%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP768-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 150.33s 150.19s
% Output : CNFRefutation 150.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of clauses : 80 ( 80 unt; 0 nHn; 6 RR)
% Number of literals : 80 ( 79 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 : 135 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(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(c9,plain,
eta(one) = i(one),
inference(equational,[status(thm)],[c1,c8]) ).
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(c12,plain,
j(one) = i(one),
inference(equational,[status(thm)],[c2,c9,c11]) ).
cnf(c13,axiom,
quotient(product(X,Y),Y) = X,
file('theBenchmark.p',sos05) ).
cnf(c14,plain,
quotient(X,X) = one,
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c15,plain,
i(one) = one,
inference(equational,[status(thm)],[c6,c12,c14]) ).
cnf(c16,plain,
quotient(X,one) = X,
inference(equational,[status(thm)],[c1,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(c20,plain,
difference(one,X) = X,
inference(equational,[status(thm)],[c2,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(c37,plain,
quotient(X,difference(Y,X)) = Y,
inference(equational,[status(thm)],[c13,c25]) ).
cnf(c39,plain,
difference(i(X),eta(X)) = X,
inference(equational,[status(thm)],[c8,c18]) ).
cnf(c49,axiom,
product(X,product(eta(X),Y)) = product(j(j(X)),Y),
file('theBenchmark.p',sos14) ).
cnf(c50,plain,
product(X,eta(X)) = j(j(X)),
inference(equational,[status(thm)],[c1,c49]) ).
cnf(c52,axiom,
product(i(i(X)),Y) = product(eta(X),product(X,Y)),
file('theBenchmark.p',sos13) ).
cnf(c53,plain,
product(eta(X),product(X,Y)) = product(i(i(X)),Y),
inference(equational,[status(thm)],[c52]) ).
cnf(c59,axiom,
product(eta(X),product(Y,Z)) = product(product(eta(X),Y),Z),
file('theBenchmark.p',sos16) ).
cnf(c60,plain,
product(product(eta(X),Y),Z) = product(eta(X),product(Y,Z)),
inference(equational,[status(thm)],[c59]) ).
cnf(c61,axiom,
product(X,product(Y,eta(X))) = product(product(X,Y),eta(X)),
file('theBenchmark.p',sos15) ).
cnf(c62,plain,
product(product(X,Y),eta(X)) = product(X,product(Y,eta(X))),
inference(equational,[status(thm)],[c61]) ).
cnf(c76,plain,
product(i(X),eta(X)) = j(X),
inference(equational,[status(thm)],[c27,c28,c50]) ).
cnf(c92,axiom,
difference(X,product(product(X,Y),Z)) = quotient(product(Y,product(Z,X)),X),
file('theBenchmark.p',sos07) ).
cnf(c93,plain,
quotient(product(X,product(Y,Z)),Z) = difference(Z,product(product(Z,X),Y)),
inference(equational,[status(thm)],[c92]) ).
cnf(c95,plain,
product(j(j(X)),i(eta(X))) = X,
inference(equational,[status(thm)],[c1,c26,c49]) ).
cnf(c98,plain,
quotient(X,i(eta(X))) = j(j(X)),
inference(equational,[status(thm)],[c13,c95]) ).
cnf(c102,plain,
product(j(X),i(eta(X))) = i(X),
inference(equational,[status(thm)],[c27,c28,c95]) ).
cnf(c104,plain,
difference(X,product(product(X,X),Y)) = t(X,product(Y,X)),
inference(equational,[status(thm)],[c31,c93]) ).
cnf(c116,plain,
quotient(i(X),i(eta(X))) = j(X),
inference(equational,[status(thm)],[c27,c28,c98]) ).
cnf(c118,plain,
product(j(X),eta(eta(X))) = j(X),
inference(equational,[status(thm)],[c8,c29,c62,c76,c102]) ).
cnf(c119,plain,
eta(eta(X)) = one,
inference(equational,[status(thm)],[c18,c19,c118]) ).
cnf(c120,plain,
j(eta(X)) = i(eta(X)),
inference(equational,[status(thm)],[c15,c16,c116,c119]) ).
cnf(c121,plain,
i(i(eta(X))) = eta(X),
inference(equational,[status(thm)],[c4,c39,c119]) ).
cnf(c129,plain,
t(eta(X),product(Y,eta(X))) = product(eta(X),Y),
inference(equational,[status(thm)],[c18,c60,c104]) ).
cnf(c156,plain,
difference(eta(X),product(i(i(X)),Y)) = product(X,Y),
inference(equational,[status(thm)],[c18,c53]) ).
cnf(c166,plain,
product(X,difference(i(i(X)),Y)) = difference(eta(X),Y),
inference(equational,[status(thm)],[c25,c156]) ).
cnf(c184,plain,
difference(X,product(product(X,eta(Y)),Z)) = product(eta(Y),Z),
inference(equational,[status(thm)],[c13,c60,c93]) ).
cnf(c185,plain,
difference(i(eta(X)),Y) = product(eta(X),Y),
inference(equational,[status(thm)],[c2,c8,c119,c184]) ).
cnf(c186,plain,
quotient(X,product(eta(Y),X)) = i(eta(Y)),
inference(equational,[status(thm)],[c37,c185]) ).
cnf(c189,plain,
quotient(difference(eta(X),Y),Y) = i(eta(X)),
inference(equational,[status(thm)],[c20,c119,c121,c166,c186]) ).
cnf(c190,plain,
product(i(eta(X)),Y) = difference(eta(X),Y),
inference(equational,[status(thm)],[c22,c189]) ).
cnf(c219,plain,
product(eta(X),quotient(Y,eta(X))) = t(eta(X),Y),
inference(equational,[status(thm)],[c22,c129]) ).
cnf(c238,plain,
difference(X,product(product(X,Y),j(X))) = quotient(Y,X),
inference(equational,[status(thm)],[c1,c23,c93]) ).
cnf(c243,plain,
product(X,i(eta(Y))) = quotient(X,eta(Y)),
inference(equational,[status(thm)],[c18,c60,c120,c238]) ).
cnf(c309,plain,
difference(X,product(product(X,Y),i(X))) = quotient(product(Y,eta(X)),X),
inference(equational,[status(thm)],[c8,c93]) ).
cnf(c311,plain,
difference(eta(X),t(eta(X),Y)) = quotient(Y,eta(X)),
inference(equational,[status(thm)],[c1,c60,c119,c219,c243,c309]) ).
cnf(c324,plain,
difference(quotient(X,eta(Y)),product(X,Z)) = product(eta(Y),Z),
inference(equational,[status(thm)],[c22,c184]) ).
cnf(c325,plain,
product(eta(X),difference(Y,Z)) = difference(quotient(Y,eta(X)),Z),
inference(equational,[status(thm)],[c25,c324]) ).
cnf(c360,plain,
product(eta(X),product(difference(eta(X),Y),Z)) = product(Y,Z),
inference(equational,[status(thm)],[c25,c60]) ).
cnf(c361,plain,
product(difference(eta(X),Y),Z) = difference(eta(X),product(Y,Z)),
inference(equational,[status(thm)],[c18,c360]) ).
cnf(c428,plain,
product(difference(X,product(product(X,Y),Z)),X) = product(Y,product(Z,X)),
inference(equational,[status(thm)],[c22,c93]) ).
cnf(c433,plain,
product(X,quotient(Y,eta(Z))) = quotient(product(X,Y),eta(Z)),
inference(equational,[status(thm)],[c14,c20,c185,c190,c243,c325,c361,c428]) ).
cnf(c535,plain,
difference(X,product(product(X,Y),quotient(Z,X))) = quotient(product(Y,Z),X),
inference(equational,[status(thm)],[c22,c93]) ).
cnf(c536,plain,
product(eta(X),quotient(Y,Z)) = quotient(product(eta(X),Y),Z),
inference(equational,[status(thm)],[c184,c535]) ).
cnf(c588,plain,
quotient(product(X,Y),product(eta(Z),Y)) = quotient(X,eta(Z)),
inference(equational,[status(thm)],[c37,c324]) ).
cnf(c1124,plain,
quotient(product(X,difference(eta(Y),Z)),Z) = quotient(X,eta(Y)),
inference(equational,[status(thm)],[c25,c588]) ).
cnf(c1125,plain,
product(quotient(X,eta(Y)),Z) = product(X,difference(eta(Y),Z)),
inference(equational,[status(thm)],[c22,c1124]) ).
cnf(c1451,plain,
product(eta(X),product(Y,difference(eta(X),Z))) = product(t(eta(X),Y),Z),
inference(equational,[status(thm)],[c1,c60,c119,c219,c243,c309,c360,c1125]) ).
cnf(c2601,plain,
product(t(eta(X),Y),t(eta(X),Z)) = t(eta(X),product(Y,Z)),
inference(equational,[status(thm)],[c31,c311,c433,c536,c1451]) ).
cnf(g1,plain,
t(eta(x0),product(x1,x2)) = product(t(eta(x0),x1),t(eta(x0),x2)),
inference(equational,[status(thm)],[c2601]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : GRP768-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.09 % Command : run_Leo-III %s %d THM
% 0.08/0.29 % Computer : n003.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30 % CPULimit : 300
% 0.08/0.30 % WCLimit : 300
% 0.08/0.30 % DateTime : Mon Jul 14 09:04:19 EDT 2025
% 0.08/0.30 % CPUTime :
% 150.33/150.19 % SZS status Unsatisfiable
% 150.33/150.19 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------