# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:s(t_h4s_pairs_prod(X1,t_bool),happ(s(t_fun(X1,t_h4s_pairs_prod(X1,t_bool)),X2),s(X1,X3)))=s(t_h4s_pairs_prod(X1,t_bool),h4s_pairs_u_2c(s(X1,X3),s(t_bool,f)))=>s(t_fun(X1,t_bool),h4s_predu_u_sets_gspec(s(t_fun(X1,t_h4s_pairs_prod(X1,t_bool)),X2)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/GSPEC__F', ch4s_predu_u_sets_GSPECu_u_F)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/GSPEC__F', aHLu_TRUTH)).
fof(4, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/pred_set/GSPEC__F', aHLu_BOOLu_CASES)).
fof(11, axiom,![X4]:(s(t_bool,f)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/pred_set/GSPEC__F', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(12, axiom,![X1]:![X3]:~(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/GSPEC__F', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(14, axiom,![X1]:![X4]:![X11]:(s(t_fun(X1,t_bool),X11)=s(t_fun(X1,t_bool),X4)<=>![X3]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X11)))=s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4)))),file('i/f/pred_set/GSPEC__F', ah4s_predu_u_sets_EXTENSION)).
fof(15, axiom,![X1]:![X12]:![X13]:![X9]:(p(s(t_bool,h4s_bools_in(s(X1,X13),s(t_fun(X1,t_bool),h4s_predu_u_sets_gspec(s(t_fun(X12,t_h4s_pairs_prod(X1,t_bool)),X9))))))<=>?[X3]:s(t_h4s_pairs_prod(X1,t_bool),h4s_pairs_u_2c(s(X1,X13),s(t_bool,t)))=s(t_h4s_pairs_prod(X1,t_bool),happ(s(t_fun(X12,t_h4s_pairs_prod(X1,t_bool)),X9),s(X12,X3)))),file('i/f/pred_set/GSPEC__F', ah4s_predu_u_sets_GSPECIFICATION)).
fof(16, axiom,![X1]:![X12]:![X14]:![X3]:![X15]:![X16]:(s(t_h4s_pairs_prod(X1,X12),h4s_pairs_u_2c(s(X1,X3),s(X12,X14)))=s(t_h4s_pairs_prod(X1,X12),h4s_pairs_u_2c(s(X1,X16),s(X12,X15)))<=>(s(X1,X3)=s(X1,X16)&s(X12,X14)=s(X12,X15))),file('i/f/pred_set/GSPEC__F', ah4s_pairs_PAIRu_u_EQ)).
# SZS output end CNFRefutation
