# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:~(p(s(t_bool,h4s_pairs_snd(s(t_h4s_pairs_prod(X2,t_bool),happ(s(t_fun(X1,t_h4s_pairs_prod(X2,t_bool)),X3),s(X1,X4)))))))=>s(t_fun(X2,t_bool),h4s_predu_u_sets_gspec(s(t_fun(X1,t_h4s_pairs_prod(X2,t_bool)),X3)))=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/GSPEC__F__COND', ch4s_predu_u_sets_GSPECu_u_Fu_u_COND)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/GSPEC__F__COND', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/pred_set/GSPEC__F__COND', aHLu_FALSITY)).
fof(4, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f0)),file('i/f/pred_set/GSPEC__F__COND', aHLu_BOOLu_CASES)).
fof(6, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/pred_set/GSPEC__F__COND', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X5]:(s(t_bool,t)=s(t_bool,X5)<=>p(s(t_bool,X5))),file('i/f/pred_set/GSPEC__F__COND', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(13, axiom,![X5]:(s(t_bool,f0)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/pred_set/GSPEC__F__COND', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(16, axiom,![X1]:![X4]:~(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/GSPEC__F__COND', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(19, axiom,![X1]:![X5]:![X16]:(s(t_fun(X1,t_bool),X16)=s(t_fun(X1,t_bool),X5)<=>![X4]:s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X16)))=s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X5)))),file('i/f/pred_set/GSPEC__F__COND', ah4s_predu_u_sets_EXTENSION)).
fof(20, axiom,![X1]:![X2]:![X17]:![X3]:(p(s(t_bool,h4s_bools_in(s(X1,X17),s(t_fun(X1,t_bool),h4s_predu_u_sets_gspec(s(t_fun(X2,t_h4s_pairs_prod(X1,t_bool)),X3))))))<=>?[X4]:s(t_h4s_pairs_prod(X1,t_bool),h4s_pairs_u_2c(s(X1,X17),s(t_bool,t)))=s(t_h4s_pairs_prod(X1,t_bool),happ(s(t_fun(X2,t_h4s_pairs_prod(X1,t_bool)),X3),s(X2,X4)))),file('i/f/pred_set/GSPEC__F__COND', ah4s_predu_u_sets_GSPECIFICATION)).
fof(21, axiom,![X1]:![X2]:![X8]:![X4]:![X18]:![X19]:(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X8)))=s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X19),s(X2,X18)))<=>(s(X1,X4)=s(X1,X19)&s(X2,X8)=s(X2,X18))),file('i/f/pred_set/GSPEC__F__COND', ah4s_pairs_CLOSEDu_u_PAIRu_u_EQ)).
fof(22, axiom,![X1]:![X2]:![X4]:?[X20]:?[X21]:s(t_h4s_pairs_prod(X1,X2),X4)=s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X20),s(X2,X21))),file('i/f/pred_set/GSPEC__F__COND', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
fof(23, axiom,![X1]:![X2]:![X8]:![X4]:s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X8)))))=s(X2,X8),file('i/f/pred_set/GSPEC__F__COND', ah4s_pairs_SND0)).
# SZS output end CNFRefutation
