# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty)))=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ch4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_EMPTY)).
fof(6, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(27, axiom,![X6]:s(t_fun(X6,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X6),h4s_lists_nil)))=s(t_fun(X6,t_bool),h4s_predu_u_sets_empty),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_lists_LISTu_u_TOu_u_SET0u_c0)).
fof(28, axiom,![X6]:![X25]:s(t_fun(X6,t_bool),h4s_predu_u_sets_union(s(t_fun(X6,t_bool),X25),s(t_fun(X6,t_bool),h4s_predu_u_sets_empty)))=s(t_fun(X6,t_bool),X25),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_predu_u_sets_UNIONu_u_EMPTYu_c1)).
fof(29, axiom,![X13]:s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13)))=s(t_fun(t_h4s_nums_num,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13))))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_def)).
fof(30, axiom,![X13]:![X26]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13))))=>s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X26),s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13)))))=s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X26),s(t_h4s_patricias_ptree(t_h4s_ones_one),X13)))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_INu_u_NUMSETu_u_OFu_u_PTREE)).
fof(31, axiom,![X13]:![X25]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X25)))))=>s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_union(s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13))),s(t_fun(t_h4s_nums_num,t_bool),X25)))))=s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13),s(t_fun(t_h4s_nums_num,t_bool),X25)))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_NUMSETu_u_OFu_u_PTREE)).
fof(34, axiom,![X13]:![X25]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X25)))))=>s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13),s(t_fun(t_h4s_nums_num,t_bool),X25)))))=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_union(s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13))),s(t_fun(t_h4s_nums_num,t_bool),X25)))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_PTREEu_u_OFu_u_NUMSET)).
fof(36, axiom,![X26]:~(p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X26),s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty))))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_INu_u_PTREEu_u_EMPTY)).
fof(37, axiom,![X25]:p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty),s(t_fun(t_h4s_nums_num,t_bool),X25)))))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_ISu_u_PTREEu_u_EMPTY)).
fof(38, axiom,![X6]:p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X6),h4s_patricias_empty)))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_EMPTYu_u_ISu_u_PTREE)).
fof(39, axiom,![X25]:![X26]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X25))))=>s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X26),s(t_fun(t_h4s_nums_num,t_bool),X25)))=s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X26),s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty),s(t_fun(t_h4s_nums_num,t_bool),X25)))))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_INu_u_PTREEu_u_OFu_u_NUMSETu_u_EMPTY)).
fof(41, axiom,![X6]:s(t_h4s_patricias_ptree(X6),h4s_patricias_empty)=s(t_h4s_patricias_ptree(X6),h4s_patricias_u_20u_40indu_u_typepatricia0),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_Empty0)).
fof(45, axiom,![X6]:![X30]:p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X6,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X6),X30)))))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_lists_FINITEu_u_LISTu_u_TOu_u_SET)).
fof(53, axiom,![X6]:s(t_h4s_lists_list(X6),h4s_lists_reverse(s(t_h4s_lists_list(X6),h4s_lists_nil)))=s(t_h4s_lists_list(X6),h4s_lists_nil),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_lists_REVERSEu_u_DEFu_c0)).
fof(57, axiom,![X6]:s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X6),h4s_lists_nil)))=s(t_bool,t),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_lists_ALLu_u_DISTINCT0u_c0)).
fof(61, axiom,![X6]:![X13]:![X27]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X6),X13))))=>s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X27),s(t_fun(t_h4s_nums_num,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X6),X13)))))))=s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X6),h4s_patricias_peek(s(t_h4s_patricias_ptree(X6),X13),s(t_h4s_nums_num,X27)))))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_MEMu_u_TRAVERSEu_u_PEEK)).
fof(62, axiom,![X13]:![X26]:s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X26),s(t_h4s_patricias_ptree(t_h4s_ones_one),X13)))=s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(t_h4s_ones_one),h4s_patricias_peek(s(t_h4s_patricias_ptree(t_h4s_ones_one),X13),s(t_h4s_nums_num,X26))))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_patricias_INu_u_PTREEu_u_def)).
fof(63, axiom,![X6]:![X13]:![X25]:(s(t_fun(X6,t_bool),X25)=s(t_fun(X6,t_bool),X13)<=>![X5]:s(t_bool,h4s_bools_in(s(X6,X5),s(t_fun(X6,t_bool),X25)))=s(t_bool,h4s_bools_in(s(X6,X5),s(t_fun(X6,t_bool),X13)))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_predu_u_sets_EXTENSION)).
fof(77, axiom,p(s(t_bool,t)),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', aHLu_TRUTH)).
fof(78, axiom,![X13]:(s(t_bool,X13)=s(t_bool,t)|s(t_bool,X13)=s(t_bool,f)),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', aHLu_BOOLu_CASES)).
fof(79, axiom,![X13]:(s(t_bool,X13)=s(t_bool,t)<=>p(s(t_bool,X13))),file('i/f/patricia/NUMSET__OF__PTREE__EMPTY', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
