# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:s(X1,happ(s(t_fun(X1,X1),X2),s(X1,X3)))=s(X1,X3)=>![X4]:p(s(t_bool,h4s_predu_u_sets_bij(s(t_fun(X1,X1),X2),s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X4))))),file('i/f/pred_set/BIJ__ID', ch4s_predu_u_sets_BIJu_u_ID)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/BIJ__ID', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/BIJ__ID', aHLu_FALSITY)).
fof(7, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/pred_set/BIJ__ID', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(8, axiom,![X1]:![X2]:(![X3]:s(X1,happ(s(t_fun(X1,X1),X2),s(X1,X3)))=s(X1,X3)=>![X4]:p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,X1),X2),s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X4))))),file('i/f/pred_set/BIJ__ID', ah4s_predu_u_sets_INJu_u_ID)).
fof(9, axiom,![X1]:![X2]:(![X3]:s(X1,happ(s(t_fun(X1,X1),X2),s(X1,X3)))=s(X1,X3)=>![X4]:p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X1,X1),X2),s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X4))))),file('i/f/pred_set/BIJ__ID', ah4s_predu_u_sets_SURJu_u_ID)).
fof(10, axiom,![X1]:![X6]:![X5]:![X4]:![X7]:(p(s(t_bool,h4s_predu_u_sets_bij(s(t_fun(X1,X6),X7),s(t_fun(X1,t_bool),X4),s(t_fun(X6,t_bool),X5))))<=>(p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,X6),X7),s(t_fun(X1,t_bool),X4),s(t_fun(X6,t_bool),X5))))&p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X1,X6),X7),s(t_fun(X1,t_bool),X4),s(t_fun(X6,t_bool),X5)))))),file('i/f/pred_set/BIJ__ID', ah4s_predu_u_sets_BIJu_u_DEF)).
fof(12, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/pred_set/BIJ__ID', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
