# 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(X2,t_fun(X2,t_bool)),X5),s(t_fun(X2,X1),X4),s(t_fun(X1,X2),X3))))=>![X6]:![X7]:![X8]:![X9]:![X10]:![X11]:((s(t_bool,X6)=s(t_bool,X7)&(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X8))),s(X2,X9))))&p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X10))),s(X2,X11))))))=>p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,h4s_bools_cond(s(t_bool,X6),s(X2,X8),s(X2,X10))))),s(X2,h4s_bools_cond(s(t_bool,X7),s(X2,X9),s(X2,X11)))))))),file('i/f/quotient/COND__RSP', ch4s_quotients_CONDu_u_RSP)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/quotient/COND__RSP', aHLu_FALSITY)).
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/quotient/COND__RSP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(4, axiom,(p(s(t_bool,f))<=>![X14]:p(s(t_bool,X14))),file('i/f/quotient/COND__RSP', ah4s_bools_Fu_u_DEF)).
fof(7, axiom,![X15]:![X16]:![X17]:((p(s(t_bool,X17))<=>s(t_bool,X16)=s(t_bool,X15))<=>((p(s(t_bool,X17))|(p(s(t_bool,X16))|p(s(t_bool,X15))))&((p(s(t_bool,X17))|(~(p(s(t_bool,X15)))|~(p(s(t_bool,X16)))))&((p(s(t_bool,X16))|(~(p(s(t_bool,X15)))|~(p(s(t_bool,X17)))))&(p(s(t_bool,X15))|(~(p(s(t_bool,X16)))|~(p(s(t_bool,X17))))))))),file('i/f/quotient/COND__RSP', ah4s_sats_dcu_u_eq)).
fof(30, axiom,![X14]:(s(t_bool,X14)=s(t_bool,f)<=>~(p(s(t_bool,X14)))),file('i/f/quotient/COND__RSP', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(72, 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/quotient/COND__RSP', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(73, axiom,![X2]:![X12]:![X13]:s(X2,h4s_bools_cond(s(t_bool,f),s(X2,X13),s(X2,X12)))=s(X2,X12),file('i/f/quotient/COND__RSP', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(75, axiom,![X14]:(s(t_bool,X14)=s(t_bool,t)|s(t_bool,X14)=s(t_bool,f)),file('i/f/quotient/COND__RSP', aHLu_BOOLu_CASES)).
fof(81, axiom,p(s(t_bool,t)),file('i/f/quotient/COND__RSP', aHLu_TRUTH)).
# SZS output end CNFRefutation
