# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))<=>s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,X1)),file('i/f/arithmetic/SUC__PRE', ch4s_arithmetics_SUCu_u_PRE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/SUC__PRE', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/SUC__PRE', aHLu_FALSITY)).
fof(6, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/arithmetic/SUC__PRE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X2]:(s(t_bool,t)=s(t_bool,X2)<=>p(s(t_bool,X2))),file('i/f/arithmetic/SUC__PRE', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(12, axiom,![X2]:(s(t_bool,f)=s(t_bool,X2)<=>~(p(s(t_bool,X2)))),file('i/f/arithmetic/SUC__PRE', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(13, axiom,![X7]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/SUC__PRE', ah4s_nums_NOTu_u_SUC)).
fof(14, axiom,![X1]:(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0)|?[X7]:s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7)))),file('i/f/arithmetic/SUC__PRE', ah4s_arithmetics_numu_u_CASES)).
fof(15, axiom,![X7]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/SUC__PRE', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(16, axiom,![X7]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7)))))),file('i/f/arithmetic/SUC__PRE', ah4s_primu_u_recs_LESSu_u_0)).
fof(17, axiom,![X1]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,X1),file('i/f/arithmetic/SUC__PRE', ah4s_primu_u_recs_PRE0u_c1)).
# SZS output end CNFRefutation
