# 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,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),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,h4s_nums_0),s(t_h4s_nums_num,X2))))&s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', ch4s_arithmetics_LTu_u_MULTu_u_CANCELu_u_RBAREu_c0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', aHLu_BOOLu_CASES)).
fof(10, axiom,![X3]:(s(t_bool,t)=s(t_bool,X3)<=>p(s(t_bool,X3))),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(12, axiom,![X3]:(s(t_bool,f)=s(t_bool,X3)<=>~(p(s(t_bool,X3)))),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(14, axiom,![X1]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(15, axiom,![X1]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', ah4s_primu_u_recs_LESSu_u_0)).
fof(16, axiom,![X2]:(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', ah4s_arithmetics_numu_u_CASES)).
fof(17, axiom,![X1]:![X2]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=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/LT__MULT__CANCEL__RBARE_c0', ah4s_arithmetics_LESSu_u_MONOu_u_EQ)).
fof(18, 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/LT__MULT__CANCEL__RBARE_c0', ah4s_arithmetics_ONE)).
fof(19, axiom,![X8]:![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X8))))))<=>(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,X1),s(t_h4s_nums_num,X8)))))),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', ah4s_arithmetics_LTu_u_MULTu_u_LCANCEL)).
fof(20, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(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)))))))=s(t_h4s_nums_num,X2),file('i/f/arithmetic/LT__MULT__CANCEL__RBARE_c0', ah4s_arithmetics_MULTu_u_CLAUSESu_c3)).
# SZS output end CNFRefutation
