# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(X2,happ(s(t_fun(t_h4s_nums_num,X2),happ(s(t_fun(t_h4s_fcps_cart(X2,X1),t_fun(t_h4s_nums_num,X2)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(X2,X1),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,X2),X4))))),s(t_h4s_nums_num,X3)))=s(X2,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))),s(X2,happ(s(t_fun(t_h4s_nums_num,X2),X4),s(t_h4s_nums_num,X3))),s(X2,happ(s(t_fun(t_h4s_nums_num,X2),happ(s(t_fun(t_h4s_fcps_cart(X2,X1),t_fun(t_h4s_nums_num,X2)),h4s_combins_fail(s(t_fun(t_h4s_fcps_cart(X2,X1),t_fun(t_h4s_nums_num,X2)),h4s_fcps_fcpu_u_index),s(t_bool,X5))),s(t_h4s_fcps_cart(X2,X1),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,X2),X4))))),s(t_h4s_nums_num,X3))))),file('i/f/fcp/index__comp', ch4s_fcps_indexu_u_comp)).
fof(31, axiom,![X2]:![X6]:![X7]:s(X2,h4s_bools_cond(s(t_bool,f0),s(X2,X7),s(X2,X6)))=s(X2,X6),file('i/f/fcp/index__comp', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(32, axiom,![X2]:![X6]:![X7]:s(X2,h4s_bools_cond(s(t_bool,t),s(X2,X7),s(X2,X6)))=s(X2,X7),file('i/f/fcp/index__comp', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(35, axiom,![X6]:![X7]:![X22]:(p(s(t_bool,h4s_bools_cond(s(t_bool,X22),s(t_bool,X7),s(t_bool,X6))))<=>((~(p(s(t_bool,X22)))|p(s(t_bool,X7)))&(p(s(t_bool,X22))|p(s(t_bool,X6))))),file('i/f/fcp/index__comp', ah4s_bools_CONDu_u_EXPAND)).
fof(37, axiom,![X1]:![X2]:![X10]:![X23]:![X4]:![X22]:s(X1,happ(s(t_fun(X2,X1),h4s_bools_cond(s(t_bool,X22),s(t_fun(X2,X1),X4),s(t_fun(X2,X1),X23))),s(X2,X10)))=s(X1,h4s_bools_cond(s(t_bool,X22),s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X10))),s(X1,happ(s(t_fun(X2,X1),X23),s(X2,X10))))),file('i/f/fcp/index__comp', ah4s_bools_CONDu_u_RATOR)).
fof(51, axiom,![X1]:![X2]:![X27]:![X23]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X27),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))))=>s(X2,happ(s(t_fun(t_h4s_nums_num,X2),happ(s(t_fun(t_h4s_fcps_cart(X2,X1),t_fun(t_h4s_nums_num,X2)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(X2,X1),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,X2),X23))))),s(t_h4s_nums_num,X27)))=s(X2,happ(s(t_fun(t_h4s_nums_num,X2),X23),s(t_h4s_nums_num,X27)))),file('i/f/fcp/index__comp', ah4s_fcps_FCPu_u_BETA)).
fof(54, axiom,![X1]:![X2]:![X9]:![X10]:s(X2,h4s_combins_fail(s(X2,X10),s(X1,X9)))=s(X2,X10),file('i/f/fcp/index__comp', ah4s_combins_FAILu_u_THM)).
fof(55, axiom,![X3]:![X30]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X30),s(t_h4s_nums_num,X3)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X30))),s(t_h4s_nums_num,X3))),file('i/f/fcp/index__comp', ah4s_arithmetics_LESSu_u_EQ)).
fof(56, axiom,![X3]:![X30]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X30),s(t_h4s_nums_num,X3)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X30))))),file('i/f/fcp/index__comp', ah4s_arithmetics_NOTu_u_LESS)).
fof(58, axiom,![X3]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X3))))),file('i/f/fcp/index__comp', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(60, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)|s(t_bool,X11)=s(t_bool,f0)),file('i/f/fcp/index__comp', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
