%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP184-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 06:43:42 AM UTC 2025
% Result : Unsatisfiable 0.94s 1.10s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 4 RR)
% Number of literals : 25 ( 24 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('theBenchmark.p',prove_p21) ).
cnf(c1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p21_1) ).
cnf(c4,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c5,axiom,
inverse(inverse(X)) = X,
file('theBenchmark.p',p21_2) ).
cnf(c6,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c7,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c8,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c9,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c14,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('theBenchmark.p',p21_3) ).
cnf(c15,plain,
multiply(inverse(X),identity) = inverse(X),
inference(equational,[status(thm)],[c1,c4,c14]) ).
cnf(c30,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c31,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c32,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c33,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c69,plain,
inverse(greatest_lower_bound(multiply(X,Y),multiply(Z,Y))) = multiply(inverse(Y),inverse(greatest_lower_bound(X,Z))),
inference(equational,[status(thm)],[c14,c32]) ).
cnf(c70,plain,
inverse(greatest_lower_bound(identity,multiply(X,inverse(Y)))) = multiply(Y,inverse(greatest_lower_bound(Y,X))),
inference(equational,[status(thm)],[c5,c9,c69]) ).
cnf(c71,plain,
inverse(greatest_lower_bound(identity,inverse(X))) = multiply(X,inverse(greatest_lower_bound(X,identity))),
inference(equational,[status(thm)],[c4,c70]) ).
cnf(c72,plain,
inverse(greatest_lower_bound(X,multiply(Y,X))) = multiply(inverse(X),inverse(greatest_lower_bound(identity,Y))),
inference(equational,[status(thm)],[c4,c69]) ).
cnf(c73,plain,
inverse(greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(inverse(greatest_lower_bound(Y,Z)),inverse(X)),
inference(equational,[status(thm)],[c14,c31]) ).
cnf(c74,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X),Y))) = multiply(inverse(greatest_lower_bound(X,Y)),X),
inference(equational,[status(thm)],[c5,c8,c73]) ).
cnf(c75,plain,
multiply(inverse(greatest_lower_bound(X,identity)),X) = multiply(X,inverse(greatest_lower_bound(X,identity))),
inference(equational,[status(thm)],[c1,c4,c71,c72,c74]) ).
cnf(c76,plain,
multiply(inverse(greatest_lower_bound(identity,X)),X) = multiply(X,inverse(greatest_lower_bound(X,identity))),
inference(equational,[status(thm)],[c7,c75]) ).
cnf(c82,plain,
multiply(inverse(greatest_lower_bound(identity,X)),X) = multiply(X,inverse(greatest_lower_bound(identity,X))),
inference(equational,[status(thm)],[c7,c76]) ).
cnf(g1,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(equational,[status(thm)],[c4,c6,c7,c15,c30,c33,c82]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP184-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:15:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.94/1.10 % SZS status Unsatisfiable
% 0.94/1.10 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------