# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:?[X7]:((p(s(t_bool,X7))<=>s(X2,X6)=s(X2,X4))&s(X1,h4s_combins_update(s(X2,X6),s(X1,X5),s(t_fun(X2,X1),X3),s(X2,X4)))=s(X1,h4s_bools_cond(s(t_bool,X7),s(X1,X5),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X4)))))),file('i/f/combin/APPLY__UPDATE__THM', ch4s_combins_APPLYu_u_UPDATEu_u_THM)).
fof(3, 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/combin/APPLY__UPDATE__THM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(38, axiom,![X2]:![X12]:![X13]:s(X2,h4s_bools_cond(s(t_bool,t),s(X2,X13),s(X2,X12)))=s(X2,X13),file('i/f/combin/APPLY__UPDATE__THM', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(39, axiom,![X2]:![X12]:![X13]:s(X2,h4s_bools_cond(s(t_bool,f0),s(X2,X13),s(X2,X12)))=s(X2,X12),file('i/f/combin/APPLY__UPDATE__THM', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(55, axiom,![X27]:![X28]:![X11]:![X3]:![X5]:![X6]:(~(s(X28,X6)=s(X28,X5))=>s(X27,h4s_combins_update(s(X28,X6),s(X27,X11),s(t_fun(X28,X27),X3),s(X28,X5)))=s(X27,happ(s(t_fun(X28,X27),X3),s(X28,X5)))),file('i/f/combin/APPLY__UPDATE__THM', ah4s_combins_UPDATEu_u_APPLYu_c1)).
fof(56, axiom,![X2]:![X1]:![X11]:![X3]:![X6]:s(X1,h4s_combins_update(s(X2,X6),s(X1,X11),s(t_fun(X2,X1),X3),s(X2,X6)))=s(X1,X11),file('i/f/combin/APPLY__UPDATE__THM', ah4s_combins_UPDATEu_u_APPLYu_c0)).
fof(57, axiom,p(s(t_bool,t)),file('i/f/combin/APPLY__UPDATE__THM', aHLu_TRUTH)).
fof(65, axiom,~(p(s(t_bool,f0))),file('i/f/combin/APPLY__UPDATE__THM', aHLu_FALSITY)).
fof(67, axiom,(p(s(t_bool,f0))<=>![X14]:p(s(t_bool,X14))),file('i/f/combin/APPLY__UPDATE__THM', ah4s_bools_Fu_u_DEF)).
# SZS output end CNFRefutation
