# 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)))))=>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),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)))))))),file('i/f/integral/INTEGRABLE__CMUL', ch4s_integrals_INTEGRABLEu_u_CMUL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/integral/INTEGRABLE__CMUL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/integral/INTEGRABLE__CMUL', aHLu_FALSITY)).
fof(5, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/integral/INTEGRABLE__CMUL', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(6, 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))))<=>?[X8]: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,X8))))),file('i/f/integral/INTEGRABLE__CMUL', ah4s_integrals_integrableu_u_def)).
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)))))=>![X8]:![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,X8))))=>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,X8)))))))),file('i/f/integral/INTEGRABLE__CMUL', ah4s_integrals_DINTu_u_CMUL)).
fof(8, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f0)),file('i/f/integral/INTEGRABLE__CMUL', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
