# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/INV__PRE__LESS__EQ', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/INV__PRE__LESS__EQ', 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/INV__PRE__LESS__EQ', aHLu_BOOLu_CASES)).
fof(8, 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/INV__PRE__LESS__EQ', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(9, 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/arithmetic/INV__PRE__LESS__EQ', ah4s_primu_u_recs_PRE0u_c0)).
fof(10, axiom,![X9]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9)))))=s(t_h4s_nums_num,X9),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_primu_u_recs_PRE0u_c1)).
fof(11, axiom,![X10]:![X11]:((p(s(t_bool,X11))=>p(s(t_bool,X10)))=>((p(s(t_bool,X10))=>p(s(t_bool,X11)))=>s(t_bool,X11)=s(t_bool,X10))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(17, axiom,![X8]:![X9]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X8))))=>(s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X8)))<=>s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9)))=s(t_h4s_nums_num,X8))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_PREu_u_SUCu_u_EQ)).
fof(21, axiom,![X8]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X8))))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(32, axiom,![X8]:![X9]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X8))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_PREu_u_SUB)).
fof(36, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(46, axiom,![X9]:(s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_nums_0)|?[X8]:s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8)))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_numu_u_CASES)).
fof(49, axiom,![X8]:![X9]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(50, 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/INV__PRE__LESS__EQ', ah4s_arithmetics_NOTu_u_LESS)).
fof(63, axiom,![X8]:![X9]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X9))))=>s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,X9)),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_SUBu_u_ADD)).
fof(67, axiom,![X20]:![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,X20)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X20))))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(69, axiom,![X8]:![X9]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X9))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))))=>s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X9)),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_LESSu_u_EQUALu_u_ANTISYM)).
fof(72, axiom,![X8]:![X9]:(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)))))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_primu_u_recs_NOTu_u_LESSu_u_EQ)).
fof(80, 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/INV__PRE__LESS__EQ', ah4s_arithmetics_LESSu_u_CASESu_u_IMP)).
fof(87, axiom,![X8]:![X9]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X9))))=>?[X20]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,X9)),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_LESSu_u_ADD)).
fof(88, 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/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_ADDu_c0)).
fof(97, axiom,![X8]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8)))))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_primu_u_recs_LESSu_u_SUCu_u_REFL)).
fof(98, 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,h4s_nums_suc(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,h4s_nums_suc(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X8))))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_LESSu_u_SUCu_u_EQu_u_COR)).
fof(100, axiom,![X8]:![X9]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_nums_suc(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,X9),s(t_h4s_nums_num,X8)))))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_primu_u_recs_LESSu_u_THM)).
fof(102, 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_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9)))))))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_LESSu_u_LESSu_u_SUC)).
fof(108, 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/INV__PRE__LESS__EQ', ah4s_arithmetics_ADDu_u_SYM)).
fof(110, axiom,![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X9),file('i/f/arithmetic/INV__PRE__LESS__EQ', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(133, conjecture,![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X8))))=>![X9]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X8)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))),file('i/f/arithmetic/INV__PRE__LESS__EQ', ch4s_arithmetics_INVu_u_PREu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
