%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP175-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 2.08s 2.27s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 4 RR)
% Number of literals : 11 ( 10 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
file('theBenchmark.p',prove_p06a) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
least_upper_bound(identity,b) = b,
file('theBenchmark.p',p06a_1) ).
cnf(c7,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c41,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c42,plain,
least_upper_bound(X,multiply(b,X)) = multiply(b,X),
inference(equational,[status(thm)],[c3,c4,c41]) ).
cnf(c52,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c282,plain,
least_upper_bound(multiply(X,Y),multiply(X,multiply(b,Y))) = multiply(X,multiply(b,Y)),
inference(equational,[status(thm)],[c42,c52]) ).
cnf(c308,plain,
least_upper_bound(identity,multiply(inverse(X),multiply(b,X))) = multiply(inverse(X),multiply(b,X)),
inference(equational,[status(thm)],[c7,c282]) ).
cnf(g1,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(equational,[status(thm)],[c308]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP175-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.09/0.28 % Computer : n007.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon Jul 14 08:13:49 EDT 2025
% 0.09/0.28 % CPUTime :
% 2.08/2.27 % SZS status Unsatisfiable
% 2.08/2.27 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------