# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(t_fun(X1,X2),X4),s(t_fun(X2,X1),X3))))=>![X6]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X2),X6)))=s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),happ(s(t_fun(t_h4s_options_option(X2),t_h4s_options_option(X1)),h4s_options_optionu_u_map(s(t_fun(X2,X1),X3))),s(t_h4s_options_option(X2),X6)))))),file('i/f/quotient_option/IS__SOME__PRS', ch4s_quotientu_u_options_ISu_u_SOMEu_u_PRS)).
fof(7, axiom,![X15]:![X16]:((p(s(t_bool,X16))=>p(s(t_bool,X15)))=>((p(s(t_bool,X15))=>p(s(t_bool,X16)))=>s(t_bool,X16)=s(t_bool,X15))),file('i/f/quotient_option/IS__SOME__PRS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(34, axiom,![X1]:![X6]:(~(p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),X6)))))<=>s(t_h4s_options_option(X1),X6)=s(t_h4s_options_option(X1),h4s_options_none)),file('i/f/quotient_option/IS__SOME__PRS', ah4s_options_NOTu_u_ISu_u_SOMEu_u_EQu_u_NONE)).
fof(42, axiom,![X2]:![X1]:![X6]:![X9]:(s(t_h4s_options_option(X2),happ(s(t_fun(t_h4s_options_option(X1),t_h4s_options_option(X2)),h4s_options_optionu_u_map(s(t_fun(X1,X2),X9))),s(t_h4s_options_option(X1),X6)))=s(t_h4s_options_option(X2),h4s_options_none)<=>s(t_h4s_options_option(X1),X6)=s(t_h4s_options_option(X1),h4s_options_none)),file('i/f/quotient_option/IS__SOME__PRS', ah4s_options_OPTIONu_u_MAPu_u_EQu_u_NONE)).
fof(50, axiom,![X2]:![X1]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(t_fun(X1,X2),X4),s(t_fun(X2,X1),X3))))<=>(![X24]:s(X2,happ(s(t_fun(X1,X2),X4),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X24)))))=s(X2,X24)&(![X24]:p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X24))))),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X24))))))&![X18]:![X37]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X18))),s(X1,X37))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X18))),s(X1,X18))))&(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X37))),s(X1,X37))))&s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X18)))=s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X37))))))))),file('i/f/quotient_option/IS__SOME__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(61, axiom,![X2]:![X1]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(t_fun(X1,X2),X4),s(t_fun(X2,X1),X3))))=>p(s(t_bool,h4s_quotients_quotient(s(t_fun(t_h4s_options_option(X1),t_fun(t_h4s_options_option(X1),t_bool)),h4s_options_optrel(s(t_fun(X1,t_fun(X1,t_bool)),X5))),s(t_fun(t_h4s_options_option(X1),t_h4s_options_option(X2)),h4s_options_optionu_u_map(s(t_fun(X1,X2),X4))),s(t_fun(t_h4s_options_option(X2),t_h4s_options_option(X1)),h4s_options_optionu_u_map(s(t_fun(X2,X1),X3))))))),file('i/f/quotient_option/IS__SOME__PRS', ah4s_quotientu_u_options_OPTIONu_u_QUOTIENT)).
fof(63, axiom,p(s(t_bool,t)),file('i/f/quotient_option/IS__SOME__PRS', aHLu_TRUTH)).
fof(64, axiom,~(p(s(t_bool,f))),file('i/f/quotient_option/IS__SOME__PRS', aHLu_FALSITY)).
fof(65, axiom,![X17]:(s(t_bool,X17)=s(t_bool,t)|s(t_bool,X17)=s(t_bool,f)),file('i/f/quotient_option/IS__SOME__PRS', aHLu_BOOLu_CASES)).
fof(74, axiom,![X17]:(s(t_bool,t)=s(t_bool,X17)<=>p(s(t_bool,X17))),file('i/f/quotient_option/IS__SOME__PRS', ah4s_bools_EQu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
