%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP170-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.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 2.15s 2.30s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 6 RR)
% Number of literals : 27 ( 26 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
file('theBenchmark.p',prove_p03a) ).
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',p03a_1) ).
cnf(c5,axiom,
least_upper_bound(c,d) = d,
file('theBenchmark.p',p03a_2) ).
cnf(c8,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c17,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
file('GRP004-2.ax',associativity_of_lub) ).
cnf(c18,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c17]) ).
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(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(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(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(c371,plain,
least_upper_bound(multiply(a,X),least_upper_bound(multiply(b,X),Y)) = least_upper_bound(multiply(b,X),Y),
inference(equational,[status(thm)],[c18,c71]) ).
cnf(c372,plain,
least_upper_bound(multiply(a,c),inverse(multiply(inverse(d),inverse(b)))) = inverse(multiply(inverse(d),inverse(b))),
inference(equational,[status(thm)],[c73,c277,c371]) ).
cnf(g1,plain,
least_upper_bound(multiply(a,c),multiply(b,d)) = multiply(b,d),
inference(equational,[status(thm)],[c277,c372]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP170-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n010.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 08:13:19 EDT 2025
% 0.12/0.32 % CPUTime :
% 2.15/2.30 % SZS status Unsatisfiable
% 2.15/2.30 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------