# 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,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_c1', ch4s_Pastu_u_Temporalu_u_Logics_SEPARATEu_u_NEXTu_u_THMu_c1)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', aHLu_FALSITY)).
fof(27, axiom,![X12]:![X8]:(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X12)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X12))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X8)))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', 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_c1', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(33, axiom,![X4]:(s(t_bool,X4)=s(t_bool,f)<=>~(p(s(t_bool,X4)))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(45, 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_c1', ah4s_Temporalu_u_Logics_NEXT0)).
fof(63, 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,![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(66, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t0))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_bools_NOTu_u_CLAUSESu_c2)).
fof(72, axiom,![X12]:![X8]:(~(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X12))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X12))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,X8)))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(73, axiom,![X12]:![X8]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X12)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X8))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_NOTu_u_LESS)).
fof(74, axiom,![X12]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X12)))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(76, axiom,![X12]:![X8]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X12)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X12))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_LESSu_u_EQ)).
fof(78, axiom,![X8]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,X8),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(80, axiom,![X12]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12)))=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,X12))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(84, axiom,![X8]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_arithmetics_ADD1)).
fof(91, axiom,![X8]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8)))))=s(t_h4s_nums_num,X8),file('i/f/Past_Temporal_Logic/SEPARATE__NEXT__THM_c1', ah4s_primu_u_recs_PRE0u_c1)).
# SZS output end CNFRefutation
