%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM592+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 05:21:30 AM UTC 2025
% Result : Theorem 1.31s 1.50s
% Output : Proof 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 36
% Syntax : Number of formulae : 104 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 2546 ( 433 equ)
% Maximal formula atoms : 84 ( 24 avg)
% Number of connectives : 4197 (1919 ~;1648 |; 450 &)
% ( 149 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 164 ( 164 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 19 usr; 1 prp; 0-6 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 467 ( 433 !; 20 ?; 467 :)
% Comments :
%------------------------------------------------------------------------------
tff(xu_type,type,
xu: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(tptp_fun_W2_38_type,type,
tptp_fun_W2_38: ( $i * $i ) > $i ).
tff(xX_type,type,
xX: $i ).
tff(xi_type,type,
xi: $i ).
tff(xC_type,type,
xC: $i ).
tff(xd_type,type,
xd: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W1_36_type,type,
tptp_fun_W1_36: $i > $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(tptp_fun_W2_37_type,type,
tptp_fun_W2_37: $i > $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xY_type,type,
xY: $i ).
tff(xT_type,type,
xT: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(1,plain,
( ( xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) )
<=> ( xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(xY)
& ! [W0: $i] :
( aElementOf0(W0,xY)
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& ( xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) )
& ( xd = sdtlpdtrp0(xC,xi) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4448_02) ).
tff(3,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(xY)
& ! [W0: $i] :
( aElementOf0(W0,xY)
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& ( xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) = xY,
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> aSubsetOf0(xX,xY) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( aSubsetOf0(xX,xY)
<=> aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( aSubsetOf0(xX,xY)
<=> aSubsetOf0(xX,xY) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [W0: $i] :
( aElementOf0(W0,xX)
=> aElementOf0(W0,xY) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [W0: $i] :
( ( aSet0(W0)
& ( ( ( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xX) )
| aSubsetOf0(W0,xX) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = xu ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4545) ).
tff(11,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [W0: $i] :
( aElementOf0(W0,xX)
=> aElementOf0(W0,xY) )
& aSubsetOf0(xX,xY)
& isCountable0(xX) ),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [W0: $i] :
( aElementOf0(W0,xX)
=> aElementOf0(W0,xY) )
& aSubsetOf0(xX,xY) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
aSubsetOf0(xX,xY),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
aSubsetOf0(xX,xY),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(modus_ponens,[status(thm)],[14,8]) ).
tff(16,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(32,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[34,29]) ).
tff(36,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aElementOf0(W0,xT),~ aElementOf0(W0,xT))),
nnf_neg(proof_bind(^ [W1: $i] :
nnf_neg(nnf_neg(refl($oeq(~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))))),
nnf_neg(refl($oeq(~ aSet0(W1),~ aSet0(W1))),
sk($oeq(~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ))),
$oeq(~ ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ))),
nnf_neg(monotonicity(refl($oeq(aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))))),
nnf_pos(proof_bind(^ [W2: $i] :
refl($oeq(( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ),
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )))),
$oeq(! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ),
! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ))),
$oeq(( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ),
( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ))),
$oeq(~ ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ),
( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ))),
nnf_neg(monotonicity(refl($oeq(aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)))),
nnf_pos(proof_bind(^ [W2: $i] :
refl($oeq(( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ),
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )))),
$oeq(! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ),
! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ))),
$oeq(( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ),
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ))),
$oeq(~ ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ),
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ))),
$oeq(~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) ),
( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ))),refl($oeq(~ isCountable0(W1),~ isCountable0(W1))),
trans(sk($oeq(~ ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ),
~ ( ~ ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 ) ))),
nnf_neg(nnf_neg(monotonicity(refl($oeq(aSet0(tptp_fun_W2_38(W1,W0)),aSet0(tptp_fun_W2_38(W1,W0)))),
nnf_pos(proof_bind(^ [W3: $i] :
refl($oeq(( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ),
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )))),
$oeq(! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ),
! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ))),
refl($oeq(aSubsetOf0(tptp_fun_W2_38(W1,W0),W1),aSubsetOf0(tptp_fun_W2_38(W1,W0),W1))),refl($oeq(sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk,sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk)),refl($oeq(aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)),aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)))),
$oeq(( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ),
( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ))),
$oeq(~ ~ ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ),
( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ))),refl($oeq(sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0,sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0)),
$oeq(~ ( ~ ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 ) ),
( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ))),
$oeq(~ ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ),
( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ))),
$oeq(~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ),
( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) )))),
$oeq(~ ? [W1: $i] :
( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ),
! [W1: $i] :
( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) ))),
$oeq(~ ( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) ) )
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& ! [W3: $i] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& ( sbrdtbr0(W2) = xk )
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) ) ))),
inference(bind,[status(th)],[]) ).
tff(37,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) ) ),
inference(nnf-neg,[status(sab)],[35,36]) ).
tff(38,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2: $i] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ( aSet0(tptp_fun_W2_38(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) = xk )
& aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) != W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[37,28]) ).
tff(39,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ),
inference(modus_ponens,[status(thm)],[38,26]) ).
tff(40,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) ) )
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ),
inference(modus_ponens,[status(thm)],[39,24]) ).
tff(41,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ),
inference(modus_ponens,[status(thm)],[40,19]) ).
tff(42,plain,
( aElementOf0(xu,xT)
<=> aElementOf0(xu,xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [W0: $i] :
( aElementOf0(W0,xX)
=> aElementOf0(W0,xY) ) ),
inference(and_elim,[status(thm)],[12]) ).
tff(44,plain,
( aElementOf0(xu,xT)
& aSet0(xX) ),
inference(and_elim,[status(thm)],[43]) ).
tff(45,plain,
aElementOf0(xu,xT),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
aElementOf0(xu,xT),
inference(modus_ponens,[status(thm)],[45,42]) ).
tff(47,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
<=> ( ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ) ),
inference(transitivity,[status(thm)],[49,47]) ).
tff(51,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_38(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_38(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_38(W1,W0)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(W1,W0),slbdtsldtrb0(W1,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,W0))
| aElementOf0(W3,W1) ) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ),
inference(unit_resolution,[status(thm)],[52,46,41]) ).
tff(54,plain,
( isCountable0(xX)
<=> isCountable0(xX) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
isCountable0(xX),
inference(and_elim,[status(thm)],[11]) ).
tff(56,plain,
isCountable0(xX),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
| ~ isCountable0(xX)
| ~ ( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
| ~ isCountable0(xX)
| ~ ( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ isCountable0(xX)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu)) )
| ~ ( aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
<=> ( ~ isCountable0(xX)
| ~ ( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
| ~ isCountable0(xX)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu)) )
| ~ ( aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
| ~ isCountable0(xX)
| ~ ( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
| ~ isCountable0(xX)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu)) )
| ~ ( aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
| ~ isCountable0(xX)
| ~ ( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
| ~ isCountable0(xX)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu)) )
| ~ ( aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(W1,xu))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_38(W1,xu),slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(tptp_fun_W2_38(W1,xu)) != xk )
| ~ aSubsetOf0(tptp_fun_W2_38(W1,xu),W1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(W1,xu)) )
| ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(W1),W1)
| aElementOf0(tptp_fun_W2_37(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
| ~ isCountable0(xX)
| ~ ( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) ) )
| ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
| ~ ! [W2: $i] :
~ ( ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi))
| ( W2 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ aSet0(xX)
| ~ ( ~ aElementOf0(tptp_fun_W2_37(xX),xX)
| aElementOf0(tptp_fun_W2_37(xX),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ ( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) ) ),
inference(unit_resolution,[status(thm)],[62,56,53,17]) ).
tff(64,plain,
( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) )
| aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk)) ),
inference(tautology,[status(thm)],[]) ).
tff(65,plain,
aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk)),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk)) ),
inference(tautology,[status(thm)],[]) ).
tff(67,plain,
( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) )
| aSet0(tptp_fun_W2_38(xX,xu)) ),
inference(tautology,[status(thm)],[]) ).
tff(69,plain,
aSet0(tptp_fun_W2_38(xX,xu)),
inference(unit_resolution,[status(thm)],[68,63]) ).
tff(70,plain,
^ [W0: $i] :
refl(( ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
<=> ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
<=> ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) )
<=> ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) )),
( ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )),
rewrite(( ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )),
( ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
<=> ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )),
( ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) )
<=> ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) )),
rewrite(( ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
<=> ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) )),
( ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) )
<=> ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) )
<=> ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) )
| ( sbrdtbr0(W0) != xk ) ) ) )
<=> ( ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) ) )),
( ( ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) )
| ( sbrdtbr0(W0) != xk ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ( ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) ) )),
rewrite(( ( ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) ) )),
( ( ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) )
| ( sbrdtbr0(W0) != xk ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) )
| ( sbrdtbr0(W0) != xk ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( ( aSubsetOf0(W0,xX)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xX) ) )
& ( sbrdtbr0(W0) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( ( aSubsetOf0(W0,xX)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xX) ) )
& ( sbrdtbr0(W0) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aSet0(W0)
& ( ( ( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xX) )
| aSubsetOf0(W0,xX) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )
<=> ( aSet0(W0)
& ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( ( aSubsetOf0(W0,xX)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xX) ) )
& ( sbrdtbr0(W0) = xk ) ) ) ) )),
( ( ( aSet0(W0)
& ( ( ( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xX) )
| aSubsetOf0(W0,xX) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ( ( aSet0(W0)
& ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( ( aSubsetOf0(W0,xX)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xX) ) )
& ( sbrdtbr0(W0) = xk ) ) ) )
=> ( sdtlpdtrp0(xd,W0) = xu ) ) )),
rewrite(( ( ( aSet0(W0)
& ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( ( aSubsetOf0(W0,xX)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xX) ) )
& ( sbrdtbr0(W0) = xk ) ) ) )
=> ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ( ~ ( aSet0(W0)
& ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( ( aSubsetOf0(W0,xX)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xX) ) )
& ( sbrdtbr0(W0) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) ) )),
( ( ( aSet0(W0)
& ( ( ( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xX) )
| aSubsetOf0(W0,xX) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ( ~ ( aSet0(W0)
& ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( ( aSubsetOf0(W0,xX)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xX) ) )
& ( sbrdtbr0(W0) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& ( ( ( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xX) )
| aSubsetOf0(W0,xX) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( ( aSubsetOf0(W0,xX)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xX) ) )
& ( sbrdtbr0(W0) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
! [W0: $i] :
( ( aSet0(W0)
& ( ( ( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xX) )
| aSubsetOf0(W0,xX) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )
=> ( sdtlpdtrp0(xd,W0) = xu ) ),
inference(and_elim,[status(thm)],[10]) ).
tff(80,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( ( aSubsetOf0(W0,xX)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xX) ) )
& ( sbrdtbr0(W0) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( ( aSubsetOf0(W0,xX)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xX) ) )
& ( sbrdtbr0(W0) = xk ) ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) )
| ( sbrdtbr0(W0) != xk ) ) )
| ( sdtlpdtrp0(xd,W0) = xu ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xX)
& ~ ( ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ),
inference(modus_ponens,[status(thm)],[83,73]) ).
tff(85,plain,
! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) ),
inference(modus_ponens,[status(thm)],[84,71]) ).
tff(86,plain,
( ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) )
<=> ( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) )
<=> ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) )
<=> ( ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) )
<=> ( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
| ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) ) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
| ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) ) ),
inference(transitivity,[status(thm)],[91,86]) ).
tff(93,plain,
( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
| ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xX)
| ~ aElementOf0(tptp_fun_W1_36(W0),W0)
| aElementOf0(tptp_fun_W1_36(W0),xX) ) ) ) )
| ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu )
| ~ ( aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ( ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ ( aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ~ aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),tptp_fun_W2_38(xX,xu))
| aElementOf0(tptp_fun_W1_36(tptp_fun_W2_38(xX,xu)),xX) ) ) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = xu,
inference(unit_resolution,[status(thm)],[94,85,69,67]) ).
tff(96,plain,
( ( xd = sdtlpdtrp0(xC,xi) )
<=> ( xd = sdtlpdtrp0(xC,xi) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
xd = sdtlpdtrp0(xC,xi),
inference(and_elim,[status(thm)],[2]) ).
tff(98,plain,
xd = sdtlpdtrp0(xC,xi),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)) = sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = sdtlpdtrp0(xd,tptp_fun_W2_38(xX,xu)),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu,
inference(transitivity,[status(thm)],[100,95]) ).
tff(102,plain,
( ~ aSet0(tptp_fun_W2_38(xX,xu))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) = xu )
| ~ aSubsetOf0(tptp_fun_W2_38(xX,xu),xX)
| ( sbrdtbr0(tptp_fun_W2_38(xX,xu)) != xk )
| ~ aElementOf0(tptp_fun_W2_38(xX,xu),slbdtsldtrb0(xX,xk))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_38(xX,xu))
| aElementOf0(W3,xX) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) != xu ) ),
inference(tautology,[status(thm)],[]) ).
tff(103,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_38(xX,xu)) != xu,
inference(unit_resolution,[status(thm)],[102,63]) ).
tff(104,plain,
$false,
inference(unit_resolution,[status(thm)],[103,101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM592+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 01:31:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.31/1.50 % SZS status Theorem
% 1.31/1.50 % SZS output start Proof
% See solution above
% 1.38/1.55 % E exiting
%------------------------------------------------------------------------------