# 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]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X6))),s(X2,X6))))=>(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X7))),s(X2,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,X6))),s(X2,X7))))<=>s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X6)))=s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X7))))))),file('i/f/quotient/QUOTIENT__REL__ABS__EQ', ch4s_quotients_QUOTIENTu_u_RELu_u_ABSu_u_EQ)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/quotient/QUOTIENT__REL__ABS__EQ', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/quotient/QUOTIENT__REL__ABS__EQ', aHLu_FALSITY)).
fof(4, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/quotient/QUOTIENT__REL__ABS__EQ', aHLu_BOOLu_CASES)).
fof(9, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/quotient/QUOTIENT__REL__ABS__EQ', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, axiom,![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))))<=>(![X14]:s(X1,happ(s(t_fun(X2,X1),X4),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X14)))))=s(X1,X14)&(![X14]:p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X14))))),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X14))))))&![X6]:![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,X6))),s(X2,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,X6))),s(X2,X6))))&(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X7))),s(X2,X7))))&s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X6)))=s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X7))))))))),file('i/f/quotient/QUOTIENT__REL__ABS__EQ', ah4s_quotients_QUOTIENTu_u_def)).
# SZS output end CNFRefutation
