# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(X1,h4s_primu_u_recs_primu_u_rec(s(X1,X2),s(t_fun(X1,t_fun(t_h4s_nums_num,X1)),X3),s(t_h4s_nums_num,h4s_nums_0)))=s(X1,X2),file('i/f/prim_rec/PRIM__REC__THM_c0', ch4s_primu_u_recs_PRIMu_u_RECu_u_THMu_c0)).
fof(4, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/prim_rec/PRIM__REC__THM_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X1]:![X15]:![X16]:(?[X2]:(s(X1,X2)=s(X1,X15)&p(s(t_bool,happ(s(t_fun(X1,t_bool),X16),s(X1,X2)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X16),s(X1,X15))))),file('i/f/prim_rec/PRIM__REC__THM_c0', ah4s_bools_UNWINDu_u_THM2)).
fof(22, axiom,![X1]:![X2]:![X14]:![X3]:s(X1,h4s_primu_u_recs_primu_u_rec(s(X1,X2),s(t_fun(X1,t_fun(t_h4s_nums_num,X1)),X3),s(t_h4s_nums_num,X14)))=s(X1,happ(s(t_fun(t_h4s_nums_num,X1),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,X1)),h4s_primu_u_recs_primu_u_recu_u_fun(s(X1,X2),s(t_fun(X1,t_fun(t_h4s_nums_num,X1)),X3))),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X14))))),file('i/f/prim_rec/PRIM__REC__THM_c0', ah4s_primu_u_recs_PRIMu_u_REC0)).
fof(23, axiom,![X1]:![X2]:![X13]:![X3]:s(X1,happ(s(t_fun(t_h4s_nums_num,X1),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,X1)),h4s_primu_u_recs_primu_u_recu_u_fun(s(X1,X2),s(t_fun(X1,t_fun(t_h4s_nums_num,X1)),X3))),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,X13)))=s(X1,X2),file('i/f/prim_rec/PRIM__REC__THM_c0', ah4s_primu_u_recs_PRIMu_u_RECu_u_EQNu_c0)).
fof(24, axiom,![X1]:![X2]:![X3]:s(X1,happ(s(t_fun(t_h4s_nums_num,X1),h4s_primu_u_recs_simpu_u_rec(s(X1,X2),s(t_fun(X1,X1),X3))),s(t_h4s_nums_num,h4s_nums_0)))=s(X1,X2),file('i/f/prim_rec/PRIM__REC__THM_c0', ah4s_primu_u_recs_SIMPu_u_RECu_u_THMu_c0)).
fof(28, axiom,s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_nums_absu_u_num(s(t_h4s_mins_ind,h4s_nums_zerou_u_rep))),file('i/f/prim_rec/PRIM__REC__THM_c0', ah4s_nums_ZEROu_u_DEF)).
fof(30, axiom,s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/prim_rec/PRIM__REC__THM_c0', ah4s_primu_u_recs_PRE0u_c0)).
fof(33, axiom,![X13]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/prim_rec/PRIM__REC__THM_c0', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(53, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)<=>p(s(t_bool,X10))),file('i/f/prim_rec/PRIM__REC__THM_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(66, axiom,![X1]:![X2]:![X13]:![X25]:?[X6]:(p(s(t_bool,h4s_primu_u_recs_simpu_u_recu_u_rel(s(t_fun(t_h4s_nums_num,X1),X6),s(X1,X2),s(t_fun(X1,X1),X25),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13))))))&s(X1,happ(s(t_fun(t_h4s_nums_num,X1),h4s_primu_u_recs_simpu_u_rec(s(X1,X2),s(t_fun(X1,X1),X25))),s(t_h4s_nums_num,X13)))=s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X6),s(t_h4s_nums_num,X13)))),file('i/f/prim_rec/PRIM__REC__THM_c0', ah4s_primu_u_recs_SIMPu_u_REC0)).
# SZS output end CNFRefutation
