# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/ZERO__EXP', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/ZERO__EXP', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/arithmetic/ZERO__EXP', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X4]:![X8]:?[X9]:(s(X7,happ(s(t_fun(t_h4s_nums_num,X7),X9),s(t_h4s_nums_num,h4s_nums_0)))=s(X7,X8)&![X10]:s(X7,happ(s(t_fun(t_h4s_nums_num,X7),X9),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))))=s(X7,happ(s(t_fun(X7,X7),happ(s(t_fun(t_h4s_nums_num,t_fun(X7,X7)),X4),s(t_h4s_nums_num,X10))),s(X7,happ(s(t_fun(t_h4s_nums_num,X7),X9),s(t_h4s_nums_num,X10)))))),file('i/f/arithmetic/ZERO__EXP', ah4s_primu_u_recs_numu_u_Axiom)).
fof(6, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0)))=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/arithmetic/ZERO__EXP', ah4s_arithmetics_EXP0u_c0)).
fof(16, axiom,![X10]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10))))),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_EXP0u_c1)).
fof(23, axiom,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(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_ONE)).
fof(35, axiom,![X10]:![X11]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X11))))&p(s(t_bool,h4s_primu_u_recs_u_3c(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(t_h4s_nums_num,X10)))))),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_LTu_u_MULTu_u_CANCELu_u_LBAREu_c1)).
fof(54, axiom,![X11]:(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_0)|?[X10]:s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_numu_u_CASES)).
fof(55, axiom,![X10]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/ZERO__EXP', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(58, axiom,![X10]:(~(s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_nums_0))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10))))),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(76, axiom,![X7]:![X6]:![X14]:(p(s(t_bool,happ(s(t_fun(X7,t_bool),X14),s(X7,X6))))=>p(s(t_bool,happ(s(t_fun(X7,t_bool),X14),s(X7,h4s_mins_u_40(s(t_fun(X7,t_bool),X14))))))),file('i/f/arithmetic/ZERO__EXP', ah4s_bools_SELECTu_u_AX)).
fof(88, axiom,![X7]:![X6]:s(t_bool,d_exists(s(t_fun(X7,t_bool),X6)))=s(t_bool,happ(s(t_fun(X7,t_bool),X6),s(X7,h4s_mins_u_40(s(t_fun(X7,t_bool),X6))))),file('i/f/arithmetic/ZERO__EXP', ah4s_bools_EXISTSu_u_DEF)).
fof(92, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_MULTu_u_CLAUSESu_c0)).
fof(125, axiom,![X7]:![X17]:![X18]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X18),s(X7,X17)))=s(X7,X18),file('i/f/arithmetic/ZERO__EXP', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(126, axiom,![X7]:![X17]:![X18]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X18),s(X7,X17)))=s(X7,X17),file('i/f/arithmetic/ZERO__EXP', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(131, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_ALTu_u_ZERO)).
fof(132, axiom,![X6]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,X6),file('i/f/arithmetic/ZERO__EXP', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(133, conjecture,![X6]:?[X31]:((p(s(t_bool,X31))<=>s(t_h4s_nums_num,X6)=s(t_h4s_nums_num,h4s_nums_0))&s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,X31),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(t_h4s_nums_num,h4s_nums_0)))),file('i/f/arithmetic/ZERO__EXP', ch4s_arithmetics_ZEROu_u_EXP)).
# SZS output end CNFRefutation
