%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM563+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:21:24 AM UTC 2025
% Result : Theorem 14.89s 15.08s
% Output : Proof 14.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 134
% Syntax : Number of formulae : 358 ( 84 unt; 0 typ; 0 def)
% Number of atoms : 5090 (1026 equ)
% Maximal formula atoms : 52 ( 14 avg)
% Number of connectives : 9145 (4672 ~;3304 |; 580 &)
% ( 495 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 259 ( 259 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 : 19 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 1118 (1034 !; 29 ?;1118 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(xc_type,type,
xc: $i ).
tff(tptp_fun_W2_30_type,type,
tptp_fun_W2_30: ( $i * $i ) > $i ).
tff(xS_type,type,
xS: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xK_type,type,
xK: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_29_type,type,
tptp_fun_W2_29: $i > $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(xT_type,type,
xT: $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(tptp_fun_W1_0_type,type,
tptp_fun_W1_0: $i > $i ).
tff(tptp_fun_W1_19_type,type,
tptp_fun_W1_19: $i > $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(tptp_fun_W3_10_type,type,
tptp_fun_W3_10: ( $i * $i * $i ) > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(1,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
refl(( ~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) ) )),
trans(monotonicity(rewrite(( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
<=> ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) )),
( ( aElementOf0(W0,szDzozmdt0(xc))
| ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK ) )
<=> ( aElementOf0(W0,szDzozmdt0(xc))
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK ) ) )),
rewrite(( ( aElementOf0(W0,szDzozmdt0(xc))
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK ) )
<=> ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )),
( ( aElementOf0(W0,szDzozmdt0(xc))
| ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK ) )
<=> ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )),
( ( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( aElementOf0(W0,szDzozmdt0(xc))
| ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK ) ) )
<=> ( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
& ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) )),
rewrite(( ( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
& ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) )),
( ( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( aElementOf0(W0,szDzozmdt0(xc))
| ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( aElementOf0(W0,szDzozmdt0(xc))
| ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK )
| aElementOf0(W0,szDzozmdt0(xc)) ) )
<=> ( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( aElementOf0(W0,szDzozmdt0(xc))
| ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK )
| aElementOf0(W0,szDzozmdt0(xc)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( aElementOf0(W0,szDzozmdt0(xc))
| ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ~ ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = xK ) )
| aElementOf0(W0,szDzozmdt0(xc)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ~ ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = xK ) )
| aElementOf0(W0,szDzozmdt0(xc)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(( ( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
<=> ( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ~ ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = xK ) )
| aElementOf0(W0,szDzozmdt0(xc)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ~ ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = xK ) )
| aElementOf0(W0,szDzozmdt0(xc)) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [W0: $i] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(W0,xT) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
tff(16,plain,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [W0: $i] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(W0,xT) ) ),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [W0: $i] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [W1: $i] :
( aElementOf0(W1,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W1) = W0 ) ) ) ),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(and_elim,[status(thm)],[17]) ).
tff(19,plain,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) )
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(and_elim,[status(thm)],[18]) ).
tff(20,plain,
( aFunction0(xc)
& ! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) ) ),
inference(and_elim,[status(thm)],[19]) ).
tff(21,plain,
! [W0: $i] :
( ( aElementOf0(W0,szDzozmdt0(xc))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xK ) )
=> aElementOf0(W0,szDzozmdt0(xc)) ) ),
inference(and_elim,[status(thm)],[20]) ).
tff(22,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ~ ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = xK ) )
| aElementOf0(W0,szDzozmdt0(xc)) ) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ~ ( ( aSubsetOf0(W0,xS)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
& ( sbrdtbr0(W0) = xK ) )
| aElementOf0(W0,szDzozmdt0(xc)) ) ),
inference(modus_ponens,[status(thm)],[22,12]) ).
tff(24,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK )
| aElementOf0(W0,szDzozmdt0(xc)) ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xK ) ) )
& ( aElementOf0(W0,szDzozmdt0(xc))
| ( ~ aSubsetOf0(W0,xS)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) )
| ( sbrdtbr0(W0) != xK ) ) ),
inference(modus_ponens,[status(thm)],[24,11]) ).
tff(26,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,9]) ).
tff(27,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
| ( sbrdtbr0(W0) != xK ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,7]) ).
tff(28,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,2]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK ) ) ) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK ) ) ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ~ ( ~ aSet0(W0)
| ~ aSubsetOf0(W0,xS)
| ( sbrdtbr0(W0) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(W0,szDzozmdt0(xc))
| ( sbrdtbr0(W0) != xK )
| ~ ( aSubsetOf0(W0,xS)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_19(W0),W0)
| aElementOf0(tptp_fun_W1_19(W0),xS) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK ) ) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ ( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK ) ) ),
inference(unit_resolution,[status(thm)],[34,28]) ).
tff(36,plain,
( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ ( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ ( ~ aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(tptp_fun_W1_19(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),xS) ) ) )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK ) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(37,plain,
( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
<=> ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(and_elim,[status(thm)],[19]) ).
tff(40,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK))
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc)) ),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
^ [W0: $i] :
refl(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
<=> ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )),
rewrite(( ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
<=> ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )),
( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
rewrite(( ( ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
^ [W0: $i] :
rewrite(( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
tff(56,plain,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[59,49]) ).
tff(61,plain,
! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[60,44]) ).
tff(62,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ~ ( ~ ( ( slbdtsldtrb0(xS,xK) = slcrc0 )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) )
<=> ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( slbdtsldtrb0(xS,xK) = slcrc0 )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( slbdtsldtrb0(xS,xK) = slcrc0 )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( slbdtsldtrb0(xS,xK) = slcrc0 )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) ) ),
inference(unit_resolution,[status(thm)],[67,61]) ).
tff(69,plain,
( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slcrc0 )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtsldtrb0(xS,xK)) ) )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(70,plain,
( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
( aSet0(xS)
<=> aSet0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
tff(73,plain,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0) ),
inference(and_elim,[status(thm)],[72]) ).
tff(74,plain,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) ) ),
inference(and_elim,[status(thm)],[73]) ).
tff(75,plain,
aSet0(xS),
inference(and_elim,[status(thm)],[74]) ).
tff(76,plain,
aSet0(xS),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
rewrite(( ~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )
<=> ~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ))),
( ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )),
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) )),
rewrite(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) )),
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0) ) )),
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0) ) )),
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0) ) )),
quant_intro(proof_bind(^ [W2: $i] :
trans(monotonicity(rewrite(( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
<=> ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) )),
trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite(( ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) )
<=> ~ ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) )),
( ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ~ ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) ) )),
rewrite(( ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ~ ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) ) )
<=> ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
( ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
rewrite(( ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) )
<=> ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
( ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
( ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ~ ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
rewrite(( ~ ~ ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) )
<=> ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
( ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) )
<=> ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )),
( ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) )
<=> ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )),
rewrite(( ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
<=> ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )),
( ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) )
<=> ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )),
( ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) )
<=> ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )),
rewrite(( ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) )
<=> ~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )),
( ( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) )
<=> ~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ))),
( ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )),
( ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) )),
rewrite(( ( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) )),
( ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,axiom,
! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
tff(92,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[94,87]) ).
tff(96,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[95,85]) ).
tff(97,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[96,83]) ).
tff(98,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[97,78]) ).
tff(99,plain,
( aElementOf0(sz00,szNzAzT0)
<=> aElementOf0(sz00,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
tff(101,plain,
aElementOf0(sz00,szNzAzT0),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
^ [W2: $i] :
rewrite(( ~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) )
<=> ~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[106,103]) ).
tff(108,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[108,102]) ).
tff(110,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) != W1 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) ),
inference(unit_resolution,[status(thm)],[111,101,98,76]) ).
tff(113,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),slbdtsldtrb0(xS,xK)) ) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),slbdtsldtrb0(xS,xK)) ) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,sz00) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS)) != sz00 ) )
<=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),sz00,xS),slbdtsldtrb0(xS,xK)) ) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) )
| ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(116,plain,
( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
( ( xK = sz00 )
<=> ( xK = sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ~ ( ( xK = sz00 )
=> ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,xS) ) )
| aSubsetOf0(W1,xS) )
& 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(xc,W2) = W0 ) ) ) ) )
<=> ~ ( ( xK != sz00 )
| ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,axiom,
~ ( ( xK = sz00 )
=> ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,xS) ) )
| aSubsetOf0(W1,xS) )
& 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(xc,W2) = W0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(120,plain,
~ ( ( xK != sz00 )
| ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
xK = sz00,
inference(or_elim,[status(thm)],[120]) ).
tff(122,plain,
xK = sz00,
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
sz00 = xK,
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
slbdtsldtrb0(xS,sz00) = slbdtsldtrb0(xS,xK),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,sz00),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) )
| ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(127,plain,
( ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ),
inference(unit_resolution,[status(thm)],[126,125]) ).
tff(128,plain,
~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ),
inference(unit_resolution,[status(thm)],[127,116]) ).
tff(129,plain,
( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) )
| aSet0(slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(130,plain,
aSet0(slbdtsldtrb0(xS,xK)),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
( ( slbdtrb0(sz00) = slcrc0 )
<=> ( slbdtrb0(sz00) = slcrc0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegZero) ).
tff(133,plain,
slbdtrb0(sz00) = slcrc0,
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
slcrc0 = slbdtrb0(sz00),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ( slbdtsldtrb0(xS,xK) = slcrc0 )
<=> ( slbdtsldtrb0(xS,xK) = slbdtrb0(sz00) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( slbdtsldtrb0(xS,xK) = slbdtrb0(sz00) )
<=> ( slbdtsldtrb0(xS,xK) = slcrc0 ) ),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ( slbdtsldtrb0(xS,sz00) = slcrc0 )
<=> ( slbdtsldtrb0(xS,xK) = slbdtrb0(sz00) ) ),
inference(monotonicity,[status(thm)],[124,134]) ).
tff(138,plain,
( ( slbdtsldtrb0(xS,sz00) = slcrc0 )
<=> ( slbdtsldtrb0(xS,xK) = slcrc0 ) ),
inference(transitivity,[status(thm)],[137,136]) ).
tff(139,plain,
( ( slbdtsldtrb0(xS,sz00) != slcrc0 )
<=> ( slbdtsldtrb0(xS,xK) != slcrc0 ) ),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( isCountable0(xS)
<=> isCountable0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
isCountable0(xS),
inference(and_elim,[status(thm)],[72]) ).
tff(142,plain,
isCountable0(xS),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
^ [W0: $i] :
refl(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(144,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(146,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
^ [W0: $i] :
rewrite(( ( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) )
<=> ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(149,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
tff(151,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(skolemize,[status(sab)],[152]) ).
tff(154,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[153,146]) ).
tff(155,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[154,144]) ).
tff(156,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(xS)
| ~ isCountable0(xS)
| ~ isFinite0(xS) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(xS)
| ~ isCountable0(xS)
| ~ isFinite0(xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
( ( ~ isFinite0(xS)
| ~ aSet0(xS)
| ~ isCountable0(xS) )
<=> ( ~ aSet0(xS)
| ~ isCountable0(xS)
| ~ isFinite0(xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(xS)
| ~ aSet0(xS)
| ~ isCountable0(xS) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(xS)
| ~ isCountable0(xS)
| ~ isFinite0(xS) ) ),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(xS)
| ~ aSet0(xS)
| ~ isCountable0(xS) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(xS)
| ~ isCountable0(xS)
| ~ isFinite0(xS) ) ),
inference(transitivity,[status(thm)],[158,156]) ).
tff(160,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(xS)
| ~ aSet0(xS)
| ~ isCountable0(xS) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(xS)
| ~ isCountable0(xS)
| ~ isFinite0(xS) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
~ isFinite0(xS),
inference(unit_resolution,[status(thm)],[161,155,76,142]) ).
tff(163,plain,
^ [W0: $i] :
refl(( ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(164,plain,
( ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[163]) ).
tff(165,plain,
^ [W0: $i] :
rewrite(( ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(166,plain,
( ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[165]) ).
tff(167,plain,
( ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(transitivity,[status(thm)],[166,164]) ).
tff(168,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& ~ isFinite0(W0) )
<=> ~ ( isFinite0(W0)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
<=> ~ ~ ( isFinite0(W0)
| ~ aSet0(W0) ) )),
rewrite(( ~ ~ ( isFinite0(W0)
| ~ aSet0(W0) )
<=> ( isFinite0(W0)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
<=> ( isFinite0(W0)
| ~ aSet0(W0) ) )),
( ( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
rewrite(( ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
( ( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(169,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[168]) ).
tff(170,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) )
<=> ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )),
( ( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
rewrite(( ( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
( ( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(172,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[171]) ).
tff(173,axiom,
! [W0: $i] :
( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,szNzAzT0)
=> ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSelNSet) ).
tff(174,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[174,170]) ).
tff(176,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& ~ isFinite0(W0) )
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
inference(skolemize,[status(sab)],[175]) ).
tff(177,plain,
! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[176,169]) ).
tff(178,plain,
! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[177,167]) ).
tff(179,plain,
( ( ~ ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
| isFinite0(xS)
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
| isFinite0(xS)
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,plain,
( ~ ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
| isFinite0(xS)
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
( ~ ! [W0: $i] :
( isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) )
| isFinite0(xS)
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
( isFinite0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ) ),
inference(unit_resolution,[status(thm)],[181,178,76]) ).
tff(183,plain,
! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) ),
inference(unit_resolution,[status(thm)],[182,162]) ).
tff(184,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( slbdtsldtrb0(xS,sz00) != slcrc0 ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( slbdtsldtrb0(xS,sz00) != slcrc0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(185,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( slbdtsldtrb0(xS,sz00) != slcrc0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ( slbdtsldtrb0(xS,W1) != slcrc0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( slbdtsldtrb0(xS,sz00) != slcrc0 ) ),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
slbdtsldtrb0(xS,sz00) != slcrc0,
inference(unit_resolution,[status(thm)],[186,101,183]) ).
tff(188,plain,
slbdtsldtrb0(xS,xK) != slcrc0,
inference(modus_ponens,[status(thm)],[187,139]) ).
tff(189,plain,
( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slcrc0 )
| aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(190,plain,
aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)),
inference(unit_resolution,[status(thm)],[189,188,130,70]) ).
tff(191,plain,
aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc)),
inference(modus_ponens,[status(thm)],[190,42]) ).
tff(192,plain,
( ~ ( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| ~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(193,plain,
~ ( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) ) ),
inference(unit_resolution,[status(thm)],[192,191,37]) ).
tff(194,plain,
( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != xK )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| aElementOf0(W1,xS) )
| aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) ),
inference(tautology,[status(thm)],[]) ).
tff(195,plain,
aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),
inference(unit_resolution,[status(thm)],[194,193]) ).
tff(196,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(197,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[196]) ).
tff(198,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(199,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(200,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[199]) ).
tff(201,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
tff(202,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[202,198]) ).
tff(204,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(skolemize,[status(sab)],[203]) ).
tff(205,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[204,197]) ).
tff(206,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(208,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
( ~ aSet0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)))
| ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ) ),
inference(unit_resolution,[status(thm)],[208,205]) ).
tff(210,plain,
( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[209,195]) ).
tff(211,plain,
( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) )
| ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(212,plain,
! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[211,128]) ).
tff(213,plain,
( ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) )
| ~ ( ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) )
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
~ ( ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) )
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[213,212]) ).
tff(215,plain,
( ( ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) )
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(216,plain,
( ( ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) )
<=> aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),slbdtsldtrb0(xS,xK)) )
| ~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) ) ),
inference(unit_resolution,[status(thm)],[215,190]) ).
tff(217,plain,
~ ( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 ) ),
inference(unit_resolution,[status(thm)],[216,214]) ).
tff(218,plain,
( ~ aSubsetOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),xS)
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(219,plain,
sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00,
inference(unit_resolution,[status(thm)],[218,217]) ).
tff(220,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) )
| ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) != sz00 )
| ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ),
inference(tautology,[status(thm)],[]) ).
tff(221,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sz00 )
<=> ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) )
| ( tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[220,219]) ).
tff(222,plain,
tptp_fun_W1_0(slbdtsldtrb0(xS,xK)) = slcrc0,
inference(unit_resolution,[status(thm)],[221,210]) ).
tff(223,plain,
sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))) = sdtlpdtrp0(xc,slcrc0),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
( aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
( aFunction0(xc)
<=> aFunction0(xc) ),
inference(rewrite,[status(thm)],[]) ).
tff(226,plain,
aFunction0(xc),
inference(and_elim,[status(thm)],[20]) ).
tff(227,plain,
aFunction0(xc),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
^ [W0: $i] :
refl(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(229,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[228]) ).
tff(230,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(231,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[230]) ).
tff(232,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(transitivity,[status(thm)],[231,229]) ).
tff(233,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(234,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
rewrite(( ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(235,plain,
( ! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[234]) ).
tff(236,axiom,
! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgRng) ).
tff(237,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[236,235]) ).
tff(238,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[237,233]) ).
tff(239,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(skolemize,[status(sab)],[238]) ).
tff(240,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[239,232]) ).
tff(241,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(242,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(243,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(modus_ponens,[status(thm)],[242,241]) ).
tff(244,plain,
! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(unit_resolution,[status(thm)],[243,240,227]) ).
tff(245,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(246,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(247,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(modus_ponens,[status(thm)],[246,245]) ).
tff(248,plain,
( ~ aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS,xK)),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(unit_resolution,[status(thm)],[247,244]) ).
tff(249,plain,
aElementOf0(sdtlpdtrp0(xc,tptp_fun_W1_0(slbdtsldtrb0(xS,xK))),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(unit_resolution,[status(thm)],[248,191]) ).
tff(250,plain,
aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(modus_ponens,[status(thm)],[249,224]) ).
tff(251,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(252,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
tff(253,plain,
aSet0(xT),
inference(and_elim,[status(thm)],[252]) ).
tff(254,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[253,251]) ).
tff(255,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(256,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[255]) ).
tff(257,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(258,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[257]) ).
tff(259,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(260,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[259]) ).
tff(261,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[260,258]) ).
tff(262,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(263,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[262]) ).
tff(264,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(265,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[264]) ).
tff(266,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(267,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(268,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[267]) ).
tff(269,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
tff(270,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[269,268]) ).
tff(271,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[270,266]) ).
tff(272,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(skolemize,[status(sab)],[271]) ).
tff(273,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[272,265]) ).
tff(274,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[273,263]) ).
tff(275,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[274,261]) ).
tff(276,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[275,256]) ).
tff(277,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(278,plain,
( ( ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(279,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[279,277]) ).
tff(281,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(282,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[281,280]) ).
tff(283,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[282,276,254]) ).
tff(284,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(285,plain,
( ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(286,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[286,284]) ).
tff(288,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(289,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[288,287]) ).
tff(290,plain,
~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[289,283]) ).
tff(291,plain,
( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(292,plain,
( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[291,290]) ).
tff(293,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
<=> aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(294,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(and_elim,[status(thm)],[15]) ).
tff(295,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(modus_ponens,[status(thm)],[294,293]) ).
tff(296,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(297,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[296,295]) ).
tff(298,plain,
~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ),
inference(unit_resolution,[status(thm)],[297,292]) ).
tff(299,plain,
( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ),
inference(tautology,[status(thm)],[]) ).
tff(300,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ),
inference(unit_resolution,[status(thm)],[299,298]) ).
tff(301,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(302,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(303,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(modus_ponens,[status(thm)],[302,301]) ).
tff(304,plain,
aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(unit_resolution,[status(thm)],[303,300,250]) ).
tff(305,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(306,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) ) ),
inference(quant_intro,[status(thm)],[305]) ).
tff(307,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(308,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(quant_intro,[status(thm)],[307]) ).
tff(309,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(310,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(quant_intro,[status(thm)],[309]) ).
tff(311,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(transitivity,[status(thm)],[310,308]) ).
tff(312,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(313,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ) ),
inference(quant_intro,[status(thm)],[312]) ).
tff(314,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(315,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[314]) ).
tff(316,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(317,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ) ),
inference(or_elim,[status(thm)],[120]) ).
tff(318,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[317,316]) ).
tff(319,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[318,316]) ).
tff(320,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[319,316]) ).
tff(321,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,xS),~ aSubsetOf0(W1,xS))),
nnf_neg(refl($oeq(~ aSet0(W1),~ aSet0(W1))),
sk($oeq(~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ),
~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ))),
$oeq(~ ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ),
( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ))),
$oeq(~ ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ),
( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) ))),refl($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(xc,W2) = W0 ) ),
~ ( ~ ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 ) ))),
nnf_neg(nnf_neg(monotonicity(refl($oeq(aSet0(tptp_fun_W2_30(W1,W0)),aSet0(tptp_fun_W2_30(W1,W0)))),
nnf_pos(proof_bind(^ [W3: $i] :
refl($oeq(( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ),
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )))),
$oeq(! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ),
! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ))),
refl($oeq(aSubsetOf0(tptp_fun_W2_30(W1,W0),W1),aSubsetOf0(tptp_fun_W2_30(W1,W0),W1))),refl($oeq(sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK,sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK)),refl($oeq(aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)),aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)))),
$oeq(( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ),
( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ))),
$oeq(~ ~ ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ),
( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ))),refl($oeq(sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0,sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0)),
$oeq(~ ( ~ ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 ) ),
( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(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(xc,W2) = W0 ) ),
( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ))),
$oeq(~ ( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ),
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) )))),
$oeq(~ ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ),
! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ))),
$oeq(~ ( aElementOf0(W0,xT)
& ? [W1: $i] :
( ( aSubsetOf0(W1,xS)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) )
& 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(xc,W2) = W0 ) ) ) ),
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) ))),
inference(bind,[status(th)],[]) ).
tff(322,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ isCountable0(W1)
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) ),
inference(nnf-neg,[status(sab)],[320,321]) ).
tff(323,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,xS)
& ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ( aSet0(tptp_fun_W2_30(W1,W0))
& ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
& aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
& ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) = xK )
& aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
& ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) != W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[322,315]) ).
tff(324,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ),
inference(modus_ponens,[status(thm)],[323,313]) ).
tff(325,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK)) ) ) ),
inference(modus_ponens,[status(thm)],[324,311]) ).
tff(326,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) ),
inference(modus_ponens,[status(thm)],[325,306]) ).
tff(327,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(328,plain,
( ( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) ) ) ) )
<=> ( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(329,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ) ),
inference(monotonicity,[status(thm)],[328]) ).
tff(330,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ) ),
inference(transitivity,[status(thm)],[329,327]) ).
tff(331,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(332,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_30(W1,W0))
| ~ aSubsetOf0(tptp_fun_W2_30(W1,W0),W1)
| ( sbrdtbr0(tptp_fun_W2_30(W1,W0)) != xK )
| ~ aElementOf0(tptp_fun_W2_30(W1,W0),slbdtsldtrb0(W1,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,W0))
| aElementOf0(W3,W1) ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ) ),
inference(modus_ponens,[status(thm)],[331,330]) ).
tff(333,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(unit_resolution,[status(thm)],[332,326,304]) ).
tff(334,plain,
( aSet0(xS)
| aSubsetOf0(xS,xS)
| ~ aSet0(xS) ),
inference(tautology,[status(thm)],[]) ).
tff(335,plain,
( aSet0(xS)
| aSubsetOf0(xS,xS) ),
inference(unit_resolution,[status(thm)],[334,76]) ).
tff(336,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(337,plain,
( ( ~ isCountable0(xS)
| ~ ( aSubsetOf0(xS,xS)
| ~ ( ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(xS),xS)
| aElementOf0(tptp_fun_W2_29(xS),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(338,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSubsetOf0(xS,xS)
| ~ ( ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(xS),xS)
| aElementOf0(tptp_fun_W2_29(xS),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) ) ),
inference(monotonicity,[status(thm)],[337]) ).
tff(339,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSubsetOf0(xS,xS)
| ~ ( ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(xS),xS)
| aElementOf0(tptp_fun_W2_29(xS),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) ) ),
inference(transitivity,[status(thm)],[338,336]) ).
tff(340,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSubsetOf0(xS,xS)
| ~ ( ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(xS),xS)
| aElementOf0(tptp_fun_W2_29(xS),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(341,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ ( aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_29(W1),W1)
| aElementOf0(tptp_fun_W2_29(W1),xS) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,W1) )
| ~ aElementOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(W1,xK))
| ( sbrdtbr0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aSubsetOf0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)),W1)
| ~ aSet0(tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(W1,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) ) ) )
| ~ isCountable0(xS)
| ~ ( aSet0(xS)
| aSubsetOf0(xS,xS) )
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ) ),
inference(modus_ponens,[status(thm)],[340,339]) ).
tff(342,plain,
~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) ) ),
inference(unit_resolution,[status(thm)],[341,142,335,333]) ).
tff(343,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) ),
inference(tautology,[status(thm)],[]) ).
tff(344,plain,
aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))),
inference(unit_resolution,[status(thm)],[343,342]) ).
tff(345,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(346,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(347,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[346,345]) ).
tff(348,plain,
( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[347,205,344]) ).
tff(349,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = xK ) ),
inference(tautology,[status(thm)],[]) ).
tff(350,plain,
sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = xK,
inference(unit_resolution,[status(thm)],[349,342]) ).
tff(351,plain,
sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sz00,
inference(transitivity,[status(thm)],[350,122]) ).
tff(352,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) )
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sz00 )
| ( tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ),
inference(tautology,[status(thm)],[]) ).
tff(353,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sz00 )
<=> ( tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) )
| ( tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[352,351]) ).
tff(354,plain,
tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)) = slcrc0,
inference(unit_resolution,[status(thm)],[353,348]) ).
tff(355,plain,
sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0),
inference(monotonicity,[status(thm)],[354]) ).
tff(356,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) = sdtlpdtrp0(xc,slcrc0) )
| ~ aSet0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| ~ aSubsetOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),xS)
| ( sbrdtbr0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != xK )
| ~ aElementOf0(tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)),slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
( ~ aElementOf0(W3,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0)))
| aElementOf0(W3,xS) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0) ) ),
inference(tautology,[status(thm)],[]) ).
tff(357,plain,
sdtlpdtrp0(xc,tptp_fun_W2_30(xS,sdtlpdtrp0(xc,slcrc0))) != sdtlpdtrp0(xc,slcrc0),
inference(unit_resolution,[status(thm)],[356,342]) ).
tff(358,plain,
$false,
inference(unit_resolution,[status(thm)],[357,355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM563+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 01:27:18 EDT 2025
% 0.13/0.33 % CPUTime :
% 14.89/15.08 % SZS status Theorem
% 14.89/15.08 % SZS output start Proof
% See solution above
% 15.02/15.20 % E exiting
%------------------------------------------------------------------------------