# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3))),s(X1,X2))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X4))))&~(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X3))))))),file('i/f/pred_set/DIFF__applied', ch4s_predu_u_sets_DIFFu_u_applied)).
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/DIFF__applied', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, axiom,![X1]:![X2]:![X24]:s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X24)))=s(t_bool,happ(s(t_fun(X1,t_bool),X24),s(X1,X2))),file('i/f/pred_set/DIFF__applied', ah4s_bools_INu_u_DEF)).
fof(35, axiom,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X4))))&~(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X3))))))),file('i/f/pred_set/DIFF__applied', ah4s_predu_u_sets_INu_u_DIFF)).
fof(40, axiom,p(s(t_bool,t0)),file('i/f/pred_set/DIFF__applied', aHLu_TRUTH)).
fof(41, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)|s(t_bool,X3)=s(t_bool,f)),file('i/f/pred_set/DIFF__applied', aHLu_BOOLu_CASES)).
fof(42, axiom,![X3]:(s(t_bool,t0)=s(t_bool,X3)<=>p(s(t_bool,X3))),file('i/f/pred_set/DIFF__applied', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(61, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/DIFF__applied', aHLu_FALSITY)).
fof(63, axiom,![X3]:(s(t_bool,X3)=s(t_bool,f)<=>~(p(s(t_bool,X3)))),file('i/f/pred_set/DIFF__applied', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(65, axiom,(p(s(t_bool,f))<=>![X3]:p(s(t_bool,X3))),file('i/f/pred_set/DIFF__applied', ah4s_bools_Fu_u_DEF)).
# SZS output end CNFRefutation
