(Z,X))) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c14,c26]) ).
cnf(c61,plain,
least_upper_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(least_upper_bound(X,Z),least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c7,c55]) ).
cnf(c63,plain,
least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Z,X))) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c16,c25]) ).
cnf(c65,plain,
greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(Z,X)) = greatest_lower_bound(X,Z),
inference(equational,[status(thm)],[c41,c46,c59]) ).
cnf(c66,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,least_upper_bound(Y,Z))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c10,c35]) ).
cnf(c67,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(equational,[status(thm)],[c17,c31]) ).
cnf(c68,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c22,c28,c67]) ).
cnf(c69,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c22,c68]) ).
cnf(c70,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
inference(equational,[status(thm)],[c32,c68]) ).
cnf(c71,plain,
multiply(inverse(multiply(X,Y)),X) = inverse(Y),
inference(equational,[status(thm)],[c30,c68]) ).
cnf(c72,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference(equational,[status(thm)],[c32,c71]) ).
cnf(c74,plain,
least_upper_bound(X,Y) = greatest_lower_bound(least_upper_bound(Y,X),least_upper_bound(Y,least_upper_bound(Z,X))),
inference(equational,[status(thm)],[c11,c45]) ).
cnf(c76,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,least_upper_bound(Z,Y))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c11,c20]) ).
cnf(c81,plain,
inverse(multiply(inverse(X),inverse(Y))) = multiply(Y,X),
inference(equational,[status(thm)],[c24,c28,c69]) ).
cnf(c83,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(least_upper_bound(X,Z),W))) = greatest_lower_bound(X,greatest_lower_bound(Y,W)),
inference(equational,[status(thm)],[c21,c41]) ).
cnf(c84,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,Z))) = Z,
inference(equational,[status(thm)],[c17,c22]) ).
cnf(c85,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(Y),Z),
inference(equational,[status(thm)],[c32,c84]) ).
cnf(c87,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(Z,least_upper_bound(W,X)))) = greatest_lower_bound(Y,X),
inference(equational,[status(thm)],[c16,c47]) ).
cnf(c92,plain,
multiply(inverse(multiply(X,Y)),Z) = multiply(inverse(Y),multiply(inverse(X),Z)),
inference(equational,[status(thm)],[c32,c85]) ).
cnf(c108,plain,
greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(Z,greatest_lower_bound(X,W))) = greatest_lower_bound(X,greatest_lower_bound(Z,W)),
inference(equational,[status(thm)],[c14,c41,c59,c60,c83]) ).
cnf(c143,plain,
least_upper_bound(inverse(least_upper_bound(identity,multiply(inverse(X),Y))),inverse(least_upper_bound(identity,multiply(inverse(Y),X)))) = identity,
inference(equational,[status(thm)],[c8,c33,c72,c74,c76]) ).
cnf(c144,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X),Y)))) = identity,
inference(equational,[status(thm)],[c18,c74,c76,c143]) ).
cnf(c145,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,X))) = identity,
inference(equational,[status(thm)],[c23,c144]) ).
cnf(c146,plain,
least_upper_bound(identity,inverse(least_upper_bound(X,identity))) = identity,
inference(equational,[status(thm)],[c49,c66,c145]) ).
cnf(c149,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X,identity))) = inverse(least_upper_bound(X,identity)),
inference(equational,[status(thm)],[c6,c11,c146]) ).
cnf(c151,plain,
least_upper_bound(X,multiply(inverse(least_upper_bound(identity,Y)),X)) = X,
inference(equational,[status(thm)],[c3,c34,c145]) ).
cnf(c153,plain,
least_upper_bound(X,multiply(inverse(least_upper_bound(Y,identity)),X)) = X,
inference(equational,[status(thm)],[c74,c76,c151]) ).
cnf(c159,plain,
least_upper_bound(inverse(least_upper_bound(identity,X)),inverse(least_upper_bound(identity,inverse(X)))) = identity,
inference(equational,[status(thm)],[c8,c22,c28,c92,c143]) ).
cnf(c160,plain,
least_upper_bound(inverse(least_upper_bound(identity,X)),least_upper_bound(Y,identity)) = least_upper_bound(Y,identity),
inference(equational,[status(thm)],[c51,c159]) ).
cnf(c161,plain,
least_upper_bound(inverse(least_upper_bound(X,identity)),least_upper_bound(Y,identity)) = least_upper_bound(Y,identity),
inference(equational,[status(thm)],[c74,c76,c160]) ).
cnf(c177,plain,
least_upper_bound(inverse(least_upper_bound(identity,X)),inverse(least_upper_bound(inverse(X),identity))) = identity,
inference(equational,[status(thm)],[c7,c159]) ).
cnf(c214,plain,
least_upper_bound(inverse(X),inverse(least_upper_bound(X,multiply(X,Y)))) = inverse(X),
inference(equational,[status(thm)],[c7,c28,c30,c33,c70,c153]) ).
cnf(c216,plain,
least_upper_bound(inverse(X),inverse(least_upper_bound(X,Y))) = inverse(X),
inference(equational,[status(thm)],[c32,c214]) ).
cnf(c219,plain,
greatest_lower_bound(inverse(X),inverse(least_upper_bound(X,Y))) = inverse(least_upper_bound(X,Y)),
inference(equational,[status(thm)],[c6,c11,c216]) ).
cnf(c226,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X),Y))),inverse(greatest_lower_bound(identity,multiply(inverse(Y),X)))) = identity,
inference(equational,[status(thm)],[c6,c8,c38,c72]) ).
cnf(c227,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),Y)))) = identity,
inference(equational,[status(thm)],[c6,c19,c226]) ).
cnf(c228,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X))) = identity,
inference(equational,[status(thm)],[c23,c227]) ).
cnf(c229,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X,identity))) = identity,
inference(equational,[status(thm)],[c87,c228]) ).
cnf(c230,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,X))) = inverse(greatest_lower_bound(identity,X)),
inference(equational,[status(thm)],[c7,c12,c228]) ).
cnf(c232,plain,
greatest_lower_bound(X,multiply(X,inverse(greatest_lower_bound(identity,Y)))) = X,
inference(equational,[status(thm)],[c28,c38,c228]) ).
cnf(c237,plain,
greatest_lower_bound(X,multiply(X,inverse(greatest_lower_bound(Y,identity)))) = X,
inference(equational,[status(thm)],[c28,c38,c229]) ).
cnf(c239,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(identity,X)),Y)) = greatest_lower_bound(identity,Y),
inference(equational,[status(thm)],[c14,c228]) ).
cnf(c240,plain,
greatest_lower_bound(identity,greatest_lower_bound(X,inverse(greatest_lower_bound(identity,Y)))) = greatest_lower_bound(X,identity),
inference(equational,[status(thm)],[c21,c228]) ).
cnf(c243,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X)),inverse(greatest_lower_bound(identity,inverse(X)))) = identity,
inference(equational,[status(thm)],[c8,c22,c28,c92,c226]) ).
cnf(c262,plain,
least_upper_bound(X,multiply(X,inverse(greatest_lower_bound(identity,Y)))) = multiply(X,inverse(greatest_lower_bound(identity,Y))),
inference(equational,[status(thm)],[c28,c33,c230]) ).
cnf(c282,plain,
greatest_lower_bound(X,multiply(X,inverse(greatest_lower_bound(Y,greatest_lower_bound(identity,Z))))) = X,
inference(equational,[status(thm)],[c53,c232]) ).
cnf(c299,plain,
greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(X,inverse(greatest_lower_bound(identity,Y)))) = least_upper_bound(X,identity),
inference(equational,[status(thm)],[c35,c228]) ).
cnf(c307,plain,
greatest_lower_bound(inverse(X),inverse(greatest_lower_bound(X,multiply(Y,X)))) = inverse(X),
inference(equational,[status(thm)],[c3,c6,c39,c69,c237]) ).
cnf(c312,plain,
greatest_lower_bound(inverse(X),inverse(greatest_lower_bound(X,inverse(Y)))) = inverse(X),
inference(equational,[status(thm)],[c71,c307]) ).
cnf(c313,plain,
greatest_lower_bound(inverse(X),inverse(greatest_lower_bound(X,Y))) = inverse(X),
inference(equational,[status(thm)],[c30,c312]) ).
cnf(c318,plain,
greatest_lower_bound(X,greatest_lower_bound(multiply(X,inverse(greatest_lower_bound(identity,Y))),Z)) = greatest_lower_bound(X,Z),
inference(equational,[status(thm)],[c14,c232]) ).
cnf(c320,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,multiply(X,inverse(greatest_lower_bound(identity,Z))))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c65,c108,c232]) ).
cnf(c356,plain,
inverse(greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(inverse(greatest_lower_bound(Y,Z)),inverse(X)),
inference(equational,[status(thm)],[c38,c69]) ).
cnf(c358,plain,
multiply(inverse(greatest_lower_bound(identity,X)),inverse(Y)) = inverse(greatest_lower_bound(Y,multiply(Y,X))),
inference(equational,[status(thm)],[c28,c38,c239,c318,c356]) ).
cnf(c361,plain,
inverse(greatest_lower_bound(multiply(X,Y),multiply(Z,Y))) = multiply(inverse(Y),inverse(greatest_lower_bound(X,Z))),
inference(equational,[status(thm)],[c39,c69]) ).
cnf(c372,plain,
inverse(least_upper_bound(multiply(X,Y),multiply(Z,Y))) = multiply(inverse(Y),inverse(least_upper_bound(X,Z))),
inference(equational,[status(thm)],[c34,c69]) ).
cnf(c378,plain,
inverse(least_upper_bound(identity,multiply(X,inverse(Y)))) = multiply(Y,inverse(least_upper_bound(X,Y))),
inference(equational,[status(thm)],[c7,c30,c31,c372]) ).
cnf(c429,plain,
inverse(multiply(X,inverse(least_upper_bound(Y,X)))) = least_upper_bound(identity,multiply(Y,inverse(X))),
inference(equational,[status(thm)],[c30,c378]) ).
cnf(c513,plain,
inverse(greatest_lower_bound(identity,multiply(X,Y))) = multiply(inverse(Y),inverse(greatest_lower_bound(inverse(Y),X))),
inference(equational,[status(thm)],[c8,c361]) ).
cnf(c535,plain,
multiply(X,inverse(least_upper_bound(multiply(Y,X),multiply(Z,X)))) = inverse(least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c34,c68]) ).
cnf(c537,plain,
multiply(X,inverse(greatest_lower_bound(multiply(Y,X),multiply(Z,X)))) = inverse(greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c39,c68]) ).
cnf(c538,plain,
multiply(X,inverse(greatest_lower_bound(identity,multiply(Y,X)))) = inverse(greatest_lower_bound(Y,inverse(X))),
inference(equational,[status(thm)],[c6,c8,c537]) ).
cnf(c539,plain,
least_upper_bound(X,inverse(greatest_lower_bound(Y,inverse(X)))) = inverse(greatest_lower_bound(Y,inverse(X))),
inference(equational,[status(thm)],[c262,c538]) ).
cnf(c543,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,inverse(greatest_lower_bound(Z,inverse(X))))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c320,c538]) ).
cnf(c544,plain,
greatest_lower_bound(X,inverse(greatest_lower_bound(identity,X))) = greatest_lower_bound(X,identity),
inference(equational,[status(thm)],[c243,c543]) ).
cnf(c546,plain,
greatest_lower_bound(X,greatest_lower_bound(inverse(X),identity)) = greatest_lower_bound(X,inverse(X)),
inference(equational,[status(thm)],[c543,c544]) ).
cnf(c547,plain,
greatest_lower_bound(X,greatest_lower_bound(identity,inverse(X))) = greatest_lower_bound(X,inverse(X)),
inference(equational,[status(thm)],[c6,c546]) ).
cnf(c594,plain,
inverse(multiply(inverse(X),inverse(least_upper_bound(Y,Z)))) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
inference(equational,[status(thm)],[c34,c81]) ).
cnf(c683,plain,
inverse(multiply(X,inverse(least_upper_bound(X,Y)))) = least_upper_bound(identity,inverse(multiply(X,inverse(Y)))),
inference(equational,[status(thm)],[c3,c17,c22,c30,c429]) ).
cnf(c687,plain,
multiply(X,inverse(least_upper_bound(multiply(Y,X),inverse(Z)))) = inverse(least_upper_bound(Y,inverse(multiply(X,Z)))),
inference(equational,[status(thm)],[c71,c535]) ).
cnf(c693,plain,
multiply(X,inverse(least_upper_bound(multiply(Y,X),Z))) = inverse(least_upper_bound(Y,inverse(multiply(X,inverse(Z))))),
inference(equational,[status(thm)],[c30,c687]) ).
cnf(c694,plain,
least_upper_bound(X,inverse(multiply(inverse(Y),inverse(Z)))) = least_upper_bound(X,multiply(Z,Y)),
inference(equational,[status(thm)],[c8,c17,c28,c30,c594,c693]) ).
cnf(c696,plain,
inverse(multiply(X,inverse(least_upper_bound(Y,X)))) = least_upper_bound(identity,inverse(multiply(X,inverse(Y)))),
inference(equational,[status(thm)],[c30,c429,c694]) ).
cnf(c795,plain,
multiply(X,inverse(greatest_lower_bound(X,Y))) = inverse(greatest_lower_bound(identity,inverse(multiply(X,inverse(Y))))),
inference(equational,[status(thm)],[c30,c70,c513]) ).
cnf(c905,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),Y) = inverse(greatest_lower_bound(inverse(Y),inverse(multiply(X,Y)))),
inference(equational,[status(thm)],[c30,c69,c358]) ).
cnf(c995,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(X,identity)) = least_upper_bound(X,identity),
inference(equational,[status(thm)],[c6,c299,c539]) ).
cnf(c996,plain,
inverse(least_upper_bound(X,identity)) = greatest_lower_bound(identity,inverse(X)),
inference(equational,[status(thm)],[c14,c30,c149,c219,c313,c995]) ).
cnf(c998,plain,
least_upper_bound(identity,inverse(X)) = inverse(greatest_lower_bound(X,identity)),
inference(equational,[status(thm)],[c28,c29,c31,c38,c683,c996]) ).
cnf(c999,plain,
least_upper_bound(inverse(X),identity) = inverse(greatest_lower_bound(X,identity)),
inference(equational,[status(thm)],[c7,c998]) ).
cnf(c1000,plain,
least_upper_bound(X,identity) = inverse(greatest_lower_bound(identity,inverse(X))),
inference(equational,[status(thm)],[c24,c28,c29,c905,c996]) ).
cnf(c1024,plain,
least_upper_bound(identity,X) = inverse(greatest_lower_bound(identity,inverse(X))),
inference(equational,[status(thm)],[c3,c30,c696,c996]) ).
cnf(c1025,plain,
inverse(least_upper_bound(X,inverse(Y))) = greatest_lower_bound(Y,inverse(X)),
inference(equational,[status(thm)],[c28,c29,c38,c68,c693,c996]) ).
cnf(c1029,plain,
least_upper_bound(X,inverse(Y)) = inverse(greatest_lower_bound(Y,inverse(X))),
inference(equational,[status(thm)],[c30,c1025]) ).
cnf(c1036,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X),inverse(Y)))),greatest_lower_bound(inverse(greatest_lower_bound(Y,greatest_lower_bound(inverse(X),inverse(Y)))),inverse(greatest_lower_bound(identity,inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),inverse(greatest_lower_bound(Y,inverse(X))))))))) = inverse(greatest_lower_bound(identity,inverse(X))),
inference(equational,[status(thm)],[c14,c30,c35,c61,c63,c161,c177,c999,c1000,c1024,c1029]) ).
cnf(c1037,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X,greatest_lower_bound(inverse(Y),inverse(X))))) = identity,
inference(equational,[status(thm)],[c6,c228,c239,c240,c1036]) ).
cnf(c1038,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X,greatest_lower_bound(Y,inverse(X))))) = identity,
inference(equational,[status(thm)],[c30,c1037]) ).
cnf(c1042,plain,
inverse(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),identity)))) = inverse(greatest_lower_bound(X,greatest_lower_bound(Y,inverse(X)))),
inference(equational,[status(thm)],[c12,c14,c999,c1038]) ).
cnf(c1044,plain,
greatest_lower_bound(X,multiply(X,inverse(greatest_lower_bound(Y,inverse(Y))))) = X,
inference(equational,[status(thm)],[c282,c547,c1042]) ).
cnf(c1053,plain,
greatest_lower_bound(X,inverse(greatest_lower_bound(identity,inverse(multiply(X,X))))) = X,
inference(equational,[status(thm)],[c30,c795,c1044]) ).
cnf(g1,plain,
a = multiply(positive_part(a),negative_part(a)),
inference(equational,[status(thm)],[c1,c3,c4,c5,c6,c7,c11,c28,c34,c35,c38,c44,c1024,c1053]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP167-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:12:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 47.48/47.58 % SZS status Unsatisfiable
% 47.48/47.58 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------