TSTP Solution File: NUM628+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM628+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Sun Sep 18 13:11:01 EDT 2022
% Result : Theorem 4.27s 2.94s
% Output : Proof 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 176
% Syntax : Number of formulae : 401 ( 86 unt; 36 typ; 0 def)
% Number of atoms : 12807 (1649 equ)
% Maximal formula atoms : 180 ( 35 avg)
% Number of connectives : 20971 (8880 ~;7552 |;3106 &)
% (1035 <=>; 398 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 11 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 351 ( 351 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 21 >; 11 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 29 ( 29 usr; 15 con; 0-2 aty)
% Number of variables : 2912 (2853 !; 0 ?;2912 :)
% Comments :
%------------------------------------------------------------------------------
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xN_type,type,
xN: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(tptp_fun_W3_33_type,type,
tptp_fun_W3_33: ( $i * $i ) > $i ).
tff(xP_type,type,
xP: $i ).
tff(tptp_fun_W2_31_type,type,
tptp_fun_W2_31: ( $i * $i ) > $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(xp_type,type,
xp: $i ).
tff(xe_type,type,
xe: $i ).
tff(tptp_fun_W1_29_type,type,
tptp_fun_W1_29: $i > $i ).
tff(xS_type,type,
xS: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(xk_type,type,
xk: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xc_type,type,
xc: $i ).
tff(xC_type,type,
xC: $i ).
tff(xO_type,type,
xO: $i ).
tff(xK_type,type,
xK: $i ).
tff(tptp_fun_W2_39_type,type,
tptp_fun_W2_39: ( $i * $i ) > $i ).
tff(1,plain,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
<=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
<=> aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
& aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
tff(4,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(tautology,[status(thm)],]) ).
tff(8,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
( aElementOf0(xn,szDzozmdt0(xd))
<=> aElementOf0(xn,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( aElementOf0(xn,szDzozmdt0(xd))
<=> aElementOf0(xn,szDzozmdt0(xd)) ),
inference(rewrite,[status(thm)],]) ).
tff(11,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/sandbox/benchmark/theBenchmark.p',m__5309) ).
tff(12,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) ) ),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aElementOf0(xn,szDzozmdt0(xd)),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
aElementOf0(xn,szDzozmdt0(xd)),
inference(modus_ponens,[status(thm)],[15,10]) ).
tff(17,plain,
aElementOf0(xn,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )),
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) )),
rewrite(
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) )),
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) )),
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )),
rewrite(
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )),
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
tff(33,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[34,28]) ).
tff(36,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[36,26]) ).
tff(38,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[37,24]) ).
tff(39,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(modus_ponens,[status(thm)],[38,19]) ).
tff(40,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN)) ) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN)) ) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN)) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ ( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN)) ),
inference(unit_resolution,[status(thm)],[45,39,17]) ).
tff(47,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| isCountable0(sdtlpdtrp0(xN,xn)) ),
inference(tautology,[status(thm)],]) ).
tff(48,plain,
isCountable0(sdtlpdtrp0(xN,xn)),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| aElementOf0(W1,szDzozmdt0(xN)) )
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(50,plain,
aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[49,46]) ).
tff(51,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(52,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) ),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ~ ( ~ 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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
<=> ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
rewrite(
( ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
<=> ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )),
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ) )),
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )),
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
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)) ) ) ) )),
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
rewrite(
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
rewrite(
( ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
<=> ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) )),
( ( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )),
rewrite(
( ( ~ ( ~ 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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ) )),
( ( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [W0: $i] :
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
rewrite(
( ( ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ( ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )),
rewrite(
( ( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [W0: $i] :
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ! [W0: $i] :
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ~ aElementOf0(W0,szNzAzT0)
<=> ~ aElementOf0(W0,szDzozmdt0(xN)) )),
rewrite(
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
rewrite(
( ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
& isCountable0(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] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
& isCountable0(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] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(65,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] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,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] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(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] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) )),
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) ) )),
( ( 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)))) )
<=> ( 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(
( ( 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)))) )
<=> ( 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)))) ) )),
( ( 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)))) )
<=> ( 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)) ) ) ) )),
( ( 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)) ) ) ) )
<=> ( 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(
( ( 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)) ) ) ) )
<=> ( 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)) ) ) ) ) )),
( ( 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)) ) ) ) )
<=> ( 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)) ) ) ) ) )),
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
rewrite(
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
rewrite(
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
rewrite(
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
rewrite(
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
( ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
<=> ( ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )),
rewrite(
( ( ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
<=> ( ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )),
( ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
<=> ( ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ( ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) )),
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
( aFunction0(xN)
& ( szDzozmdt0(xN) = szNzAzT0 )
& ( sdtlpdtrp0(xN,sz00) = xS )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
tff(70,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ),
inference(and_elim,[status(thm)],[69]) ).
tff(71,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] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[70,68]) ).
tff(72,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] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[71,66]) ).
tff(73,plain,
! [W0: $i] :
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
! [W0: $i] :
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [W0: $i] :
( ( 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)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ),
inference(modus_ponens,[status(thm)],[74,63]) ).
tff(76,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ),
inference(modus_ponens,[status(thm)],[75,61]) ).
tff(77,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,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)) ) ) )
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) ) ),
inference(modus_ponens,[status(thm)],[76,59]) ).
tff(78,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ),
inference(modus_ponens,[status(thm)],[77,54]) ).
tff(79,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
<=> ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
<=> ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
<=> ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
<=> ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(monotonicity,[status(thm)],[82,81]) ).
tff(84,plain,
( ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
<=> ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(transitivity,[status(thm)],[83,80]) ).
tff(85,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(transitivity,[status(thm)],[85,79]) ).
tff(87,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
| aElementOf0(tptp_fun_W1_29(W0),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
| aElementOf0(tptp_fun_W1_29(xn),szDzozmdt0(xN)) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(unit_resolution,[status(thm)],[88,78,17]) ).
tff(90,plain,
~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(unit_resolution,[status(thm)],[89,52,48]) ).
tff(91,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(tautology,[status(thm)],]) ).
tff(92,plain,
aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(tautology,[status(thm)],]) ).
tff(94,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(unit_resolution,[status(thm)],[93,92]) ).
tff(95,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
tff(105,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[106,100]) ).
tff(108,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[108,98]) ).
tff(110,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[109,96]) ).
tff(111,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ),
inference(unit_resolution,[status(thm)],[113,110,17]) ).
tff(115,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 )
| aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(116,plain,
aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ) ),
inference(transitivity,[status(thm)],[119,117]) ).
tff(121,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szDzozmdt0(xN))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(unit_resolution,[status(thm)],[122,39]) ).
tff(124,plain,
~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(unit_resolution,[status(thm)],[123,116]) ).
tff(125,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szDzozmdt0(xN))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(W1,szDzozmdt0(xN)) )
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(tautology,[status(thm)],]) ).
tff(126,plain,
isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(unit_resolution,[status(thm)],[125,124]) ).
tff(127,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(130,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[132,130]) ).
tff(134,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,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) )
& 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)) ) ) )
& ( ~ 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)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ( ~ aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ aSubsetOf0(W2,W1)
& ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(135,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,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) )
& 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)) ) ) )
& ( ~ 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)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ( ~ aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ aSubsetOf0(W2,W1)
& ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,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) )
& 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)) ) ) )
& ( ~ 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)))) ) ) )
| ~ isCountable0(W1)
| ! [W2: $i] :
( ~ aSet0(W2)
| ( ~ aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ aSubsetOf0(W2,W1)
& ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) )
| ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,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) )
& 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)) ) ) )
& ( ~ 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)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ( ~ aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ aSubsetOf0(W2,W1)
& ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(137,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,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) )
& 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)) ) ) )
& ( ~ 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)))) ) ) )
| ~ isCountable0(W1)
| ! [W2: $i] :
( ~ aSet0(W2)
| ( ~ aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ aSubsetOf0(W2,W1)
& ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) )
| ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,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) )
& 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)) ) ) )
& ( ~ 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)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ( ~ aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ aSubsetOf0(W2,W1)
& ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(139,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) ) ) ) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( ( 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)) ) ) ) )
=> ( ( 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)))) ) ) )
& isCountable0(W1) )
<=> ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) ) )),
quant_intro(
proof_bind(
^ [W2: $i] :
trans(
monotonicity(
rewrite(
( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
<=> ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) ) )),
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) ) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) ) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
rewrite(
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
quant_intro(
proof_bind(
^ [W3: $i] :
rewrite(
( ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ))),
( ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
rewrite(
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
quant_intro(
proof_bind(
^ [W3: $i] :
rewrite(
( ( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ))),
( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
rewrite(
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
rewrite(
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )),
rewrite(
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )),
( ( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )
<=> ( ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )),
rewrite(
( ( ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )
<=> ( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )),
( ( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )
<=> ( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ))),
( ! [W2: $i] :
( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )
<=> ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,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) ) )
=> ( ( 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)) ) ) ) )
=> ( ( 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)))) ) ) )
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
<=> ( ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
=> ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )),
rewrite(
( ( ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
=> ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
<=> ( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,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) ) )
=> ( ( 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)) ) ) ) )
=> ( ( 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)))) ) ) )
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
<=> ( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ))),
( ! [W1: $i] :
( ( ( ( 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)) ) ) ) )
=> ( ( 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)))) ) ) )
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
<=> ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( ( ( 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)) ) ) ) )
=> ( ( 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)))) ) ) )
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) )),
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( ( ( 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)) ) ) ) )
=> ( ( 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)))) ) ) )
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(142,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( ( ( 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)) ) ) ) )
=> ( ( 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)))) ) ) )
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( ( ( 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)) ) ) ) )
=> ( ( 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)))) ) ) )
& isCountable0(W1) )
=> ! [W2: $i] :
( ( aSet0(W2)
& ( ( ( ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
| aSubsetOf0(W2,W1) )
& ( sbrdtbr0(W2) = xk ) )
| aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4331) ).
tff(144,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = xk ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
inference(modus_ponens,[status(thm)],[144,140]) ).
tff(146,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( ( aSubsetOf0(W1,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) ) )
| ~ ( 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)) ) ) ) )
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& isCountable0(W1) )
| ! [W2: $i] :
( ~ ( aSet0(W2)
& ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ( ( aSubsetOf0(W2,W1)
| ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) ) )
& ( sbrdtbr0(W2) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) ) ) ) ),
inference(modus_ponens,[status(thm)],[145,139]) ).
tff(147,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,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) )
& 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)) ) ) )
& ( ~ 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)))) ) ) )
| ~ isCountable0(W1)
| ! [W2: $i] :
( ~ aSet0(W2)
| ( ~ aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ aSubsetOf0(W2,W1)
& ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) )
| ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) ) ) ) ),
inference(skolemize,[status(sab)],[146]) ).
tff(148,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,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) )
& 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)) ) ) )
& ( ~ 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)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ( ~ aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ aSubsetOf0(W2,W1)
& ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[147,137]) ).
tff(149,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[148,135]) ).
tff(150,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,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) )
| ~ ( ~ 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)))) ) )
| ~ 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] :
( ~ aSet0(W2)
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[149,133]) ).
tff(151,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[150,128]) ).
tff(152,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,plain,
( ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
<=> ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(154,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[154,152]) ).
tff(156,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),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)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(unit_resolution,[status(thm)],[157,151,17]) ).
tff(159,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
( ( ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
<=> ( ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( aElementOf0(W2,slbdtsldtrb0(W1,sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,W1)
| ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
| aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(unit_resolution,[status(thm)],[164,158,126,94]) ).
tff(166,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(rewrite,[status(thm)],]) ).
tff(167,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],]) ).
tff(168,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/sandbox/benchmark/theBenchmark.p',m__5164) ).
tff(169,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)],[168]) ).
tff(170,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(and_elim,[status(thm)],[169]) ).
tff(171,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[170]) ).
tff(172,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[171,167]) ).
tff(173,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[172,166]) ).
tff(174,plain,
( ( ~ ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
<=> ( ~ ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(175,plain,
( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
<=> ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,plain,
( ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
<=> ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,plain,
( ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
<=> ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
<=> ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(monotonicity,[status(thm)],[177,176]) ).
tff(179,plain,
( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
<=> ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(transitivity,[status(thm)],[178,175]) ).
tff(180,plain,
( ( ~ ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
<=> ( ~ ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ( ~ ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
<=> ( ~ ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(transitivity,[status(thm)],[180,174]) ).
tff(182,plain,
( ~ ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
( ~ ! [W2: $i] :
( ~ aSet0(W2)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W2) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
| aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(unit_resolution,[status(thm)],[183,173,165,8]) ).
tff(185,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
| ~ ! [W3: $i] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
| ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(W3,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(186,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(unit_resolution,[status(thm)],[185,184]) ).
tff(187,plain,
( ( szDzizrdt0(xd) = sdtlpdtrp0(xc,xQ) )
<=> ( sdtlpdtrp0(xc,xQ) = szDzizrdt0(xd) ) ),
inference(commutativity,[status(thm)],]) ).
tff(188,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(189,axiom,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK )
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
tff(190,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK ) ),
inference(and_elim,[status(thm)],[189]) ).
tff(191,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO) ),
inference(and_elim,[status(thm)],[190]) ).
tff(192,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) ) ),
inference(and_elim,[status(thm)],[191]) ).
tff(193,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[192]) ).
tff(194,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[193,188]) ).
tff(195,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(196,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[195]) ).
tff(197,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(198,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[197]) ).
tff(199,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(transitivity,[status(thm)],[198,196]) ).
tff(200,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(201,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) )
<=> ( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) )
<=> ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
rewrite(
( ( aSet0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(202,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
tff(204,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[204,200]) ).
tff(206,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(skolemize,[status(sab)],[205]) ).
tff(207,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[206,199]) ).
tff(208,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(209,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(210,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ),
inference(unit_resolution,[status(thm)],[210,207,194]) ).
tff(212,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(szmzizndt0(xQ),xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(xp,xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(214,axiom,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& ( xp = szmzizndt0(xQ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
tff(215,plain,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) ) ),
inference(and_elim,[status(thm)],[214]) ).
tff(216,plain,
aElementOf0(xp,xQ),
inference(and_elim,[status(thm)],[215]) ).
tff(217,plain,
aElementOf0(xp,xQ),
inference(modus_ponens,[status(thm)],[216,213]) ).
tff(218,plain,
aElementOf0(szmzizndt0(xQ),xQ),
inference(modus_ponens,[status(thm)],[217,212]) ).
tff(219,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(220,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) ),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ,
inference(unit_resolution,[status(thm)],[221,218,211]) ).
tff(223,plain,
( ( sdtlpdtrp0(xe,xn) = xp )
<=> ( sdtlpdtrp0(xe,xn) = szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(224,plain,
( ( sdtlpdtrp0(xe,xn) = xp )
<=> ( sdtlpdtrp0(xe,xn) = xp ) ),
inference(rewrite,[status(thm)],]) ).
tff(225,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(and_elim,[status(thm)],[11]) ).
tff(226,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(modus_ponens,[status(thm)],[225,224]) ).
tff(227,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[226,223]) ).
tff(228,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(229,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[228]) ).
tff(230,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(231,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[230]) ).
tff(232,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(233,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[232]) ).
tff(234,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(transitivity,[status(thm)],[233,231]) ).
tff(235,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(236,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[235]) ).
tff(237,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(238,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[237]) ).
tff(239,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(240,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )),
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
rewrite(
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(241,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[240]) ).
tff(242,axiom,
( aFunction0(xe)
& ( szDzozmdt0(xe) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
tff(243,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(and_elim,[status(thm)],[242]) ).
tff(244,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[243,241]) ).
tff(245,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[244,239]) ).
tff(246,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[245,238]) ).
tff(247,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(skolemize,[status(sab)],[246]) ).
tff(248,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[247,236]) ).
tff(249,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[248,234]) ).
tff(250,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[249,229]) ).
tff(251,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(252,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(253,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) ),
inference(modus_ponens,[status(thm)],[252,251]) ).
tff(254,plain,
~ ( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ),
inference(unit_resolution,[status(thm)],[253,250,17]) ).
tff(255,plain,
( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ( sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ),
inference(tautology,[status(thm)],]) ).
tff(256,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(unit_resolution,[status(thm)],[255,254]) ).
tff(257,plain,
szmzizndt0(sdtlpdtrp0(xN,xn)) = sdtlpdtrp0(xe,xn),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
szmzizndt0(sdtlpdtrp0(xN,xn)) = szmzizndt0(xQ),
inference(transitivity,[status(thm)],[257,227]) ).
tff(259,plain,
sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))) = sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))) = xQ,
inference(transitivity,[status(thm)],[259,222]) ).
tff(261,plain,
sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(xc,xQ),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
( ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
<=> ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) ) ),
inference(rewrite,[status(thm)],]) ).
tff(263,plain,
sdtlpdtrp0(xd,xn) = szDzizrdt0(xd),
inference(and_elim,[status(thm)],[14]) ).
tff(264,plain,
sdtlpdtrp0(xd,xn) = szDzizrdt0(xd),
inference(modus_ponens,[status(thm)],[263,262]) ).
tff(265,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(tautology,[status(thm)],]) ).
tff(266,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(unit_resolution,[status(thm)],[265,6]) ).
tff(267,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(268,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[267]) ).
tff(269,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(270,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[269]) ).
tff(271,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[270,268]) ).
tff(272,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(273,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[272]) ).
tff(274,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(275,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[274]) ).
tff(276,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(277,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[276]) ).
tff(278,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(279,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
trans(
monotonicity(
rewrite(
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
<=> ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) ) )),
( ( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
<=> ( ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )),
rewrite(
( ( ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
<=> ( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )),
( ( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
<=> ( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ))),
( ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
<=> ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) )),
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(280,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[279]) ).
tff(281,axiom,
( aFunction0(xd)
& ( szDzozmdt0(xd) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
tff(282,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& ( ( ( ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ( sbrdtbr0(W1) = xk ) )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(and_elim,[status(thm)],[281]) ).
tff(283,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[282,280]) ).
tff(284,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[283,278]) ).
tff(285,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ ( aSet0(W1)
& ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
& ( sbrdtbr0(W1) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[284,277]) ).
tff(286,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(skolemize,[status(sab)],[285]) ).
tff(287,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[286,275]) ).
tff(288,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[287,273]) ).
tff(289,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[288,271]) ).
tff(290,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(291,plain,
( ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
<=> ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(292,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[291]) ).
tff(293,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[292,290]) ).
tff(294,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(295,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ! [W1: $i] :
( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
| ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
| aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[294,293]) ).
tff(296,plain,
! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(unit_resolution,[status(thm)],[295,289,17]) ).
tff(297,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(298,plain,
( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
<=> ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(299,plain,
( ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
<=> ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(300,plain,
( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
<=> ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
<=> ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(transitivity,[status(thm)],[300,298]) ).
tff(302,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(monotonicity,[status(thm)],[301]) ).
tff(303,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(transitivity,[status(thm)],[302,297]) ).
tff(304,plain,
( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(305,plain,
( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
| aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(modus_ponens,[status(thm)],[304,303]) ).
tff(306,plain,
sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),
inference(unit_resolution,[status(thm)],[305,173,296,266]) ).
tff(307,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xd,xn),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = szDzizrdt0(xd),
inference(transitivity,[status(thm)],[307,264]) ).
tff(309,plain,
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
<=> ( szDzizrdt0(xd) = sdtlpdtrp0(xc,xQ) ) ),
inference(monotonicity,[status(thm)],[308,261]) ).
tff(310,plain,
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
<=> ( sdtlpdtrp0(xc,xQ) = szDzizrdt0(xd) ) ),
inference(transitivity,[status(thm)],[309,187]) ).
tff(311,plain,
( ( sdtlpdtrp0(xc,xQ) = szDzizrdt0(xd) )
<=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
( ( sdtlpdtrp0(xc,xQ) != szDzizrdt0(xd) )
<=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
inference(monotonicity,[status(thm)],[311]) ).
tff(313,plain,
( ( sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn) )
<=> ( sdtlpdtrp0(xc,xQ) != szDzizrdt0(xd) ) ),
inference(rewrite,[status(thm)],]) ).
tff(314,plain,
( ( sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn) )
<=> ( sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn) ) ),
inference(rewrite,[status(thm)],]) ).
tff(315,axiom,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(316,plain,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(modus_ponens,[status(thm)],[315,314]) ).
tff(317,plain,
sdtlpdtrp0(xc,xQ) != szDzizrdt0(xd),
inference(modus_ponens,[status(thm)],[316,313]) ).
tff(318,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(modus_ponens,[status(thm)],[317,312]) ).
tff(319,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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = 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(320,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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[319,318]) ).
tff(321,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(322,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[321]) ).
tff(323,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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(324,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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)],[323]) ).
tff(325,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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(326,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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)],[325]) ).
tff(327,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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(transitivity,[status(thm)],[326,324]) ).
tff(328,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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(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)) ) ) )
& ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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(329,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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(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)) ) ) )
& ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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)],[328]) ).
tff(330,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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)) ) ) )
& ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( 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,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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(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)) ) ) )
& ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(331,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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)) ) ) )
& ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( 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,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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(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)) ) ) )
& ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[330]) ).
tff(332,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)
& ! [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,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( ~ ( ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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)) ) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ( ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
| ( 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(333,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,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( ~ ( ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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)) ) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ( ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
| ( 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)],[332]) ).
tff(334,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(335,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(336,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)],[335]) ).
tff(337,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/sandbox/benchmark/theBenchmark.p',m__4151) ).
tff(338,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)],[337]) ).
tff(339,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)],[338,336]) ).
tff(340,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)],[339,334]) ).
tff(341,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( ~ ( ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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)) ) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ( ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
| ( 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)],[340,333]) ).
tff(342,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
& ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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)) ) ) )
& ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( 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)],[341]) ).
tff(343,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( 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) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
& ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
& ! [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(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)) ) ) )
& ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
& ( ( ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[342,331]) ).
tff(344,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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)],[343,329]) ).
tff(345,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))
| ~ ! [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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ 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)) ) ) )
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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)],[344,327]) ).
tff(346,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[345,322]) ).
tff(347,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| 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)))) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| 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)))) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(348,plain,
( ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
<=> ( ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| 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)))) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(349,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| 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)))) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[348]) ).
tff(350,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| 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)))) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[349,347]) ).
tff(351,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(352,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ 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))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
| ~ ! [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] :
( ~ aSet0(W1)
| ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [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))
| ( 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
| ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) ) ) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| 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)))) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[351,350]) ).
tff(353,plain,
~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| 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)))) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[352,346,17]) ).
tff(354,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) )
| ~ aFunction0(sdtlpdtrp0(xC,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
| ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| ( 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) )
| ~ ! [W1: $i] :
~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
| ~ ( ~ aSet0(W1)
| ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ 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) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(355,plain,
! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[354,353]) ).
tff(356,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| 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(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| 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(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(357,plain,
( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = 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] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| 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(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(358,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| 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(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[357]) ).
tff(359,plain,
( ( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = 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))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| 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(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[358,356]) ).
tff(360,plain,
( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(361,plain,
( ~ ! [W1: $i] :
( ~ aSet0(W1)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ ( ( sbrdtbr0(W1) != sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( 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)))) ) ) )
| ~ ( ~ 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] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,W1)
| ( W2 = 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] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| 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(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[360,359]) ).
tff(362,plain,
( ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| 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(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(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] :
( aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[361,173,355]) ).
tff(363,plain,
~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| 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(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))))) ),
inference(unit_resolution,[status(thm)],[362,320]) ).
tff(364,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
| ~ ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
| 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(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(tautology,[status(thm)],]) ).
tff(365,plain,
$false,
inference(unit_resolution,[status(thm)],[364,363,186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM628+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 12:30:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 4.27/2.94 % SZS status Theorem
% 4.27/2.94 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------