# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', 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/arithmetic/LESS__EQ__LESS__EQ__MONO', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X8]:![X9]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ah4s_arithmetics_LESSu_u_EQu_u_MONOu_u_ADDu_u_EQ)).
fof(6, axiom,![X8]:![X9]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))))|s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,X8))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(10, axiom,![X7]:![X8]:![X9]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ah4s_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ)).
fof(11, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(16, axiom,![X8]:![X9]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X9))))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ah4s_arithmetics_NOTu_u_LESS)).
fof(23, axiom,![X7]:![X8]:![X9]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7))))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(42, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(44, axiom,![X8]:![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),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,X9))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ah4s_arithmetics_ADDu_u_SYM)).
fof(77, axiom,![X8]:![X9]:((~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))))&~(s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,X8)))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X9))))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ah4s_arithmetics_LESSu_u_CASESu_u_IMP)).
fof(93, axiom,![X7]:![X8]:![X9]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ah4s_arithmetics_LTu_u_ADDu_u_LCANCEL)).
fof(133, conjecture,![X29]:![X7]:![X8]:![X9]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X29)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X29))))))),file('i/f/arithmetic/LESS__EQ__LESS__EQ__MONO', ch4s_arithmetics_LESSu_u_EQu_u_LESSu_u_EQu_u_MONO)).
# SZS output end CNFRefutation
