%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP170-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 2.29s 2.49s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 7 RR)
% Number of literals : 22 ( 21 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; 4 con; 0-2 aty)
% Number of variables : 31 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('theBenchmark.p',prove_p03b) ).
cnf(c4,axiom,
greatest_lower_bound(a,b) = a,
file('theBenchmark.p',p03b_1) ).
cnf(c5,axiom,
greatest_lower_bound(c,d) = c,
file('theBenchmark.p',p03b_2) ).
cnf(c6,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c7,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c11,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c14,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c15,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(equational,[status(thm)],[c7,c14]) ).
cnf(c19,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(c20,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c19]) ).
cnf(c64,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c65,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c69,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X,Y),Z)) = least_upper_bound(X,Z),
inference(equational,[status(thm)],[c11,c20]) ).
cnf(c76,plain,
greatest_lower_bound(multiply(X,d),multiply(X,c)) = multiply(X,c),
inference(equational,[status(thm)],[c5,c6,c65]) ).
cnf(c79,plain,
greatest_lower_bound(multiply(b,X),multiply(a,X)) = multiply(a,X),
inference(equational,[status(thm)],[c4,c6,c64]) ).
cnf(c92,plain,
least_upper_bound(multiply(b,X),multiply(a,X)) = multiply(b,X),
inference(equational,[status(thm)],[c11,c79]) ).
cnf(c100,plain,
least_upper_bound(multiply(X,d),multiply(X,c)) = multiply(X,d),
inference(equational,[status(thm)],[c11,c76]) ).
cnf(c382,plain,
least_upper_bound(multiply(b,X),least_upper_bound(multiply(a,X),Y)) = least_upper_bound(multiply(b,X),Y),
inference(equational,[status(thm)],[c69,c79]) ).
cnf(c384,plain,
least_upper_bound(multiply(b,d),multiply(a,c)) = multiply(b,d),
inference(equational,[status(thm)],[c92,c100,c382]) ).
cnf(c385,plain,
greatest_lower_bound(multiply(b,d),multiply(a,c)) = multiply(a,c),
inference(equational,[status(thm)],[c6,c15,c384]) ).
cnf(g1,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) = multiply(a,c),
inference(equational,[status(thm)],[c6,c385]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP170-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.11/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n016.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 08:13:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 2.29/2.49 % SZS status Unsatisfiable
% 2.29/2.49 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------