# 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(4, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/relation/WeakOrder__EQ', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(73, axiom,![X31]:![X32]:(p(s(t_bool,h4s_relations_weakorder(s(t_fun(X31,t_fun(X31,t_bool)),X32))))<=>(p(s(t_bool,h4s_relations_reflexive(s(t_fun(X31,t_fun(X31,t_bool)),X32))))&(p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(X31,t_fun(X31,t_bool)),X32))))&p(s(t_bool,h4s_relations_transitive(s(t_fun(X31,t_fun(X31,t_bool)),X32))))))),file('i/f/relation/WeakOrder__EQ', ah4s_relations_WeakOrder0)).
fof(80, axiom,![X1]:![X2]:(p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(X1,t_fun(X1,t_bool)),X2))))<=>![X10]:![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,X10))),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,X10)))))=>s(X1,X10)=s(X1,X3))),file('i/f/relation/WeakOrder__EQ', ah4s_relations_antisymmetricu_u_def)).
fof(81, axiom,![X1]:![X2]:(p(s(t_bool,h4s_relations_reflexive(s(t_fun(X1,t_fun(X1,t_bool)),X2))))<=>![X10]:p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(X1,X10))),s(X1,X10))))),file('i/f/relation/WeakOrder__EQ', ah4s_relations_reflexiveu_u_def)).
# SZS output end CNFRefutation
