0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.04	% Command    : satallax -s schedule_3_1 -E eprover -P picomus -M modes -p tstp -t %d %s
0.02/0.24	% Computer   : n131.star.cs.uiowa.edu
0.02/0.24	% Model      : x86_64 x86_64
0.02/0.24	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.24	% Memory     : 32218.625MB
0.02/0.24	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.24	% CPULimit   : 300
0.02/0.24	% DateTime   : Sun Jul 15 13:49:10 CDT 2018
0.02/0.24	% CPUTime    : 
277.09/276.88	% SZS status Theorem
277.09/276.88	% Mode: mode498
277.09/276.88	% Inferences: 84
277.09/276.88	% SZS output start Proof
277.09/276.88	thf(ty_$i, type, $i : $tType).
277.09/276.88	thf(ty_univof, type, univof : ($i>$i)).
277.09/276.88	thf(ty_l_some, type, l_some : ($i>($i>$o)>$o)).
277.09/276.88	thf(ty_if, type, if : ($o>$i>$i>$i)).
277.09/276.88	thf(ty_power, type, power : ($i>$i)).
277.09/276.88	thf(ty_eps, type, eps : (($i>$o)>$i)).
277.09/276.88	thf(ty_union, type, union : ($i>$i)).
277.09/276.88	thf(ty_d_ReplSep, type, d_ReplSep : ($i>($i>$o)>($i>$i)>$i)).
277.09/276.88	thf(ty_eigen__1, type, eigen__1 : $i).
277.09/276.88	thf(ty_eigen__0, type, eigen__0 : $i).
277.09/276.88	thf(ty_emptyset, type, emptyset : $i).
277.09/276.88	thf(ty_ind, type, ind : ($i>($i>$o)>$i)).
277.09/276.88	thf(ty_pair, type, pair : ($i>$i>$i)).
277.09/276.88	thf(ty_proj1, type, proj1 : ($i>$i)).
277.09/276.88	thf(ty_d_Sigma, type, d_Sigma : ($i>($i>$i)>$i)).
277.09/276.88	thf(ty_imp, type, imp : ($o>$o>$o)).
277.09/276.88	thf(ty_d_24_prop2, type, d_24_prop2 : ($i>$i>$o)).
277.09/276.88	thf(ty_repl, type, repl : ($i>($i>$i)>$i)).
277.09/276.88	thf(ty_in, type, in : ($i>$i>$o)).
277.09/276.88	thf(ty_d_Sing, type, d_Sing : ($i>$i)).
277.09/276.88	thf(ty_nat_p, type, nat_p : ($i>$o)).
277.09/276.88	thf(ty_e_is, type, e_is : ($i>$i>$i>$o)).
277.09/276.88	thf(ty_binunion, type, binunion : ($i>$i>$i)).
277.09/276.88	thf(sP1,plain,(sP1 <=> ((imp @ ((imp @ ((l_some @ (((if @ (~((![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) => (X1 = emptyset)))))) @ ((repl @ (((if @ (~((![X1:$i]:(((in @ X1) @ (univof @ emptyset)) => (~((nat_p @ X1)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X1:$i]:(((if @ (nat_p @ X1)) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))))))) @ emptyset)) @ (^[X1:$i]:(((if @ (~((X1 = emptyset)))) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))))))) @ emptyset)) @ (^[X1:$i]:(((e_is @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) @ eigen__1) @ (((d_ReplSep @ ((ind @ (((if @ (~((![X2:$i]:(((in @ X2) @ (power @ ((d_Sigma @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))))))) @ emptyset)) @ (^[X3:$i]:(union @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)))))) => (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X2) @ (^[X4:$i]:(~((![X5:$i]:(~((X4 = ((pair @ X3) @ X5))))))))) @ proj1)) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset))))))))))) @ ((repl @ (power @ ((d_Sigma @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) @ (^[X2:$i]:(union @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))))))) @ emptyset)))))) @ (^[X2:$i]:(((if @ (![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X2) @ (^[X4:$i]:(~((![X5:$i]:(~((X4 = ((pair @ X3) @ X5))))))))) @ proj1)) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset))))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (power @ ((d_Sigma @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) @ (^[X4:$i]:(union @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)))))) => (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X3) @ (^[X5:$i]:(~((![X6:$i]:(~((X5 = ((pair @ X4) @ X6))))))))) @ proj1)) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset))))))))))))))) @ emptyset)) @ (d_24_prop2 @ eigen__0))) @ (^[X2:$i]:(~((![X3:$i]:(~((X2 = ((pair @ X1) @ X3))))))))) @ proj1))))) @ $false)) @ (((e_is @ (((if @ (~((![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) => (X1 = emptyset)))))) @ ((repl @ (((if @ (~((![X1:$i]:(((in @ X1) @ (univof @ emptyset)) => (~((nat_p @ X1)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X1:$i]:(((if @ (nat_p @ X1)) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))))))) @ emptyset)) @ (^[X1:$i]:(((if @ (~((X1 = 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277.09/276.88	thf(sP2,plain,(sP2 <=> ((in @ eigen__0) @ (((if @ (~((![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) => (X1 = emptyset)))))) @ ((repl @ (((if @ (~((![X1:$i]:(((in @ X1) @ (univof @ emptyset)) => (~((nat_p @ X1)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X1:$i]:(((if @ (nat_p @ X1)) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))))))) @ emptyset)) @ (^[X1:$i]:(((if @ (~((X1 = emptyset)))) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))))))) @ emptyset)),introduced(definition,[new_symbols(definition,[sP2])]))).
277.09/276.88	thf(sP3,plain,(sP3 <=> (((imp @ ((imp @ ((l_some @ (((if @ (~((![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) => (X1 = emptyset)))))) @ ((repl @ (((if @ (~((![X1:$i]:(((in @ X1) @ (univof @ emptyset)) => (~((nat_p @ X1)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X1:$i]:(((if @ (nat_p @ X1)) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))))))) @ emptyset)) @ (^[X1:$i]:(((if @ (~((X1 = emptyset)))) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))))))) @ emptyset)) @ (^[X1:$i]:(((e_is @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ 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(univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X2) @ (^[X4:$i]:(~((![X5:$i]:(~((X4 = ((pair @ X3) @ X5))))))))) @ proj1)) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset))))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (power @ ((d_Sigma @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) @ (^[X4:$i]:(union @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)))))) => (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X3) @ (^[X5:$i]:(~((![X6:$i]:(~((X5 = ((pair @ X4) @ X6))))))))) @ proj1)) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset))))))))))))))) @ emptyset)) @ (d_24_prop2 @ eigen__0))) @ (^[X2:$i]:(~((![X3:$i]:(~((X2 = ((pair @ X1) @ X3))))))))) @ proj1))))) @ $false)) @ (((e_is @ (((if @ (~((![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) => (X1 = emptyset)))))) @ ((repl @ (((if @ (~((![X1:$i]:(((in @ X1) @ (univof @ emptyset)) => (~((nat_p @ X1)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X1:$i]:(((if @ (nat_p @ X1)) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))))))) @ emptyset)) @ (^[X1:$i]:(((if @ (~((X1 = emptyset)))) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))))))) @ emptyset)) @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP7])]))).
277.09/276.89	thf(sP8,plain,(sP8 <=> (sP2 => (sP4 => sP7)),introduced(definition,[new_symbols(definition,[sP8])]))).
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emptyset)))))))))) @ emptyset)) => (![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = 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emptyset)) @ (^[X3:$i]:(((e_is @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) @ 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@ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset))))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (power @ ((d_Sigma @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)) @ (^[X6:$i]:(union @ (((if @ (~((![X7:$i]:(((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))) @ ((repl @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) @ (^[X7:$i]:(((if @ (~((X7 = emptyset)))) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (((if @ (~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X9:$i]:(((if @ (nat_p @ X9)) @ X9) @ (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10)))))))))))) @ emptyset)) => (X8 = emptyset)))))))))) @ emptyset)))))) => (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))) @ ((repl @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) @ (^[X7:$i]:(((if @ (~((X7 = emptyset)))) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (((if @ (~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X9:$i]:(((if @ (nat_p @ X9)) @ X9) @ (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10)))))))))))) @ emptyset)) => (X8 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X5) @ (^[X7:$i]:(~((![X8:$i]:(~((X7 = ((pair @ X6) @ X8))))))))) @ proj1)) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))) @ ((repl @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) @ (^[X7:$i]:(((if @ (~((X7 = emptyset)))) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (((if @ (~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X9:$i]:(((if @ (nat_p @ X9)) @ X9) @ (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10)))))))))))) @ emptyset)) => (X8 = emptyset)))))))))) @ emptyset))))))))))))))) @ emptyset)) @ (d_24_prop2 @ X2))) @ (^[X4:$i]:(~((![X5:$i]:(~((X4 = ((pair @ X3) @ X5))))))))) @ proj1))))) @ $false)) @ (((e_is @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))))))) @ emptyset)) @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP9])]))).
277.09/276.89	thf(sP10,plain,(sP10 <=> (sP4 => sP7),introduced(definition,[new_symbols(definition,[sP10])]))).
277.09/276.89	thf(sP11,plain,(sP11 <=> (((in @ eigen__1) @ (((if @ (~((![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) => (X1 = emptyset)))))) @ ((repl @ (((if @ (~((![X1:$i]:(((in @ X1) @ (univof @ emptyset)) => (~((nat_p @ X1)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X1:$i]:(((if @ (nat_p @ X1)) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))))))) @ emptyset)) @ (^[X1:$i]:(((if @ (~((X1 = emptyset)))) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))))))) @ emptyset)) => (![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) => (((l_some @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) @ (^[X2:$i]:(((e_is @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))))))) @ emptyset)) @ (((d_ReplSep @ ((ind @ (((if @ (~((![X3:$i]:(((in @ X3) @ (power @ ((d_Sigma @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) @ (^[X4:$i]:(union @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)))))) => (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = 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X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)) @ (^[X5:$i]:(union @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)))))) => (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X4) @ (^[X6:$i]:(~((![X7:$i]:(~((X6 = ((pair @ X5) @ X7))))))))) @ proj1)) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset))))))))))))))) @ emptyset)) @ (d_24_prop2 @ X1))) @ (^[X3:$i]:(~((![X4:$i]:(~((X3 = ((pair @ X2) @ X4))))))))) @ proj1))))) @ $false)) @ (((e_is @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) @ X1) @ eigen__1)))))),introduced(definition,[new_symbols(definition,[sP11])]))).
277.09/276.89	thf(sP12,plain,(sP12 <=> ((in @ eigen__1) @ (((if @ (~((![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) => (X1 = emptyset)))))) @ ((repl @ (((if @ (~((![X1:$i]:(((in @ X1) @ (univof @ emptyset)) => (~((nat_p @ X1)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X1:$i]:(((if @ (nat_p @ X1)) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))))))) @ emptyset)) @ (^[X1:$i]:(((if @ (~((X1 = emptyset)))) @ X1) @ (eps @ (^[X2:$i]:(~((((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))))))) @ emptyset)),introduced(definition,[new_symbols(definition,[sP12])]))).
277.09/276.89	thf(sP13,plain,(sP13 <=> (![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) => (((imp @ ((imp @ ((l_some @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) @ (^[X2:$i]:(((e_is @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))))))) @ emptyset)) @ X1) @ (((d_ReplSep @ ((ind @ (((if @ (~((![X3:$i]:(((in @ X3) @ (power @ ((d_Sigma @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) @ (^[X4:$i]:(union @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)))))) => (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = 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(^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)))))) @ (^[X3:$i]:(((if @ (![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X3) @ (^[X5:$i]:(~((![X6:$i]:(~((X5 = ((pair @ X4) @ X6))))))))) @ proj1)) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset))))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (power @ ((d_Sigma @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)) @ (^[X5:$i]:(union @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)))))) => (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X4) @ (^[X6:$i]:(~((![X7:$i]:(~((X6 = ((pair @ X5) @ X7))))))))) @ proj1)) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset))))))))))))))) @ emptyset)) @ (d_24_prop2 @ X1))) @ (^[X3:$i]:(~((![X4:$i]:(~((X3 = ((pair @ X2) @ X4))))))))) @ proj1))))) @ $false)) @ (((e_is @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) @ X1) @ eigen__1))))),introduced(definition,[new_symbols(definition,[sP14])]))).
277.09/276.90	thf(sP15,plain,(sP15 <=> (sP12 => sP3),introduced(definition,[new_symbols(definition,[sP15])]))).
277.09/276.90	thf(def_is_of,definition,(is_of = (^[X1:$i]:(^[X2:$i>$o]:(X2 @ X1))))).
277.09/276.90	thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))).
277.09/276.90	thf(def_d_Sep,definition,(d_Sep = (^[X1:$i]:(^[X2:$i>$o]:(((if @ (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) @ ((repl @ X1) @ (^[X3:$i]:(((if @ (X2 @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ X1) => (~((X2 @ X4)))))))))))) @ emptyset))))).
277.09/276.90	thf(def_ordsucc,definition,(ordsucc = (^[X1:$i]:((binunion @ X1) @ (d_Sing @ X1))))).
277.09/276.90	thf(def_omega,definition,(omega = ((d_Sep @ (univof @ emptyset)) @ nat_p))).
277.09/276.90	thf(def_ap,definition,(ap = (^[X1:$i]:(^[X2:$i]:(((d_ReplSep @ X1) @ (^[X3:$i]:(~((![X4:$i]:(~((X3 = ((pair @ X2) @ X4))))))))) @ proj1))))).
277.09/276.90	thf(def_d_Pi,definition,(d_Pi = (^[X1:$i]:(^[X2:$i>$i]:((d_Sep @ (power @ ((d_Sigma @ X1) @ (^[X3:$i]:(union @ (X2 @ X3)))))) @ (^[X3:$i]:(![X4:$i]:(((in @ X4) @ X1) => ((in @ ((ap @ X3) @ X4)) @ (X2 @ X4)))))))))).
277.09/276.90	thf(def_d_not,definition,(d_not = (^[X1:$o]:((imp @ X1) @ $false)))).
277.09/276.90	thf(def_d_and,definition,(d_and = (^[X1:$o]:(^[X2:$o]:(d_not @ ((l_ec @ X1) @ X2)))))).
277.09/276.90	thf(def_l_or,definition,(l_or = (^[X1:$o]:(imp @ (d_not @ X1))))).
277.09/276.90	thf(def_one,definition,(one = (^[X1:$i]:(^[X2:$i>$o]:((d_and @ ((amone @ X1) @ X2)) @ ((l_some @ X1) @ X2)))))).
277.09/276.90	thf(def_nat,definition,(nat = ((d_Sep @ omega) @ (^[X1:$i]:(~((X1 = emptyset))))))).
277.09/276.90	thf(def_n_is,definition,(n_is = (e_is @ nat))).
277.09/276.90	thf(def_nis,definition,(nis = (^[X1:$i]:(^[X2:$i]:(d_not @ ((n_is @ X1) @ X2)))))).
277.09/276.90	thf(def_n_some,definition,(n_some = (l_some @ nat))).
277.09/276.90	thf(def_n_all,definition,(n_all = (all @ nat))).
277.09/276.90	thf(def_n_1,definition,(n_1 = (ordsucc @ emptyset))).
277.09/276.90	thf(def_plus,definition,(plus = (^[X1:$i]:((ind @ ((d_Pi @ nat) @ (^[X2:$i]:nat))) @ (d_24_prop2 @ X1))))).
277.09/276.90	thf(def_n_pl,definition,(n_pl = (^[X1:$i]:(ap @ (plus @ X1))))).
277.09/276.90	thf(def_diffprop,definition,(diffprop = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((n_is @ X1) @ ((n_pl @ X2) @ X3))))))).
277.09/276.90	thf(def_d_29_ii,definition,(d_29_ii = (^[X1:$i]:(^[X2:$i]:(n_some @ ((diffprop @ X1) @ X2)))))).
277.09/276.90	thf(def_iii,definition,(iii = (^[X1:$i]:(^[X2:$i]:(n_some @ ((diffprop @ X2) @ X1)))))).
277.09/276.90	thf(def_moreis,definition,(moreis = (^[X1:$i]:(^[X2:$i]:((l_or @ ((d_29_ii @ X1) @ X2)) @ ((n_is @ X1) @ X2)))))).
277.09/276.90	thf(def_lessis,definition,(lessis = (^[X1:$i]:(^[X2:$i]:((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)))))).
277.09/276.90	thf(satz26b,conjecture,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((d_29_ii @ ((n_pl @ X2) @ n_1)) @ X1) => ((moreis @ X2) @ X1))))))).
277.09/276.90	thf(h0,negated_conjecture,(~((![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) => (![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))))))) @ emptyset)) => (((l_some @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))))))) @ emptyset)) @ (^[X3:$i]:(((e_is @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) @ (((d_ReplSep @ ((ind @ (((if @ (~((![X4:$i]:(((in @ X4) @ (power @ ((d_Sigma @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => 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(nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) @ (^[X4:$i]:(union @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)))))) @ (^[X4:$i]:(((if @ (![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X4) @ (^[X6:$i]:(~((![X7:$i]:(~((X6 = ((pair @ X5) @ X7))))))))) @ proj1)) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset))))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (power @ ((d_Sigma @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)) @ (^[X6:$i]:(union @ (((if @ (~((![X7:$i]:(((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))) @ ((repl @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) @ (^[X7:$i]:(((if @ (~((X7 = emptyset)))) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (((if @ (~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X9:$i]:(((if @ (nat_p @ X9)) @ X9) @ (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10)))))))))))) @ emptyset)) => (X8 = emptyset)))))))))) @ emptyset)))))) => (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))) @ ((repl @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) @ (^[X7:$i]:(((if @ (~((X7 = emptyset)))) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (((if @ (~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X9:$i]:(((if @ (nat_p @ X9)) @ X9) @ (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10)))))))))))) @ emptyset)) => (X8 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X5) @ (^[X7:$i]:(~((![X8:$i]:(~((X7 = ((pair @ X6) @ X8))))))))) @ proj1)) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))) @ ((repl @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) @ (^[X7:$i]:(((if @ (~((X7 = emptyset)))) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (((if @ (~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X9:$i]:(((if @ (nat_p @ X9)) @ X9) @ (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10)))))))))))) @ emptyset)) => (X8 = emptyset)))))))))) @ emptyset))))))))))))))) @ emptyset)) @ (d_24_prop2 @ X1))) @ (^[X4:$i]:(~((![X5:$i]:(~((X4 = ((pair @ X3) @ X5))))))))) @ proj1))))) @ $false)) @ (((e_is @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))))))) @ emptyset)) @ X2) @ X1))))))))),inference(assume_negation,[status(cth)],[satz26b])).
277.16/276.91	thf(h1,assumption,(~((sP2 => (![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) => (((l_some @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) @ (^[X2:$i]:(((e_is @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))))))) @ emptyset)) @ (((d_ReplSep @ ((ind @ (((if @ (~((![X3:$i]:(((in @ X3) @ (power @ ((d_Sigma @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => 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(eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X3) @ (^[X5:$i]:(~((![X6:$i]:(~((X5 = ((pair @ X4) @ X6))))))))) @ proj1)) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset))))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (power @ ((d_Sigma @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)) @ (^[X5:$i]:(union @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)))))) => (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X4) @ (^[X6:$i]:(~((![X7:$i]:(~((X6 = ((pair @ X5) @ X7))))))))) @ proj1)) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset))))))))))))))) @ emptyset)) @ (d_24_prop2 @ eigen__0))) @ (^[X3:$i]:(~((![X4:$i]:(~((X3 = ((pair @ X2) @ X4))))))))) @ proj1))))) @ $false)) @ (((e_is @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) @ X1) @ eigen__0)))))))),introduced(assumption,[])).
277.16/276.91	thf(h2,assumption,sP2,introduced(assumption,[])).
277.16/276.91	thf(h3,assumption,(~((![X1:$i]:(((in @ X1) @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) => (((l_some @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) @ (^[X2:$i]:(((e_is @ (((if @ (~((![X3:$i]:(((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))) @ ((repl @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) @ (^[X3:$i]:(((if @ (~((X3 = emptyset)))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))))))) @ emptyset)) @ (((d_ReplSep @ ((ind @ (((if @ (~((![X3:$i]:(((in @ X3) @ (power @ ((d_Sigma @ (((if @ (~((![X4:$i]:(((in @ X4) @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) => (X4 = emptyset)))))) @ ((repl @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) @ (^[X4:$i]:(((if @ (~((X4 = emptyset)))) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))))))) @ emptyset)) @ (^[X4:$i]:(union @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = 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(univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset))))) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (power @ ((d_Sigma @ (((if @ (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) => (X5 = emptyset)))))) @ ((repl @ (((if @ (~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(((if @ (nat_p @ X5)) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))))))) @ emptyset)) @ (^[X5:$i]:(((if @ (~((X5 = emptyset)))) @ X5) @ (eps @ (^[X6:$i]:(~((((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))))))) @ emptyset)) @ (^[X5:$i]:(union @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)))))) => (~((![X5:$i]:(((in @ X5) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset)) => ((in @ (((d_ReplSep @ X4) @ (^[X6:$i]:(~((![X7:$i]:(~((X6 = ((pair @ X5) @ X7))))))))) @ proj1)) @ (((if @ (~((![X6:$i]:(((in @ X6) @ (((if @ (~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(((if @ (nat_p @ X7)) @ X7) @ (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))))))) @ emptyset)) => (X6 = emptyset)))))) @ ((repl @ (((if @ (~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(((if @ (nat_p @ X6)) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7)))))))))))) @ emptyset)) @ (^[X6:$i]:(((if @ (~((X6 = emptyset)))) @ X6) @ (eps @ (^[X7:$i]:(~((((in @ X7) @ (((if @ (~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(((if @ (nat_p @ X8)) @ X8) @ (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9)))))))))))) @ emptyset)) => (X7 = emptyset)))))))))) @ emptyset))))))))))))))) @ emptyset)) @ (d_24_prop2 @ eigen__0))) @ (^[X3:$i]:(~((![X4:$i]:(~((X3 = ((pair @ X2) @ X4))))))))) @ proj1))))) @ $false)) @ (((e_is @ (((if @ (~((![X2:$i]:(((in @ X2) @ (((if @ (~((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(((if @ (nat_p @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))))))) @ emptyset)) => (X2 = emptyset)))))) @ ((repl @ (((if @ (~((![X2:$i]:(((in @ X2) @ (univof @ emptyset)) => (~((nat_p @ X2)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X2:$i]:(((if @ (nat_p @ X2)) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (univof @ emptyset)) => (~((nat_p @ X3)))))))))))) @ emptyset)) @ (^[X2:$i]:(((if @ (~((X2 = emptyset)))) @ X2) @ (eps @ (^[X3:$i]:(~((((in @ X3) @ (((if @ (~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4)))))))) @ ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(((if @ (nat_p @ X4)) @ X4) @ (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5)))))))))))) @ emptyset)) => (X3 = emptyset)))))))))) @ emptyset)) @ X1) @ eigen__0))))))),introduced(assumption,[])).
277.16/276.93	thf(h4,assumption,(~((sP12 => (sP4 => sP1)))),introduced(assumption,[])).
277.16/276.93	thf(h5,assumption,sP12,introduced(assumption,[])).
277.16/276.93	thf(h6,assumption,(~((sP4 => sP1))),introduced(assumption,[])).
277.16/276.93	thf(h7,assumption,sP4,introduced(assumption,[])).
277.16/276.93	thf(h8,assumption,(~(sP1)),introduced(assumption,[])).
277.16/276.93	thf(satz14,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((lessis @ X1) @ X2) => ((moreis @ X2) @ X1))))))).
277.16/276.93	thf(1,plain,sP5,inference(preprocess,[status(thm)],[satz14]).
277.16/276.93	thf(satz26,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((iii @ X2) @ ((n_pl @ X1) @ n_1)) => ((lessis @ X2) @ X1))))))).
277.16/276.93	thf(2,plain,sP9,inference(preprocess,[status(thm)],[satz26]).
277.16/276.93	thf(3,plain,((~(sP10) | ~(sP4)) | sP7),inference(prop_rule,[status(thm)],[])).
277.16/276.93	thf(4,plain,((~(sP8) | ~(sP2)) | sP10),inference(prop_rule,[status(thm)],[])).
277.16/276.93	thf(5,plain,(~(sP14) | sP8),inference(all_rule,[status(thm)],[])).
277.16/276.93	thf(6,plain,((~(sP11) | ~(sP12)) | sP14),inference(prop_rule,[status(thm)],[])).
277.16/276.93	thf(7,plain,(~(sP9) | sP11),inference(all_rule,[status(thm)],[])).
277.16/276.93	thf(8,plain,((~(sP3) | ~(sP7)) | sP1),inference(prop_rule,[status(thm)],[])).
277.16/276.93	thf(9,plain,((~(sP15) | ~(sP12)) | sP3),inference(prop_rule,[status(thm)],[])).
277.16/276.93	thf(10,plain,(~(sP13) | sP15),inference(all_rule,[status(thm)],[])).
277.16/276.93	thf(11,plain,((~(sP6) | ~(sP2)) | sP13),inference(prop_rule,[status(thm)],[])).
277.16/276.93	thf(12,plain,(~(sP5) | sP6),inference(all_rule,[status(thm)],[])).
277.16/276.93	thf(13,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,h8,h7,h5,h2,3,4,5,6,7,8,9,10,11,12])).
277.16/276.93	thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,13,h7,h8])).
277.16/276.93	thf(15,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,14,h5,h6])).
277.16/276.93	thf(16,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,15,h4])).
277.16/276.93	thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,16,h2,h3])).
277.16/276.93	thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,17,h1])).
277.16/276.93	thf(0,theorem,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((d_29_ii @ ((n_pl @ X2) @ n_1)) @ X1) => ((moreis @ X2) @ X1)))))),inference(contra,[status(thm),contra(discharge,[h0])],[18,h0])).
277.16/276.93	% SZS output end Proof
277.16/276.93	EOF