%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP555-1 : 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 06:44:19 AM UTC 2025
% Result : Unsatisfiable 0.42s 0.61s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% 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 : 9 ( 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 : 57 ( 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,
multiply(X,Y) = divide(X,inverse(Y)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
divide(divide(X,inverse(divide(Y,divide(X,Z)))),Z) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
divide(divide(X,inverse(Y)),Z) = divide(W,inverse(divide(Y,divide(W,divide(X,Z))))),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
divide(divide(divide(X,inverse(Y)),Z),divide(X,Z)) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
divide(X,divide(Y,inverse(divide(X,divide(Y,divide(Y,divide(Y,inverse(Z)))))))) = Z,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c6,plain,
divide(divide(divide(X,inverse(Y)),Z),inverse(divide(W,Y))) = divide(divide(X,inverse(W)),Z),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c8,plain,
divide(X,inverse(divide(divide(Y,divide(Z,W)),divide(X,divide(Z,W))))) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c9,plain,
divide(X,inverse(divide(divide(Y,Z),divide(X,Z)))) = Y,
inference(equational,[status(thm)],[c8]) ).
cnf(c12,plain,
divide(divide(X,divide(Y,divide(Y,inverse(Z)))),X) = Z,
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c14,plain,
divide(X,divide(Y,divide(Y,inverse(Z)))) = divide(X,inverse(Z)),
inference(equational,[status(thm)],[c9,c12]) ).
cnf(c15,plain,
divide(divide(X,inverse(Y)),X) = Y,
inference(equational,[status(thm)],[c12,c14]) ).
cnf(c16,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c17,plain,
divide(X,inverse(divide(Y,X))) = Y,
inference(equational,[status(thm)],[c6,c15]) ).
cnf(c18,plain,
divide(divide(X,X),inverse(Y)) = Y,
inference(equational,[status(thm)],[c16,c17]) ).
cnf(c20,plain,
divide(X,divide(inverse(Y),inverse(X))) = Y,
inference(equational,[status(thm)],[c15]) ).
cnf(c21,plain,
divide(divide(X,Y),X) = inverse(Y),
inference(equational,[status(thm)],[c12,c20]) ).
cnf(c22,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c15,c21]) ).
cnf(c26,plain,
divide(divide(X,X),Y) = inverse(Y),
inference(equational,[status(thm)],[c18,c22]) ).
cnf(c34,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(X,Z),
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c35,plain,
divide(X,divide(Y,inverse(X))) = inverse(Y),
inference(equational,[status(thm)],[c18,c26,c34]) ).
cnf(c38,plain,
divide(divide(X,Y),Z) = divide(X,divide(Y,inverse(Z))),
inference(equational,[status(thm)],[c15,c34]) ).
cnf(c41,plain,
divide(inverse(X),Y) = inverse(divide(X,inverse(Y))),
inference(equational,[status(thm)],[c21,c35]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c1,c22,c38,c41]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP555-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n006.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 08:31:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.42/0.61 % SZS status Unsatisfiable
% 0.42/0.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------