%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM584+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:21:29 AM UTC 2025
% Result : Theorem 0.60s 0.77s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 45
% Syntax : Number of formulae : 104 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 1758 ( 422 equ)
% Maximal formula atoms : 48 ( 16 avg)
% Number of connectives : 3353 (1777 ~;1102 |; 134 &)
% ( 325 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 78 ( 78 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 422 ( 400 !; 0 ?; 422 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xK_type,type,
xK: $i ).
tff(xS_type,type,
xS: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xi_type,type,
xi: $i ).
tff(xN_type,type,
xN: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(tptp_fun_W3_10_type,type,
tptp_fun_W3_10: ( $i * $i * $i ) > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(1,plain,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
<=> aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4024) ).
tff(3,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )
<=> ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4007) ).
tff(6,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ~ ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ) )
| ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ) ),
inference(tautology,[status(thm)],[]) ).
tff(8,plain,
~ ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ) ),
inference(unit_resolution,[status(thm)],[7,6,3]) ).
tff(9,plain,
( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
<=> ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(11,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
( ( ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ) )
<=> aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) )
| ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK )
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(13,plain,
( ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ) )
<=> aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[12,11,8]) ).
tff(14,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(16,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[16,14]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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)],[20]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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)],[23,21]) ).
tff(25,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(26,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)],[25]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,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(31,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)],[30]) ).
tff(32,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(33,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)],[32,31]) ).
tff(34,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)],[33,29]) ).
tff(35,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)],[34]) ).
tff(36,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)],[35,28]) ).
tff(37,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)],[36,26]) ).
tff(38,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)],[37,24]) ).
tff(39,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)],[38,19]) ).
tff(40,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(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) )
<=> ( ~ ! [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(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,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(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,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(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[42,39,17]) ).
tff(44,plain,
( ~ ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xS,szNzAzT0)
| ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),xS)
| aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
~ ( ~ ( aSubsetOf0(xS,szNzAzT0)
| ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),xS)
| aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
( ~ ( aSubsetOf0(xS,szNzAzT0)
| ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),xS)
| aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(47,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
( aSubsetOf0(xS,szNzAzT0)
<=> aSubsetOf0(xS,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
tff(50,plain,
aSubsetOf0(xS,szNzAzT0),
inference(and_elim,[status(thm)],[49]) ).
tff(51,plain,
aSubsetOf0(xS,szNzAzT0),
inference(modus_ponens,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(53,plain,
( ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ),
inference(unit_resolution,[status(thm)],[53,47]) ).
tff(55,plain,
( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) )
| aSet0(xS) ),
inference(tautology,[status(thm)],[]) ).
tff(56,plain,
aSet0(xS),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(xK,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
tff(59,plain,
aElementOf0(xK,szNzAzT0),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,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(61,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)],[60]) ).
tff(62,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(63,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)],[62]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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)],[65,63]) ).
tff(67,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(68,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)],[67]) ).
tff(69,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(70,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)],[69]) ).
tff(71,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(72,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(73,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)],[72]) ).
tff(74,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/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
tff(75,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)],[74,73]) ).
tff(76,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)],[75,71]) ).
tff(77,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)],[76]) ).
tff(78,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)],[77,70]) ).
tff(79,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)],[78,68]) ).
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) ) ) ) ),
inference(modus_ponens,[status(thm)],[79,66]) ).
tff(81,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)],[80,61]) ).
tff(82,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(xK,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> 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(xK,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
^ [W2: $i] :
rewrite(( ~ ( ~ ( ( W2 = slbdtsldtrb0(xS,xK) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) )
<=> ~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,xK) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ( ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,xK) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,xK) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[86,83]) ).
tff(88,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(xK,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,xK) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> 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(xK,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,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(xK,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,xK) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> 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(xK,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[88,82]) ).
tff(90,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(xK,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,xK) )
| ~ aSet0(W2)
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,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(xK,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[91,81,59]) ).
tff(93,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) ),
inference(unit_resolution,[status(thm)],[92,56]) ).
tff(94,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS),slbdtsldtrb0(xS,xK)) ) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) )
<=> ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS),slbdtsldtrb0(xS,xK)) ) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS),slbdtsldtrb0(xS,xK)) ) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ( slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,xK),xK,xS),slbdtsldtrb0(xS,xK)) ) )
| ~ ( ( slbdtsldtrb0(xS,xK) != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,xK) )
| ( ( ~ aSubsetOf0(tptp_fun_W3_10(W2,xK,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,xK,xS)) != xK ) )
<=> aElementOf0(tptp_fun_W3_10(W2,xK,xS),W2) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,xK) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ),
inference(unit_resolution,[status(thm)],[99,93]) ).
tff(101,plain,
( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) )
| ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(102,plain,
! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
( ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != xK ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) )
| ~ ( ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ) )
<=> aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
$false,
inference(unit_resolution,[status(thm)],[103,102,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM584+1 : TPTP v9.0.0. Released v4.0.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:31:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.60/0.77 % SZS status Theorem
% 0.60/0.77 % SZS output start Proof
% See solution above
% 0.60/0.80 % E exiting
%------------------------------------------------------------------------------