↑ Up

Z3---4.15.1.THM-Prf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz 
%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : NUM587+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n005.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  : 300s
% DateTime : Sat Jun 21 05:21:29 AM UTC 2025

% Result   : Theorem 0.45s 0.61s
% Output   : Proof 0.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : NUM587+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n005.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri Jun 20 01:31:05 EDT 2025
% 0.11/0.33  % CPUTime    : 
% 0.45/0.61  % SZS status Theorem
% 0.45/0.61  % SZS output start Proof
% 0.45/0.61  tff(aElementOf0_type, type, (
% 0.45/0.61     aElementOf0: ( $i * $i ) > $o)).
% 0.45/0.61  tff(sdtlcdtrc0_type, type, (
% 0.45/0.61     sdtlcdtrc0: ( $i * $i ) > $i)).
% 0.45/0.61  tff(szDzozmdt0_type, type, (
% 0.45/0.61     szDzozmdt0: $i > $i)).
% 0.45/0.61  tff(xc_type, type, (
% 0.45/0.61     xc: $i)).
% 0.45/0.61  tff(sdtlpdtrp0_type, type, (
% 0.45/0.61     sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.45/0.61  tff(tptp_fun_W0_33_type, type, (
% 0.45/0.61     tptp_fun_W0_33: $i)).
% 0.45/0.61  tff(xx_type, type, (
% 0.45/0.61     xx: $i)).
% 0.45/0.61  tff(xQ_type, type, (
% 0.45/0.61     xQ: $i)).
% 0.45/0.61  tff(xi_type, type, (
% 0.45/0.61     xi: $i)).
% 0.45/0.61  tff(xC_type, type, (
% 0.45/0.61     xC: $i)).
% 0.45/0.61  tff(slbdtsldtrb0_type, type, (
% 0.45/0.61     slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.45/0.61  tff(xk_type, type, (
% 0.45/0.61     xk: $i)).
% 0.45/0.61  tff(sdtmndt0_type, type, (
% 0.45/0.61     sdtmndt0: ( $i * $i ) > $i)).
% 0.45/0.61  tff(szmzizndt0_type, type, (
% 0.45/0.61     szmzizndt0: $i > $i)).
% 0.45/0.61  tff(xN_type, type, (
% 0.45/0.61     xN: $i)).
% 0.45/0.61  tff(sbrdtbr0_type, type, (
% 0.45/0.61     sbrdtbr0: $i > $i)).
% 0.45/0.61  tff(aSubsetOf0_type, type, (
% 0.45/0.61     aSubsetOf0: ( $i * $i ) > $o)).
% 0.45/0.61  tff(aSet0_type, type, (
% 0.45/0.61     aSet0: $i > $o)).
% 0.45/0.61  tff(aElement0_type, type, (
% 0.45/0.61     aElement0: $i > $o)).
% 0.45/0.61  tff(sdtlseqdt0_type, type, (
% 0.45/0.61     sdtlseqdt0: ( $i * $i ) > $o)).
% 0.45/0.61  tff(sdtpldt0_type, type, (
% 0.45/0.61     sdtpldt0: ( $i * $i ) > $i)).
% 0.45/0.61  tff(tptp_fun_W2_31_type, type, (
% 0.45/0.61     tptp_fun_W2_31: ( $i * $i ) > $i)).
% 0.45/0.61  tff(aFunction0_type, type, (
% 0.45/0.61     aFunction0: $i > $o)).
% 0.45/0.61  tff(szNzAzT0_type, type, (
% 0.45/0.61     szNzAzT0: $i)).
% 0.45/0.61  tff(xT_type, type, (
% 0.45/0.61     xT: $i)).
% 0.45/0.61  tff(xK_type, type, (
% 0.45/0.61     xK: $i)).
% 0.45/0.61  tff(xS_type, type, (
% 0.45/0.61     xS: $i)).
% 0.45/0.61  tff(1,plain,
% 0.45/0.61      ((sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = xx) <=> (sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = xx)),
% 0.45/0.61      inference(rewrite,[status(thm)],[])).
% 0.45/0.61  tff(2,axiom,(((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & (sbrdtbr0(xQ) = xk)) & aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) & (sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = xx)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4237')).
% 0.45/0.61  tff(3,plain,
% 0.45/0.61      (sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = xx),
% 0.45/0.61      inference(and_elim,[status(thm)],[2])).
% 0.45/0.61  tff(4,plain,
% 0.45/0.61      (sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = xx),
% 0.45/0.61      inference(modus_ponens,[status(thm)],[3, 1])).
% 0.45/0.61  tff(5,plain,
% 0.45/0.61      (aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) <=> aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))),
% 0.45/0.61      inference(rewrite,[status(thm)],[])).
% 0.45/0.61  tff(6,plain,
% 0.45/0.61      ((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & (sbrdtbr0(xQ) = xk)) & aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))),
% 0.45/0.61      inference(and_elim,[status(thm)],[2])).
% 0.45/0.61  tff(7,plain,
% 0.45/0.61      (aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))),
% 0.45/0.61      inference(and_elim,[status(thm)],[6])).
% 0.45/0.61  tff(8,plain,
% 0.45/0.61      (aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))),
% 0.45/0.61      inference(modus_ponens,[status(thm)],[7, 5])).
% 0.45/0.61  tff(9,plain,
% 0.45/0.61      ((aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ))))))) | (~aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)))),
% 0.45/0.62      inference(tautology,[status(thm)],[])).
% 0.45/0.62  tff(10,plain,
% 0.45/0.62      (aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ))))))),
% 0.45/0.62      inference(unit_resolution,[status(thm)],[9, 8])).
% 0.45/0.62  tff(11,plain,
% 0.45/0.62      (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szNzAzT0)),
% 0.45/0.62      inference(rewrite,[status(thm)],[])).
% 0.45/0.62  tff(12,axiom,(aElementOf0(xi, szNzAzT0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4200')).
% 0.45/0.62  tff(13,plain,
% 0.45/0.62      (aElementOf0(xi, szNzAzT0)),
% 0.45/0.62      inference(modus_ponens,[status(thm)],[12, 11])).
% 0.45/0.62  tff(14,plain,
% 0.45/0.62      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))))),
% 0.45/0.62      inference(bind,[status(th)],[])).
% 0.45/0.62  tff(15,plain,
% 0.45/0.62      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 0.45/0.62      inference(quant_intro,[status(thm)],[14])).
% 0.45/0.62  tff(16,plain,
% 0.45/0.62      (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 0.45/0.62      inference(bind,[status(th)],[])).
% 0.45/0.62  tff(17,plain,
% 0.45/0.62      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.45/0.62      inference(quant_intro,[status(thm)],[16])).
% 0.45/0.62  tff(18,plain,
% 0.45/0.62      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 0.47/0.63      inference(bind,[status(th)],[])).
% 0.47/0.63  tff(19,plain,
% 0.47/0.63      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.47/0.63      inference(quant_intro,[status(thm)],[18])).
% 0.47/0.63  tff(20,plain,
% 0.47/0.63      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.47/0.63      inference(transitivity,[status(thm)],[19, 17])).
% 0.47/0.63  tff(21,plain,
% 0.47/0.63      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & (aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 0.47/0.63      inference(bind,[status(th)],[])).
% 0.47/0.63  tff(22,plain,
% 0.47/0.63      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & (aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.47/0.63      inference(quant_intro,[status(thm)],[21])).
% 0.47/0.63  tff(23,plain,
% 0.47/0.63      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & (aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 0.47/0.64      inference(bind,[status(th)],[])).
% 0.47/0.64  tff(24,plain,
% 0.47/0.64      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & (aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))),
% 0.47/0.64      inference(quant_intro,[status(thm)],[23])).
% 0.47/0.64  tff(25,plain,
% 0.47/0.64      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.47/0.64      inference(rewrite,[status(thm)],[])).
% 0.47/0.64  tff(26,plain,
% 0.47/0.64      (^[W0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) <=> ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) <=> ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))))), ((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))), ((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), quant_intro(proof_bind(^[W1: $i] : rewrite(((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) <=> (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))))), (![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) <=> ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))))), ((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))))), ((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))))), (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))), (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) <=> (aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))), trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))), ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite(((aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), (![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))), ((((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))), ((((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), ((aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> (aElementOf0(W0, szNzAzT0) => (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))), rewrite((aElementOf0(W0, szNzAzT0) => (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), ((aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 0.47/0.66      inference(bind,[status(th)],[])).
% 0.47/0.66  tff(27,plain,
% 0.47/0.66      (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.47/0.66      inference(quant_intro,[status(thm)],[26])).
% 0.47/0.66  tff(28,axiom,((aFunction0(xC) & (szDzozmdt0(xC) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4151')).
% 0.47/0.67  tff(29,plain,
% 0.47/0.67      (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.47/0.67      inference(and_elim,[status(thm)],[28])).
% 0.47/0.67  tff(30,plain,
% 0.47/0.67      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.47/0.67      inference(modus_ponens,[status(thm)],[29, 27])).
% 0.47/0.67  tff(31,plain,
% 0.47/0.67      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.47/0.67      inference(modus_ponens,[status(thm)],[30, 25])).
% 0.47/0.67  tff(32,plain,(
% 0.47/0.67      ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 0.47/0.67      inference(skolemize,[status(sab)],[31])).
% 0.47/0.67  tff(33,plain,
% 0.47/0.67      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & (aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))),
% 0.47/0.67      inference(modus_ponens,[status(thm)],[32, 24])).
% 0.47/0.67  tff(34,plain,
% 0.47/0.67      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.47/0.67      inference(modus_ponens,[status(thm)],[33, 22])).
% 0.47/0.67  tff(35,plain,
% 0.47/0.67      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 0.47/0.67      inference(modus_ponens,[status(thm)],[34, 20])).
% 0.47/0.67  tff(36,plain,
% 0.47/0.67      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 0.47/0.67      inference(modus_ponens,[status(thm)],[35, 15])).
% 0.47/0.67  tff(37,plain,
% 0.47/0.67      (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))),
% 0.47/0.68      inference(rewrite,[status(thm)],[])).
% 0.47/0.68  tff(38,plain,
% 0.47/0.68      (((~aElementOf0(xi, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))) <=> ((~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))),
% 0.47/0.68      inference(rewrite,[status(thm)],[])).
% 0.47/0.68  tff(39,plain,
% 0.47/0.68      (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))))),
% 0.47/0.69      inference(monotonicity,[status(thm)],[38])).
% 0.47/0.69  tff(40,plain,
% 0.47/0.69      (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))),
% 0.47/0.69      inference(transitivity,[status(thm)],[39, 37])).
% 0.47/0.69  tff(41,plain,
% 0.47/0.69      ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | ((~aElementOf0(xi, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))),
% 0.47/0.69      inference(quant_inst,[status(thm)],[])).
% 0.47/0.69  tff(42,plain,
% 0.47/0.69      ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~aElementOf0(xi, szNzAzT0)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))))),
% 0.47/0.70      inference(modus_ponens,[status(thm)],[41, 40])).
% 0.47/0.70  tff(43,plain,
% 0.47/0.70      (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))),
% 0.47/0.70      inference(unit_resolution,[status(thm)],[42, 36, 13])).
% 0.47/0.70  tff(44,plain,
% 0.47/0.70      (((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W1: $i] : (~(((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W1))) | (~(szDzozmdt0(sdtlpdtrp0(xC, xi)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk))) | (~aFunction0(sdtlpdtrp0(xC, xi))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, xi))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, xi), W1)) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))),
% 0.47/0.70      inference(tautology,[status(thm)],[])).
% 0.47/0.70  tff(45,plain,
% 0.47/0.70      (![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))),
% 0.54/0.70      inference(unit_resolution,[status(thm)],[44, 43])).
% 0.54/0.70  tff(46,plain,
% 0.54/0.70      (aSet0(xQ) <=> aSet0(xQ)),
% 0.54/0.70      inference(rewrite,[status(thm)],[])).
% 0.54/0.70  tff(47,plain,
% 0.54/0.70      (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & (sbrdtbr0(xQ) = xk)),
% 0.54/0.70      inference(and_elim,[status(thm)],[6])).
% 0.54/0.70  tff(48,plain,
% 0.54/0.70      ((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))) & aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.54/0.70      inference(and_elim,[status(thm)],[47])).
% 0.54/0.70  tff(49,plain,
% 0.54/0.70      (((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.54/0.70      inference(and_elim,[status(thm)],[48])).
% 0.54/0.70  tff(50,plain,
% 0.54/0.70      ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> ((aElement0(W0) & aElementOf0(W0, sdtlpdtrp0(xN, xi))) & (~(W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aSet0(xQ)),
% 0.54/0.70      inference(and_elim,[status(thm)],[49])).
% 0.54/0.70  tff(51,plain,
% 0.54/0.70      (aSet0(xQ)),
% 0.54/0.70      inference(and_elim,[status(thm)],[50])).
% 0.54/0.70  tff(52,plain,
% 0.54/0.70      (aSet0(xQ)),
% 0.54/0.70      inference(modus_ponens,[status(thm)],[51, 46])).
% 0.54/0.70  tff(53,plain,
% 0.54/0.70      (((~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | ((~aSet0(xQ)) | (~(aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~aSet0(xQ)) | (~(aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))),
% 0.54/0.70      inference(rewrite,[status(thm)],[])).
% 0.54/0.70  tff(54,plain,
% 0.54/0.70      (((~aSet0(xQ)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))))))) <=> ((~aSet0(xQ)) | (~(aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))),
% 0.54/0.70      inference(rewrite,[status(thm)],[])).
% 0.54/0.70  tff(55,plain,
% 0.54/0.70      (((~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | ((~aSet0(xQ)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | ((~aSet0(xQ)) | (~(aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))))))))),
% 0.54/0.71      inference(monotonicity,[status(thm)],[54])).
% 0.54/0.71  tff(56,plain,
% 0.54/0.71      (((~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | ((~aSet0(xQ)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~aSet0(xQ)) | (~(aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))),
% 0.54/0.71      inference(transitivity,[status(thm)],[55, 53])).
% 0.54/0.71  tff(57,plain,
% 0.54/0.71      ((~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | ((~aSet0(xQ)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))),
% 0.54/0.71      inference(quant_inst,[status(thm)],[])).
% 0.54/0.71  tff(58,plain,
% 0.54/0.71      ((~![W1: $i] : ((~aSet0(W1)) | (~((~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(W1, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(W1, xi), W1)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, xi))))))))))) | (~aSet0(xQ)) | (~(aElementOf0(xQ, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))), xk)) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))))))) | (~((~(sbrdtbr0(xQ) = xk)) | (~(aSubsetOf0(xQ, sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | aElementOf0(tptp_fun_W2_31(xQ, xi), sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi)))) | (~aElementOf0(tptp_fun_W2_31(xQ, xi), xQ)))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))))))),
% 0.54/0.71      inference(modus_ponens,[status(thm)],[57, 56])).
% 0.54/0.71  tff(59,plain,
% 0.54/0.71      (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))))),
% 0.54/0.71      inference(unit_resolution,[status(thm)],[58, 52, 45, 10])).
% 0.54/0.71  tff(60,plain,
% 0.54/0.71      (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, xi))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W2))) | (~![W2: $i] : (~(((~aElement0(W2)) | (~(aElementOf0(W2, xQ) | (W2 = szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> aElementOf0(W2, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.54/0.71      inference(tautology,[status(thm)],[])).
% 0.54/0.71  tff(61,plain,
% 0.54/0.71      (sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.54/0.71      inference(unit_resolution,[status(thm)],[60, 59])).
% 0.54/0.71  tff(62,plain,
% 0.54/0.71      (sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), xQ)),
% 0.54/0.71      inference(symmetry,[status(thm)],[61])).
% 0.54/0.71  tff(63,plain,
% 0.54/0.71      (?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))) <=> ?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.54/0.71      inference(rewrite,[status(thm)],[])).
% 0.54/0.71  tff(64,axiom,((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi))) & ![W0: $i] : (aElementOf0(W0, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0))) & aSet0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) <=> (aElement0(W0) & (aElementOf0(W0, xQ) | (W0 = szmzizndt0(sdtlpdtrp0(xN, xi))))))) & ?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4263')).
% 0.54/0.71  tff(65,plain,
% 0.54/0.71      (?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.54/0.71      inference(and_elim,[status(thm)],[64])).
% 0.54/0.71  tff(66,plain,
% 0.54/0.71      (?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))))),
% 0.54/0.71      inference(modus_ponens,[status(thm)],[65, 63])).
% 0.54/0.71  tff(67,plain,(
% 0.54/0.71      aElementOf0(W0!33, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W0!33) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))))),
% 0.54/0.71      inference(skolemize,[status(sab)],[66])).
% 0.54/0.71  tff(68,plain,
% 0.54/0.71      (sdtlpdtrp0(xc, W0!33) = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))),
% 0.54/0.71      inference(and_elim,[status(thm)],[67])).
% 0.54/0.71  tff(69,plain,
% 0.54/0.71      (sdtlpdtrp0(xc, W0!33) = xx),
% 0.54/0.71      inference(transitivity,[status(thm)],[68, 62, 4])).
% 0.54/0.71  tff(70,plain,
% 0.54/0.71      (aElementOf0(sdtlpdtrp0(xc, W0!33), sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> aElementOf0(xx, sdtlcdtrc0(xc, szDzozmdt0(xc)))),
% 0.54/0.71      inference(monotonicity,[status(thm)],[69])).
% 0.54/0.71  tff(71,plain,
% 0.54/0.71      (aElementOf0(xx, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> aElementOf0(sdtlpdtrp0(xc, W0!33), sdtlcdtrc0(xc, szDzozmdt0(xc)))),
% 0.54/0.71      inference(symmetry,[status(thm)],[70])).
% 0.54/0.71  tff(72,plain,
% 0.54/0.71      ((~aElementOf0(xx, sdtlcdtrc0(xc, szDzozmdt0(xc)))) <=> (~aElementOf0(sdtlpdtrp0(xc, W0!33), sdtlcdtrc0(xc, szDzozmdt0(xc))))),
% 0.54/0.72      inference(monotonicity,[status(thm)],[71])).
% 0.54/0.72  tff(73,plain,
% 0.54/0.72      ((~aElementOf0(xx, xT)) <=> (~aElementOf0(xx, xT))),
% 0.54/0.72      inference(rewrite,[status(thm)],[])).
% 0.54/0.72  tff(74,axiom,(~aElementOf0(xx, xT)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.54/0.72  tff(75,plain,
% 0.54/0.72      (~aElementOf0(xx, xT)),
% 0.54/0.72      inference(modus_ponens,[status(thm)],[74, 73])).
% 0.54/0.72  tff(76,plain,
% 0.54/0.72      (^[W0: $i] : refl(((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)))),
% 0.54/0.72      inference(bind,[status(th)],[])).
% 0.54/0.72  tff(77,plain,
% 0.54/0.72      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 0.54/0.72      inference(quant_intro,[status(thm)],[76])).
% 0.54/0.72  tff(78,plain,
% 0.54/0.72      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 0.54/0.72      inference(rewrite,[status(thm)],[])).
% 0.54/0.72  tff(79,plain,
% 0.54/0.72      (^[W0: $i] : rewrite((aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)))),
% 0.54/0.72      inference(bind,[status(th)],[])).
% 0.54/0.72  tff(80,plain,
% 0.54/0.72      (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 0.54/0.72      inference(quant_intro,[status(thm)],[79])).
% 0.54/0.72  tff(81,axiom,((((((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT))) & aSubsetOf0(sdtlcdtrc0(xc, szDzozmdt0(xc)), xT)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3453')).
% 0.54/0.72  tff(82,plain,
% 0.54/0.72      (((((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT))),
% 0.54/0.72      inference(and_elim,[status(thm)],[81])).
% 0.54/0.72  tff(83,plain,
% 0.54/0.72      (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT))),
% 0.54/0.72      inference(and_elim,[status(thm)],[82])).
% 0.54/0.72  tff(84,plain,
% 0.54/0.72      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 0.54/0.72      inference(modus_ponens,[status(thm)],[83, 80])).
% 0.54/0.72  tff(85,plain,
% 0.54/0.72      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 0.54/0.72      inference(modus_ponens,[status(thm)],[84, 78])).
% 0.54/0.72  tff(86,plain,(
% 0.54/0.72      ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 0.54/0.72      inference(skolemize,[status(sab)],[85])).
% 0.54/0.72  tff(87,plain,
% 0.54/0.72      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 0.54/0.72      inference(modus_ponens,[status(thm)],[86, 77])).
% 0.54/0.72  tff(88,plain,
% 0.54/0.72      (((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | ((~aElementOf0(xx, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(xx, xT))) <=> ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | (~aElementOf0(xx, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(xx, xT))),
% 0.54/0.72      inference(rewrite,[status(thm)],[])).
% 0.54/0.72  tff(89,plain,
% 0.54/0.72      ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | ((~aElementOf0(xx, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(xx, xT))),
% 0.54/0.72      inference(quant_inst,[status(thm)],[])).
% 0.54/0.72  tff(90,plain,
% 0.54/0.72      ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | (~aElementOf0(xx, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(xx, xT)),
% 0.54/0.72      inference(modus_ponens,[status(thm)],[89, 88])).
% 0.54/0.72  tff(91,plain,
% 0.54/0.72      (~aElementOf0(xx, sdtlcdtrc0(xc, szDzozmdt0(xc)))),
% 0.54/0.72      inference(unit_resolution,[status(thm)],[90, 87, 75])).
% 0.54/0.72  tff(92,plain,
% 0.54/0.72      (~aElementOf0(sdtlpdtrp0(xc, W0!33), sdtlcdtrc0(xc, szDzozmdt0(xc)))),
% 0.54/0.72      inference(modus_ponens,[status(thm)],[91, 72])).
% 0.54/0.72  tff(93,plain,
% 0.54/0.72      (aFunction0(xc) <=> aFunction0(xc)),
% 0.54/0.72      inference(rewrite,[status(thm)],[])).
% 0.54/0.72  tff(94,plain,
% 0.54/0.72      ((((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))),
% 0.54/0.72      inference(and_elim,[status(thm)],[82])).
% 0.54/0.72  tff(95,plain,
% 0.54/0.72      (((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))),
% 0.54/0.72      inference(and_elim,[status(thm)],[94])).
% 0.54/0.72  tff(96,plain,
% 0.54/0.72      ((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))),
% 0.54/0.72      inference(and_elim,[status(thm)],[95])).
% 0.54/0.72  tff(97,plain,
% 0.54/0.72      (aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))),
% 0.54/0.72      inference(and_elim,[status(thm)],[96])).
% 0.54/0.72  tff(98,plain,
% 0.54/0.72      (aFunction0(xc)),
% 0.54/0.72      inference(and_elim,[status(thm)],[97])).
% 0.54/0.72  tff(99,plain,
% 0.54/0.72      (aFunction0(xc)),
% 0.54/0.72      inference(modus_ponens,[status(thm)],[98, 93])).
% 0.54/0.72  tff(100,plain,
% 0.54/0.72      (^[W0: $i] : refl(((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))))),
% 0.54/0.72      inference(bind,[status(th)],[])).
% 0.54/0.72  tff(101,plain,
% 0.54/0.72      (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.54/0.72      inference(quant_intro,[status(thm)],[100])).
% 0.54/0.72  tff(102,plain,
% 0.54/0.72      (^[W0: $i] : rewrite(((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))))),
% 0.54/0.72      inference(bind,[status(th)],[])).
% 0.54/0.72  tff(103,plain,
% 0.54/0.72      (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.54/0.72      inference(quant_intro,[status(thm)],[102])).
% 0.54/0.72  tff(104,plain,
% 0.54/0.72      (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.54/0.72      inference(transitivity,[status(thm)],[103, 101])).
% 0.54/0.72  tff(105,plain,
% 0.54/0.72      (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.54/0.72      inference(rewrite,[status(thm)],[])).
% 0.54/0.72  tff(106,plain,
% 0.54/0.72      (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))) <=> ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))), (![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))) <=> ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))), ((aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> (aFunction0(W0) => ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))))), rewrite((aFunction0(W0) => ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))), ((aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))))),
% 0.54/0.72      inference(bind,[status(th)],[])).
% 0.54/0.72  tff(107,plain,
% 0.54/0.72      (![W0: $i] : (aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.54/0.72      inference(quant_intro,[status(thm)],[106])).
% 0.54/0.72  tff(108,axiom,(![W0: $i] : (aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mImgRng')).
% 0.54/0.72  tff(109,plain,
% 0.54/0.72      (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.54/0.72      inference(modus_ponens,[status(thm)],[108, 107])).
% 0.54/0.72  tff(110,plain,
% 0.54/0.72      (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.54/0.72      inference(modus_ponens,[status(thm)],[109, 105])).
% 0.54/0.72  tff(111,plain,(
% 0.54/0.72      ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.54/0.72      inference(skolemize,[status(sab)],[110])).
% 0.54/0.72  tff(112,plain,
% 0.54/0.72      (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.54/0.72      inference(modus_ponens,[status(thm)],[111, 104])).
% 0.54/0.72  tff(113,plain,
% 0.54/0.72      (((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))) | ((~aFunction0(xc)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W1), sdtlcdtrc0(xc, szDzozmdt0(xc)))))) <=> ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))) | (~aFunction0(xc)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W1), sdtlcdtrc0(xc, szDzozmdt0(xc)))))),
% 0.54/0.72      inference(rewrite,[status(thm)],[])).
% 0.54/0.72  tff(114,plain,
% 0.54/0.72      ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))) | ((~aFunction0(xc)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W1), sdtlcdtrc0(xc, szDzozmdt0(xc)))))),
% 0.54/0.73      inference(quant_inst,[status(thm)],[])).
% 0.54/0.73  tff(115,plain,
% 0.54/0.73      ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))) | (~aFunction0(xc)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W1), sdtlcdtrc0(xc, szDzozmdt0(xc))))),
% 0.54/0.73      inference(modus_ponens,[status(thm)],[114, 113])).
% 0.54/0.73  tff(116,plain,
% 0.54/0.73      (![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W1), sdtlcdtrc0(xc, szDzozmdt0(xc))))),
% 0.54/0.73      inference(unit_resolution,[status(thm)],[115, 112, 99])).
% 0.54/0.73  tff(117,plain,
% 0.54/0.73      (aElementOf0(W0!33, szDzozmdt0(xc))),
% 0.54/0.73      inference(and_elim,[status(thm)],[67])).
% 0.54/0.73  tff(118,plain,
% 0.54/0.73      (((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W1), sdtlcdtrc0(xc, szDzozmdt0(xc))))) | ((~aElementOf0(W0!33, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W0!33), sdtlcdtrc0(xc, szDzozmdt0(xc))))) <=> ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W1), sdtlcdtrc0(xc, szDzozmdt0(xc))))) | (~aElementOf0(W0!33, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W0!33), sdtlcdtrc0(xc, szDzozmdt0(xc))))),
% 0.54/0.73      inference(rewrite,[status(thm)],[])).
% 0.54/0.73  tff(119,plain,
% 0.54/0.73      ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W1), sdtlcdtrc0(xc, szDzozmdt0(xc))))) | ((~aElementOf0(W0!33, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W0!33), sdtlcdtrc0(xc, szDzozmdt0(xc))))),
% 0.54/0.73      inference(quant_inst,[status(thm)],[])).
% 0.54/0.73  tff(120,plain,
% 0.54/0.73      ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W1), sdtlcdtrc0(xc, szDzozmdt0(xc))))) | (~aElementOf0(W0!33, szDzozmdt0(xc))) | aElementOf0(sdtlpdtrp0(xc, W0!33), sdtlcdtrc0(xc, szDzozmdt0(xc)))),
% 0.54/0.73      inference(modus_ponens,[status(thm)],[119, 118])).
% 0.54/0.73  tff(121,plain,
% 0.54/0.73      (aElementOf0(sdtlpdtrp0(xc, W0!33), sdtlcdtrc0(xc, szDzozmdt0(xc)))),
% 0.54/0.73      inference(unit_resolution,[status(thm)],[120, 117, 116])).
% 0.54/0.73  tff(122,plain,
% 0.54/0.73      ($false),
% 0.54/0.73      inference(unit_resolution,[status(thm)],[121, 92])).
% 0.54/0.73  % SZS output end Proof
% 0.54/0.73  % E exiting
%------------------------------------------------------------------------------