# 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,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/pred_set/IN__DELETE__EQ', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(20, axiom,![X1]:![X13]:![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,X13))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4))))&~(s(X1,X3)=s(X1,X13)))),file('i/f/pred_set/IN__DELETE__EQ', ah4s_predu_u_sets_INu_u_DELETE)).
fof(22, axiom,![X1]:![X3]:![X4]:(~(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4)))))<=>s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X4),s(X1,X3)))=s(t_fun(X1,t_bool),X4)),file('i/f/pred_set/IN__DELETE__EQ', ah4s_predu_u_sets_DELETEu_u_NONu_u_ELEMENT)).
fof(59, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/IN__DELETE__EQ', aHLu_FALSITY)).
fof(60, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/pred_set/IN__DELETE__EQ', aHLu_BOOLu_CASES)).
fof(65, axiom,![X7]:(s(t_bool,X7)=s(t_bool,f)<=>~(p(s(t_bool,X7)))),file('i/f/pred_set/IN__DELETE__EQ', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(74, axiom,(p(s(t_bool,f))<=>![X7]:p(s(t_bool,X7))),file('i/f/pred_set/IN__DELETE__EQ', ah4s_bools_Fu_u_DEF)).
fof(79, axiom,p(s(t_bool,t)),file('i/f/pred_set/IN__DELETE__EQ', aHLu_TRUTH)).
fof(82, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/pred_set/IN__DELETE__EQ', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
