# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X1))))=>(s(t_h4s_integers_int,X3)=s(t_h4s_integers_int,X2)<=>s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))),file('i/f/intExtension/INT__EQ__RMUL__EXP', ch4s_intExtensions_INTu_u_EQu_u_RMULu_u_EXP)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/intExtension/INT__EQ__RMUL__EXP', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/intExtension/INT__EQ__RMUL__EXP', aHLu_FALSITY)).
fof(4, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/intExtension/INT__EQ__RMUL__EXP', aHLu_BOOLu_CASES)).
fof(16, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/intExtension/INT__EQ__RMUL__EXP', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(20, axiom,![X13]:![X9]:![X8]:((~(s(t_h4s_integers_int,X13)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))&s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X13)))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X9),s(t_h4s_integers_int,X13))))=>s(t_h4s_integers_int,X8)=s(t_h4s_integers_int,X9)),file('i/f/intExtension/INT__EQ__RMUL__EXP', ah4s_integers_INTu_u_EQu_u_RMULu_u_IMP)).
fof(21, axiom,![X1]:![X14]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X14))),file('i/f/intExtension/INT__EQ__RMUL__EXP', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(22, 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/intExtension/INT__EQ__RMUL__EXP', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
# SZS output end CNFRefutation
