# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X7),s(t_fun(X1,X3),X6),s(t_fun(X3,X1),X5))))=>![X8]:![X9]:![X10]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X8),s(t_fun(X2,X4),X9),s(t_fun(X4,X2),X10))))=>![X11]:s(X4,h4s_pairs_snd(s(t_h4s_pairs_prod(X3,X4),X11)))=s(X4,happ(s(t_fun(X2,X4),X9),s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),happ(s(t_fun(t_h4s_pairs_prod(X3,X4),t_h4s_pairs_prod(X1,X2)),h4s_pairs_u_23u_23(s(t_fun(X3,X1),X5),s(t_fun(X4,X2),X10))),s(t_h4s_pairs_prod(X3,X4),X11))))))))),file('i/f/quotient_pair/SND__PRS', ch4s_quotientu_u_pairs_SNDu_u_PRS)).
fof(31, axiom,![X2]:![X1]:![X29]:![X30]:![X31]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X31),s(t_fun(X1,X2),X30),s(t_fun(X2,X1),X29))))<=>(![X32]:s(X2,happ(s(t_fun(X1,X2),X30),s(X1,happ(s(t_fun(X2,X1),X29),s(X2,X32)))))=s(X2,X32)&(![X32]:p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X31),s(X1,happ(s(t_fun(X2,X1),X29),s(X2,X32))))),s(X1,happ(s(t_fun(X2,X1),X29),s(X2,X32))))))&![X23]:![X33]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X31),s(X1,X23))),s(X1,X33))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X31),s(X1,X23))),s(X1,X23))))&(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X31),s(X1,X33))),s(X1,X33))))&s(X2,happ(s(t_fun(X1,X2),X30),s(X1,X23)))=s(X2,happ(s(t_fun(X1,X2),X30),s(X1,X33))))))))),file('i/f/quotient_pair/SND__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(33, axiom,![X3]:![X4]:![X1]:![X2]:![X11]:![X15]:![X14]:s(X4,h4s_pairs_snd(s(t_h4s_pairs_prod(X3,X4),happ(s(t_fun(t_h4s_pairs_prod(X1,X2),t_h4s_pairs_prod(X3,X4)),h4s_pairs_u_23u_23(s(t_fun(X1,X3),X14),s(t_fun(X2,X4),X15))),s(t_h4s_pairs_prod(X1,X2),X11)))))=s(X4,happ(s(t_fun(X2,X4),X15),s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),X11))))),file('i/f/quotient_pair/SND__PRS', ah4s_pairs_SNDu_u_PAIRu_u_MAP)).
fof(45, axiom,~(p(s(t_bool,f))),file('i/f/quotient_pair/SND__PRS', aHLu_FALSITY)).
fof(77, axiom,![X17]:(s(t_bool,X17)=s(t_bool,t)|s(t_bool,X17)=s(t_bool,f)),file('i/f/quotient_pair/SND__PRS', aHLu_BOOLu_CASES)).
fof(78, axiom,(~(p(s(t_bool,t)))<=>p(s(t_bool,f))),file('i/f/quotient_pair/SND__PRS', ah4s_bools_NOTu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
