# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:~(s(t_h4s_ringNorms_polynom(X1),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_pvar),s(t_h4s_quotes_index,X3)))=s(t_h4s_ringNorms_polynom(X1),happ(s(t_fun(t_h4s_ringNorms_polynom(X1),t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_popp),s(t_h4s_ringNorms_polynom(X1),X2)))),file('i/f/ringNorm/polynom__distinct_c3', ch4s_ringNorms_polynomu_u_distinctu_c3)).
fof(20, axiom,![X1]:s(t_fun(t_h4s_ringNorms_polynom(X1),t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_popp)=s(t_fun(t_h4s_ringNorms_polynom(X1),t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_u_20u_40indu_u_typeringnorm4),file('i/f/ringNorm/polynom__distinct_c3', ah4s_ringNorms_Popp0)).
fof(22, axiom,![X9]:![X1]:![X30]:![X31]:![X32]:![X33]:![X6]:![X3]:s(X9,h4s_ringnorms_polynomu_u_case(s(t_h4s_ringNorms_polynom(X1),happ(s(t_fun(t_h4s_ringNorms_polynom(X1),t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_popp),s(t_h4s_ringNorms_polynom(X1),X3))),s(t_fun(t_h4s_quotes_index,X9),X6),s(t_fun(X1,X9),X33),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X9)),X32),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X9)),X31),s(t_fun(t_h4s_ringNorms_polynom(X1),X9),X30)))=s(X9,happ(s(t_fun(t_h4s_ringNorms_polynom(X1),X9),X30),s(t_h4s_ringNorms_polynom(X1),X3))),file('i/f/ringNorm/polynom__distinct_c3', ah4s_ringNorms_polynomu_u_caseu_u_defu_c4)).
fof(23, axiom,![X1]:s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_pvar)=s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_u_20u_40indu_u_typeringnorm0),file('i/f/ringNorm/polynom__distinct_c3', ah4s_ringNorms_Pvar0)).
fof(25, axiom,![X1]:![X34]:![X35]:![X3]:~(s(t_h4s_ringNorms_polynom(X1),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_pvar),s(t_h4s_quotes_index,X3)))=s(t_h4s_ringNorms_polynom(X1),happ(s(t_fun(t_h4s_ringNorms_polynom(X1),t_h4s_ringNorms_polynom(X1)),happ(s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),t_h4s_ringNorms_polynom(X1))),h4s_ringnorms_pplus),s(t_h4s_ringNorms_polynom(X1),X35))),s(t_h4s_ringNorms_polynom(X1),X34)))),file('i/f/ringNorm/polynom__distinct_c3', ah4s_ringNorms_polynomu_u_distinctu_c1)).
fof(28, axiom,![X1]:![X9]:![X30]:![X31]:![X32]:![X33]:![X6]:![X3]:s(X9,h4s_ringnorms_polynomu_u_case(s(t_h4s_ringNorms_polynom(X1),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_pvar),s(t_h4s_quotes_index,X3))),s(t_fun(t_h4s_quotes_index,X9),X6),s(t_fun(X1,X9),X33),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X9)),X32),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X9)),X31),s(t_fun(t_h4s_ringNorms_polynom(X1),X9),X30)))=s(X9,happ(s(t_fun(t_h4s_quotes_index,X9),X6),s(t_h4s_quotes_index,X3))),file('i/f/ringNorm/polynom__distinct_c3', ah4s_ringNorms_polynomu_u_caseu_u_defu_c0)).
fof(70, axiom,![X1]:s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),t_h4s_ringNorms_polynom(X1))),h4s_ringnorms_pplus)=s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),t_h4s_ringNorms_polynom(X1))),h4s_ringnorms_u_20u_40indu_u_typeringnorm2),file('i/f/ringNorm/polynom__distinct_c3', ah4s_ringNorms_Pplus0)).
# SZS output end CNFRefutation
