# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/MIN__LE_c0', ch4s_arithmetics_MINu_u_LEu_c0)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MIN__LE_c0', aHLu_FALSITY)).
fof(3, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/arithmetic/MIN__LE_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(5, axiom,![X2]:![X3]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_NOTu_u_LESS)).
fof(22, axiom,![X2]:![X3]:~((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3)))))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_LESSu_u_ANTISYM)).
fof(23, axiom,![X6]:(s(t_bool,X6)=s(t_bool,f)<=>~(p(s(t_bool,X6)))),file('i/f/arithmetic/MIN__LE_c0', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(27, axiom,![X2]:![X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))|s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,X2))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(36, axiom,![X2]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/MIN__LE_c0', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(38, axiom,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(42, axiom,![X2]:![X3]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(44, axiom,![X2]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/MIN__LE_c0', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(46, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(48, axiom,![X3]:(s(t_h4s_nums_num,h4s_nums_0)=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))))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_LESSu_u_0u_u_CASES)).
fof(58, axiom,![X2]:![X3]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(63, axiom,![X2]:![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_ADDu_u_COMM)).
fof(65, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X3),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(66, axiom,![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))=>?[X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X3)),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_LESSu_u_ADD)).
fof(78, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_MINu_u_LTu_c1)).
fof(79, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_MINu_u_LTu_c0)).
fof(80, axiom,![X2]:![X3]:s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))),file('i/f/arithmetic/MIN__LE_c0', ah4s_arithmetics_MINu_u_COMM)).
# SZS output end CNFRefutation
