%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP524-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 0.76s 0.93s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 3 RR)
% Number of literals : 25 ( 24 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 : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
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(c10,plain,
divide(X,divide(Y,divide(Z,Z))) = divide(X,Y),
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c11,plain,
divide(X,divide(X,Y)) = Y,
inference(equational,[status(thm)],[c6,c10]) ).
cnf(c12,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c18,plain,
divide(X,divide(divide(X,X),divide(Y,X))) = Y,
inference(equational,[status(thm)],[c2,c7,c11,c12]) ).
cnf(c21,plain,
divide(X,divide(divide(Y,Y),Z)) = divide(X,divide(divide(X,X),Z)),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c22,plain,
inverse(divide(divide(X,X),Y)) = Y,
inference(equational,[status(thm)],[c1,c11,c12,c21]) ).
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(c32,plain,
divide(divide(X,X),divide(Y,multiply(Z,Y))) = Z,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c33,plain,
inverse(X) = divide(Y,divide(X,divide(divide(X,X),Y))),
inference(equational,[status(thm)],[c2,c22,c32]) ).
cnf(c35,plain,
divide(divide(X,Y),X) = inverse(Y),
inference(equational,[status(thm)],[c18,c33]) ).
cnf(c37,plain,
divide(multiply(X,Y),X) = Y,
inference(equational,[status(thm)],[c2,c22,c35]) ).
cnf(c39,plain,
divide(X,divide(divide(Y,divide(Z,X)),Y)) = Z,
inference(equational,[status(thm)],[c6]) ).
cnf(c44,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(X,Z),
inference(equational,[status(thm)],[c6,c39]) ).
cnf(c46,plain,
divide(divide(X,Y),inverse(Y)) = X,
inference(equational,[status(thm)],[c3,c12,c44]) ).
cnf(c82,plain,
divide(X,inverse(Y)) = multiply(Y,X),
inference(equational,[status(thm)],[c37,c46]) ).
cnf(g1,plain,
multiply(a,b) = multiply(b,a),
inference(equational,[status(thm)],[c30,c82]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP524-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n002.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 08:31:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.76/0.93 % SZS status Unsatisfiable
% 0.76/0.93 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------