# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:![X5]:s(t_fun(X1,t_bool),happ(s(t_fun(X2,t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X2,t_fun(X1,t_bool)),t_fun(X2,t_fun(X1,t_bool))),X3),s(t_fun(X2,t_fun(X1,t_bool)),X4))),s(X2,X5)))=s(t_fun(X1,t_bool),happ(s(t_fun(X2,t_fun(X1,t_bool)),X4),s(X2,X5)))=>![X4]:(p(s(t_bool,d_forall(s(t_fun(t_h4s_pairs_prod(X2,X1),t_bool),h4s_pairs_uncurry(s(t_fun(X2,t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X2,t_fun(X1,t_bool)),t_fun(X2,t_fun(X1,t_bool))),X3),s(t_fun(X2,t_fun(X1,t_bool)),X4))))))))<=>![X5]:p(s(t_bool,d_forall(s(t_fun(X1,t_bool),happ(s(t_fun(X2,t_fun(X1,t_bool)),X4),s(X2,X5)))))))),file('i/f/pair/ELIM__PFORALL__EVAL', ch4s_pairs_ELIMu_u_PFORALLu_u_EVAL)).
fof(3, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/pair/ELIM__PFORALL__EVAL', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(26, axiom,![X2]:![X5]:(p(s(t_bool,d_forall(s(t_fun(X2,t_bool),X5))))<=>![X19]:s(t_bool,happ(s(t_fun(X2,t_bool),X5),s(X2,X19)))=s(t_bool,t)),file('i/f/pair/ELIM__PFORALL__EVAL', ah4s_bools_FORALLu_u_DEF)).
fof(28, axiom,![X2]:![X21]:(p(s(t_bool,d_forall(s(t_fun(X2,t_bool),X21))))<=>![X5]:p(s(t_bool,happ(s(t_fun(X2,t_bool),X21),s(X2,X5))))),file('i/f/pair/ELIM__PFORALL__EVAL', ah4s_bools_FORALLu_u_THM)).
fof(29, axiom,![X22]:![X23]:![X21]:![X24]:(![X5]:s(X23,happ(s(t_fun(X22,X23),X21),s(X22,X5)))=s(X23,happ(s(t_fun(X22,X23),X24),s(X22,X5)))=>s(t_fun(X22,X23),X21)=s(t_fun(X22,X23),X24)),file('i/f/pair/ELIM__PFORALL__EVAL', aHLu_EXT)).
fof(38, axiom,![X27]:![X2]:![X1]:![X13]:![X5]:![X21]:s(X27,happ(s(t_fun(t_h4s_pairs_prod(X2,X1),X27),h4s_pairs_uncurry(s(t_fun(X2,t_fun(X1,X27)),X21))),s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X5),s(X1,X13)))))=s(X27,happ(s(t_fun(X1,X27),happ(s(t_fun(X2,t_fun(X1,X27)),X21),s(X2,X5))),s(X1,X13))),file('i/f/pair/ELIM__PFORALL__EVAL', ah4s_pairs_UNCURRYu_u_DEF)).
fof(42, axiom,p(s(t_bool,t)),file('i/f/pair/ELIM__PFORALL__EVAL', aHLu_TRUTH)).
fof(46, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/pair/ELIM__PFORALL__EVAL', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(63, axiom,![X2]:![X1]:![X4]:(![X16]:p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(X2,X1),t_bool),X4),s(t_h4s_pairs_prod(X2,X1),X16))))<=>![X34]:![X35]:p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(X2,X1),t_bool),X4),s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X34),s(X1,X35))))))),file('i/f/pair/ELIM__PFORALL__EVAL', ah4s_pairs_FORALLu_u_PROD)).
fof(65, axiom,~(p(s(t_bool,f))),file('i/f/pair/ELIM__PFORALL__EVAL', aHLu_FALSITY)).
fof(67, axiom,(p(s(t_bool,f))<=>![X6]:p(s(t_bool,X6))),file('i/f/pair/ELIM__PFORALL__EVAL', ah4s_bools_Fu_u_DEF)).
# SZS output end CNFRefutation
