%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM578+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:27 AM UTC 2025
% Result : Theorem 3.91s 4.10s
% Output : Proof 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 27
% Syntax : Number of formulae : 73 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 2568 ( 280 equ)
% Maximal formula atoms : 84 ( 35 avg)
% Number of connectives : 4597 (2164 ~;1813 |; 404 &)
% ( 189 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 12 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 62 ( 62 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 573 ( 562 !; 0 ?; 573 :)
% Comments :
%------------------------------------------------------------------------------
tff(xj_type,type,
xj: $i ).
tff(xi_type,type,
xi: $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xN_type,type,
xN: $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(tptp_fun_W2_30_type,type,
tptp_fun_W2_30: ( $i * $i ) > $i ).
tff(1,plain,
( ( xi != xj )
<=> ( xi != xj ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W0),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,sdtlpdtrp0(xN,W1))
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
& ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
=> ( ( xi != xj )
=> ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xj))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) ) ) ) )
<=> ~ ( ( xi = xj )
| ~ ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W0),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,sdtlpdtrp0(xN,W1))
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
& ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
=> ( ( xi != xj )
=> ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xj))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ ( ( xi = xj )
| ~ ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) ) ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
xi != xj,
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
xi != xj,
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
<=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) ) ),
inference(or_elim,[status(thm)],[4]) ).
tff(9,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)),
inference(and_elim,[status(thm)],[8]) ).
tff(10,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)),
inference(modus_ponens,[status(thm)],[9,7]) ).
tff(11,plain,
szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) )
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(13,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ),
inference(unit_resolution,[status(thm)],[12,11]) ).
tff(14,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )),
rewrite(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )),
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
rewrite(( ~ ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(trans(monotonicity(rewrite(( ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
rewrite(( ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ~ ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
( ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
rewrite(( ~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
<=> ~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
( ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ( 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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
( ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
( ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )),
rewrite(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )),
( ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
( ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
rewrite(( ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
( ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
( ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
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)) ) ) )
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
( ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
<=> ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )),
( ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) )
<=> ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) ) )),
rewrite(( ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) )
<=> ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )),
( ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) )
<=> ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) ),
inference(or_elim,[status(thm)],[4]) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ( 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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),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,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,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] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) ),
inference(modus_ponens,[status(thm)],[31,15]) ).
tff(33,plain,
( aElementOf0(xj,szNzAzT0)
<=> aElementOf0(xj,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3856) ).
tff(35,plain,
aElementOf0(xj,szNzAzT0),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
aElementOf0(xj,szNzAzT0),
inference(modus_ponens,[status(thm)],[35,33]) ).
tff(37,plain,
( aElementOf0(xi,szNzAzT0)
<=> aElementOf0(xi,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
aElementOf0(xi,szNzAzT0),
inference(and_elim,[status(thm)],[34]) ).
tff(39,plain,
aElementOf0(xi,szNzAzT0),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ) )
<=> ( ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) ) )
<=> ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) ) ) )
<=> ( ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) ) ) )
<=> ( ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ) ) ),
inference(transitivity,[status(thm)],[45,40]) ).
tff(47,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ( szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xj),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xi))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xj,xi),sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),tptp_fun_W2_30(xj,xi)) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ sdtlseqdt0(szszuzczcdt0(xi),xj),
inference(unit_resolution,[status(thm)],[48,39,36,32,13]) ).
tff(50,plain,
( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) )
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ),
inference(unit_resolution,[status(thm)],[50,10]) ).
tff(52,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ) )
<=> ( ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
<=> ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
<=> ( ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
<=> ( ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ) ) ),
inference(transitivity,[status(thm)],[57,52]) ).
tff(59,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(W1,W0),sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),tptp_fun_W2_30(W1,W0)) ) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xj)),sdtlpdtrp0(xN,xj))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xj)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xj)),W2) )
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj))))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xj),szmzizndt0(sdtlpdtrp0(xN,xj)))) )
| ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
| ~ ( ~ aElementOf0(tptp_fun_W2_30(xi,xj),sdtlpdtrp0(xN,xj))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),tptp_fun_W2_30(xi,xj)) ) ) ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
~ sdtlseqdt0(szszuzczcdt0(xj),xi),
inference(unit_resolution,[status(thm)],[60,39,36,32,51]) ).
tff(62,plain,
( ( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) )
<=> ( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ( xi != xj )
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) )
<=> ( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) )
<=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ( ( xi != xj )
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) )
<=> ( ( xi != xj )
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ( xi != xj )
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) )
<=> ( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,axiom,
( ( xi != xj )
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3856_02) ).
tff(68,plain,
( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ),
inference(modus_ponens,[status(thm)],[68,62]) ).
tff(70,plain,
( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ),
inference(modus_ponens,[status(thm)],[70,62]) ).
tff(72,plain,
( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ),
inference(modus_ponens,[status(thm)],[71,62]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,61,49,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM578+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 01:30:05 EDT 2025
% 0.13/0.33 % CPUTime :
% 3.91/4.10 % SZS status Theorem
% 3.91/4.10 % SZS output start Proof
% See solution above
% 4.01/4.18 % E exiting
%------------------------------------------------------------------------------