%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP521-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 06:44:15 AM UTC 2025
% Result : Unsatisfiable 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 3 RR)
% Number of literals : 11 ( 10 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 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,
inverse(X) = divide(divide(Y,Y),X),
file('theBenchmark.p',inverse) ).
cnf(c2,axiom,
multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('theBenchmark.p',multiply) ).
cnf(c3,plain,
divide(X,inverse(Y)) = divide(X,divide(divide(X,X),Y)),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c6,axiom,
divide(X,divide(Y,divide(Z,divide(X,Y)))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c7,plain,
divide(X,multiply(Y,divide(X,Y))) = divide(Z,Z),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c2,c6,c7]) ).
cnf(c29,plain,
divide(X,divide(divide(Y,Y),Z)) = divide(X,inverse(Z)),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c30,plain,
divide(X,inverse(Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c2,c29]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c8,c30]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP521-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.31 % Computer : n006.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Jul 14 08:31:04 EDT 2025
% 0.16/0.31 % CPUTime :
% 0.17/0.46 % SZS status Unsatisfiable
% 0.17/0.46 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------