# 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(t_bool,h4s_sums_isl(s(t_h4s_sums_sum(X3,X4),X11)))=s(t_bool,h4s_sums_isl(s(t_h4s_sums_sum(X1,X2),h4s_sums_u_2bu_2b(s(t_fun(X3,X1),X5),s(t_fun(X4,X2),X10),s(t_h4s_sums_sum(X3,X4),X11))))))),file('i/f/quotient_sum/ISL__PRS', ch4s_quotientu_u_sums_ISLu_u_PRS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/quotient_sum/ISL__PRS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/quotient_sum/ISL__PRS', aHLu_FALSITY)).
fof(4, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)|s(t_bool,X12)=s(t_bool,f)),file('i/f/quotient_sum/ISL__PRS', aHLu_BOOLu_CASES)).
fof(6, axiom,![X13]:![X14]:((p(s(t_bool,X14))=>p(s(t_bool,X13)))=>((p(s(t_bool,X13))=>p(s(t_bool,X14)))=>s(t_bool,X14)=s(t_bool,X13))),file('i/f/quotient_sum/ISL__PRS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X12]:(s(t_bool,t)=s(t_bool,X12)<=>p(s(t_bool,X12))),file('i/f/quotient_sum/ISL__PRS', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(11, axiom,![X12]:(s(t_bool,f)=s(t_bool,X12)<=>~(p(s(t_bool,X12)))),file('i/f/quotient_sum/ISL__PRS', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(12, axiom,![X2]:![X1]:![X15]:p(s(t_bool,h4s_sums_isl(s(t_h4s_sums_sum(X1,X2),h4s_sums_inl(s(X1,X15)))))),file('i/f/quotient_sum/ISL__PRS', ah4s_sums_ISL0u_c0)).
fof(13, axiom,![X1]:![X2]:![X16]:~(p(s(t_bool,h4s_sums_isl(s(t_h4s_sums_sum(X1,X2),h4s_sums_inr(s(X2,X16))))))),file('i/f/quotient_sum/ISL__PRS', ah4s_sums_ISL0u_c1)).
fof(14, axiom,![X2]:![X4]:![X3]:![X1]:![X17]:![X18]:![X11]:s(t_h4s_sums_sum(X3,X4),h4s_sums_u_2bu_2b(s(t_fun(X1,X3),X18),s(t_fun(X2,X4),X17),s(t_h4s_sums_sum(X1,X2),h4s_sums_inl(s(X1,X11)))))=s(t_h4s_sums_sum(X3,X4),h4s_sums_inl(s(X3,happ(s(t_fun(X1,X3),X18),s(X1,X11))))),file('i/f/quotient_sum/ISL__PRS', ah4s_sums_SUMu_u_MAPu_u_defu_c0)).
fof(15, axiom,![X1]:![X3]:![X4]:![X2]:![X17]:![X18]:![X19]:s(t_h4s_sums_sum(X3,X4),h4s_sums_u_2bu_2b(s(t_fun(X1,X3),X18),s(t_fun(X2,X4),X17),s(t_h4s_sums_sum(X1,X2),h4s_sums_inr(s(X2,X19)))))=s(t_h4s_sums_sum(X3,X4),h4s_sums_inr(s(X4,happ(s(t_fun(X2,X4),X17),s(X2,X19))))),file('i/f/quotient_sum/ISL__PRS', ah4s_sums_SUMu_u_MAPu_u_defu_c1)).
fof(16, axiom,![X1]:![X2]:![X20]:(?[X15]:s(t_h4s_sums_sum(X1,X2),X20)=s(t_h4s_sums_sum(X1,X2),h4s_sums_inl(s(X1,X15)))|?[X16]:s(t_h4s_sums_sum(X1,X2),X20)=s(t_h4s_sums_sum(X1,X2),h4s_sums_inr(s(X2,X16)))),file('i/f/quotient_sum/ISL__PRS', ah4s_sums_sumu_u_CASES)).
# SZS output end CNFRefutation
