%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM630+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:21:40 AM UTC 2025
% Result : Theorem 0.70s 0.88s
% Output : Proof 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 33
% Syntax : Number of formulae : 97 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 4426 ( 788 equ)
% Maximal formula atoms : 180 ( 45 avg)
% Number of connectives : 7335 (3092 ~;2567 |;1139 &)
% ( 376 <=>; 161 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 10 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 86 ( 86 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-2 aty)
% Number of variables : 973 ( 963 !; 0 ?; 973 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xP_type,type,
xP: $i ).
tff(xn_type,type,
xn: $i ).
tff(xC_type,type,
xC: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(xc_type,type,
xc: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(tptp_fun_W2_31_type,type,
tptp_fun_W2_31: ( $i * $i ) > $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xD_type,type,
xD: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(xp_type,type,
xp: $i ).
tff(xe_type,type,
xe: $i ).
tff(1,plain,
( ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) )
<=> ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != szmzizndt0(xQ) ) ) )
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
tff(3,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) )
<=> ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0) )
& aSet0(xD)
& ! [W0: $i] :
( aElementOf0(W0,xD)
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xn))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
& ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5585) ).
tff(9,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(and_elim,[status(thm)],[8]) ).
tff(10,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(modus_ponens,[status(thm)],[9,7]) ).
tff(11,plain,
sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) = xD,
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(symmetry,[status(thm)],[4]) ).
tff(13,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> aSubsetOf0(xP,xD) ),
inference(monotonicity,[status(thm)],[12,11]) ).
tff(14,plain,
( aSubsetOf0(xP,xD)
<=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( aSubsetOf0(xP,xD)
<=> aSubsetOf0(xP,xD) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xD) )
& aSubsetOf0(xP,xD)
& aElementOf0(xP,slbdtsldtrb0(xD,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5599) ).
tff(17,plain,
( ! [W0: $i] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xD) )
& aSubsetOf0(xP,xD) ),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
aSubsetOf0(xP,xD),
inference(and_elim,[status(thm)],[17]) ).
tff(19,plain,
aSubsetOf0(xP,xD),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(modus_ponens,[status(thm)],[19,14]) ).
tff(21,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(tautology,[status(thm)],[]) ).
tff(22,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
( ( sbrdtbr0(xP) = xk )
<=> ( sbrdtbr0(xP) = xk ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5217) ).
tff(25,plain,
sbrdtbr0(xP) = xk,
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = sbrdtbr0(xP),
inference(monotonicity,[status(thm)],[12]) ).
tff(27,plain,
sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk,
inference(transitivity,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(29,plain,
~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(unit_resolution,[status(thm)],[28,27,22]) ).
tff(30,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( aElementOf0(xn,szNzAzT0)
<=> aElementOf0(xn,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& ( sdtlpdtrp0(xe,xn) = xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
tff(34,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0) ),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
aElementOf0(xn,szNzAzT0),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
aElementOf0(xn,szNzAzT0),
inference(modus_ponens,[status(thm)],[35,32]) ).
tff(37,plain,
^ [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)))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [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)))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [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)))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [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)))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
^ [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)))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [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)))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [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)))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
^ [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)))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [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)))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
^ [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)) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [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)) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [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)))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [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)))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [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)))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,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) ).
tff(52,plain,
! [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)))) ) ) ) ) ),
inference(and_elim,[status(thm)],[51]) ).
tff(53,plain,
! [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)))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[52,50]) ).
tff(54,plain,
! [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)))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[53,48]) ).
tff(55,plain,
! [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)))) ) ) ) ) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [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)) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[55,47]) ).
tff(57,plain,
! [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)))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[56,45]) ).
tff(58,plain,
! [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)))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[57,43]) ).
tff(59,plain,
! [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)))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[58,38]) ).
tff(60,plain,
( ( ~ ! [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(xn,szNzAzT0)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != xk )
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ( sbrdtbr0(W1) != xk )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
<=> ( ~ ! [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(xn,szNzAzT0)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != xk )
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ( sbrdtbr0(W1) != xk )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ( ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( sbrdtbr0(W1) != xk )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
<=> ( ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != xk )
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ( sbrdtbr0(W1) != xk )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ( ~ ! [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(xn,szNzAzT0)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( sbrdtbr0(W1) != xk )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
<=> ( ~ ! [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(xn,szNzAzT0)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != xk )
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ( sbrdtbr0(W1) != xk )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ( ~ ! [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(xn,szNzAzT0)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( sbrdtbr0(W1) != xk )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
<=> ( ~ ! [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(xn,szNzAzT0)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != xk )
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ( sbrdtbr0(W1) != xk )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ~ ! [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(xn,szNzAzT0)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( sbrdtbr0(W1) != xk )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [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(xn,szNzAzT0)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != xk )
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ( sbrdtbr0(W1) != xk )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != xk )
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ( sbrdtbr0(W1) != xk )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(unit_resolution,[status(thm)],[65,59,36]) ).
tff(67,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
~ ( ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != xk )
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ( sbrdtbr0(W1) != xk )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(68,plain,
! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
<=> aSet0(xP) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(70,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != szmzizndt0(xQ) ) ) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(73,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(and_elim,[status(thm)],[72]) ).
tff(74,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[73]) ).
tff(75,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[74,71]) ).
tff(76,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[75,70]) ).
tff(77,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) )
| aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) )
| aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
<=> ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) )
| aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) )
| aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) )
| aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ( ( sbrdtbr0(W1) != xk )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) )
| aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) )
| aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(unit_resolution,[status(thm)],[82,76,68,31]) ).
tff(84,plain,
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) )
| aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(85,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))) = sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(monotonicity,[status(thm)],[12]) ).
tff(88,plain,
sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))) = sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(transitivity,[status(thm)],[89,86,6]) ).
tff(91,plain,
( ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) )
<=> ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0) )
=> ( ( aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [W0: $i] :
( aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xP)
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) )
=> ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ) )
<=> ~ ( ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) )
| ~ ( aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [W0: $i] :
( aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xP)
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) )
| ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
~ ( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0) )
=> ( ( aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [W0: $i] :
( aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xP)
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) )
=> ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(94,plain,
~ ( ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) )
| ~ ( aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [W0: $i] :
( aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xP)
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) )
| ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(or_elim,[status(thm)],[94]) ).
tff(96,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
$false,
inference(unit_resolution,[status(thm)],[96,90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM630+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:38:46 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.70/0.88 % SZS status Theorem
% 0.70/0.88 % SZS output start Proof
% See solution above
% 0.79/0.97 % E exiting
%------------------------------------------------------------------------------