# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:((p(s(t_bool,happ(s(t_fun(t_h4s_totos_cpn,t_bool),X1),s(t_h4s_totos_cpn,h4s_totos_equal))))&(p(s(t_bool,happ(s(t_fun(t_h4s_totos_cpn,t_bool),X1),s(t_h4s_totos_cpn,h4s_totos_greater))))&p(s(t_bool,happ(s(t_fun(t_h4s_totos_cpn,t_bool),X1),s(t_h4s_totos_cpn,h4s_totos_less))))))=>![X2]:p(s(t_bool,happ(s(t_fun(t_h4s_totos_cpn,t_bool),X1),s(t_h4s_totos_cpn,X2))))),file('i/f/toto/cpn__induction', ch4s_totos_cpnu_u_induction)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/toto/cpn__induction', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/toto/cpn__induction', aHLu_FALSITY)).
fof(37, axiom,![X10]:((p(s(t_bool,X10))=>p(s(t_bool,f)))<=>s(t_bool,X10)=s(t_bool,f)),file('i/f/toto/cpn__induction', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(43, axiom,![X10]:(s(t_bool,f)=s(t_bool,X10)<=>~(p(s(t_bool,X10)))),file('i/f/toto/cpn__induction', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(58, axiom,![X2]:(s(t_h4s_totos_cpn,X2)=s(t_h4s_totos_cpn,h4s_totos_less)|(s(t_h4s_totos_cpn,X2)=s(t_h4s_totos_cpn,h4s_totos_equal)|s(t_h4s_totos_cpn,X2)=s(t_h4s_totos_cpn,h4s_totos_greater))),file('i/f/toto/cpn__induction', ah4s_totos_cpnu_u_nchotomy)).
fof(70, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)|s(t_bool,X10)=s(t_bool,f)),file('i/f/toto/cpn__induction', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
