# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:![X3]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3)))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X2)))))=>![X2]:p(s(t_bool,h4s_encodes_wfu_u_predu_u_bnum(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X1),s(t_h4s_nums_num,X2))))))),file('i/f/Encode/wf__pred__bnum__total', ch4s_Encodes_wfu_u_predu_u_bnumu_u_total)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/Encode/wf__pred__bnum__total', aHLu_TRUTH)).
fof(7, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/Encode/wf__pred__bnum__total', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X10]:![X2]:(p(s(t_bool,h4s_encodes_wfu_u_predu_u_bnum(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X10))))<=>(p(s(t_bool,h4s_encodes_wfu_u_pred(s(t_fun(t_h4s_nums_num,t_bool),X10))))&![X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X10),s(t_h4s_nums_num,X3))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X2))))))))),file('i/f/Encode/wf__pred__bnum__total', ah4s_Encodes_wfu_u_predu_u_bnumu_u_def)).
fof(10, axiom,![X4]:![X10]:(p(s(t_bool,h4s_encodes_wfu_u_pred(s(t_fun(X4,t_bool),X10))))<=>?[X3]:p(s(t_bool,happ(s(t_fun(X4,t_bool),X10),s(X4,X3))))),file('i/f/Encode/wf__pred__bnum__total', ah4s_Encodes_wfu_u_predu_u_def)).
fof(11, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(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/Encode/wf__pred__bnum__total', ah4s_arithmetics_TWO)).
fof(12, axiom,![X11]:![X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X2)))))),file('i/f/Encode/wf__pred__bnum__total', ah4s_arithmetics_ZEROu_u_LESSu_u_EXP)).
fof(13, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/Encode/wf__pred__bnum__total', aHLu_BOOLu_CASES)).
fof(14, axiom,~(p(s(t_bool,f))),file('i/f/Encode/wf__pred__bnum__total', aHLu_FALSITY)).
# SZS output end CNFRefutation
