# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((~(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X3)))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2)))))=>~(s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))),file('i/f/pred_set/INFINITE__DIFF__FINITE', ch4s_predu_u_sets_INFINITEu_u_DIFFu_u_FINITE)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/pred_set/INFINITE__DIFF__FINITE', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/INFINITE__DIFF__FINITE', aHLu_FALSITY)).
fof(4, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t0)|s(t_bool,X2)=s(t_bool,f)),file('i/f/pred_set/INFINITE__DIFF__FINITE', aHLu_BOOLu_CASES)).
fof(11, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t0)<=>p(s(t_bool,X2))),file('i/f/pred_set/INFINITE__DIFF__FINITE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X2]:(s(t_bool,X2)=s(t_bool,f)<=>~(p(s(t_bool,X2)))),file('i/f/pred_set/INFINITE__DIFF__FINITE', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(14, axiom,![X1]:![X6]:~(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/INFINITE__DIFF__FINITE', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(15, axiom,![X1]:![X6]:![X2]:![X3]:(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X3))))&~(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X2))))))),file('i/f/pred_set/INFINITE__DIFF__FINITE', ah4s_predu_u_sets_INu_u_DIFF)).
fof(16, axiom,![X1]:![X2]:![X3]:((~(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X3)))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2)))))=>?[X6]:(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X3))))&~(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X2))))))),file('i/f/pred_set/INFINITE__DIFF__FINITE', ah4s_predu_u_sets_INu_u_INFINITEu_u_NOTu_u_FINITE)).
# SZS output end CNFRefutation
