%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP453-1 : TPTP v9.0.0. Released v2.6.0.
% 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 06:44:05 AM UTC 2025
% Result : Unsatisfiable 0.50s 0.70s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 3 RR)
% Number of literals : 32 ( 31 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c1,axiom,
inverse(X) = divide(divide(Y,Y),X),
file('theBenchmark.p',inverse) ).
cnf(c2,plain,
divide(divide(X,X),Y) = inverse(Y),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
divide(inverse(divide(X,X)),Y) = inverse(Y),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,axiom,
multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('theBenchmark.p',multiply) ).
cnf(c5,plain,
multiply(X,Y) = divide(X,inverse(Y)),
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
divide(inverse(inverse(divide(X,X))),Y) = inverse(Y),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c7,plain,
divide(inverse(inverse(inverse(divide(X,X)))),Y) = inverse(Y),
inference(equational,[status(thm)],[c3]) ).
cnf(c13,axiom,
divide(divide(divide(X,X),divide(X,divide(Y,divide(divide(divide(X,X),X),Z)))),Z) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c14,plain,
divide(inverse(divide(X,divide(Y,divide(inverse(X),Z)))),Z) = Y,
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c15,plain,
divide(inverse(inverse(divide(X,inverse(Y)))),Y) = X,
inference(equational,[status(thm)],[c2,c3,c14]) ).
cnf(c16,plain,
divide(inverse(inverse(inverse(inverse(X)))),X) = divide(Y,Y),
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c21,plain,
inverse(inverse(inverse(inverse(inverse(X))))) = inverse(X),
inference(equational,[status(thm)],[c6,c15,c16]) ).
cnf(c24,plain,
divide(inverse(inverse(X)),Y) = inverse(inverse(divide(X,inverse(inverse(Y))))),
inference(equational,[status(thm)],[c15]) ).
cnf(c25,plain,
inverse(inverse(inverse(inverse(divide(X,inverse(inverse(inverse(inverse(X))))))))) = inverse(divide(Y,Y)),
inference(equational,[status(thm)],[c2,c16,c24]) ).
cnf(c27,plain,
inverse(inverse(divide(divide(X,inverse(Y)),inverse(inverse(Y))))) = X,
inference(equational,[status(thm)],[c6,c7,c14,c24]) ).
cnf(c28,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(equational,[status(thm)],[c21,c27]) ).
cnf(c29,plain,
inverse(inverse(divide(divide(X,Y),inverse(Y)))) = X,
inference(equational,[status(thm)],[c27]) ).
cnf(c30,plain,
divide(divide(X,Y),inverse(Y)) = inverse(inverse(X)),
inference(equational,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
divide(inverse(divide(X,inverse(divide(inverse(X),Y)))),Y) = divide(Z,Z),
inference(equational,[status(thm)],[c2,c14]) ).
cnf(c32,plain,
inverse(divide(X,inverse(divide(inverse(X),inverse(Y))))) = inverse(Y),
inference(equational,[status(thm)],[c2,c15,c24,c28,c31]) ).
cnf(c33,plain,
inverse(divide(X,divide(Y,Y))) = inverse(X),
inference(equational,[status(thm)],[c25,c28,c32]) ).
cnf(c34,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c28,c33]) ).
cnf(c35,plain,
inverse(divide(X,inverse(divide(Y,Y)))) = inverse(X),
inference(equational,[status(thm)],[c16,c28,c32]) ).
cnf(c36,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c29,c34,c35]) ).
cnf(c39,plain,
inverse(divide(X,inverse(divide(inverse(X),Y)))) = Y,
inference(equational,[status(thm)],[c27,c28,c30,c32]) ).
cnf(c40,plain,
divide(inverse(X),divide(inverse(Y),X)) = Y,
inference(equational,[status(thm)],[c15,c39]) ).
cnf(c41,plain,
divide(inverse(X),Y) = inverse(divide(Y,inverse(X))),
inference(equational,[status(thm)],[c15,c40]) ).
cnf(c48,plain,
divide(inverse(divide(X,Y)),Z) = divide(Y,inverse(divide(inverse(X),Z))),
inference(equational,[status(thm)],[c14,c15,c36]) ).
cnf(c49,plain,
divide(divide(X,inverse(Y)),Z) = divide(X,inverse(divide(Y,Z))),
inference(equational,[status(thm)],[c36,c41,c48]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c5,c49]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP453-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.14/0.33 % Computer : n009.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Jul 14 08:29:04 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.50/0.70 % SZS status Unsatisfiable
% 0.50/0.70 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------