# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(X1,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_equal),s(X1,X4),s(X1,X3),s(X1,X2)))=s(X1,X3),file('i/f/toto/cpn__case__def_c1', ch4s_totos_cpnu_u_caseu_u_defu_c1)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/toto/cpn__case__def_c1', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/toto/cpn__case__def_c1', aHLu_FALSITY)).
fof(4, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/toto/cpn__case__def_c1', aHLu_BOOLu_CASES)).
fof(6, axiom,![X1]:![X7]:![X8]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X8),s(X1,X7)))=s(X1,X8),file('i/f/toto/cpn__case__def_c1', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(7, axiom,![X1]:![X7]:![X8]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X8),s(X1,X7)))=s(X1,X7),file('i/f/toto/cpn__case__def_c1', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(8, axiom,![X9]:![X10]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X10)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10))),file('i/f/toto/cpn__case__def_c1', ah4s_numerals_numeralu_u_distribu_c22)).
fof(9, axiom,![X9]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/toto/cpn__case__def_c1', ah4s_numerals_numeralu_u_ltu_c2)).
fof(10, axiom,![X9]:![X10]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X10)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10))),file('i/f/toto/cpn__case__def_c1', ah4s_numerals_numeralu_u_ltu_c3)).
fof(11, axiom,![X1]:![X6]:![X2]:![X3]:![X4]:?[X11]:((p(s(t_bool,X11))<=>s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,X6)))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))&s(X1,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,X6),s(X1,X4),s(X1,X3),s(X1,X2)))=s(X1,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,X6))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(X1,X4),s(X1,h4s_bools_cond(s(t_bool,X11),s(X1,X3),s(X1,X2)))))),file('i/f/toto/cpn__case__def_c1', ah4s_totos_cpnu_u_CASE0)).
fof(12, axiom,s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,h4s_totos_equal)))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),file('i/f/toto/cpn__case__def_c1', ah4s_totos_cpn2numu_u_thmu_c1)).
# SZS output end CNFRefutation
