# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:![X5]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X3),s(X1,X4))),s(X1,X5))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X3),s(X1,happ(s(t_fun(X1,X1),X2),s(X1,X4))))),s(X1,happ(s(t_fun(X1,X1),X2),s(X1,X5)))))))=>![X4]:![X5]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),h4s_relations_rc(s(t_fun(X1,t_fun(X1,t_bool)),X3))),s(X1,X4))),s(X1,X5))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),h4s_relations_rc(s(t_fun(X1,t_fun(X1,t_bool)),X3))),s(X1,happ(s(t_fun(X1,X1),X2),s(X1,X4))))),s(X1,happ(s(t_fun(X1,X1),X2),s(X1,X5)))))))),file('i/f/relation/RC__lifts__monotonicities', ch4s_relations_RCu_u_liftsu_u_monotonicities)).
fof(2, 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/RC__lifts__monotonicities', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(46, axiom,![X1]:![X5]:![X4]:![X3]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),h4s_relations_rc(s(t_fun(X1,t_fun(X1,t_bool)),X3))),s(X1,X4))),s(X1,X5))))<=>(s(X1,X4)=s(X1,X5)|p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X3),s(X1,X4))),s(X1,X5)))))),file('i/f/relation/RC__lifts__monotonicities', ah4s_relations_RCu_u_DEF)).
fof(47, axiom,![X1]:![X3]:p(s(t_bool,h4s_relations_reflexive(s(t_fun(X1,t_fun(X1,t_bool)),h4s_relations_rc(s(t_fun(X1,t_fun(X1,t_bool)),X3)))))),file('i/f/relation/RC__lifts__monotonicities', ah4s_relations_RCu_u_REFLEXIVE)).
fof(50, axiom,~(p(s(t_bool,f0))),file('i/f/relation/RC__lifts__monotonicities', aHLu_FALSITY)).
fof(51, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f0)),file('i/f/relation/RC__lifts__monotonicities', aHLu_BOOLu_CASES)).
fof(64, axiom,![X8]:(s(t_bool,X8)=s(t_bool,f0)<=>~(p(s(t_bool,X8)))),file('i/f/relation/RC__lifts__monotonicities', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(65, axiom,(p(s(t_bool,f0))<=>![X8]:p(s(t_bool,X8))),file('i/f/relation/RC__lifts__monotonicities', ah4s_bools_Fu_u_DEF)).
fof(69, axiom,p(s(t_bool,t)),file('i/f/relation/RC__lifts__monotonicities', aHLu_TRUTH)).
fof(71, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/relation/RC__lifts__monotonicities', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(79, axiom,![X1]:![X3]:(p(s(t_bool,h4s_relations_reflexive(s(t_fun(X1,t_fun(X1,t_bool)),X3))))<=>![X4]:p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X3),s(X1,X4))),s(X1,X4))))),file('i/f/relation/RC__lifts__monotonicities', ah4s_relations_reflexiveu_u_def)).
# SZS output end CNFRefutation
