# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))))<=>(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_suc(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/LE_c1', ch4s_arithmetics_LEu_c1)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/LE_c1', aHLu_TRUTH)).
fof(4, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/arithmetic/LE_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(8, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/LE_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))))=>(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,X2),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/LE_c1', ah4s_primu_u_recs_LESSu_u_LEMMA1)).
fof(10, axiom,![X1]:![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_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))|s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1))),file('i/f/arithmetic/LE_c1', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(11, axiom,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),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,h4s_nums_suc(s(t_h4s_nums_num,X2))))))),file('i/f/arithmetic/LE_c1', ah4s_arithmetics_LESSu_u_EQu_u_IMPu_u_LESSu_u_SUC)).
fof(13, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/LE_c1', aHLu_FALSITY)).
# SZS output end CNFRefutation
