# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/relation/RTC__CASES__TC', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/relation/RTC__CASES__TC', aHLu_FALSITY)).
fof(6, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/relation/RTC__CASES__TC', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(34, axiom,![X12]:![X14]:![X6]:![X13]:(p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),X13),s(X12,X6))),s(X12,X14))))=>p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_tc(s(t_fun(X12,t_fun(X12,t_bool)),X13))),s(X12,X6))),s(X12,X14))))),file('i/f/relation/RTC__CASES__TC', ah4s_relations_TCu_u_RULESu_c0)).
fof(40, axiom,![X12]:![X14]:![X6]:![X13]:(p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_rtc(s(t_fun(X12,t_fun(X12,t_bool)),X13))),s(X12,X6))),s(X12,X14))))=>(p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_rc(s(t_fun(X12,t_fun(X12,t_bool)),X13))),s(X12,X6))),s(X12,X14))))|p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_tc(s(t_fun(X12,t_fun(X12,t_bool)),X13))),s(X12,X6))),s(X12,X14)))))),file('i/f/relation/RTC__CASES__TC', ah4s_relations_RTCu_u_TCu_u_RC)).
fof(70, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/relation/RTC__CASES__TC', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(78, axiom,![X12]:![X14]:![X6]:![X13]:(p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_rc(s(t_fun(X12,t_fun(X12,t_bool)),X13))),s(X12,X6))),s(X12,X14))))<=>(s(X12,X6)=s(X12,X14)|p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),X13),s(X12,X6))),s(X12,X14)))))),file('i/f/relation/RTC__CASES__TC', ah4s_relations_RCu_u_DEF)).
fof(87, axiom,![X12]:![X14]:![X6]:![X13]:(p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_rtc(s(t_fun(X12,t_fun(X12,t_bool)),X13))),s(X12,X6))),s(X12,X14))))<=>(s(X12,X6)=s(X12,X14)|?[X21]:(p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),X13),s(X12,X6))),s(X12,X21))))&p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_rtc(s(t_fun(X12,t_fun(X12,t_bool)),X13))),s(X12,X21))),s(X12,X14))))))),file('i/f/relation/RTC__CASES__TC', ah4s_relations_RTCu_u_CASES1)).
fof(92, axiom,![X12]:![X13]:s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_rc(s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_tc(s(t_fun(X12,t_fun(X12,t_bool)),X13)))))=s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_rtc(s(t_fun(X12,t_fun(X12,t_bool)),X13))),file('i/f/relation/RTC__CASES__TC', ah4s_relations_TCu_u_RCu_u_EQNSu_c0)).
fof(133, conjecture,![X12]:![X14]:![X6]:![X13]:(p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_rtc(s(t_fun(X12,t_fun(X12,t_bool)),X13))),s(X12,X6))),s(X12,X14))))<=>(s(X12,X6)=s(X12,X14)|p(s(t_bool,happ(s(t_fun(X12,t_bool),happ(s(t_fun(X12,t_fun(X12,t_bool)),h4s_relations_tc(s(t_fun(X12,t_fun(X12,t_bool)),X13))),s(X12,X6))),s(X12,X14)))))),file('i/f/relation/RTC__CASES__TC', ch4s_relations_RTCu_u_CASESu_u_TC)).
# SZS output end CNFRefutation
