# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),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,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3)))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))))))),file('i/f/arithmetic/MOD__LIFT__PLUS__IFF', ch4s_arithmetics_MODu_u_LIFTu_u_PLUSu_u_IFF)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MOD__LIFT__PLUS__IFF', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MOD__LIFT__PLUS__IFF', aHLu_FALSITY)).
fof(18, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/arithmetic/MOD__LIFT__PLUS__IFF', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(19, axiom,![X6]:(s(t_bool,X6)=s(t_bool,f)<=>~(p(s(t_bool,X6)))),file('i/f/arithmetic/MOD__LIFT__PLUS__IFF', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(38, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/arithmetic/MOD__LIFT__PLUS__IFF', aHLu_BOOLu_CASES)).
fof(41, axiom,![X13]:![X2]:![X15]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X13)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/MOD__LIFT__PLUS__IFF', ah4s_arithmetics_SUBu_u_LEFTu_u_LESS)).
fof(42, axiom,![X2]:![X15]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/MOD__LIFT__PLUS__IFF', ah4s_arithmetics_MODu_u_LESS)).
fof(43, axiom,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),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,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),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,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3)))),file('i/f/arithmetic/MOD__LIFT__PLUS__IFF', ah4s_arithmetics_MODu_u_LIFTu_u_PLUS)).
fof(44, axiom,![X2]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),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,X15))),file('i/f/arithmetic/MOD__LIFT__PLUS__IFF', ah4s_arithmetics_ADDu_u_SYM)).
# SZS output end CNFRefutation
