%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP770-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 06:44:52 AM UTC 2025
% Result : Unsatisfiable 278.51s 278.20s
% Output : CNFRefutation 278.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of clauses : 96 ( 96 unt; 0 nHn; 3 RR)
% Number of literals : 96 ( 95 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 : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 165 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
product(x0,product(x1,x2)) != product(quotient(product(x0,x1),x0),product(x0,x2)),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
product(X,one) = X,
file('theBenchmark.p',sos01) ).
cnf(c2,axiom,
product(one,X) = X,
file('theBenchmark.p',sos02) ).
cnf(c3,axiom,
i(X) = difference(X,one),
file('theBenchmark.p',sos09) ).
cnf(c4,plain,
difference(X,one) = i(X),
inference(equational,[status(thm)],[c3]) ).
cnf(c5,axiom,
j(X) = quotient(one,X),
file('theBenchmark.p',sos10) ).
cnf(c6,plain,
quotient(one,X) = j(X),
inference(equational,[status(thm)],[c5]) ).
cnf(c7,axiom,
eta(X) = product(i(X),X),
file('theBenchmark.p',sos12) ).
cnf(c8,plain,
product(i(X),X) = eta(X),
inference(equational,[status(thm)],[c7]) ).
cnf(c10,axiom,
product(i(X),X) = product(X,j(X)),
file('theBenchmark.p',sos11) ).
cnf(c11,plain,
product(X,j(X)) = eta(X),
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c13,axiom,
quotient(product(X,Y),Y) = X,
file('theBenchmark.p',sos05) ).
cnf(c17,plain,
quotient(eta(X),X) = i(X),
inference(equational,[status(thm)],[c8,c13]) ).
cnf(c18,axiom,
difference(X,product(X,Y)) = Y,
file('theBenchmark.p',sos04) ).
cnf(c19,plain,
difference(X,X) = one,
inference(equational,[status(thm)],[c1,c18]) ).
cnf(c22,axiom,
product(quotient(X,Y),Y) = X,
file('theBenchmark.p',sos06) ).
cnf(c23,plain,
product(j(X),X) = one,
inference(equational,[status(thm)],[c6,c22]) ).
cnf(c24,plain,
i(j(X)) = X,
inference(equational,[status(thm)],[c4,c18,c23]) ).
cnf(c25,axiom,
product(X,difference(X,Y)) = Y,
file('theBenchmark.p',sos03) ).
cnf(c26,plain,
product(X,i(X)) = one,
inference(equational,[status(thm)],[c4,c25]) ).
cnf(c27,plain,
j(i(X)) = X,
inference(equational,[status(thm)],[c6,c13,c26]) ).
cnf(c28,plain,
eta(i(X)) = eta(X),
inference(equational,[status(thm)],[c8,c11,c27]) ).
cnf(c29,plain,
eta(j(X)) = eta(X),
inference(equational,[status(thm)],[c8,c11,c24]) ).
cnf(c30,axiom,
t(X,Y) = quotient(product(X,Y),X),
file('theBenchmark.p',sos19) ).
cnf(c31,plain,
quotient(product(X,Y),X) = t(X,Y),
inference(equational,[status(thm)],[c30]) ).
cnf(c35,plain,
t(X,j(X)) = i(X),
inference(equational,[status(thm)],[c11,c17,c31]) ).
cnf(c37,plain,
quotient(X,difference(Y,X)) = Y,
inference(equational,[status(thm)],[c13,c25]) ).
cnf(c38,plain,
difference(quotient(X,Y),X) = Y,
inference(equational,[status(thm)],[c18,c22]) ).
cnf(c40,plain,
quotient(eta(X),j(X)) = X,
inference(equational,[status(thm)],[c11,c13]) ).
cnf(c45,plain,
product(t(X,Y),X) = product(X,Y),
inference(equational,[status(thm)],[c22,c31]) ).
cnf(c46,axiom,
product(X,i(product(Y,X))) = i(Y),
file('theBenchmark.p',sos23) ).
cnf(c47,plain,
i(product(X,Y)) = difference(Y,i(X)),
inference(equational,[status(thm)],[c18,c46]) ).
cnf(c48,plain,
product(X,i(Y)) = i(quotient(Y,X)),
inference(equational,[status(thm)],[c22,c46]) ).
cnf(c49,axiom,
product(j(product(X,Y)),X) = j(Y),
file('theBenchmark.p',sos24) ).
cnf(c50,plain,
j(product(X,Y)) = quotient(j(Y),X),
inference(equational,[status(thm)],[c13,c49]) ).
cnf(c51,plain,
product(j(X),Y) = j(difference(Y,X)),
inference(equational,[status(thm)],[c25,c49]) ).
cnf(c52,plain,
j(difference(X,i(Y))) = product(Y,X),
inference(equational,[status(thm)],[c27,c46,c47,c49]) ).
cnf(c53,plain,
t(i(X),X) = i(i(X)),
inference(equational,[status(thm)],[c27,c35]) ).
cnf(c54,plain,
quotient(eta(X),i(X)) = i(i(X)),
inference(equational,[status(thm)],[c8,c31,c53]) ).
cnf(c58,plain,
quotient(j(X),i(X)) = j(eta(X)),
inference(equational,[status(thm)],[c8,c50]) ).
cnf(c60,plain,
j(difference(i(eta(X)),X)) = i(X),
inference(equational,[status(thm)],[c11,c46,c51]) ).
cnf(c61,axiom,
product(i(i(X)),Y) = product(eta(X),product(X,Y)),
file('theBenchmark.p',sos13) ).
cnf(c62,plain,
product(eta(X),product(X,Y)) = product(i(i(X)),Y),
inference(equational,[status(thm)],[c61]) ).
cnf(c63,plain,
product(eta(X),X) = i(i(X)),
inference(equational,[status(thm)],[c1,c62]) ).
cnf(c66,plain,
product(i(X),eta(X)) = j(X),
inference(equational,[status(thm)],[c27,c49,c63]) ).
cnf(c70,plain,
i(quotient(X,j(eta(X)))) = j(X),
inference(equational,[status(thm)],[c8,c48,c49]) ).
cnf(c79,plain,
difference(i(X),j(X)) = eta(X),
inference(equational,[status(thm)],[c18,c66]) ).
cnf(c80,axiom,
product(X,product(Y,eta(X))) = product(product(X,Y),eta(X)),
file('theBenchmark.p',sos15) ).
cnf(c81,plain,
product(product(X,Y),eta(X)) = product(X,product(Y,eta(X))),
inference(equational,[status(thm)],[c80]) ).
cnf(c82,axiom,
product(eta(X),product(Y,Z)) = product(product(eta(X),Y),Z),
file('theBenchmark.p',sos16) ).
cnf(c83,plain,
product(product(eta(X),Y),Z) = product(eta(X),product(Y,Z)),
inference(equational,[status(thm)],[c82]) ).
cnf(c88,plain,
difference(eta(X),i(i(X))) = X,
inference(equational,[status(thm)],[c18,c63]) ).
cnf(c89,plain,
difference(eta(X),i(X)) = j(X),
inference(equational,[status(thm)],[c24,c29,c88]) ).
cnf(c90,plain,
difference(eta(X),X) = j(j(X)),
inference(equational,[status(thm)],[c24,c29,c89]) ).
cnf(c94,plain,
quotient(X,i(i(X))) = j(eta(X)),
inference(equational,[status(thm)],[c27,c28,c58]) ).
cnf(c96,plain,
difference(i(eta(X)),X) = i(i(X)),
inference(equational,[status(thm)],[c24,c60]) ).
cnf(c97,plain,
j(eta(X)) = i(eta(X)),
inference(equational,[status(thm)],[c37,c94,c96]) ).
cnf(c98,plain,
eta(eta(X)) = one,
inference(equational,[status(thm)],[c19,c79,c97]) ).
cnf(c100,plain,
i(i(eta(X))) = eta(X),
inference(equational,[status(thm)],[c40,c54,c97]) ).
cnf(c101,plain,
quotient(j(X),quotient(Y,X)) = j(Y),
inference(equational,[status(thm)],[c22,c50]) ).
cnf(c102,plain,
difference(j(X),j(Y)) = quotient(X,Y),
inference(equational,[status(thm)],[c38,c101]) ).
cnf(c103,plain,
quotient(i(X),Y) = difference(X,j(Y)),
inference(equational,[status(thm)],[c27,c102]) ).
cnf(c104,plain,
quotient(X,i(Y)) = difference(j(X),Y),
inference(equational,[status(thm)],[c27,c102]) ).
cnf(c105,plain,
difference(j(X),eta(X)) = j(j(X)),
inference(equational,[status(thm)],[c27,c58,c97,c101,c104]) ).
cnf(c107,plain,
difference(X,i(quotient(Y,X))) = i(Y),
inference(equational,[status(thm)],[c18,c48]) ).
cnf(c130,plain,
quotient(j(X),t(X,Y)) = quotient(j(Y),X),
inference(equational,[status(thm)],[c45,c50]) ).
cnf(c132,plain,
difference(quotient(X,Y),j(Y)) = t(Y,i(X)),
inference(equational,[status(thm)],[c31,c48,c103]) ).
cnf(c150,axiom,
difference(X,product(product(X,Y),Z)) = quotient(product(Y,product(Z,X)),X),
file('theBenchmark.p',sos07) ).
cnf(c151,plain,
quotient(product(X,product(Y,Z)),Z) = difference(Z,product(product(Z,X),Y)),
inference(equational,[status(thm)],[c150]) ).
cnf(c167,plain,
product(i(i(X)),difference(X,Y)) = product(eta(X),Y),
inference(equational,[status(thm)],[c25,c62]) ).
cnf(c205,plain,
quotient(X,t(i(X),Y)) = difference(j(j(Y)),X),
inference(equational,[status(thm)],[c27,c104,c130]) ).
cnf(c220,plain,
product(X,difference(j(j(X)),Y)) = product(eta(X),Y),
inference(equational,[status(thm)],[c24,c29,c70,c97,c104,c105,c167]) ).
cnf(c225,plain,
i(difference(j(j(X)),Y)) = product(i(Y),X),
inference(equational,[status(thm)],[c45,c48,c205]) ).
cnf(c234,plain,
difference(difference(X,j(Y)),j(X)) = product(Y,eta(X)),
inference(equational,[status(thm)],[c18,c48,c63,c81,c103,c151]) ).
cnf(c235,plain,
difference(difference(X,Y),j(X)) = product(i(Y),eta(X)),
inference(equational,[status(thm)],[c27,c234]) ).
cnf(c272,plain,
product(i(X),eta(Y)) = i(difference(eta(Y),X)),
inference(equational,[status(thm)],[c27,c97,c225]) ).
cnf(c305,plain,
difference(X,product(product(X,eta(Y)),Z)) = product(eta(Y),Z),
inference(equational,[status(thm)],[c13,c83,c151]) ).
cnf(c306,plain,
difference(i(eta(X)),Y) = product(eta(X),Y),
inference(equational,[status(thm)],[c2,c8,c98,c305]) ).
cnf(c309,plain,
quotient(X,product(eta(Y),X)) = i(eta(Y)),
inference(equational,[status(thm)],[c37,c306]) ).
cnf(c313,plain,
quotient(difference(eta(X),Y),Y) = i(eta(X)),
inference(equational,[status(thm)],[c2,c27,c97,c98,c220,c309]) ).
cnf(c315,plain,
i(difference(eta(X),Y)) = difference(Y,eta(X)),
inference(equational,[status(thm)],[c100,c107,c313]) ).
cnf(c317,plain,
difference(product(X,eta(Y)),X) = i(eta(Y)),
inference(equational,[status(thm)],[c46,c47,c52,c104,c309]) ).
cnf(c318,plain,
difference(j(X),eta(Y)) = product(X,eta(Y)),
inference(equational,[status(thm)],[c37,c104,c317]) ).
cnf(c635,plain,
product(eta(X),product(difference(eta(X),Y),Z)) = product(Y,Z),
inference(equational,[status(thm)],[c25,c83]) ).
cnf(c636,plain,
product(difference(eta(X),Y),Z) = difference(eta(X),product(Y,Z)),
inference(equational,[status(thm)],[c18,c635]) ).
cnf(c637,plain,
difference(product(X,Y),eta(Z)) = difference(Y,difference(X,eta(Z))),
inference(equational,[status(thm)],[c47,c315,c636]) ).
cnf(c640,plain,
product(difference(X,Y),eta(Z)) = difference(X,product(Y,eta(Z))),
inference(equational,[status(thm)],[c51,c318,c637]) ).
cnf(c903,plain,
product(difference(X,product(product(X,Y),Z)),X) = product(Y,product(Z,X)),
inference(equational,[status(thm)],[c22,c151]) ).
cnf(c932,plain,
product(difference(X,product(Y,Z)),X) = product(difference(X,Y),product(Z,X)),
inference(equational,[status(thm)],[c25,c903]) ).
cnf(c1512,plain,
quotient(j(difference(product(X,Y),Z)),Y) = difference(Y,product(product(Y,j(Z)),X)),
inference(equational,[status(thm)],[c51,c151]) ).
cnf(c1513,plain,
t(X,difference(product(Y,X),Z)) = difference(Y,quotient(Z,X)),
inference(equational,[status(thm)],[c24,c47,c90,c102,c132,c235,c272,c640,c1512]) ).
cnf(c2966,plain,
product(difference(X,quotient(Y,Z)),product(Z,X)) = product(difference(X,Y),X),
inference(equational,[status(thm)],[c22,c932]) ).
cnf(c3318,plain,
difference(X,quotient(product(product(X,Y),Z),Y)) = t(Y,Z),
inference(equational,[status(thm)],[c18,c1513]) ).
cnf(c3320,plain,
product(t(X,Y),product(X,Z)) = product(X,product(Y,Z)),
inference(equational,[status(thm)],[c18,c932,c2966,c3318]) ).
cnf(g1,plain,
product(x0,product(x1,x2)) = product(quotient(product(x0,x1),x0),product(x0,x2)),
inference(equational,[status(thm)],[c31,c3320]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP770-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n001.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 09:04:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 278.51/278.20 % SZS status Unsatisfiable
% 278.51/278.20 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------