# 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_pmult),s(t_h4s_ringNorms_polynom(X1),X3))),s(t_h4s_ringNorms_polynom(X1),X2)))),file('i/f/ringNorm/polynom__distinct_c2', ch4s_ringNorms_polynomu_u_distinctu_c2)).
fof(18, axiom,![X1]:s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),t_h4s_ringNorms_polynom(X1))),h4s_ringnorms_pmult)=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_typeringnorm3),file('i/f/ringNorm/polynom__distinct_c2', ah4s_ringNorms_Pmult0)).
fof(20, axiom,![X10]:![X1]:![X32]:![X33]:![X34]:![X35]:![X7]:![X2]:![X3]:s(X10,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_pmult),s(t_h4s_ringNorms_polynom(X1),X3))),s(t_h4s_ringNorms_polynom(X1),X2))),s(t_fun(t_h4s_quotes_index,X10),X7),s(t_fun(X1,X10),X35),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X10)),X34),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X10)),X33),s(t_fun(t_h4s_ringNorms_polynom(X1),X10),X32)))=s(X10,happ(s(t_fun(t_h4s_ringNorms_polynom(X1),X10),happ(s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X10)),X33),s(t_h4s_ringNorms_polynom(X1),X3))),s(t_h4s_ringNorms_polynom(X1),X2))),file('i/f/ringNorm/polynom__distinct_c2', ah4s_ringNorms_polynomu_u_caseu_u_defu_c3)).
fof(21, 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_c2', ah4s_ringNorms_Pvar0)).
fof(22, axiom,![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_c2', ah4s_ringNorms_polynomu_u_distinctu_c1)).
fof(24, axiom,![X1]:![X10]:![X32]:![X33]:![X34]:![X35]:![X7]:![X4]:s(X10,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,X10),X7),s(t_fun(X1,X10),X35),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X10)),X34),s(t_fun(t_h4s_ringNorms_polynom(X1),t_fun(t_h4s_ringNorms_polynom(X1),X10)),X33),s(t_fun(t_h4s_ringNorms_polynom(X1),X10),X32)))=s(X10,happ(s(t_fun(t_h4s_quotes_index,X10),X7),s(t_h4s_quotes_index,X4))),file('i/f/ringNorm/polynom__distinct_c2', ah4s_ringNorms_polynomu_u_caseu_u_defu_c0)).
fof(67, 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_c2', ah4s_ringNorms_Pplus0)).
# SZS output end CNFRefutation
