%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP456-1 : TPTP v9.0.0. Released v2.6.0.
% 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 06:44:05 AM UTC 2025
% Result : Unsatisfiable 0.47s 0.68s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 3 RR)
% Number of literals : 21 ( 20 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 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,
identity = divide(X,X),
file('theBenchmark.p',identity) ).
cnf(c2,plain,
divide(X,X) = identity,
inference(equational,[status(thm)],[c1]) ).
cnf(c4,axiom,
multiply(X,Y) = divide(X,divide(identity,Y)),
file('theBenchmark.p',multiply) ).
cnf(c5,axiom,
divide(divide(identity,divide(X,divide(Y,divide(divide(divide(X,X),X),Z)))),Z) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c6,plain,
divide(divide(identity,divide(X,divide(Y,divide(divide(identity,X),Z)))),Z) = Y,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
divide(divide(identity,divide(X,identity)),Y) = divide(divide(identity,X),Y),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
divide(identity,divide(X,identity)) = divide(identity,X),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
divide(divide(identity,divide(X,divide(Y,identity))),divide(identity,X)) = Y,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c10,plain,
divide(identity,divide(identity,X)) = X,
inference(equational,[status(thm)],[c2,c8,c9]) ).
cnf(c11,plain,
divide(X,identity) = X,
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
divide(divide(X,divide(identity,Y)),Y) = X,
inference(equational,[status(thm)],[c2,c6,c10]) ).
cnf(c13,plain,
divide(X,Y) = divide(identity,divide(Y,X)),
inference(equational,[status(thm)],[c9,c11,c12]) ).
cnf(c14,plain,
divide(divide(X,Y),divide(identity,Y)) = X,
inference(equational,[status(thm)],[c10,c12]) ).
cnf(c16,plain,
divide(divide(identity,X),divide(Y,X)) = divide(identity,Y),
inference(equational,[status(thm)],[c13,c14]) ).
cnf(c17,plain,
divide(identity,divide(divide(identity,X),divide(identity,divide(X,Y)))) = Y,
inference(equational,[status(thm)],[c9,c11,c12,c13]) ).
cnf(c34,plain,
divide(divide(identity,divide(X,Y)),Z) = divide(Y,divide(identity,divide(divide(identity,X),Z))),
inference(equational,[status(thm)],[c6,c12]) ).
cnf(c36,plain,
divide(divide(X,Y),divide(identity,divide(Y,Z))) = divide(X,Z),
inference(equational,[status(thm)],[c10,c16,c34]) ).
cnf(c37,plain,
divide(divide(X,divide(identity,Y)),Z) = divide(X,divide(identity,divide(Y,Z))),
inference(equational,[status(thm)],[c17,c36]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c4,c37]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP456-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.12 % 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 08:28:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.47/0.68 % SZS status Unsatisfiable
% 0.47/0.68 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------