# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/intto/apintto__thm', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/intto/apintto__thm', 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/intto/apintto__thm', aHLu_BOOLu_CASES)).
fof(15, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/intto/apintto__thm', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(16, axiom,![X9]:![X11]:(p(s(t_bool,h4s_relations_transitive(s(t_fun(X9,t_fun(X9,t_bool)),X11))))<=>![X6]:![X10]:![X12]:((p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X11),s(X9,X6))),s(X9,X10))))&p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X11),s(X9,X10))),s(X9,X12)))))=>p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X11),s(X9,X6))),s(X9,X12)))))),file('i/f/intto/apintto__thm', ah4s_relations_transitiveu_u_def)).
fof(17, axiom,![X9]:![X11]:(p(s(t_bool,h4s_relations_irreflexive(s(t_fun(X9,t_fun(X9,t_bool)),X11))))<=>![X6]:~(p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X11),s(X9,X6))),s(X9,X6)))))),file('i/f/intto/apintto__thm', ah4s_relations_irreflexiveu_u_def)).
fof(18, axiom,![X9]:![X11]:(p(s(t_bool,h4s_relations_trichotomous(s(t_fun(X9,t_fun(X9,t_bool)),X11))))<=>![X13]:![X14]:(p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X11),s(X9,X13))),s(X9,X14))))|(p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X11),s(X9,X14))),s(X9,X13))))|s(X9,X13)=s(X9,X14)))),file('i/f/intto/apintto__thm', ah4s_relations_trichotomous0)).
fof(19, axiom,![X9]:![X11]:(p(s(t_bool,h4s_relations_stronglinearorder(s(t_fun(X9,t_fun(X9,t_bool)),X11))))<=>(p(s(t_bool,h4s_relations_strongorder(s(t_fun(X9,t_fun(X9,t_bool)),X11))))&p(s(t_bool,h4s_relations_trichotomous(s(t_fun(X9,t_fun(X9,t_bool)),X11)))))),file('i/f/intto/apintto__thm', ah4s_relations_StrongLinearOrder0)).
fof(20, axiom,![X10]:![X6]:(s(t_h4s_integers_int,X6)=s(t_h4s_integers_int,X10)|(p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt),s(t_h4s_integers_int,X6))),s(t_h4s_integers_int,X10))))|p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt),s(t_h4s_integers_int,X10))),s(t_h4s_integers_int,X6)))))),file('i/f/intto/apintto__thm', ah4s_integers_INTu_u_LTu_u_TOTAL)).
fof(21, axiom,![X6]:~(p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt),s(t_h4s_integers_int,X6))),s(t_h4s_integers_int,X6))))),file('i/f/intto/apintto__thm', ah4s_integers_INTu_u_LTu_u_REFL)).
fof(22, axiom,![X12]:![X10]:![X6]:((p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt),s(t_h4s_integers_int,X6))),s(t_h4s_integers_int,X10))))&p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt),s(t_h4s_integers_int,X10))),s(t_h4s_integers_int,X12)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt),s(t_h4s_integers_int,X6))),s(t_h4s_integers_int,X12))))),file('i/f/intto/apintto__thm', ah4s_integers_INTu_u_LTu_u_TRANS)).
fof(23, axiom,![X9]:![X15]:(p(s(t_bool,h4s_totos_totord(s(t_fun(X9,t_fun(X9,t_h4s_totos_cpn)),X15))))<=>s(t_fun(X9,t_fun(X9,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(X9),h4s_totos_to(s(t_fun(X9,t_fun(X9,t_h4s_totos_cpn)),X15)))))=s(t_fun(X9,t_fun(X9,t_h4s_totos_cpn)),X15)),file('i/f/intto/apintto__thm', ah4s_totos_TOu_u_aptou_u_TOu_u_ID)).
fof(24, axiom,![X9]:![X15]:(p(s(t_bool,h4s_relations_stronglinearorder(s(t_fun(X9,t_fun(X9,t_bool)),X15))))=>p(s(t_bool,h4s_totos_totord(s(t_fun(X9,t_fun(X9,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(X9,t_fun(X9,t_bool)),X15))))))),file('i/f/intto/apintto__thm', ah4s_totos_TotOrdu_u_TOu_u_ofu_u_Strong)).
fof(25, axiom,![X9]:![X16]:(p(s(t_bool,h4s_relations_strongorder(s(t_fun(X9,t_fun(X9,t_bool)),X16))))<=>(p(s(t_bool,h4s_relations_irreflexive(s(t_fun(X9,t_fun(X9,t_bool)),X16))))&p(s(t_bool,h4s_relations_transitive(s(t_fun(X9,t_fun(X9,t_bool)),X16)))))),file('i/f/intto/apintto__thm', ah4s_totos_StrongOrderu_u_ALT)).
fof(26, axiom,s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_inttos_intord)=s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt))),file('i/f/intto/apintto__thm', ah4s_inttos_intOrd0)).
fof(27, axiom,s(t_h4s_totos_toto(t_h4s_integers_int),h4s_inttos_intto)=s(t_h4s_totos_toto(t_h4s_integers_int),h4s_totos_to(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_inttos_intord))),file('i/f/intto/apintto__thm', ah4s_inttos_intto0)).
fof(28, conjecture,s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(t_h4s_integers_int),h4s_inttos_intto)))=s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_inttos_intord),file('i/f/intto/apintto__thm', ch4s_inttos_apinttou_u_thm)).
# SZS output end CNFRefutation
