%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP766-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.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 06:44:51 AM UTC 2025
% Result : Unsatisfiable 211.00s 211.00s
% Output : CNFRefutation 211.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 3 RR)
% Number of literals : 23 ( 22 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2),
file('theBenchmark.p',goals) ).
cnf(c13,axiom,
quotient(product(X,Y),Y) = X,
file('theBenchmark.p',sos05) ).
cnf(c18,axiom,
difference(X,product(X,Y)) = Y,
file('theBenchmark.p',sos04) ).
cnf(c22,axiom,
product(quotient(X,Y),Y) = X,
file('theBenchmark.p',sos06) ).
cnf(c25,axiom,
product(X,difference(X,Y)) = Y,
file('theBenchmark.p',sos03) ).
cnf(c30,axiom,
t(X,Y) = quotient(product(X,Y),X),
file('theBenchmark.p',sos18) ).
cnf(c31,plain,
quotient(product(X,Y),X) = t(X,Y),
inference(equational,[status(thm)],[c30]) ).
cnf(c32,plain,
t(X,X) = X,
inference(equational,[status(thm)],[c13,c31]) ).
cnf(c42,plain,
t(X,difference(X,Y)) = quotient(Y,X),
inference(equational,[status(thm)],[c25,c31]) ).
cnf(c43,plain,
product(t(X,Y),X) = product(X,Y),
inference(equational,[status(thm)],[c22,c31]) ).
cnf(c84,axiom,
difference(X,product(product(X,Y),Z)) = quotient(product(Y,product(Z,X)),X),
file('theBenchmark.p',sos07) ).
cnf(c85,plain,
quotient(product(X,product(Y,Z)),Z) = difference(Z,product(product(Z,X),Y)),
inference(equational,[status(thm)],[c84]) ).
cnf(c422,axiom,
t(eta(X),product(Y,Z)) = product(t(eta(X),Y),t(eta(X),Z)),
file('theBenchmark.p',sos19) ).
cnf(c423,plain,
product(t(eta(X),Y),t(eta(X),Z)) = t(eta(X),product(Y,Z)),
inference(equational,[status(thm)],[c422]) ).
cnf(c424,plain,
t(eta(X),product(Y,eta(X))) = product(eta(X),Y),
inference(equational,[status(thm)],[c32,c43,c423]) ).
cnf(c518,plain,
product(difference(X,product(product(X,Y),Z)),X) = product(Y,product(Z,X)),
inference(equational,[status(thm)],[c22,c85]) ).
cnf(c3013,plain,
t(eta(X),product(Y,product(Z,eta(X)))) = product(product(eta(X),Y),Z),
inference(equational,[status(thm)],[c25,c424,c518]) ).
cnf(c3595,plain,
product(quotient(X,eta(Y)),t(eta(Y),Z)) = t(eta(Y),product(difference(eta(Y),X),Z)),
inference(equational,[status(thm)],[c42,c423]) ).
cnf(c3597,plain,
product(quotient(X,eta(Y)),product(eta(Y),Z)) = product(X,Z),
inference(equational,[status(thm)],[c25,c424,c3013,c3595]) ).
cnf(c3598,plain,
product(product(X,eta(Y)),Z) = product(X,product(eta(Y),Z)),
inference(equational,[status(thm)],[c13,c3597]) ).
cnf(c3603,plain,
product(product(eta(X),Y),Z) = product(eta(X),product(Y,Z)),
inference(equational,[status(thm)],[c18,c518,c3598]) ).
cnf(g1,plain,
product(eta(x0),product(x1,x2)) = product(product(eta(x0),x1),x2),
inference(equational,[status(thm)],[c3603]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP766-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.10 % Command : run_Leo-III %s %d THM
% 0.09/0.30 % Computer : n010.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Jul 14 09:03:49 EDT 2025
% 0.09/0.30 % CPUTime :
% 211.00/211.00 % SZS status Unsatisfiable
% 211.00/211.00 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------