# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:![X5]:p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),X3),s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X5))))))=>![X6]:p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),X3),s(t_h4s_pairs_prod(X1,X2),X6))))),file('i/f/pair/pair__induction', ch4s_pairs_pairu_u_induction)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pair/pair__induction', aHLu_FALSITY)).
fof(6, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/pair/pair__induction', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(16, axiom,![X1]:![X13]:![X12]:(![X10]:(s(X1,X10)=s(X1,X13)=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X12),s(X1,X10)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X12),s(X1,X13))))),file('i/f/pair/pair__induction', ah4s_bools_UNWINDu_u_FORALLu_u_THM2)).
fof(34, axiom,(p(s(t_bool,f))<=>![X7]:p(s(t_bool,X7))),file('i/f/pair/pair__induction', ah4s_bools_Fu_u_DEF)).
fof(58, axiom,![X1]:![X2]:![X10]:?[X20]:?[X21]:s(t_h4s_pairs_prod(X1,X2),X10)=s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X20),s(X2,X21))),file('i/f/pair/pair__induction', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
# SZS output end CNFRefutation
