%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM639^4 : TPTP v8.1.0. Released v7.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 13:54:27 EDT 2022

% Result   : Theorem 181.07s 177.34s
% Output   : Proof 181.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM639^4 : TPTP v8.1.0. Released v7.1.0.
% 0.03/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Wed Jul  6 07:15:23 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 181.07/177.34  % SZS status Theorem
% 181.07/177.34  % Mode: mode94:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 181.07/177.34  % Inferences: 6
% 181.07/177.34  % SZS output start Proof
% 181.07/177.34  thf(ty_univof, type, univof : ($i>$i)).
% 181.07/177.34  thf(ty_power, type, power : ($i>$i)).
% 181.07/177.34  thf(ty_eps, type, eps : (($i>$o)>$i)).
% 181.07/177.34  thf(ty_union, type, union : ($i>$i)).
% 181.07/177.34  thf(ty_d_ReplSep, type, d_ReplSep : ($i>($i>$o)>($i>$i)>$i)).
% 181.07/177.34  thf(ty_eigen__0, type, eigen__0 : $i).
% 181.07/177.34  thf(ty_famunion, type, famunion : ($i>($i>$i)>$i)).
% 181.07/177.34  thf(ty_emptyset, type, emptyset : $i).
% 181.07/177.34  thf(ty_ind, type, ind : ($i>($i>$o)>$i)).
% 181.07/177.34  thf(ty_pair, type, pair : ($i>$i>$i)).
% 181.07/177.34  thf(ty_proj1, type, proj1 : ($i>$i)).
% 181.07/177.34  thf(ty_d_24_prop2, type, d_24_prop2 : ($i>$i>$o)).
% 181.07/177.34  thf(ty_repl, type, repl : ($i>($i>$i)>$i)).
% 181.07/177.34  thf(ty_in, type, in : ($i>$i>$o)).
% 181.07/177.34  thf(ty_d_UPair, type, d_UPair : ($i>$i>$i)).
% 181.07/177.34  thf(ty_nat_p, type, nat_p : ($i>$o)).
% 181.07/177.34  thf(sP1,plain,sP1 <=> (![X1:$i]:(((((d_ReplSep @ ((ind @ (eps @ (^[X2:$i]:(((~((![X3:$i]:(((in @ X3) @ (power @ ((famunion @ (eps @ (^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))) => (~((X6 = emptyset)))))))))) => (X5 = emptyset))))) => (~((X4 = ((repl @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))))) => (~((X5 = ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((nat_p @ X6) => (~((X7 = X6)))) => (~(((~((nat_p @ X6))) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))))))))))))))))) => (~(((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))) => (~((X5 = emptyset)))))))))) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((~((X5 = emptyset))) => (~((X6 = X5)))) => (~(((X5 = emptyset) => (~((X6 = (eps @ (^[X7:$i]:(~((((in @ X7) @ (eps @ (^[X8:$i]:(((~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))) => (~((X8 = ((repl @ (univof @ emptyset)) @ (^[X9:$i]:(eps @ (^[X10:$i]:(((nat_p @ X9) => (~((X10 = X9)))) => (~(((~((nat_p @ X9))) => (~((X10 = (eps @ (^[X11:$i]:(~((((in @ X11) @ (univof @ emptyset)) => (~((nat_p @ X11))))))))))))))))))))))) => (~(((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))) => (~((X8 = emptyset)))))))))) => (X7 = emptyset))))))))))))))))))))) => (~(((![X5:$i]:(((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))) => (~((X6 = emptyset)))))))))) => (X5 = emptyset))) => (~((X4 = emptyset)))))))))) @ (^[X4:$i]:((repl @ (union @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))) => (~((X7 = emptyset)))))))))) => (X6 = emptyset))))) => (~((X5 = ((repl @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))) => (~((X6 = emptyset)))))))))) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((~((X6 = emptyset))) => (~((X7 = X6)))) => (~(((X6 = emptyset) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (eps @ (^[X9:$i]:(((~((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))) => (~((X9 = ((repl @ (univof @ emptyset)) @ (^[X10:$i]:(eps @ (^[X11:$i]:(((nat_p @ X10) => (~((X11 = X10)))) => (~(((~((nat_p @ X10))) => (~((X11 = (eps @ (^[X12:$i]:(~((((in @ X12) @ (univof @ emptyset)) => (~((nat_p @ X12))))))))))))))))))))))) => (~(((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))) => (~((X9 = emptyset)))))))))) => (X8 = emptyset))))))))))))))))))))) => (~(((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))) => (~((X7 = emptyset)))))))))) => (X6 = emptyset))) => (~((X5 = emptyset))))))))))) @ (pair @ X4)))))) => (~((![X4:$i]:(((in @ X4) @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))) => (~((X7 = emptyset)))))))))) => (X6 = emptyset))))) => (~((X5 = ((repl @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))) => (~((X6 = emptyset)))))))))) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((~((X6 = emptyset))) => (~((X7 = X6)))) => (~(((X6 = emptyset) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (eps @ (^[X9:$i]:(((~((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))) => (~((X9 = ((repl @ (univof @ emptyset)) @ (^[X10:$i]:(eps @ (^[X11:$i]:(((nat_p @ X10) => (~((X11 = X10)))) => (~(((~((nat_p @ X10))) => (~((X11 = (eps @ (^[X12:$i]:(~((((in @ X12) @ (univof @ emptyset)) => (~((nat_p @ X12))))))))))))))))))))))) => (~(((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))) => (~((X9 = emptyset)))))))))) => (X8 = emptyset))))))))))))))))))))) => (~(((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))) => (~((X7 = emptyset)))))))))) => (X6 = emptyset))) => (~((X5 = emptyset)))))))))) => ((in @ (((d_ReplSep @ X3) @ (^[X5:$i]:(~((![X6:$i]:(~((X5 = ((pair @ X4) @ X6))))))))) @ proj1)) @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))) => (~((X7 = emptyset)))))))))) => (X6 = emptyset))))) => (~((X5 = ((repl @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))) => (~((X6 = emptyset)))))))))) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((~((X6 = emptyset))) => (~((X7 = X6)))) => (~(((X6 = emptyset) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (eps @ (^[X9:$i]:(((~((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))) => (~((X9 = ((repl @ (univof @ emptyset)) @ (^[X10:$i]:(eps @ (^[X11:$i]:(((nat_p @ X10) => (~((X11 = X10)))) => (~(((~((nat_p @ X10))) => (~((X11 = (eps @ (^[X12:$i]:(~((((in @ X12) @ (univof @ emptyset)) => (~((nat_p @ X12))))))))))))))))))))))) => (~(((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))) => (~((X9 = emptyset)))))))))) => (X8 = emptyset))))))))))))))))))))) => (~(((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))) => (~((X7 = emptyset)))))))))) => (X6 = emptyset))) => (~((X5 = emptyset)))))))))))))))))) => (~((X2 = ((repl @ (power @ ((famunion @ (eps @ (^[X3:$i]:(((~((![X4:$i]:(((in @ X4) @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))))) => (~((X5 = ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((nat_p @ X6) => (~((X7 = X6)))) => (~(((~((nat_p @ X6))) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))))))))))))))))) => (~(((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))) => (~((X5 = emptyset)))))))))) => (X4 = emptyset))))) => (~((X3 = ((repl @ (eps @ (^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5))))))) => (~((X4 = ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((nat_p @ X5) => (~((X6 = X5)))) => (~(((~((nat_p @ X5))) => (~((X6 = (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))))))))))))))))))) => (~(((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5))))) => (~((X4 = emptyset)))))))))) @ (^[X4:$i]:(eps @ (^[X5:$i]:(((~((X4 = emptyset))) => (~((X5 = X4)))) => (~(((X4 = emptyset) => (~((X5 = (eps @ (^[X6:$i]:(~((((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ 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(^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))) => (~((X6 = emptyset)))))))))) => (X5 = emptyset))))) => (~((X4 = ((repl @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))))) => (~((X5 = ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((nat_p @ X6) => (~((X7 = X6)))) => (~(((~((nat_p @ X6))) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))))))))))))))))) => (~(((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))) => (~((X5 = emptyset)))))))))) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((~((X5 = 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emptyset)))))))))) => (X5 = emptyset))) => (~((X4 = emptyset))))))))))) @ (pair @ X3)))))) => (~((![X3:$i]:(((in @ X3) @ (eps @ (^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))) => (~((X6 = emptyset)))))))))) => (X5 = emptyset))))) => (~((X4 = ((repl @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))))) => (~((X5 = ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((nat_p @ X6) => (~((X7 = X6)))) => (~(((~((nat_p @ X6))) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))))))))))))))))) => (~(((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))) => (~((X5 = emptyset)))))))))) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((~((X5 = emptyset))) => (~((X6 = X5)))) => (~(((X5 = emptyset) => (~((X6 = (eps @ (^[X7:$i]:(~((((in @ X7) @ (eps @ (^[X8:$i]:(((~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))) => (~((X8 = ((repl @ (univof @ emptyset)) @ (^[X9:$i]:(eps @ (^[X10:$i]:(((nat_p @ X9) => (~((X10 = X9)))) => (~(((~((nat_p @ X9))) => (~((X10 = (eps @ (^[X11:$i]:(~((((in @ X11) @ (univof @ emptyset)) => (~((nat_p @ X11))))))))))))))))))))))) => (~(((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))) => (~((X8 = emptyset)))))))))) => (X7 = emptyset))))))))))))))))))))) => (~(((![X5:$i]:(((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))) => (~((X6 = emptyset)))))))))) => (X5 = emptyset))) => (~((X4 = emptyset)))))))))) => ((in @ (((d_ReplSep @ X2) @ (^[X4:$i]:(~((![X5:$i]:(~((X4 = ((pair @ X3) @ X5))))))))) @ proj1)) @ (eps @ (^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))) => (~((X6 = emptyset)))))))))) => (X5 = emptyset))))) => (~((X4 = ((repl @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))))) => (~((X5 = ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((nat_p @ X6) => (~((X7 = X6)))) => (~(((~((nat_p @ X6))) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))))))))))))))))) => (~(((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))) => (~((X5 = emptyset)))))))))) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((~((X5 = emptyset))) => (~((X6 = X5)))) => (~(((X5 = emptyset) => (~((X6 = (eps @ (^[X7:$i]:(~((((in @ X7) @ (eps @ (^[X8:$i]:(((~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))) => (~((X8 = ((repl @ (univof @ emptyset)) @ (^[X9:$i]:(eps @ (^[X10:$i]:(((nat_p @ X9) => (~((X10 = X9)))) => (~(((~((nat_p @ X9))) => (~((X10 = (eps @ (^[X11:$i]:(~((((in @ X11) @ (univof @ emptyset)) => (~((nat_p @ X11))))))))))))))))))))))) => (~(((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))) => (~((X8 = emptyset)))))))))) => (X7 = emptyset))))))))))))))))))))) => (~(((![X5:$i]:(((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))) => (~((X6 = emptyset)))))))))) => (X5 = emptyset))) => (~((X4 = emptyset)))))))))))))))) => (~((X1 = emptyset)))))))))) @ (d_24_prop2 @ eigen__0))) @ (^[X1:$i]:(~((![X2:$i]:(~((X1 = ((pair @ (union @ ((d_UPair @ emptyset) @ ((d_UPair @ emptyset) @ emptyset)))) @ X2))))))))) @ proj1) = (union @ ((d_UPair @ eigen__0) @ ((d_UPair @ eigen__0) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 181.15/177.42  thf(def_is_of,definition,(is_of = (^[X1:$i]:(^[X2:$i>$o]:(X2 @ X1))))).
% 181.15/177.42  thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))).
% 181.15/177.42  thf(def_if,definition,(if = (^[X1:$o]:(^[X2:$i]:(^[X3:$i]:(eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3)))))))))))))).
% 181.15/177.42  thf(def_d_Sing,definition,(d_Sing = (^[X1:$i]:((d_UPair @ X1) @ X1)))).
% 181.15/177.42  thf(def_binunion,definition,(binunion = (^[X1:$i]:(^[X2:$i]:(union @ ((d_UPair @ X1) @ X2)))))).
% 181.15/177.42  thf(def_d_Sep,definition,(d_Sep = (^[X1:$i]:(^[X2:$i>$o]:(((if @ (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) @ ((repl @ X1) @ (^[X3:$i]:(((if @ (X2 @ X3)) @ X3) @ (eps @ (^[X4:$i]:(~((((in @ X4) @ X1) => (~((X2 @ X4)))))))))))) @ emptyset))))).
% 181.15/177.42  thf(def_ordsucc,definition,(ordsucc = (^[X1:$i]:((binunion @ X1) @ (d_Sing @ X1))))).
% 181.15/177.42  thf(def_omega,definition,(omega = ((d_Sep @ (univof @ emptyset)) @ nat_p))).
% 181.15/177.42  thf(def_d_Sigma,definition,(d_Sigma = (^[X1:$i]:(^[X2:$i>$i]:((famunion @ X1) @ (^[X3:$i]:((repl @ (X2 @ X3)) @ (pair @ X3)))))))).
% 181.15/177.42  thf(def_setprod,definition,(setprod = (^[X1:$i]:(^[X2:$i]:((d_Sigma @ X1) @ (^[X3:$i]:X2)))))).
% 181.15/177.42  thf(def_ap,definition,(ap = (^[X1:$i]:(^[X2:$i]:(((d_ReplSep @ X1) @ (^[X3:$i]:(~((![X4:$i]:(~((X3 = ((pair @ X2) @ X4))))))))) @ proj1))))).
% 181.15/177.42  thf(def_d_Pi,definition,(d_Pi = (^[X1:$i]:(^[X2:$i>$i]:((d_Sep @ (power @ ((d_Sigma @ X1) @ (^[X3:$i]:(union @ (X2 @ X3)))))) @ (^[X3:$i]:(![X4:$i]:(((in @ X4) @ X1) => ((in @ ((ap @ X3) @ X4)) @ (X2 @ X4)))))))))).
% 181.15/177.42  thf(def_d_and,definition,(d_and = (^[X1:$o]:(^[X2:$o]:(d_not @ ((l_ec @ X1) @ X2)))))).
% 181.15/177.42  thf(def_e_is,definition,(e_is = (^[X1:$i]:(=)))).
% 181.15/177.42  thf(def_one,definition,(one = (^[X1:$i]:(^[X2:$i>$o]:((d_and @ ((amone @ X1) @ X2)) @ ((l_some @ X1) @ X2)))))).
% 181.15/177.42  thf(def_e_in,definition,(e_in = (^[X1:$i]:(^[X2:$i>$o]:(^[X3:$i]:X3))))).
% 181.15/177.42  thf(def_d_pair,definition,(d_pair = (^[X1:$i]:(^[X2:$i]:pair)))).
% 181.15/177.42  thf(def_first,definition,(first = (^[X1:$i]:(^[X2:$i]:proj0)))).
% 181.15/177.42  thf(def_second,definition,(second = (^[X1:$i]:(^[X2:$i]:proj1)))).
% 181.15/177.42  thf(def_esti,definition,(esti = (^[X1:$i]:in))).
% 181.15/177.42  thf(def_nat,definition,(nat = ((d_Sep @ omega) @ (^[X1:$i]:(~((X1 = emptyset))))))).
% 181.15/177.42  thf(def_n_is,definition,(n_is = (e_is @ nat))).
% 181.15/177.42  thf(def_nis,definition,(nis = (^[X1:$i]:(^[X2:$i]:(d_not @ ((n_is @ X1) @ X2)))))).
% 181.15/177.42  thf(def_n_in,definition,(n_in = (esti @ nat))).
% 181.15/177.42  thf(def_n_some,definition,(n_some = (l_some @ nat))).
% 181.15/177.42  thf(def_n_all,definition,(n_all = (all @ nat))).
% 181.15/177.42  thf(def_n_one,definition,(n_one = (one @ nat))).
% 181.15/177.42  thf(def_n_1,definition,(n_1 = (ordsucc @ emptyset))).
% 181.15/177.42  thf(def_cond1,definition,(cond1 = (n_in @ n_1))).
% 181.15/177.42  thf(def_cond2,definition,(cond2 = (^[X1:$i]:(n_all @ (^[X2:$i]:((imp @ ((n_in @ X2) @ X1)) @ ((n_in @ (ordsucc @ X2)) @ X1))))))).
% 181.15/177.42  thf(def_plus,definition,(plus = (^[X1:$i]:((ind @ ((d_Pi @ nat) @ (^[X2:$i]:nat))) @ (d_24_prop2 @ X1))))).
% 181.15/177.42  thf(def_n_pl,definition,(n_pl = (^[X1:$i]:(ap @ (plus @ X1))))).
% 181.15/177.42  thf(satz4e,conjecture,(![X1:$i]:(((in @ X1) @ (eps @ (^[X2:$i]:(((~((![X3:$i]:(((in @ X3) @ (eps @ (^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5))))))) => (~((X4 = ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((nat_p @ X5) => (~((X6 = X5)))) => (~(((~((nat_p @ X5))) => (~((X6 = (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))))))))))))))))))) => (~(((~((~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5))))))))) => (~((X4 = emptyset)))))))))) => (~((~((X3 = emptyset))))))))) => (~((X2 = ((repl @ (eps @ (^[X3:$i]:(((~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4))))))) => (~((X3 = ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(eps @ (^[X5:$i]:(((nat_p @ X4) => (~((X5 = X4)))) => (~(((~((nat_p @ X4))) => (~((X5 = (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))))))))))))))))))))) => (~(((~((~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((nat_p @ X4))))))))) => (~((X3 = emptyset)))))))))) @ (^[X3:$i]:(eps @ (^[X4:$i]:(((~((X3 = emptyset))) => (~((X4 = X3)))) => (~(((~((~((X3 = emptyset))))) => (~((X4 = (eps @ (^[X5:$i]:(~((((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((~((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))))) => (~((X6 = emptyset)))))))))) => (~((~((X5 = emptyset))))))))))))))))))))))))) => (~(((~((~((![X3:$i]:(((in @ X3) @ (eps @ (^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5))))))) => (~((X4 = ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((nat_p @ X5) => (~((X6 = X5)))) => (~(((~((nat_p @ X5))) => (~((X6 = (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))))))))))))))))))) => (~(((~((~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((nat_p @ X5))))))))) => (~((X4 = emptyset)))))))))) => (~((~((X3 = emptyset))))))))))) => (~((X2 = emptyset)))))))))) => ((union @ ((d_UPair @ X1) @ ((d_UPair @ X1) @ X1))) = (((d_ReplSep @ ((ind @ (eps @ (^[X2:$i]:(((~((![X3:$i]:(((in @ X3) @ (power @ ((famunion @ (eps @ (^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((~((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))))) => (~((X6 = emptyset)))))))))) => (~((~((X5 = emptyset))))))))) => (~((X4 = ((repl @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))))) => (~((X5 = ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((nat_p @ X6) => (~((X7 = X6)))) => (~(((~((nat_p @ X6))) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))))))))))))))))) => (~(((~((~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((nat_p @ X6))))))))) => (~((X5 = emptyset)))))))))) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((~((X5 = emptyset))) => (~((X6 = X5)))) => (~(((~((~((X5 = emptyset))))) => (~((X6 = (eps @ (^[X7:$i]:(~((((in @ X7) @ (eps @ (^[X8:$i]:(((~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))) => (~((X8 = ((repl @ (univof @ emptyset)) @ (^[X9:$i]:(eps @ (^[X10:$i]:(((nat_p @ X9) => (~((X10 = X9)))) => (~(((~((nat_p @ X9))) => (~((X10 = (eps @ (^[X11:$i]:(~((((in @ X11) @ (univof @ emptyset)) => (~((nat_p @ X11))))))))))))))))))))))) => (~(((~((~((![X9:$i]:(((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))) => (~((X8 = emptyset)))))))))) => (~((~((X7 = emptyset))))))))))))))))))))))))) => (~(((~((~((![X5:$i]:(((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((~((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))))) => (~((X6 = emptyset)))))))))) => (~((~((X5 = emptyset))))))))))) => (~((X4 = emptyset)))))))))) @ (^[X4:$i]:((repl @ (union @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((~((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))) => (~((X7 = emptyset)))))))))) => (~((~((X6 = emptyset))))))))) => (~((X5 = ((repl @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((~((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))))) => (~((X6 = emptyset)))))))))) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((~((X6 = emptyset))) => (~((X7 = X6)))) => (~(((~((~((X6 = emptyset))))) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (eps @ (^[X9:$i]:(((~((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))) => (~((X9 = ((repl @ (univof @ emptyset)) @ (^[X10:$i]:(eps @ (^[X11:$i]:(((nat_p @ X10) => (~((X11 = X10)))) => (~(((~((nat_p @ X10))) => (~((X11 = (eps @ (^[X12:$i]:(~((((in @ X12) @ (univof @ emptyset)) => (~((nat_p @ X12))))))))))))))))))))))) => (~(((~((~((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))) => (~((X9 = emptyset)))))))))) => (~((~((X8 = emptyset))))))))))))))))))))))))) => (~(((~((~((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((~((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))) => (~((X7 = emptyset)))))))))) => (~((~((X6 = emptyset))))))))))) => (~((X5 = emptyset))))))))))) @ (pair @ X4)))))) => (~((![X4:$i]:(((in @ X4) @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((~((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))) => (~((X7 = emptyset)))))))))) => (~((~((X6 = emptyset))))))))) => (~((X5 = ((repl @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((~((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))))) => (~((X6 = emptyset)))))))))) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((~((X6 = emptyset))) => (~((X7 = X6)))) => (~(((~((~((X6 = emptyset))))) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (eps @ (^[X9:$i]:(((~((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))) => (~((X9 = ((repl @ (univof @ emptyset)) @ (^[X10:$i]:(eps @ (^[X11:$i]:(((nat_p @ X10) => (~((X11 = X10)))) => (~(((~((nat_p @ X10))) => (~((X11 = (eps @ (^[X12:$i]:(~((((in @ X12) @ (univof @ emptyset)) => (~((nat_p @ X12))))))))))))))))))))))) => (~(((~((~((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))) => (~((X9 = emptyset)))))))))) => (~((~((X8 = emptyset))))))))))))))))))))))))) => (~(((~((~((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((~((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))) => (~((X7 = emptyset)))))))))) => (~((~((X6 = emptyset))))))))))) => (~((X5 = emptyset)))))))))) => ((in @ (((d_ReplSep @ X3) @ (^[X5:$i]:(~((![X6:$i]:(~((X5 = ((pair @ X4) @ X6))))))))) @ proj1)) @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))) => (~((X7 = ((repl @ (univof @ emptyset)) @ (^[X8:$i]:(eps @ (^[X9:$i]:(((nat_p @ X8) => (~((X9 = X8)))) => (~(((~((nat_p @ X8))) => (~((X9 = (eps @ (^[X10:$i]:(~((((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))))))))))))))))) => (~(((~((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ X8))))))))) => (~((X7 = emptyset)))))))))) => (~((~((X6 = emptyset))))))))) => (~((X5 = ((repl @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((nat_p @ X7) => (~((X8 = X7)))) => (~(((~((nat_p @ X7))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((nat_p @ X9))))))))))))))))))))))) => (~(((~((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((nat_p @ X7))))))))) => (~((X6 = emptyset)))))))))) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((~((X6 = emptyset))) => (~((X7 = X6)))) => (~(((~((~((X6 = emptyset))))) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) @ (eps @ (^[X9:$i]:(((~((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))) => (~((X9 = ((repl @ (univof @ emptyset)) @ (^[X10:$i]:(eps @ (^[X11:$i]:(((nat_p @ X10) => (~((X11 = X10)))) => (~(((~((nat_p @ X10))) => (~((X11 = (eps @ (^[X12:$i]:(~((((in @ X12) @ (univof @ emptyset)) => (~((nat_p @ X12))))))))))))))))))))))) => (~(((~((~((![X10:$i]:(((in @ X10) @ (univof @ emptyset)) => (~((nat_p @ X10))))))))) => (~((X9 = emptyset)))))))))) => (~((~((X8 = emptyset))))))))))))))))))))))))) => (~(((~((~((![X6:$i]:(((in @ X6) @ (eps @ (^[X7:$i]:(((~((![X8:$i]:(((in @ X8) @ (univof @ emptyset)) => (~((nat_p @ 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emptyset)))) @ X3))))))))) @ proj1)))))),inference(assume_negation,[status(cth)],[satz4e])).
% 181.15/177.43  thf(h1,assumption,(~((sP2 => sP3))),introduced(assumption,[])).
% 181.15/177.43  thf(h2,assumption,sP2,introduced(assumption,[])).
% 181.15/177.43  thf(h3,assumption,(~(sP3)),introduced(assumption,[])).
% 181.15/177.43  thf(1,plain,(~(sP7) | sP4),inference(all_rule,[status(thm)],[])).
% 181.15/177.43  thf(2,plain,((~(sP4) | ~(sP2)) | sP8),inference(prop_rule,[status(thm)],[])).
% 181.15/177.43  thf(3,plain,((~(sP5) | ~(sP8)) | sP3),inference(prop_rule,[status(thm)],[])).
% 181.15/177.43  thf(4,plain,(~(sP1) | sP5),inference(all_rule,[status(thm)],[])).
% 181.15/177.43  thf(5,plain,(~(sP6) | sP1),inference(all_rule,[status(thm)],[])).
% 181.15/177.43  thf(6,plain,sP6,inference(eq_sym,[status(thm)],[])).
% 181.15/177.43  thf(satz4a,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((n_is @ ((n_pl @ X1) @ n_1)) @ (ordsucc @ X1))))).
% 181.15/177.43  thf(7,plain,sP7,inference(preprocess,[status(thm)],[satz4a]).
% 181.15/177.43  thf(8,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,h2,h3,7])).
% 181.15/177.43  thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,8,h2,h3])).
% 181.15/177.43  thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1])).
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% 181.15/177.43  % SZS output end Proof
%------------------------------------------------------------------------------