%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP184-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.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 06:43:43 AM UTC 2025
% Result : Unsatisfiable 31.07s 31.27s
% Output : CNFRefutation 31.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 4 RR)
% Number of literals : 31 ( 30 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('theBenchmark.p',prove_p21x) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c5,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c6,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c15,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c20,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c6,c15]) ).
cnf(c22,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c6,c20]) ).
cnf(c25,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c20]) ).
cnf(c26,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c22,c25]) ).
cnf(c27,plain,
inverse(identity) = identity,
inference(equational,[status(thm)],[c6,c26]) ).
cnf(c28,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c22,c26]) ).
cnf(c29,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c6,c25]) ).
cnf(c30,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c20,c25]) ).
cnf(c31,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c32,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c33,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c34,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c63,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(equational,[status(thm)],[c15,c29]) ).
cnf(c64,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c20,c26,c63]) ).
cnf(c65,plain,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
inference(equational,[status(thm)],[c20,c64]) ).
cnf(c652,plain,
inverse(greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(inverse(greatest_lower_bound(Y,Z)),inverse(X)),
inference(equational,[status(thm)],[c32,c65]) ).
cnf(c653,plain,
inverse(greatest_lower_bound(X,multiply(X,Y))) = multiply(inverse(greatest_lower_bound(identity,Y)),inverse(X)),
inference(equational,[status(thm)],[c26,c652]) ).
cnf(c654,plain,
inverse(greatest_lower_bound(identity,inverse(X))) = multiply(inverse(greatest_lower_bound(identity,X)),X),
inference(equational,[status(thm)],[c4,c6,c28,c653]) ).
cnf(c656,plain,
inverse(greatest_lower_bound(X,multiply(X,Y))) = multiply(inverse(greatest_lower_bound(Y,identity)),inverse(X)),
inference(equational,[status(thm)],[c4,c26,c652]) ).
cnf(c657,plain,
inverse(greatest_lower_bound(multiply(X,Y),multiply(Z,Y))) = multiply(inverse(Y),inverse(greatest_lower_bound(X,Z))),
inference(equational,[status(thm)],[c34,c65]) ).
cnf(c658,plain,
inverse(greatest_lower_bound(identity,multiply(X,inverse(Y)))) = multiply(Y,inverse(greatest_lower_bound(Y,X))),
inference(equational,[status(thm)],[c28,c29,c657]) ).
cnf(c659,plain,
multiply(X,inverse(greatest_lower_bound(X,identity))) = multiply(inverse(greatest_lower_bound(identity,X)),X),
inference(equational,[status(thm)],[c4,c26,c27,c654,c656,c658]) ).
cnf(c660,plain,
multiply(inverse(greatest_lower_bound(identity,X)),X) = multiply(X,inverse(greatest_lower_bound(identity,X))),
inference(equational,[status(thm)],[c4,c15,c26,c29,c30,c654,c659]) ).
cnf(g1,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(equational,[status(thm)],[c3,c4,c5,c26,c31,c33,c660]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP184-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:15:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 31.07/31.27 % SZS status Unsatisfiable
% 31.07/31.27 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------