# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4)))=s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X4)))<=>s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X4),s(X1,X2)))))=s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X4),s(X1,X3)))))),file('i/f/pred_set/IN__DELETE__EQ', ch4s_predu_u_sets_INu_u_DELETEu_u_EQ)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/IN__DELETE__EQ', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/IN__DELETE__EQ', aHLu_FALSITY)).
fof(4, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/pred_set/IN__DELETE__EQ', 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/IN__DELETE__EQ', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(13, axiom,![X5]:(s(t_bool,t)=s(t_bool,X5)<=>p(s(t_bool,X5))),file('i/f/pred_set/IN__DELETE__EQ', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(14, axiom,![X1]:![X8]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X4),s(X1,X8))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4))))&~(s(X1,X3)=s(X1,X8)))),file('i/f/pred_set/IN__DELETE__EQ', ah4s_predu_u_sets_INu_u_DELETE)).
# SZS output end CNFRefutation
