# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_relations_weakorder(s(t_fun(X1,t_fun(X1,t_bool)),X2))))=>![X3]:![X4]:(s(X1,X3)=s(X1,X4)<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(X1,X3))),s(X1,X4))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(X1,X4))),s(X1,X3))))))),file('i/f/relation/WeakOrder__EQ', ch4s_relations_WeakOrderu_u_EQ)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/relation/WeakOrder__EQ', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/relation/WeakOrder__EQ', aHLu_FALSITY)).
fof(19, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/relation/WeakOrder__EQ', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(20, axiom,![X7]:(s(t_bool,X7)=s(t_bool,f)<=>~(p(s(t_bool,X7)))),file('i/f/relation/WeakOrder__EQ', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(41, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/relation/WeakOrder__EQ', aHLu_BOOLu_CASES)).
fof(45, axiom,![X1]:![X2]:(p(s(t_bool,h4s_relations_reflexive(s(t_fun(X1,t_fun(X1,t_bool)),X2))))<=>![X8]:p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(X1,X8))),s(X1,X8))))),file('i/f/relation/WeakOrder__EQ', ah4s_relations_reflexiveu_u_def)).
fof(46, axiom,![X1]:![X2]:(p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(X1,t_fun(X1,t_bool)),X2))))<=>![X8]:![X3]:((p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(X1,X8))),s(X1,X3))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(X1,X3))),s(X1,X8)))))=>s(X1,X8)=s(X1,X3))),file('i/f/relation/WeakOrder__EQ', ah4s_relations_antisymmetricu_u_def)).
fof(47, axiom,![X22]:![X23]:(p(s(t_bool,h4s_relations_weakorder(s(t_fun(X22,t_fun(X22,t_bool)),X23))))<=>(p(s(t_bool,h4s_relations_reflexive(s(t_fun(X22,t_fun(X22,t_bool)),X23))))&(p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(X22,t_fun(X22,t_bool)),X23))))&p(s(t_bool,h4s_relations_transitive(s(t_fun(X22,t_fun(X22,t_bool)),X23))))))),file('i/f/relation/WeakOrder__EQ', ah4s_relations_WeakOrder0)).
# SZS output end CNFRefutation
