# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X1,t_fun(X2,t_bool)),X3),s(X1,h4s_pairs_fst(s(t_h4s_pairs_prod(X1,X2),X4))))),s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),X4))))))<=>![X5]:![X6]:p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X1,t_fun(X2,t_bool)),X3),s(X1,X5))),s(X2,X6))))),file('i/f/pair/ELIM__PFORALL', ch4s_pairs_ELIMu_u_PFORALL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pair/ELIM__PFORALL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pair/ELIM__PFORALL', aHLu_FALSITY)).
fof(9, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/pair/ELIM__PFORALL', aHLu_BOOLu_CASES)).
fof(10, axiom,![X1]:![X2]:![X15]:![X14]:s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X14),s(X2,X15)))))=s(X2,X15),file('i/f/pair/ELIM__PFORALL', ah4s_pairs_SND0)).
fof(11, axiom,![X2]:![X1]:![X15]:![X14]:s(X1,h4s_pairs_fst(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X14),s(X2,X15)))))=s(X1,X14),file('i/f/pair/ELIM__PFORALL', ah4s_pairs_FST0)).
# SZS output end CNFRefutation
