# 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]:(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,happ(s(t_fun(X1,X2),X3),s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X6))))))),s(X2,X6)))))),file('i/f/quotient/QUOTIENT__REP__ABS', ch4s_quotients_QUOTIENTu_u_REPu_u_ABS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/quotient/QUOTIENT__REP__ABS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/quotient/QUOTIENT__REP__ABS', aHLu_FALSITY)).
fof(7, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/quotient/QUOTIENT__REP__ABS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(8, axiom,![X2]:![X1]:![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))))=>![X9]:s(X1,happ(s(t_fun(X2,X1),X4),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X9)))))=s(X1,X9)),file('i/f/quotient/QUOTIENT__REP__ABS', ah4s_quotients_QUOTIENTu_u_ABSu_u_REP)).
fof(9, axiom,![X2]:![X1]:![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))))=>![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,happ(s(t_fun(X1,X2),X3),s(X1,X9))))),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X9))))))),file('i/f/quotient/QUOTIENT__REP__ABS', ah4s_quotients_QUOTIENTu_u_REPu_u_REFL)).
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))))=>![X6]:![X10]:(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,X10))))<=>(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,X10))),s(X2,X10))))&s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X6)))=s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X10))))))),file('i/f/quotient/QUOTIENT__REP__ABS', ah4s_quotients_QUOTIENTu_u_REL)).
fof(12, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/quotient/QUOTIENT__REP__ABS', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
