# 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,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_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))),file('i/f/arithmetic/MIN__LE_c1', ch4s_arithmetics_MINu_u_LEu_c1)).
fof(2, 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_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(25, 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_c1', ah4s_arithmetics_NOTu_u_LESS)).
fof(26, 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_c1', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(27, axiom,![X2]:![X3]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))))=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X3)),file('i/f/arithmetic/MIN__LE_c1', ah4s_arithmetics_LESSu_u_EQUALu_u_ANTISYM)).
fof(30, 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_c1', ah4s_arithmetics_LESSu_u_EQu_u_ANTISYM)).
fof(33, 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_c1', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(35, 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_bools_cond(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_c1', ah4s_arithmetics_MINu_u_DEF)).
fof(36, axiom,![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_c1', ah4s_arithmetics_MINu_u_LEu_c0)).
fof(37, axiom,![X1]:![X2]:![X3]:s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_arithmetics_min(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))),file('i/f/arithmetic/MIN__LE_c1', ah4s_arithmetics_MINu_u_ASSOC)).
fof(38, 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_c1', ah4s_arithmetics_MINu_u_COMM)).
fof(40, 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_c1', ah4s_arithmetics_MINu_u_LTu_c0)).
fof(43, 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_c1', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(46, 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_c1', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(50, axiom,![X4]:![X5]:![X18]:(p(s(t_bool,h4s_bools_cond(s(t_bool,X18),s(t_bool,X5),s(t_bool,X4))))<=>((~(p(s(t_bool,X18)))|p(s(t_bool,X5)))&(p(s(t_bool,X18))|p(s(t_bool,X4))))),file('i/f/arithmetic/MIN__LE_c1', ah4s_bools_CONDu_u_EXPAND)).
fof(52, axiom,![X13]:![X4]:![X5]:s(X13,h4s_bools_cond(s(t_bool,t),s(X13,X5),s(X13,X4)))=s(X13,X5),file('i/f/arithmetic/MIN__LE_c1', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(53, axiom,![X13]:![X4]:![X5]:s(X13,h4s_bools_cond(s(t_bool,f),s(X13,X5),s(X13,X4)))=s(X13,X4),file('i/f/arithmetic/MIN__LE_c1', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
