# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:![X3]:(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)),X1),s(t_fun(t_h4s_nums_num,t_bool),X2))),s(t_h4s_nums_num,X3))))<=>~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X3))))))=>![X4]:![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,X4)))))<=>p(s(t_bool,h4s_pastu_u_temporalu_u_logics_psnext(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)),X1),s(t_fun(t_h4s_nums_num,t_bool),X2))),s(t_h4s_nums_num,X4)))))),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', ch4s_Pastu_u_Temporalu_u_Logics_NEGATIONu_u_NORMALu_u_FORMu_c9)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', aHLu_FALSITY)).
fof(14, 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/NEGATION__NORMAL__FORM_c9', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(38, axiom,![X3]:![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,X3))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3))))&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,X3)))))))),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', ah4s_Pastu_u_Temporalu_u_Logics_PSNEXT0)).
fof(54, axiom,![X3]:![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,X3))))<=>(s(t_h4s_nums_num,X3)=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,X3)))))))),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', ah4s_Pastu_u_Temporalu_u_Logics_PNEXT0)).
fof(69, axiom,![X15]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(70, axiom,![X15]:![X14]:(~(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,X15))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X15))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X14)))))),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(73, axiom,![X15]:![X14]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X15))),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', ah4s_arithmetics_LESSu_u_EQ)).
fof(75, axiom,![X15]:![X14]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))))),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', ah4s_arithmetics_NOTu_u_LESS)).
fof(80, 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/NEGATION__NORMAL__FORM_c9', ah4s_primu_u_recs_PRE0u_c0)).
fof(83, axiom,![X15]:![X14]:(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,X15)|(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))))|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))))),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', ah4s_arithmetics_LESSu_u_LESSu_u_CASES)).
fof(95, axiom,p(s(t_bool,t1)),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', aHLu_TRUTH)).
fof(100, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t1)<=>p(s(t_bool,X4))),file('i/f/Past_Temporal_Logic/NEGATION__NORMAL__FORM_c9', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
