# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:![X3]:![X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),X1),s(t_fun(t_h4s_nums_num,t_bool),X2))),s(t_fun(t_h4s_nums_num,t_bool),X3))),s(t_h4s_nums_num,X4))))<=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X4))))|p(s(t_bool,h4s_pastu_u_temporalu_u_logics_pnext(s(t_fun(t_h4s_nums_num,t_bool),X3),s(t_h4s_nums_num,X4))))))=>![X3]:![X2]:![X5]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),X1),s(t_fun(t_h4s_nums_num,t_bool),X2))),s(t_fun(t_h4s_nums_num,t_bool),X3))))),s(t_h4s_nums_num,X5))))<=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X3),s(t_h4s_nums_num,X5))))|p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),X2))),s(t_h4s_nums_num,X5))))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ch4s_Pastu_u_Temporalu_u_Logics_SEPARATEu_u_NEXTu_u_THMu_c4)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', aHLu_FALSITY)).
fof(8, axiom,![X10]:![X11]:(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,X10)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11)))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(29, axiom,![X4]:((p(s(t_bool,X4))=>p(s(t_bool,f)))<=>s(t_bool,X4)=s(t_bool,f)),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(33, axiom,![X4]:(s(t_bool,f)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(44, axiom,![X18]:![X5]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),X18))),s(t_h4s_nums_num,X5)))=s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X18),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X5))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_Temporalu_u_Logics_NEXT0)).
fof(60, axiom,![X25]:![X2]:(p(s(t_bool,h4s_pastu_u_temporalu_u_logics_pnext(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X25))))<=>(s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,h4s_nums_0)|p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X25)))))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_Pastu_u_Temporalu_u_Logics_PNEXT0)).
fof(68, axiom,![X10]:![X11]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_arithmetics_NOTu_u_LESS)).
fof(69, axiom,![X10]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10)))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(74, axiom,![X10]:![X11]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X10))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_arithmetics_LESSu_u_EQ)).
fof(76, axiom,![X11]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11)))))=s(t_h4s_nums_num,X11),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_primu_u_recs_PRE0u_c1)).
fof(77, axiom,![X10]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(80, 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/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_arithmetics_ONE)).
fof(81, axiom,s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_primu_u_recs_PRE0u_c0)).
fof(97, axiom,p(s(t_bool,t0)),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', aHLu_TRUTH)).
fof(99, axiom,![X4]:(s(t_bool,t0)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c4', ah4s_bools_EQu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
