# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),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,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),file('i/f/arithmetic/SUB__LESS__OR', ch4s_arithmetics_SUBu_u_LESSu_u_OR)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/SUB__LESS__OR', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/SUB__LESS__OR', aHLu_FALSITY)).
fof(5, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/arithmetic/SUB__LESS__OR', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(6, axiom,![X1]:![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X1)))))),file('i/f/arithmetic/SUB__LESS__OR', ah4s_arithmetics_LESSu_u_EQu_u_ADD)).
fof(7, axiom,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))=>?[X4]:s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))),file('i/f/arithmetic/SUB__LESS__OR', ah4s_arithmetics_LESSu_u_ADDu_u_1)).
fof(8, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/SUB__LESS__OR', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(9, axiom,![X2]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/arithmetic/SUB__LESS__OR', ah4s_arithmetics_PREu_u_SUB1)).
fof(10, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/SUB__LESS__OR', ah4s_arithmetics_ONE)).
fof(11, axiom,![X2]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,X2),file('i/f/arithmetic/SUB__LESS__OR', ah4s_primu_u_recs_PRE0u_c1)).
fof(12, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X2),file('i/f/arithmetic/SUB__LESS__OR', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(13, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/SUB__LESS__OR', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
