%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP175-2 : 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 06:43:39 AM UTC 2025
% Result : Unsatisfiable 14.51s 14.71s
% Output : CNFRefutation 14.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 6 RR)
% Number of literals : 23 ( 22 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 31 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
file('theBenchmark.p',prove_p06b) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
greatest_lower_bound(identity,b) = identity,
file('theBenchmark.p',p06b_1) ).
cnf(c5,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c6,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c7,plain,
greatest_lower_bound(b,identity) = identity,
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c8,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c9,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c10,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c11,plain,
least_upper_bound(b,identity) = b,
inference(equational,[status(thm)],[c7,c10]) ).
cnf(c18,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c26,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c8,c18]) ).
cnf(c28,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c8,c26]) ).
cnf(c31,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c26]) ).
cnf(c32,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c28,c31]) ).
cnf(c47,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c48,plain,
least_upper_bound(X,multiply(X,b)) = multiply(X,b),
inference(equational,[status(thm)],[c6,c11,c32,c47]) ).
cnf(c54,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c583,plain,
least_upper_bound(multiply(X,Y),multiply(X,multiply(b,Y))) = multiply(X,multiply(b,Y)),
inference(equational,[status(thm)],[c18,c48,c54]) ).
cnf(c607,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,multiply(b,Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c9,c583]) ).
cnf(c609,plain,
greatest_lower_bound(identity,multiply(inverse(X),multiply(b,X))) = identity,
inference(equational,[status(thm)],[c8,c607]) ).
cnf(g1,plain,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) = identity,
inference(equational,[status(thm)],[c609]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP175-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n009.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 08:13:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 14.51/14.71 % SZS status Unsatisfiable
% 14.51/14.71 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------