# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(X2,h4s_options_optionu_u_case(s(t_h4s_options_option(X1),X3),s(X2,X5),s(t_fun(X1,X2),X4)))=s(X2,h4s_bools_cond(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),X3))),s(X2,happ(s(t_fun(X1,X2),X4),s(X1,h4s_options_the(s(t_h4s_options_option(X1),X3))))),s(X2,X5))),file('i/f/option/option__case__compute', ch4s_options_optionu_u_caseu_u_compute)).
fof(4, axiom,![X1]:![X9]:![X10]:s(X1,h4s_bools_cond(s(t_bool,f0),s(X1,X10),s(X1,X9)))=s(X1,X9),file('i/f/option/option__case__compute', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
fof(5, axiom,![X1]:![X9]:![X10]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X10),s(X1,X9)))=s(X1,X10),file('i/f/option/option__case__compute', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(24, axiom,![X2]:![X1]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),X3))))=>s(X2,h4s_options_optionu_u_case(s(t_h4s_options_option(X1),X3),s(X2,X5),s(t_fun(X1,X2),X4)))=s(X2,happ(s(t_fun(X1,X2),X4),s(X1,h4s_options_the(s(t_h4s_options_option(X1),X3)))))),file('i/f/option/option__case__compute', ah4s_options_optionu_u_CLAUSESu_c12)).
fof(26, axiom,![X1]:![X3]:(~(p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),X3)))))<=>s(t_h4s_options_option(X1),X3)=s(t_h4s_options_option(X1),h4s_options_none)),file('i/f/option/option__case__compute', ah4s_options_NOTu_u_ISu_u_SOMEu_u_EQu_u_NONE)).
fof(33, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/option/option__case__compute', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(52, axiom,![X1]:![X2]:![X23]:![X4]:s(X2,h4s_options_optionu_u_case(s(t_h4s_options_option(X1),h4s_options_none),s(X2,X23),s(t_fun(X1,X2),X4)))=s(X2,X23),file('i/f/option/option__case__compute', ah4s_options_optionu_u_caseu_u_defu_c0)).
fof(60, axiom,~(p(s(t_bool,f0))),file('i/f/option/option__case__compute', aHLu_FALSITY)).
fof(61, axiom,![X15]:(s(t_bool,X15)=s(t_bool,t)|s(t_bool,X15)=s(t_bool,f0)),file('i/f/option/option__case__compute', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
