# 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_none(s(t_h4s_options_option(X2),X6)))=s(t_bool,h4s_options_isu_u_none(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__NONE__PRS', ch4s_quotientu_u_options_ISu_u_NONEu_u_PRS)).
fof(4, axiom,![X12]:![X13]:((p(s(t_bool,X13))=>p(s(t_bool,X12)))=>((p(s(t_bool,X12))=>p(s(t_bool,X13)))=>s(t_bool,X13)=s(t_bool,X12))),file('i/f/quotient_option/IS__NONE__PRS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(22, axiom,![X1]:![X6]:(p(s(t_bool,h4s_options_isu_u_none(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__NONE__PRS', ah4s_options_ISu_u_NONEu_u_EQu_u_NONE)).
fof(24, axiom,![X1]:s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X1),h4s_options_none)))=s(t_bool,t),file('i/f/quotient_option/IS__NONE__PRS', ah4s_options_ISu_u_NONEu_u_DEFu_c1)).
fof(31, 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__NONE__PRS', ah4s_options_OPTIONu_u_MAPu_u_EQu_u_NONE)).
fof(46, 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))))<=>(![X21]:s(X2,happ(s(t_fun(X1,X2),X4),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X21)))))=s(X2,X21)&(![X21]: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,X21))))),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X21))))))&![X15]:![X46]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X15))),s(X1,X46))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X15))),s(X1,X15))))&(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(X1,X46))),s(X1,X46))))&s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X15)))=s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X46))))))))),file('i/f/quotient_option/IS__NONE__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(57, 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__NONE__PRS', ah4s_quotientu_u_options_OPTIONu_u_QUOTIENT)).
fof(59, axiom,p(s(t_bool,t)),file('i/f/quotient_option/IS__NONE__PRS', aHLu_TRUTH)).
fof(61, axiom,![X14]:(s(t_bool,X14)=s(t_bool,t)|s(t_bool,X14)=s(t_bool,f)),file('i/f/quotient_option/IS__NONE__PRS', aHLu_BOOLu_CASES)).
fof(65, axiom,![X14]:(s(t_bool,f)=s(t_bool,X14)<=>~(p(s(t_bool,X14)))),file('i/f/quotient_option/IS__NONE__PRS', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(67, axiom,![X14]:(s(t_bool,t)=s(t_bool,X14)<=>p(s(t_bool,X14))),file('i/f/quotient_option/IS__NONE__PRS', ah4s_bools_EQu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
