# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![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),X1))))=>p(s(t_bool,h4s_encodes_collisionu_u_free(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))),file('i/f/Encode/wf__pred__bnum0', ch4s_Encodes_wfu_u_predu_u_bnum0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/Encode/wf__pred__bnum0', aHLu_TRUTH)).
fof(6, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/Encode/wf__pred__bnum0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X1]:![X2]:(p(s(t_bool,h4s_encodes_collisionu_u_free(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))<=>![X5]:![X10]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X5))))&(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X10))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X5),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)))))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X10),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)))))))=>s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,X10))),file('i/f/Encode/wf__pred__bnum0', ah4s_Encodes_collisionu_u_freeu_u_def)).
fof(12, axiom,![X1]:![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),X1))))<=>(p(s(t_bool,h4s_encodes_wfu_u_pred(s(t_fun(t_h4s_nums_num,t_bool),X1))))&![X5]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X5))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),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__bnum0', ah4s_Encodes_wfu_u_predu_u_bnumu_u_def)).
fof(13, axiom,![X16]:![X17]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16)))=s(t_h4s_nums_num,X17)),file('i/f/Encode/wf__pred__bnum0', ah4s_arithmetics_LESSu_u_MOD)).
fof(14, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/Encode/wf__pred__bnum0', aHLu_BOOLu_CASES)).
fof(15, axiom,~(p(s(t_bool,f))),file('i/f/Encode/wf__pred__bnum0', aHLu_FALSITY)).
# SZS output end CNFRefutation
