# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/relation/EQC__EQUIVALENCE', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/relation/EQC__EQUIVALENCE', aHLu_FALSITY)).
fof(7, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(21, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(22, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(44, axiom,![X9]:![X19]:(p(s(t_bool,h4s_relations_equivalence(s(t_fun(X9,t_fun(X9,t_bool)),X19))))<=>(p(s(t_bool,h4s_relations_reflexive(s(t_fun(X9,t_fun(X9,t_bool)),X19))))&(p(s(t_bool,h4s_relations_symmetric(s(t_fun(X9,t_fun(X9,t_bool)),X19))))&p(s(t_bool,h4s_relations_transitive(s(t_fun(X9,t_fun(X9,t_bool)),X19))))))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_relations_equivalenceu_u_def)).
fof(45, axiom,![X9]:![X19]:s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_eqc(s(t_fun(X9,t_fun(X9,t_bool)),X19)))=s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_rc(s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_tc(s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_sc(s(t_fun(X9,t_fun(X9,t_bool)),X19))))))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_relations_EQCu_u_DEF)).
fof(46, axiom,![X9]:![X19]:p(s(t_bool,h4s_relations_symmetric(s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_sc(s(t_fun(X9,t_fun(X9,t_bool)),X19)))))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_relations_SCu_u_SYMMETRIC)).
fof(47, axiom,![X9]:![X19]:p(s(t_bool,h4s_relations_transitive(s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_tc(s(t_fun(X9,t_fun(X9,t_bool)),X19)))))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_relations_TCu_u_TRANSITIVE)).
fof(48, axiom,![X9]:![X19]:p(s(t_bool,h4s_relations_reflexive(s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_rc(s(t_fun(X9,t_fun(X9,t_bool)),X19)))))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_relations_RCu_u_REFLEXIVE)).
fof(49, axiom,![X9]:![X19]:s(t_bool,h4s_relations_symmetric(s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_rc(s(t_fun(X9,t_fun(X9,t_bool)),X19)))))=s(t_bool,h4s_relations_symmetric(s(t_fun(X9,t_fun(X9,t_bool)),X19))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_relations_symmetricu_u_RC)).
fof(50, axiom,![X9]:![X19]:s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_rc(s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_tc(s(t_fun(X9,t_fun(X9,t_bool)),X19)))))=s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_rtc(s(t_fun(X9,t_fun(X9,t_bool)),X19))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_relations_TCu_u_RCu_u_EQNSu_c0)).
fof(51, axiom,![X9]:![X19]:s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_tc(s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_rc(s(t_fun(X9,t_fun(X9,t_bool)),X19)))))=s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_rtc(s(t_fun(X9,t_fun(X9,t_bool)),X19))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_relations_TCu_u_RCu_u_EQNSu_c1)).
fof(52, axiom,![X9]:![X19]:(p(s(t_bool,h4s_relations_symmetric(s(t_fun(X9,t_fun(X9,t_bool)),X19))))=>p(s(t_bool,h4s_relations_symmetric(s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_tc(s(t_fun(X9,t_fun(X9,t_bool)),X19))))))),file('i/f/relation/EQC__EQUIVALENCE', ah4s_relations_symmetricu_u_TC)).
fof(53, conjecture,![X9]:![X19]:p(s(t_bool,h4s_relations_equivalence(s(t_fun(X9,t_fun(X9,t_bool)),h4s_relations_eqc(s(t_fun(X9,t_fun(X9,t_bool)),X19)))))),file('i/f/relation/EQC__EQUIVALENCE', ch4s_relations_EQCu_u_EQUIVALENCE)).
# SZS output end CNFRefutation
