# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:~(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,X4)))=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),X3))),s(t_h4s_ringNorms_polynom(X1),X2)))),file('i/f/ringNorm/polynom__distinct_c1', ch4s_ringNorms_polynomu_u_distinctu_c1)).
fof(23, 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_c1', ah4s_ringNorms_Pplus0)).
fof(25, axiom,![X15]:![X1]:![X34]:![X35]:![X36]:![X37]:![X7]:![X2]:![X3]:s(X15,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)),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),X3))),s(t_h4s_ringNorms_polynom(X1),X2))),s(t_fun(t_h4s_quotes_index,X15),X7),s(t_fun(X1,X15),X37),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X15)),X36),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X15)),X35),s(t_fun(t_h4s_ringNorms_polynom(X1),X15),X34)))=s(X15,happ(s(t_fun(t_h4s_ringNorms_polynom(X1),X15),happ(s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X15)),X36),s(t_h4s_ringNorms_polynom(X1),X3))),s(t_h4s_ringNorms_polynom(X1),X2))),file('i/f/ringNorm/polynom__distinct_c1', ah4s_ringNorms_polynomu_u_caseu_u_defu_c2)).
fof(26, 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_c1', ah4s_ringNorms_Pvar0)).
fof(27, axiom,![X1]:![X30]:![X4]:~(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,X4)))=s(t_h4s_ringNorms_polynom(X1),happ(s(t_fun(X1,t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_pconst),s(X1,X30)))),file('i/f/ringNorm/polynom__distinct_c1', ah4s_ringNorms_polynomu_u_distinctu_c0)).
fof(28, axiom,![X1]:![X15]:![X34]:![X35]:![X36]:![X37]:![X7]:![X4]:s(X15,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,X4))),s(t_fun(t_h4s_quotes_index,X15),X7),s(t_fun(X1,X15),X37),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X15)),X36),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X15)),X35),s(t_fun(t_h4s_ringNorms_polynom(X1),X15),X34)))=s(X15,happ(s(t_fun(t_h4s_quotes_index,X15),X7),s(t_h4s_quotes_index,X4))),file('i/f/ringNorm/polynom__distinct_c1', ah4s_ringNorms_polynomu_u_caseu_u_defu_c0)).
fof(79, axiom,![X1]:s(t_fun(X1,t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_pconst)=s(t_fun(X1,t_h4s_ringNorms_polynom(X1)),h4s_ringnorms_u_20u_40indu_u_typeringnorm1),file('i/f/ringNorm/polynom__distinct_c1', ah4s_ringNorms_Pconst0)).
# SZS output end CNFRefutation
