# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:![X3]:![X4]:s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))))),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X4)))=s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,X2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X4)))))=>![X5]:(![X2]:![X3]:s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))))),X5),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3)))=s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))))),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3)))=>![X6]:(![X2]:s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),X6),s(t_h4s_nums_num,X2)))=s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),h4s_pairs_uncurry(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))))),X5),s(t_h4s_nums_num,X2)))))=>![X7]:![X8]:![X9]:![X10]:(?[X11]:(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),X7)=s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),h4s_pairs_uncurry(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),X6))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),X11)))&(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),X11))),s(t_h4s_nums_num,X10))))&(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),X11))))),s(t_h4s_nums_num,X9))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),X11))))),s(t_h4s_nums_num,X8)))))))=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),X7))),s(t_h4s_nums_num,X10))))&(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),X7))))),s(t_h4s_nums_num,X9))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),X7))))),s(t_h4s_nums_num,X8)))))))))),file('i/f/float/FLOAT__FIRSTCROSS1', ch4s_floats_FLOATu_u_FIRSTCROSS1)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/float/FLOAT__FIRSTCROSS1', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/float/FLOAT__FIRSTCROSS1', aHLu_FALSITY)).
fof(6, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)<=>p(s(t_bool,X12))),file('i/f/float/FLOAT__FIRSTCROSS1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X17]:![X18]:![X7]:?[X21]:?[X22]:s(t_h4s_pairs_prod(X17,X18),X7)=s(t_h4s_pairs_prod(X17,X18),h4s_pairs_u_2c(s(X17,X21),s(X18,X22))),file('i/f/float/FLOAT__FIRSTCROSS1', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
fof(12, axiom,![X17]:![X18]:![X3]:![X7]:s(X18,h4s_pairs_snd(s(t_h4s_pairs_prod(X17,X18),h4s_pairs_u_2c(s(X17,X7),s(X18,X3)))))=s(X18,X3),file('i/f/float/FLOAT__FIRSTCROSS1', ah4s_pairs_SND0)).
fof(13, axiom,![X18]:![X17]:![X3]:![X7]:s(X17,h4s_pairs_fst(s(t_h4s_pairs_prod(X17,X18),h4s_pairs_u_2c(s(X17,X7),s(X18,X3)))))=s(X17,X7),file('i/f/float/FLOAT__FIRSTCROSS1', ah4s_pairs_FST0)).
fof(14, axiom,![X23]:![X17]:![X18]:![X3]:![X7]:![X24]:s(X23,happ(s(t_fun(t_h4s_pairs_prod(X17,X18),X23),h4s_pairs_uncurry(s(t_fun(X17,t_fun(X18,X23)),X24))),s(t_h4s_pairs_prod(X17,X18),h4s_pairs_u_2c(s(X17,X7),s(X18,X3)))))=s(X23,happ(s(t_fun(X18,X23),happ(s(t_fun(X17,t_fun(X18,X23)),X24),s(X17,X7))),s(X18,X3))),file('i/f/float/FLOAT__FIRSTCROSS1', ah4s_pairs_UNCURRYu_u_DEF)).
fof(15, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)|s(t_bool,X12)=s(t_bool,f)),file('i/f/float/FLOAT__FIRSTCROSS1', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
