%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP557-1 : TPTP v9.0.0. Released v2.6.0.
% 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 06:44:19 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 3 RR)
% Number of literals : 12 ( 11 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c1,axiom,
multiply(X,Y) = divide(X,inverse(Y)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
divide(X,inverse(divide(divide(Y,Z),divide(X,Z)))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
divide(X,inverse(divide(Y,divide(X,inverse(divide(divide(Y,Z),divide(W,Z))))))) = W,
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
divide(X,inverse(divide(Y,Y))) = X,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
divide(X,inverse(divide(Y,X))) = Y,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c7,plain,
divide(inverse(divide(X,X)),inverse(Y)) = Y,
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c8,plain,
divide(X,X) = inverse(divide(Y,Y)),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c1,c10]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP557-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:32:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------