%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP116-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n012.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 06:43:25 AM UTC 2025
% Result : Unsatisfiable 0.40s 0.61s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 3 RR)
% Number of literals : 15 ( 14 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(identity,a) != a,
file('theBenchmark.p',prove_order3) ).
cnf(c1,axiom,
multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(X,multiply(multiply(X,multiply(Y,Z)),multiply(identity,multiply(Z,Z)))) = multiply(multiply(X,multiply(multiply(X,Y),W)),multiply(identity,multiply(W,W))),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(X,multiply(X,multiply(multiply(X,multiply(Y,Z)),multiply(identity,multiply(Z,Z))))) = Y,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c6,plain,
multiply(X,multiply(Y,multiply(identity,multiply(multiply(identity,multiply(Z,Z)),multiply(identity,multiply(Z,Z)))))) = multiply(multiply(X,Y),Z),
inference(equational,[status(thm)],[c1]) ).
cnf(c7,plain,
multiply(multiply(X,identity),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c9,plain,
multiply(multiply(X,Y),multiply(identity,Z)) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c10,plain,
multiply(X,multiply(X,multiply(X,Y))) = Y,
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c11,plain,
multiply(X,multiply(X,X)) = identity,
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
multiply(X,multiply(multiply(X,X),Y)) = multiply(identity,multiply(identity,Y)),
inference(equational,[status(thm)],[c9,c11]) ).
cnf(c13,plain,
multiply(multiply(X,Y),multiply(Y,Y)) = X,
inference(equational,[status(thm)],[c3,c10,c12]) ).
cnf(c14,plain,
multiply(identity,X) = X,
inference(equational,[status(thm)],[c11,c13]) ).
cnf(g1,plain,
multiply(identity,a) = a,
inference(equational,[status(thm)],[c14]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP116-1 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:08:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.40/0.61 % SZS status Unsatisfiable
% 0.40/0.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------