%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP169-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 06:43:38 AM UTC 2025
% Result : Unsatisfiable 1.41s 1.60s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 9 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(a,b) != b,
file('theBenchmark.p',prove_p02b) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c5,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c6,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c7,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c8,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c11,axiom,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
file('theBenchmark.p',p02b_1) ).
cnf(c12,plain,
greatest_lower_bound(inverse(b),inverse(a)) = inverse(a),
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c15,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c23,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c6,c15]) ).
cnf(c25,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c6,c23]) ).
cnf(c28,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c23]) ).
cnf(c29,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c25,c28]) ).
cnf(c31,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c25,c29]) ).
cnf(c35,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c36,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c99,plain,
greatest_lower_bound(multiply(X,inverse(b)),multiply(X,inverse(a))) = multiply(X,inverse(a)),
inference(equational,[status(thm)],[c12,c36]) ).
cnf(c101,plain,
greatest_lower_bound(identity,multiply(b,inverse(a))) = multiply(b,inverse(a)),
inference(equational,[status(thm)],[c6,c31,c99]) ).
cnf(c102,plain,
least_upper_bound(identity,multiply(b,inverse(a))) = identity,
inference(equational,[status(thm)],[c7,c101]) ).
cnf(c106,plain,
least_upper_bound(X,multiply(b,multiply(inverse(a),X))) = X,
inference(equational,[status(thm)],[c3,c15,c35,c102]) ).
cnf(c107,plain,
least_upper_bound(b,a) = a,
inference(equational,[status(thm)],[c5,c6,c29,c106]) ).
cnf(c108,plain,
greatest_lower_bound(b,a) = b,
inference(equational,[status(thm)],[c8,c107]) ).
cnf(g1,plain,
greatest_lower_bound(a,b) = b,
inference(equational,[status(thm)],[c4,c108]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GRP169-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.02/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.31 % Computer : n008.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Jul 14 08:13:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 1.41/1.60 % SZS status Unsatisfiable
% 1.41/1.60 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------