%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP170-3 : 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 06:43:38 AM UTC 2025
% Result : Unsatisfiable 2.01s 2.22s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 7 RR)
% Number of literals : 33 ( 32 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('theBenchmark.p',prove_p03c) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
least_upper_bound(a,b) = b,
file('theBenchmark.p',p03c_1) ).
cnf(c5,axiom,
least_upper_bound(c,d) = d,
file('theBenchmark.p',p03c_2) ).
cnf(c8,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c10,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c11,plain,
greatest_lower_bound(a,b) = a,
inference(equational,[status(thm)],[c4,c10]) ).
cnf(c15,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
file('GRP004-2.ax',associativity_of_glb) ).
cnf(c16,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c15]) ).
cnf(c19,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c28,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c8,c19]) ).
cnf(c30,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c8,c28]) ).
cnf(c33,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c28]) ).
cnf(c34,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c30,c33]) ).
cnf(c36,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c30,c34]) ).
cnf(c37,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c8,c33]) ).
cnf(c50,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c28,c33]) ).
cnf(c51,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c52,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
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(c55,plain,
greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),Z)) = greatest_lower_bound(X,Z),
inference(equational,[status(thm)],[c10,c16]) ).
cnf(c71,plain,
least_upper_bound(multiply(a,X),multiply(b,X)) = multiply(b,X),
inference(equational,[status(thm)],[c4,c54]) ).
cnf(c73,plain,
least_upper_bound(multiply(X,c),multiply(X,d)) = multiply(X,d),
inference(equational,[status(thm)],[c5,c51]) ).
cnf(c87,plain,
greatest_lower_bound(multiply(X,c),multiply(X,d)) = multiply(X,c),
inference(equational,[status(thm)],[c10,c73]) ).
cnf(c90,plain,
greatest_lower_bound(multiply(a,X),multiply(b,X)) = multiply(a,X),
inference(equational,[status(thm)],[c11,c52]) ).
cnf(c205,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(equational,[status(thm)],[c19,c37]) ).
cnf(c206,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c28,c34,c205]) ).
cnf(c208,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
inference(equational,[status(thm)],[c50,c206]) ).
cnf(c277,plain,
multiply(X,Y) = inverse(multiply(inverse(Y),inverse(X))),
inference(equational,[status(thm)],[c36,c208]) ).
cnf(c361,plain,
greatest_lower_bound(multiply(a,X),greatest_lower_bound(multiply(b,X),Y)) = greatest_lower_bound(multiply(a,X),Y),
inference(equational,[status(thm)],[c55,c71]) ).
cnf(c363,plain,
greatest_lower_bound(multiply(a,c),inverse(multiply(inverse(d),inverse(b)))) = multiply(a,c),
inference(equational,[status(thm)],[c87,c90,c277,c361]) ).
cnf(g1,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) = multiply(a,c),
inference(equational,[status(thm)],[c277,c363]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP170-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n002.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:13:34 EDT 2025
% 0.12/0.32 % CPUTime :
% 2.01/2.22 % SZS status Unsatisfiable
% 2.01/2.22 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------