# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),X2)))=s(t_h4s_integers_int,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_cs),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_simplify),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),X2))))),file('i/f/integerRing/int__ring__thms_c1', ch4s_integerRings_intu_u_ringu_u_thmsu_c1)).
fof(4, axiom,![X8]:![X10]:(p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(X8),X10))))=>![X1]:![X2]:s(X8,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X8),X8),happ(s(t_fun(t_h4s_quotes_varmap(X8),t_fun(t_h4s_canonicals_canonicalu_u_sum(X8),X8)),h4s_ringnorms_ru_u_interpu_u_cs(s(t_h4s_rings_ring(X8),X10))),s(t_h4s_quotes_varmap(X8),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X8),happ(s(t_fun(t_h4s_ringNorms_polynom(X8),t_h4s_canonicals_canonicalu_u_sum(X8)),h4s_ringnorms_polynomu_u_simplify(s(t_h4s_rings_ring(X8),X10))),s(t_h4s_ringNorms_polynom(X8),X2)))))=s(X8,happ(s(t_fun(t_h4s_ringNorms_polynom(X8),X8),happ(s(t_fun(t_h4s_quotes_varmap(X8),t_fun(t_h4s_ringNorms_polynom(X8),X8)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(X8),X10))),s(t_h4s_quotes_varmap(X8),X1))),s(t_h4s_ringNorms_polynom(X8),X2)))),file('i/f/integerRing/int__ring__thms_c1', ah4s_ringNorms_polynomu_u_simplifyu_u_ok)).
fof(5, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg))))),file('i/f/integerRing/int__ring__thms_c1', ah4s_integerRings_intu_u_interpu_u_pu_u_def)).
fof(6, axiom,s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_simplify)=s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_ringnorms_polynomu_u_simplify(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg))))),file('i/f/integerRing/int__ring__thms_c1', ah4s_integerRings_intu_u_polynomu_u_simplifyu_u_def)).
fof(7, axiom,p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))),file('i/f/integerRing/int__ring__thms_c1', ah4s_integerRings_intu_u_isu_u_ring)).
fof(8, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_cs)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_ringnorms_ru_u_interpu_u_cs(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg))))),file('i/f/integerRing/int__ring__thms_c1', ah4s_integerRings_intu_u_ru_u_interpu_u_csu_u_def)).
fof(9, axiom,p(s(t_bool,t)),file('i/f/integerRing/int__ring__thms_c1', aHLu_TRUTH)).
fof(10, axiom,~(p(s(t_bool,f))),file('i/f/integerRing/int__ring__thms_c1', aHLu_FALSITY)).
fof(11, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)|s(t_bool,X11)=s(t_bool,f)),file('i/f/integerRing/int__ring__thms_c1', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
