# 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_psnext(s(t_fun(t_h4s_nums_num,t_bool),X3),s(t_h4s_nums_num,X4))))))=>![X3]:![X2]:![X5]:(p(s(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,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_c1', ch4s_Pastu_u_Temporalu_u_Logics_SEPARATEu_u_NEXTu_u_THMu_c1)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', aHLu_FALSITY)).
fof(24, axiom,![X4]:(s(t_bool,t0)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(44, axiom,![X16]:![X17]:(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X16)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17)))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(45, axiom,![X18]:![X5]:s(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_c1', ah4s_Temporalu_u_Logics_NEXT0)).
fof(52, axiom,![X16]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X16)))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(55, axiom,![X16]:![X17]:(~(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X16))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,X16))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,X17)))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(56, axiom,![X16]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X16),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_numerals_numeralu_u_distribu_c1)).
fof(59, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t0)|s(t_bool,X4)=s(t_bool,f)),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', aHLu_BOOLu_CASES)).
fof(61, axiom,![X25]:![X2]:(p(s(t_bool,h4s_pastu_u_temporalu_u_logics_psnext(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X25))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X25))))&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_c1', ah4s_Pastu_u_Temporalu_u_Logics_PSNEXT0)).
fof(64, axiom,![X16]:![X17]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,X16))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_LESSu_u_EQ)).
fof(65, 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)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_NOTu_u_LESS)).
fof(67, axiom,![X17]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17)))))=s(t_h4s_nums_num,X17),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_primu_u_recs_PRE0u_c1)).
fof(68, axiom,![X16]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16)))=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,X16))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(69, 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_c1', ah4s_primu_u_recs_PRE0u_c0)).
fof(71, axiom,![X16]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X16)))))=s(t_h4s_nums_num,X16),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_numerals_numeralu_u_addu_c0)).
# SZS output end CNFRefutation
