# 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_arithmetics_u_2a(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,h4s_nums_0),s(t_h4s_nums_num,X3))))&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/LT__MULT__LCANCEL', ch4s_arithmetics_LTu_u_MULTu_u_LCANCEL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/LT__MULT__LCANCEL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/LT__MULT__LCANCEL', aHLu_FALSITY)).
fof(12, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/arithmetic/LT__MULT__LCANCEL', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(13, 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/LT__MULT__LCANCEL', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(14, axiom,![X2]: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,X2)))))),file('i/f/arithmetic/LT__MULT__LCANCEL', ah4s_primu_u_recs_LESSu_u_0)).
fof(15, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/arithmetic/LT__MULT__LCANCEL', aHLu_BOOLu_CASES)).
fof(16, axiom,![X2]:![X3]:![X9]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X9)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X9))),file('i/f/arithmetic/LT__MULT__LCANCEL', ah4s_arithmetics_LESSu_u_MULTu_u_MONO)).
fof(17, axiom,![X3]:(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/LT__MULT__LCANCEL', ah4s_arithmetics_numu_u_CASES)).
fof(18, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/LT__MULT__LCANCEL', ah4s_arithmetics_MULTu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
