%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM564+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:21:25 AM UTC 2025
% Result : Theorem 0.70s 0.90s
% Output : Proof 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 113
% Syntax : Number of formulae : 282 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 3261 ( 644 equ)
% Maximal formula atoms : 48 ( 11 avg)
% Number of connectives : 6110 (3262 ~;2121 |; 237 &)
% ( 452 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 131 ( 131 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 775 ( 713 !; 19 ?; 775 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(tptp_fun_W1_0_type,type,
tptp_fun_W1_0: $i > $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(xS_type,type,
xS: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xK_type,type,
xK: $i ).
tff(tptp_fun_W3_10_type,type,
tptp_fun_W3_10: ( $i * $i * $i ) > $i ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(tptp_fun_W2_5_type,type,
tptp_fun_W2_5: ( $i * $i ) > $i ).
tff(xT_type,type,
xT: $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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)],[3]) ).
tff(5,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(6,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)],[5]) ).
tff(7,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)],[6,4]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
tff(14,plain,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,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)],[14]) ).
tff(16,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)],[15,11]) ).
tff(17,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)],[16,9]) ).
tff(18,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)],[17,7]) ).
tff(19,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)],[18,2]) ).
tff(20,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ( ~ ( ( slcrc0 = slcrc0 )
| ~ aSet0(slcrc0)
| aElementOf0(tptp_fun_W1_0(slcrc0),slcrc0) )
| ~ ( ( slcrc0 != slcrc0 )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) )
<=> ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( slcrc0 = slcrc0 )
| ~ aSet0(slcrc0)
| aElementOf0(tptp_fun_W1_0(slcrc0),slcrc0) )
| ~ ( ( slcrc0 != slcrc0 )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( slcrc0 = slcrc0 )
| ~ aSet0(slcrc0)
| aElementOf0(tptp_fun_W1_0(slcrc0),slcrc0) )
| ~ ( ( slcrc0 != slcrc0 )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( slcrc0 = slcrc0 )
| ~ aSet0(slcrc0)
| aElementOf0(tptp_fun_W1_0(slcrc0),slcrc0) )
| ~ ( ( slcrc0 != slcrc0 )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ ( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ),
inference(unit_resolution,[status(thm)],[25,19]) ).
tff(27,plain,
( ~ aSet0(slcrc0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ! [W1: $i] : ~ aElementOf0(W1,slcrc0) ),
inference(tautology,[status(thm)],[]) ).
tff(28,plain,
! [W1: $i] : ~ aElementOf0(W1,slcrc0),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(31,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[31,29]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(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) ) ) ) )
<=> ! [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)],[35]) ).
tff(37,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(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) ) ) ) )
<=> ! [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)],[37]) ).
tff(39,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)],[38,36]) ).
tff(40,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(41,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)],[40]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,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(46,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)],[45]) ).
tff(47,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(48,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)],[47,46]) ).
tff(49,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)],[48,44]) ).
tff(50,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)],[49]) ).
tff(51,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)],[50,43]) ).
tff(52,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)],[51,41]) ).
tff(53,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)],[52,39]) ).
tff(54,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)],[53,34]) ).
tff(55,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(56,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(57,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)],[56,55]) ).
tff(58,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)],[57,54,32]) ).
tff(59,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(60,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)],[59,58]) ).
tff(61,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(62,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
( aSubsetOf0(xS,szNzAzT0)
<=> aSubsetOf0(xS,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
tff(65,plain,
aSubsetOf0(xS,szNzAzT0),
inference(and_elim,[status(thm)],[64]) ).
tff(66,plain,
aSubsetOf0(xS,szNzAzT0),
inference(modus_ponens,[status(thm)],[65,63]) ).
tff(67,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(68,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)],[67,66]) ).
tff(69,plain,
~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ),
inference(unit_resolution,[status(thm)],[68,62]) ).
tff(70,plain,
( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) )
| aSet0(xS) ),
inference(tautology,[status(thm)],[]) ).
tff(71,plain,
aSet0(xS),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,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(xS)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) )
<=> ( ~ ! [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(xS)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ~ aSet0(xS)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) )
<=> ( ~ aSet0(xS)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,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(xS)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) )
<=> ( ~ ! [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(xS)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,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(xS)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) )
<=> ( ~ ! [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(xS)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,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(xS)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xS)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,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(xS)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) ),
inference(unit_resolution,[status(thm)],[77,54,71]) ).
tff(79,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xS),W1)
| aElementOf0(tptp_fun_W2_1(W1,xS),xS) ) )
| ~ ( ~ aSubsetOf0(W1,xS)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xS) ) ) ) )
| ~ ( ~ ( ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS) ) )
| ~ ( ~ aSubsetOf0(slcrc0,xS)
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,slcrc0)
| aElementOf0(W2,xS) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
~ ( ~ ( ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS) ) )
| ~ ( ~ aSubsetOf0(slcrc0,xS)
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,slcrc0)
| aElementOf0(W2,xS) ) ) ) ),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
( ~ ( ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS) ) )
| ~ ( ~ aSubsetOf0(slcrc0,xS)
| ~ ( ~ aSet0(slcrc0)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,slcrc0)
| aElementOf0(W2,xS) ) ) )
| ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS) ) ),
inference(tautology,[status(thm)],[]) ).
tff(82,plain,
( ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS) ) ),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,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)],[85]) ).
tff(87,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(88,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)],[87]) ).
tff(89,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)],[88,86]) ).
tff(90,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(91,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)],[90]) ).
tff(92,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(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 ) ) ) ) )
& ( ( 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)],[92]) ).
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 ) ) ) ) ) )
<=> ! [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(95,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(96,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)],[95]) ).
tff(97,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(98,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)],[97,96]) ).
tff(99,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)],[98,94]) ).
tff(100,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)],[99]) ).
tff(101,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)],[100,93]) ).
tff(102,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)],[101,91]) ).
tff(103,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)],[102,89]) ).
tff(104,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)],[103,84]) ).
tff(105,plain,
( aElementOf0(sz00,szNzAzT0)
<=> aElementOf0(sz00,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
tff(107,plain,
aElementOf0(sz00,szNzAzT0),
inference(modus_ponens,[status(thm)],[106,105]) ).
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) ) ) ) ) )
| ~ 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(109,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(110,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(111,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)],[110]) ).
tff(112,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)],[111]) ).
tff(113,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)],[112,109]) ).
tff(114,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)],[113]) ).
tff(115,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)],[114,108]) ).
tff(116,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(117,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)],[116,115]) ).
tff(118,plain,
( ~ 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(unit_resolution,[status(thm)],[117,107,104]) ).
tff(119,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)],[118,71]) ).
tff(120,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(121,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)],[120,119]) ).
tff(122,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(123,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)],[122,121]) ).
tff(124,plain,
( ( xK = sz00 )
<=> ( xK = sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,axiom,
xK = sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
tff(126,plain,
xK = sz00,
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
sz00 = xK,
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
slbdtsldtrb0(xS,sz00) = slbdtsldtrb0(xS,xK),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
slbdtsldtrb0(xS,xK) = slbdtsldtrb0(xS,sz00),
inference(symmetry,[status(thm)],[128]) ).
tff(130,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(131,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)],[130,129]) ).
tff(132,plain,
~ ( ~ aSet0(slbdtsldtrb0(xS,xK))
| ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ) ),
inference(unit_resolution,[status(thm)],[131,123]) ).
tff(133,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(134,plain,
! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[133,132]) ).
tff(135,plain,
( ~ ! [W3: $i] :
~ ( ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) )
<=> aElementOf0(W3,slbdtsldtrb0(xS,xK)) )
| ~ ( ( ~ aSubsetOf0(slcrc0,xS)
| ( sbrdtbr0(slcrc0) != sz00 ) )
<=> aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
~ ( ( ~ aSubsetOf0(slcrc0,xS)
| ( sbrdtbr0(slcrc0) != sz00 ) )
<=> aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)) ),
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,plain,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,xK))
<=> aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
inference(monotonicity,[status(thm)],[129]) ).
tff(138,plain,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
<=> aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)) ),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
<=> ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)) ),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
<=> ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,axiom,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(142,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(modus_ponens,[status(thm)],[142,139]) ).
tff(144,plain,
( ( ( ~ aSubsetOf0(slcrc0,xS)
| ( sbrdtbr0(slcrc0) != sz00 ) )
<=> aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)) )
| ~ aSubsetOf0(slcrc0,xS)
| ( sbrdtbr0(slcrc0) != sz00 )
| aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(145,plain,
( ( ( ~ aSubsetOf0(slcrc0,xS)
| ( sbrdtbr0(slcrc0) != sz00 ) )
<=> aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)) )
| ~ aSubsetOf0(slcrc0,xS)
| ( sbrdtbr0(slcrc0) != sz00 ) ),
inference(unit_resolution,[status(thm)],[144,143]) ).
tff(146,plain,
( ~ aSubsetOf0(slcrc0,xS)
| ( sbrdtbr0(slcrc0) != sz00 ) ),
inference(unit_resolution,[status(thm)],[145,136]) ).
tff(147,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(151,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ) ),
inference(quant_intro,[status(thm)],[150]) ).
tff(152,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSeg) ).
tff(153,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
inference(modus_ponens,[status(thm)],[153,149]) ).
tff(155,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
inference(skolemize,[status(sab)],[154]) ).
tff(156,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
inference(modus_ponens,[status(thm)],[155,148]) ).
tff(157,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
sbrdtbr0(slbdtrb0(sz00)) = sz00,
inference(unit_resolution,[status(thm)],[159,107,156]) ).
tff(161,plain,
( ( slbdtrb0(sz00) = slcrc0 )
<=> ( slbdtrb0(sz00) = slcrc0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
tff(163,plain,
slbdtrb0(sz00) = slcrc0,
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
slcrc0 = slbdtrb0(sz00),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
sbrdtbr0(slcrc0) = sbrdtbr0(slbdtrb0(sz00)),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
sbrdtbr0(slcrc0) = sz00,
inference(transitivity,[status(thm)],[165,160]) ).
tff(167,plain,
( ~ ( ~ aSubsetOf0(slcrc0,xS)
| ( sbrdtbr0(slcrc0) != sz00 ) )
| ~ aSubsetOf0(slcrc0,xS)
| ( sbrdtbr0(slcrc0) != sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(168,plain,
( ~ ( ~ aSubsetOf0(slcrc0,xS)
| ( sbrdtbr0(slcrc0) != sz00 ) )
| ~ aSubsetOf0(slcrc0,xS) ),
inference(unit_resolution,[status(thm)],[167,166]) ).
tff(169,plain,
~ aSubsetOf0(slcrc0,xS),
inference(unit_resolution,[status(thm)],[168,146]) ).
tff(170,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
tff(172,plain,
aSet0(xT),
inference(and_elim,[status(thm)],[171]) ).
tff(173,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[172,170]) ).
tff(174,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(175,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(176,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)],[175]) ).
tff(177,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)],[176,174]) ).
tff(178,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(179,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)],[178,177]) ).
tff(180,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)],[179,54,173]) ).
tff(181,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(tptp_fun_W2_5(sz00,xT),xT)
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| 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(tptp_fun_W2_5(sz00,xT),xT)
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(182,plain,
( ~ ( ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(183,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(tptp_fun_W2_5(sz00,xT))
| aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| 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(tptp_fun_W2_5(sz00,xT),xT)
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,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(tptp_fun_W2_5(sz00,xT))
| aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| 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(tptp_fun_W2_5(sz00,xT),xT)
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[183,181]) ).
tff(185,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(tptp_fun_W2_5(sz00,xT))
| aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,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(tptp_fun_W2_5(sz00,xT),xT)
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
~ ( ~ ( aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[186,180]) ).
tff(188,plain,
( ~ ( aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),tptp_fun_W2_5(sz00,xT))
| aElementOf0(tptp_fun_W2_1(tptp_fun_W2_5(sz00,xT),xT),xT) ) )
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(189,plain,
( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[188,187]) ).
tff(190,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(191,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[190]) ).
tff(192,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(193,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(194,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[193]) ).
tff(195,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
tff(196,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[196,192]) ).
tff(198,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(skolemize,[status(sab)],[197]) ).
tff(199,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[198,191]) ).
tff(200,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xT)
| ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xT)
| ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xT)
| ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xT)
| ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ) ),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ),
inference(unit_resolution,[status(thm)],[202,199,173]) ).
tff(204,plain,
( isFinite0(xT)
<=> isFinite0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,plain,
isFinite0(xT),
inference(and_elim,[status(thm)],[171]) ).
tff(206,plain,
isFinite0(xT),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
( ~ ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) )
| aElementOf0(sbrdtbr0(xT),szNzAzT0)
| ~ isFinite0(xT) ),
inference(tautology,[status(thm)],[]) ).
tff(208,plain,
( ~ ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) )
| aElementOf0(sbrdtbr0(xT),szNzAzT0) ),
inference(unit_resolution,[status(thm)],[207,206]) ).
tff(209,plain,
aElementOf0(sbrdtbr0(xT),szNzAzT0),
inference(unit_resolution,[status(thm)],[208,203]) ).
tff(210,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(211,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[210]) ).
tff(212,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(214,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[213]) ).
tff(215,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
tff(216,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[216,212]) ).
tff(218,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(skolemize,[status(sab)],[217]) ).
tff(219,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[218,211]) ).
tff(220,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(sbrdtbr0(xT),szNzAzT0)
| sdtlseqdt0(sz00,sbrdtbr0(xT)) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(sbrdtbr0(xT),szNzAzT0)
| sdtlseqdt0(sz00,sbrdtbr0(xT)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(221,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(sbrdtbr0(xT),szNzAzT0)
| sdtlseqdt0(sz00,sbrdtbr0(xT)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(sbrdtbr0(xT),szNzAzT0)
| sdtlseqdt0(sz00,sbrdtbr0(xT)) ),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
sdtlseqdt0(sz00,sbrdtbr0(xT)),
inference(unit_resolution,[status(thm)],[222,219,209]) ).
tff(224,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(225,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) ) ),
inference(quant_intro,[status(thm)],[224]) ).
tff(226,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
<=> ~ ( ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0)) ) )),
( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
<=> ~ ~ ( ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0)) ) )),
rewrite(( ~ ~ ( ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0)) )
<=> ( ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0)) ) )),
( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
<=> ( ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0)) ) )),
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) ) )),
rewrite(( ( aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) = W1 ) )
<=> ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )),
( ( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ( aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) = W1 ) ) )
<=> ( ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) ) )),
rewrite(( ( ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) ) )),
( ( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ( aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) = W1 ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(227,plain,
( ! [W0: $i,W1: $i] :
( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ( aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) ) ),
inference(quant_intro,[status(thm)],[226]) ).
tff(228,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) = W1 ) )
| ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ( aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) = W1 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(229,plain,
( ! [W0: $i,W1: $i] :
( ( aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) = W1 ) )
| ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ( aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) = W1 ) ) ) ),
inference(quant_intro,[status(thm)],[228]) ).
tff(230,plain,
( ! [W0: $i,W1: $i] :
( ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) )
| ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ! [W0: $i,W1: $i] :
( ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) )
| ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(231,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
=> ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) ) )
<=> ( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) ) ) )),
( ( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
=> ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) ) ) )
<=> ( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) ) ) ) )),
rewrite(( ( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) ) ) )
<=> ( ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) )
| ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) ) ) )),
( ( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
=> ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) ) ) )
<=> ( ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) )
| ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(232,plain,
( ! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
=> ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) )
| ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) ) ) ),
inference(quant_intro,[status(thm)],[231]) ).
tff(233,axiom,
! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
=> ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSubEx) ).
tff(234,plain,
! [W0: $i,W1: $i] :
( ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) )
| ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
! [W0: $i,W1: $i] :
( ? [W2: $i] :
( aSubsetOf0(W2,W0)
& ( sbrdtbr0(W2) = W1 ) )
| ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[234,230]) ).
tff(236,plain,
! [W0: $i,W1: $i] :
( ( aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) = W1 ) )
| ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(skolemize,[status(sab)],[235]) ).
tff(237,plain,
! [W0: $i,W1: $i] :
( ~ ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
| ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ( aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) = W1 ) ) ),
inference(modus_ponens,[status(thm)],[236,229]) ).
tff(238,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) ),
inference(modus_ponens,[status(thm)],[237,227]) ).
tff(239,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) ),
inference(modus_ponens,[status(thm)],[238,225]) ).
tff(240,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,sbrdtbr0(xT))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,sbrdtbr0(xT))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(241,plain,
( ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ~ sdtlseqdt0(sz00,sbrdtbr0(xT))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ) )
<=> ( ~ aSet0(xT)
| ~ isFinite0(xT)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,sbrdtbr0(xT))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(242,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ~ sdtlseqdt0(sz00,sbrdtbr0(xT))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,sbrdtbr0(xT))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ) ) ),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ~ sdtlseqdt0(sz00,sbrdtbr0(xT))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,sbrdtbr0(xT))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ) ) ),
inference(transitivity,[status(thm)],[242,240]) ).
tff(244,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ~ sdtlseqdt0(sz00,sbrdtbr0(xT))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ~ isFinite0(W0)
| ~ sdtlseqdt0(W1,sbrdtbr0(W0))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(W1,W0),W0)
| ( sbrdtbr0(tptp_fun_W2_5(W1,W0)) != W1 ) ) )
| ~ aSet0(xT)
| ~ isFinite0(xT)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,sbrdtbr0(xT))
| ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[244,243]) ).
tff(246,plain,
~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ),
inference(unit_resolution,[status(thm)],[245,107,239,173,206,223]) ).
tff(247,plain,
( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 )
| aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT) ),
inference(tautology,[status(thm)],[]) ).
tff(248,plain,
aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT),
inference(unit_resolution,[status(thm)],[247,246]) ).
tff(249,plain,
( ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(250,plain,
( ~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) )
| ~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[249,248]) ).
tff(251,plain,
~ ( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) ) ),
inference(unit_resolution,[status(thm)],[250,189]) ).
tff(252,plain,
( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,tptp_fun_W2_5(sz00,xT))
| aElementOf0(W2,xT) )
| aSet0(tptp_fun_W2_5(sz00,xT)) ),
inference(tautology,[status(thm)],[]) ).
tff(253,plain,
aSet0(tptp_fun_W2_5(sz00,xT)),
inference(unit_resolution,[status(thm)],[252,251]) ).
tff(254,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(255,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[254]) ).
tff(256,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(257,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(258,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[257]) ).
tff(259,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
tff(260,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[260,256]) ).
tff(262,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(skolemize,[status(sab)],[261]) ).
tff(263,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[262,255]) ).
tff(264,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(265,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slcrc0 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(266,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[265,264]) ).
tff(267,plain,
( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slcrc0 ) ) ),
inference(unit_resolution,[status(thm)],[266,263]) ).
tff(268,plain,
( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[267,253]) ).
tff(269,plain,
( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 )
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(270,plain,
sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00,
inference(unit_resolution,[status(thm)],[269,246]) ).
tff(271,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slcrc0 ) )
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 )
| ( tptp_fun_W2_5(sz00,xT) = slcrc0 ) ),
inference(tautology,[status(thm)],[]) ).
tff(272,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slcrc0 ) )
| ( tptp_fun_W2_5(sz00,xT) = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[271,270]) ).
tff(273,plain,
tptp_fun_W2_5(sz00,xT) = slcrc0,
inference(unit_resolution,[status(thm)],[272,268]) ).
tff(274,plain,
( aSet0(tptp_fun_W2_5(sz00,xT))
<=> aSet0(slcrc0) ),
inference(monotonicity,[status(thm)],[273]) ).
tff(275,plain,
aSet0(slcrc0),
inference(modus_ponens,[status(thm)],[253,274]) ).
tff(276,plain,
( ~ ( ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS) ) )
| ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS) ) ),
inference(tautology,[status(thm)],[]) ).
tff(277,plain,
( ~ ( ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS) ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS) ) ),
inference(unit_resolution,[status(thm)],[276,275,169]) ).
tff(278,plain,
~ ( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS) ),
inference(unit_resolution,[status(thm)],[277,82]) ).
tff(279,plain,
( ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),xS)
| aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0) ),
inference(tautology,[status(thm)],[]) ).
tff(280,plain,
aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0),
inference(unit_resolution,[status(thm)],[279,278]) ).
tff(281,plain,
( ~ ! [W1: $i] : ~ aElementOf0(W1,slcrc0)
| ~ aElementOf0(tptp_fun_W2_1(slcrc0,xS),slcrc0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(282,plain,
$false,
inference(unit_resolution,[status(thm)],[281,280,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM564+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:26:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.70/0.90 % SZS status Theorem
% 0.70/0.90 % SZS output start Proof
% See solution above
% 0.77/0.94 % E exiting
%------------------------------------------------------------------------------