%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP532-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 06:44:16 AM UTC 2025
% Result : Unsatisfiable 0.54s 0.74s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 3 RR)
% Number of literals : 20 ( 19 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 : 43 ( 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(divide(X,divide(Y,Z)),divide(X,Y)) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c7,plain,
divide(divide(X,X),X) = divide(divide(Y,Y),X),
inference(equational,[status(thm)],[c1,c3,c6]) ).
cnf(c10,plain,
divide(X,inverse(Y)) = divide(X,divide(divide(Y,Y),Y)),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c11,plain,
divide(X,divide(divide(Y,divide(Z,X)),Y)) = Z,
inference(equational,[status(thm)],[c6]) ).
cnf(c12,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c3,c10,c11]) ).
cnf(c14,plain,
divide(X,divide(multiply(Y,X),Y)) = divide(Z,Z),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c16,plain,
divide(multiply(X,Y),divide(X,divide(Z,Z))) = Y,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c17,plain,
divide(divide(X,Y),divide(X,Z)) = divide(divide(W,divide(Y,Z)),W),
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c18,plain,
divide(divide(X,divide(Y,Y)),X) = divide(Z,Z),
inference(equational,[status(thm)],[c12,c17]) ).
cnf(c19,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c11,c18]) ).
cnf(c22,plain,
divide(multiply(X,Y),X) = Y,
inference(equational,[status(thm)],[c16,c19]) ).
cnf(c53,plain,
divide(X,divide(Y,divide(Z,divide(X,Y)))) = Z,
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c54,plain,
multiply(divide(X,Y),Y) = X,
inference(equational,[status(thm)],[c14,c19,c53]) ).
cnf(c56,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c22,c54]) ).
cnf(g1,plain,
multiply(a,b) = multiply(b,a),
inference(equational,[status(thm)],[c56]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP532-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:31:19 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.54/0.74 % SZS status Unsatisfiable
% 0.54/0.74 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------