%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP191-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 06:43:45 AM UTC 2025
% Result : Unsatisfiable 1.02s 1.17s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 7 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 : 28 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
file('theBenchmark.p',prove_p39d) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
greatest_lower_bound(a,b) = b,
file('theBenchmark.p',p39d_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,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(c11,plain,
least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c17,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c24,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c7,c17]) ).
cnf(c26,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c7,c24]) ).
cnf(c29,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c24]) ).
cnf(c30,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c26,c29]) ).
cnf(c33,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c7,c29]) ).
cnf(c43,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c44,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c56,plain,
greatest_lower_bound(multiply(X,a),multiply(X,b)) = multiply(X,b),
inference(equational,[status(thm)],[c4,c43]) ).
cnf(c57,plain,
greatest_lower_bound(identity,multiply(inverse(b),a)) = identity,
inference(equational,[status(thm)],[c5,c7,c56]) ).
cnf(c117,plain,
greatest_lower_bound(X,multiply(inverse(b),multiply(a,X))) = X,
inference(equational,[status(thm)],[c3,c17,c44,c57]) ).
cnf(c118,plain,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
inference(equational,[status(thm)],[c30,c33,c117]) ).
cnf(c119,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(equational,[status(thm)],[c6,c11,c118]) ).
cnf(g1,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(equational,[status(thm)],[c119]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP191-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:16:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.02/1.17 % SZS status Unsatisfiable
% 1.02/1.17 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------