# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((![X3]:p(s(t_bool,happ(s(t_fun(t_h4s_fcps_bit0(X1),t_bool),X2),s(t_h4s_fcps_bit0(X1),happ(s(t_fun(X1,t_h4s_fcps_bit0(X1)),h4s_fcps_bit0a),s(X1,X3))))))&![X3]:p(s(t_bool,happ(s(t_fun(t_h4s_fcps_bit0(X1),t_bool),X2),s(t_h4s_fcps_bit0(X1),happ(s(t_fun(X1,t_h4s_fcps_bit0(X1)),h4s_fcps_bit0b),s(X1,X3)))))))=>![X4]:p(s(t_bool,happ(s(t_fun(t_h4s_fcps_bit0(X1),t_bool),X2),s(t_h4s_fcps_bit0(X1),X4))))),file('i/f/fcp/bit0__induction', ch4s_fcps_bit0u_u_induction)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/fcp/bit0__induction', aHLu_FALSITY)).
fof(6, axiom,![X7]:(s(t_bool,X7)=s(t_bool,f)<=>~(p(s(t_bool,X7)))),file('i/f/fcp/bit0__induction', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(38, axiom,![X1]:![X25]:(?[X3]:s(t_h4s_fcps_bit0(X1),X25)=s(t_h4s_fcps_bit0(X1),happ(s(t_fun(X1,t_h4s_fcps_bit0(X1)),h4s_fcps_bit0a),s(X1,X3)))|?[X3]:s(t_h4s_fcps_bit0(X1),X25)=s(t_h4s_fcps_bit0(X1),happ(s(t_fun(X1,t_h4s_fcps_bit0(X1)),h4s_fcps_bit0b),s(X1,X3)))),file('i/f/fcp/bit0__induction', ah4s_fcps_bit0u_u_nchotomy)).
fof(44, axiom,![X1]:s(t_fun(X1,t_h4s_fcps_bit0(X1)),h4s_fcps_bit0b)=s(t_fun(X1,t_h4s_fcps_bit0(X1)),h4s_fcps_u_20u_40indu_u_typefcp1),file('i/f/fcp/bit0__induction', ah4s_fcps_BIT0B0)).
fof(49, axiom,![X1]:s(t_fun(X1,t_h4s_fcps_bit0(X1)),h4s_fcps_bit0a)=s(t_fun(X1,t_h4s_fcps_bit0(X1)),h4s_fcps_u_20u_40indu_u_typefcp0),file('i/f/fcp/bit0__induction', ah4s_fcps_BIT0A0)).
fof(52, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/fcp/bit0__induction', aHLu_BOOLu_CASES)).
fof(53, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/fcp/bit0__induction', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
