# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:![X3]:![X4]:s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),X1),s(t_h4s_realaxs_real,X2))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3))),s(t_h4s_realaxs_real,X4)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3),s(t_h4s_realaxs_real,X4)))))=>![X3]:![X2]:![X5]:![X6]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))))&p(s(t_bool,h4s_integrals_integrable(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3)))))=>s(t_h4s_realaxs_real,h4s_integrals_integral(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),X1),s(t_h4s_realaxs_real,X2))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,h4s_integrals_integral(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3))))))),file('i/f/integral/INTEGRAL__CMUL', ch4s_integrals_INTEGRALu_u_CMUL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/integral/INTEGRAL__CMUL', aHLu_TRUTH)).
fof(6, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)<=>p(s(t_bool,X10))),file('i/f/integral/INTEGRAL__CMUL', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X1]:(![X2]:![X3]:![X4]:s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),X1),s(t_h4s_realaxs_real,X2))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3))),s(t_h4s_realaxs_real,X4)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3),s(t_h4s_realaxs_real,X4)))))=>![X11]:![X3]:![X2]:![X5]:![X6]:(p(s(t_bool,h4s_transcs_dint(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3),s(t_h4s_realaxs_real,X11))))=>p(s(t_bool,h4s_transcs_dint(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),X1),s(t_h4s_realaxs_real,X2))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X11)))))))),file('i/f/integral/INTEGRAL__CMUL', ah4s_integrals_DINTu_u_CMUL)).
fof(8, axiom,![X3]:![X5]:![X6]:(p(s(t_bool,h4s_integrals_integrable(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3))))=>p(s(t_bool,h4s_transcs_dint(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3),s(t_h4s_realaxs_real,h4s_integrals_integral(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3))))))),file('i/f/integral/INTEGRAL__CMUL', ah4s_integrals_INTEGRABLEu_u_DINT)).
fof(9, axiom,![X11]:![X3]:![X5]:![X6]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))))&p(s(t_bool,h4s_transcs_dint(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3),s(t_h4s_realaxs_real,X11)))))=>s(t_h4s_realaxs_real,h4s_integrals_integral(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),X3)))=s(t_h4s_realaxs_real,X11)),file('i/f/integral/INTEGRAL__CMUL', ah4s_integrals_DINTu_u_INTEGRAL)).
# SZS output end CNFRefutation
