TSTP Solution File: NUM564+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM564+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Sun Sep 18 13:10:33 EDT 2022
% Result : Theorem 1.11s 0.97s
% Output : Proof 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 139
% Syntax : Number of formulae : 311 ( 64 unt; 23 typ; 0 def)
% Number of atoms : 3331 ( 670 equ)
% Maximal formula atoms : 48 ( 11 avg)
% Number of connectives : 6286 (3364 ~;2170 |; 242 &)
% ( 472 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 121 ( 121 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 16 >; 9 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 803 ( 734 !; 24 ?; 803 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(tptp_fun_W1_0_type,type,
tptp_fun_W1_0: $i > $i ).
tff(slcrc0_type,type,
slcrc0: $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(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(tptp_fun_W3_10_type,type,
tptp_fun_W3_10: ( $i * $i * $i ) > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xc_type,type,
xc: $i ).
tff(xK_type,type,
xK: $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(xT_type,type,
xT: $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(tptp_fun_W2_5_type,type,
tptp_fun_W2_5: ( $i * $i ) > $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(1,plain,
^ [W0: $i] :
rewrite(
( ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
refl(
( ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(
( ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
<=> ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )),
( ( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
rewrite(
( ( ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
( ( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [W0: $i] :
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(
( ( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slbdtrb0(sz00) )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W0: $i] :
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slbdtrb0(sz00) )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(
( ( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) )
<=> ( ( W0 = slbdtrb0(sz00) )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,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(15,axiom,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
tff(16,plain,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [W0: $i] :
( ( W0 = slbdtrb0(sz00) )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
! [W0: $i] :
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slbdtrb0(sz00) )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [W0: $i] :
( ( ( W0 != slbdtrb0(sz00) )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ( ~ ( ~ aSet0(slbdtrb0(sz00))
| ( slbdtrb0(sz00) = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(slbdtrb0(sz00)),slbdtrb0(sz00)) )
| ~ ( ( slbdtrb0(sz00) != slbdtrb0(sz00) )
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ) ) )
<=> ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtrb0(sz00))
| ( slbdtrb0(sz00) = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(slbdtrb0(sz00)),slbdtrb0(sz00)) )
| ~ ( ( slbdtrb0(sz00) != slbdtrb0(sz00) )
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtrb0(sz00))
| ( slbdtrb0(sz00) = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(slbdtrb0(sz00)),slbdtrb0(sz00)) )
| ~ ( ( slbdtrb0(sz00) != slbdtrb0(sz00) )
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtrb0(sz00))
| ( slbdtrb0(sz00) = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(slbdtrb0(sz00)),slbdtrb0(sz00)) )
| ~ ( ( slbdtrb0(sz00) != slbdtrb0(sz00) )
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aSet0(W0)
| ( W0 = slbdtrb0(sz00) )
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slbdtrb0(sz00) )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00))
| ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)) ),
inference(tautology,[status(thm)],]) ).
tff(31,plain,
! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00)),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
tff(34,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[34,32]) ).
tff(36,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(37,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [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)],[36]) ).
tff(38,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(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(quant_intro,[status(thm)],[38]) ).
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] :
( ~ 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)],[41,39]) ).
tff(43,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(44,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)],[43]) ).
tff(45,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(46,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)],[45]) ).
tff(47,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(48,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(49,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)],[48]) ).
tff(50,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
tff(51,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)],[50,49]) ).
tff(52,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)],[51,47]) ).
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(skolemize,[status(sab)],[52]) ).
tff(54,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)],[53,46]) ).
tff(55,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)],[54,44]) ).
tff(56,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)],[55,42]) ).
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) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[56,37]) ).
tff(58,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(59,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(60,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)],[59,58]) ).
tff(61,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)],[60,57,35]) ).
tff(62,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(63,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)],[62,61]) ).
tff(64,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(65,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( aSubsetOf0(xS,szNzAzT0)
<=> aSubsetOf0(xS,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
tff(68,plain,
aSubsetOf0(xS,szNzAzT0),
inference(and_elim,[status(thm)],[67]) ).
tff(69,plain,
aSubsetOf0(xS,szNzAzT0),
inference(modus_ponens,[status(thm)],[68,66]) ).
tff(70,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(71,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)],[70,69]) ).
tff(72,plain,
~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ),
inference(unit_resolution,[status(thm)],[71,65]) ).
tff(73,plain,
( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) )
| aSet0(xS) ),
inference(tautology,[status(thm)],]) ).
tff(74,plain,
aSet0(xS),
inference(unit_resolution,[status(thm)],[73,72]) ).
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] :
~ ( ~ ( ~ 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(76,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(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] :
~ ( ~ ( 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)],[76]) ).
tff(78,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)],[77,75]) ).
tff(79,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(80,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)],[79,78]) ).
tff(81,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)],[80,57,74]) ).
tff(82,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(slbdtrb0(sz00))
| aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS) ) )
| ~ ( ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,slbdtrb0(sz00))
| aElementOf0(W2,xS) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
~ ( ~ ( ~ aSet0(slbdtrb0(sz00))
| aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS) ) )
| ~ ( ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,slbdtrb0(sz00))
| aElementOf0(W2,xS) ) ) ) ),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
( ~ ( ~ aSet0(slbdtrb0(sz00))
| aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS) ) )
| ~ ( ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aSet0(slbdtrb0(sz00))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,slbdtrb0(sz00))
| aElementOf0(W2,xS) ) ) )
| ~ aSet0(slbdtrb0(sz00))
| aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS) ) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
( ~ aSet0(slbdtrb0(sz00))
| aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS) ) ),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W2: $i] :
rewrite(
( ~ ( ~ ( ( 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)
| ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ))),
( ! [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)
| ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )),
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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)
| ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ) )),
rewrite(
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ) )),
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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)
| ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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)
| ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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] :
( 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(89,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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] :
( 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)],[88]) ).
tff(90,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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] :
( 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(91,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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] :
( 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)],[90]) ).
tff(92,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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] :
( 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(transitivity,[status(thm)],[91,89]) ).
tff(93,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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) )),
trans(
monotonicity(
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 ) ) )
<=> ( 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 ) ) )
<=> ( 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)
| ( ~ 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)
| ( 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(
( ( ( 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)
| ( 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)
| ( ~ 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)
| ( 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] :
( 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] :
( 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 ) ) ) ) ) )),
rewrite(
( ( ( ( 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] :
( 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] :
( 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] :
( 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] :
( 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] :
( 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 ) ) ) ) ) )
<=> ( ~ 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 ) ) ) ) ) ) )),
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 ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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 ) ) ) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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(94,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
| ! [W2: $i] :
( ( ( W2 != slbdtsldtrb0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) )
& ( ( W2 = slbdtsldtrb0(W0,W1) )
| ~ aSet0(W2)
| ( ~ aElementOf0(tptp_fun_W3_10(W2,W1,W0),W2)
<=> ( aSubsetOf0(tptp_fun_W3_10(W2,W1,W0),W0)
& ( sbrdtbr0(tptp_fun_W3_10(W2,W1,W0)) = W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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)],[93]) ).
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 ) ) ) ) )
& ( ( 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(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 ) ) ) ) )
& ( ( 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)],[95]) ).
tff(97,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(98,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(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 ) ) ) ) ) )
<=> ! [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)],[98]) ).
tff(100,axiom,
! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2: $i] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
tff(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 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,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)],[101,97]) ).
tff(103,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)],[102]) ).
tff(104,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)],[103,96]) ).
tff(105,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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)],[104,94]) ).
tff(106,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [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)],[105,92]) ).
tff(107,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[106,87]) ).
tff(108,plain,
( aElementOf0(sz00,szNzAzT0)
<=> aElementOf0(sz00,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
tff(110,plain,
aElementOf0(sz00,szNzAzT0),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) )
<=> ( ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
^ [W2: $i] :
rewrite(
( ~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
<=> ~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) )
<=> ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) )
<=> ( ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[115,112]) ).
tff(117,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[117,111]) ).
tff(119,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ( W2 = slbdtsldtrb0(xS,sz00) )
| ~ aSet0(W2)
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( 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] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,W0)
| ( sbrdtbr0(W3) != W1 ) ) ) ) ) ) )
| ~ aSet0(xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
( ~ aSet0(xS)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[120,110,107]) ).
tff(122,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[121,74]) ).
tff(123,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ( slbdtsldtrb0(xS,sz00) = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS),slbdtsldtrb0(xS,sz00))
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS)) != sz00 ) ) ) )
| ~ ( ( slbdtsldtrb0(xS,sz00) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
<=> ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ( slbdtsldtrb0(xS,sz00) = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS),slbdtsldtrb0(xS,sz00))
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS)) != sz00 ) ) ) )
| ~ ( ( slbdtsldtrb0(xS,sz00) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ( slbdtsldtrb0(xS,sz00) = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS),slbdtsldtrb0(xS,sz00))
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS)) != sz00 ) ) ) )
| ~ ( ( slbdtsldtrb0(xS,sz00) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[125,123]) ).
tff(127,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
| ~ ( ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ( slbdtsldtrb0(xS,sz00) = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS),slbdtsldtrb0(xS,sz00))
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS,sz00),sz00,xS)) != sz00 ) ) ) )
| ~ ( ( slbdtsldtrb0(xS,sz00) != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = slbdtsldtrb0(xS,sz00) )
| ( aElementOf0(tptp_fun_W3_10(W2,sz00,xS),W2)
<=> ( ~ aSubsetOf0(tptp_fun_W3_10(W2,sz00,xS),xS)
| ( sbrdtbr0(tptp_fun_W3_10(W2,sz00,xS)) != sz00 ) ) ) )
| ~ ( ( W2 != slbdtsldtrb0(xS,sz00) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ) )
| ~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
~ ( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ),
inference(unit_resolution,[status(thm)],[128,122]) ).
tff(130,plain,
( ~ aSet0(slbdtsldtrb0(xS,sz00))
| ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) )
| ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(131,plain,
! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) ),
inference(unit_resolution,[status(thm)],[130,129]) ).
tff(132,plain,
( ~ ! [W3: $i] :
( aElementOf0(W3,slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(W3,xS)
| ( sbrdtbr0(W3) != sz00 ) ) )
| ( aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ( sbrdtbr0(slbdtrb0(sz00)) != sz00 ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
( aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ( sbrdtbr0(slbdtrb0(sz00)) != sz00 ) ) ),
inference(unit_resolution,[status(thm)],[132,131]) ).
tff(134,plain,
( ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
<=> ( szDzozmdt0(xc) = slbdtsldtrb0(xS,sz00) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
<=> ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,axiom,
( aFunction0(xc)
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
tff(137,plain,
( aFunction0(xc)
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(and_elim,[status(thm)],[136]) ).
tff(138,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(and_elim,[status(thm)],[137]) ).
tff(139,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(modus_ponens,[status(thm)],[138,135]) ).
tff(140,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,sz00),
inference(modus_ponens,[status(thm)],[139,134]) ).
tff(141,plain,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00))
<=> aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc)) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc))
<=> aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00)) ),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc))
<=> ~ aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00)) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
( ~ aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00))
<=> ~ aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc)) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
<=> ~ aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00)) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
<=> ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
inference(rewrite,[status(thm)],]) ).
tff(148,axiom,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(149,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
~ aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00)),
inference(modus_ponens,[status(thm)],[149,146]) ).
tff(151,plain,
~ aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc)),
inference(modus_ponens,[status(thm)],[150,145]) ).
tff(152,plain,
~ aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00)),
inference(modus_ponens,[status(thm)],[151,144]) ).
tff(153,plain,
( ~ ( aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ( sbrdtbr0(slbdtrb0(sz00)) != sz00 ) ) )
| aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00))
| ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ( sbrdtbr0(slbdtrb0(sz00)) != sz00 ) ),
inference(tautology,[status(thm)],]) ).
tff(154,plain,
( ~ ( aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00))
<=> ~ ( ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ( sbrdtbr0(slbdtrb0(sz00)) != sz00 ) ) )
| ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ( sbrdtbr0(slbdtrb0(sz00)) != sz00 ) ),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
( ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ( sbrdtbr0(slbdtrb0(sz00)) != sz00 ) ),
inference(unit_resolution,[status(thm)],[154,133]) ).
tff(156,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ) )),
inference(bind,[status(th)],]) ).
tff(157,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ) )),
inference(bind,[status(th)],]) ).
tff(160,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardSeg) ).
tff(162,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
inference(modus_ponens,[status(thm)],[164,157]) ).
tff(166,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(167,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(W0)) = W0 ) )
| ~ aElementOf0(sz00,szNzAzT0)
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
sbrdtbr0(slbdtrb0(sz00)) = sz00,
inference(unit_resolution,[status(thm)],[168,110,165]) ).
tff(170,plain,
( ~ ( ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ( sbrdtbr0(slbdtrb0(sz00)) != sz00 ) )
| ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ( sbrdtbr0(slbdtrb0(sz00)) != sz00 ) ),
inference(tautology,[status(thm)],]) ).
tff(171,plain,
( ~ ( ~ aSubsetOf0(slbdtrb0(sz00),xS)
| ( sbrdtbr0(slbdtrb0(sz00)) != sz00 ) )
| ~ aSubsetOf0(slbdtrb0(sz00),xS) ),
inference(unit_resolution,[status(thm)],[170,169]) ).
tff(172,plain,
~ aSubsetOf0(slbdtrb0(sz00),xS),
inference(unit_resolution,[status(thm)],[171,155]) ).
tff(173,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],]) ).
tff(174,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
tff(175,plain,
aSet0(xT),
inference(and_elim,[status(thm)],[174]) ).
tff(176,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[175,173]) ).
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] :
~ ( ~ ( ~ 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(178,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(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] :
~ ( ~ ( 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)],[178]) ).
tff(180,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)],[179,177]) ).
tff(181,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(182,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)],[181,180]) ).
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) ) ) ) ),
inference(unit_resolution,[status(thm)],[182,57,176]) ).
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) ) ) ) )
| ~ ( ~ ( 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(185,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(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) ) ) ) )
| ~ ( ~ ( ~ 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)],[185]) ).
tff(187,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)],[186,184]) ).
tff(188,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(189,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)],[188,187]) ).
tff(190,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)],[189,183]) ).
tff(191,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(192,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)],[191,190]) ).
tff(193,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(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,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(196,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(197,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)],[196]) ).
tff(198,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
tff(199,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[199,195]) ).
tff(201,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(skolemize,[status(sab)],[200]) ).
tff(202,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[201,194]) ).
tff(203,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(204,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(205,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xT)
| ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ) ),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) ),
inference(unit_resolution,[status(thm)],[205,202,176]) ).
tff(207,plain,
( isFinite0(xT)
<=> isFinite0(xT) ),
inference(rewrite,[status(thm)],]) ).
tff(208,plain,
isFinite0(xT),
inference(and_elim,[status(thm)],[174]) ).
tff(209,plain,
isFinite0(xT),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
( ~ ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) )
| aElementOf0(sbrdtbr0(xT),szNzAzT0)
| ~ isFinite0(xT) ),
inference(tautology,[status(thm)],]) ).
tff(211,plain,
( ~ ( aElementOf0(sbrdtbr0(xT),szNzAzT0)
<=> isFinite0(xT) )
| aElementOf0(sbrdtbr0(xT),szNzAzT0) ),
inference(unit_resolution,[status(thm)],[210,209]) ).
tff(212,plain,
aElementOf0(sbrdtbr0(xT),szNzAzT0),
inference(unit_resolution,[status(thm)],[211,206]) ).
tff(213,plain,
^ [W0: $i] :
refl(
( ( ~ 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,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(216,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],]) ).
tff(217,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[216]) ).
tff(218,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
tff(219,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[219,215]) ).
tff(221,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(skolemize,[status(sab)],[220]) ).
tff(222,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[221,214]) ).
tff(223,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(224,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(sbrdtbr0(xT),szNzAzT0)
| sdtlseqdt0(sz00,sbrdtbr0(xT)) ),
inference(quant_inst,[status(thm)],]) ).
tff(225,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(sbrdtbr0(xT),szNzAzT0)
| sdtlseqdt0(sz00,sbrdtbr0(xT)) ),
inference(modus_ponens,[status(thm)],[224,223]) ).
tff(226,plain,
sdtlseqdt0(sz00,sbrdtbr0(xT)),
inference(unit_resolution,[status(thm)],[225,222,212]) ).
tff(227,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(228,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)],[227]) ).
tff(229,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(230,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)],[229]) ).
tff(231,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(232,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)],[231]) ).
tff(233,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(234,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(235,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)],[234]) ).
tff(236,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/sandbox/benchmark/theBenchmark.p',mCardSubEx) ).
tff(237,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)],[236,235]) ).
tff(238,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)],[237,233]) ).
tff(239,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)],[238]) ).
tff(240,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)],[239,232]) ).
tff(241,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)],[240,230]) ).
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 ) ) ),
inference(modus_ponens,[status(thm)],[241,228]) ).
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 ) ) )
| ~ 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(244,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(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 ) ) )
| ~ 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)],[244]) ).
tff(246,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)],[245,243]) ).
tff(247,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(248,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)],[247,246]) ).
tff(249,plain,
~ ( ~ aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT)
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 ) ),
inference(unit_resolution,[status(thm)],[248,110,242,176,209,226]) ).
tff(250,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(251,plain,
aSubsetOf0(tptp_fun_W2_5(sz00,xT),xT),
inference(unit_resolution,[status(thm)],[250,249]) ).
tff(252,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(253,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)],[252,251]) ).
tff(254,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)],[253,192]) ).
tff(255,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(256,plain,
aSet0(tptp_fun_W2_5(sz00,xT)),
inference(unit_resolution,[status(thm)],[255,254]) ).
tff(257,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(258,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ) ),
inference(quant_intro,[status(thm)],[257]) ).
tff(259,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(260,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ) ),
inference(quant_intro,[status(thm)],[259]) ).
tff(261,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(262,plain,
^ [W0: $i] :
rewrite(
( ( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(263,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[262]) ).
tff(264,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
tff(265,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[264,263]) ).
tff(266,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[265,261]) ).
tff(267,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ),
inference(modus_ponens,[status(thm)],[266,260]) ).
tff(268,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ),
inference(skolemize,[status(sab)],[267]) ).
tff(269,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ),
inference(modus_ponens,[status(thm)],[268,258]) ).
tff(270,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(271,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(272,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00) ) ) ),
inference(modus_ponens,[status(thm)],[271,270]) ).
tff(273,plain,
( ~ aSet0(tptp_fun_W2_5(sz00,xT))
| ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00) ) ) ),
inference(unit_resolution,[status(thm)],[272,269]) ).
tff(274,plain,
( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00) ) ),
inference(unit_resolution,[status(thm)],[273,256]) ).
tff(275,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(276,plain,
sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00,
inference(unit_resolution,[status(thm)],[275,249]) ).
tff(277,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00) ) )
| ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) != sz00 )
| ( tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00) ) ),
inference(tautology,[status(thm)],]) ).
tff(278,plain,
( ~ ( ( sbrdtbr0(tptp_fun_W2_5(sz00,xT)) = sz00 )
<=> ( tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00) ) )
| ( tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00) ) ),
inference(unit_resolution,[status(thm)],[277,276]) ).
tff(279,plain,
tptp_fun_W2_5(sz00,xT) = slbdtrb0(sz00),
inference(unit_resolution,[status(thm)],[278,274]) ).
tff(280,plain,
( aSet0(tptp_fun_W2_5(sz00,xT))
<=> aSet0(slbdtrb0(sz00)) ),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
aSet0(slbdtrb0(sz00)),
inference(modus_ponens,[status(thm)],[256,280]) ).
tff(282,plain,
( ~ ( ~ aSet0(slbdtrb0(sz00))
| aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS) ) )
| ~ aSet0(slbdtrb0(sz00))
| aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS) ) ),
inference(tautology,[status(thm)],]) ).
tff(283,plain,
( ~ ( ~ aSet0(slbdtrb0(sz00))
| aSubsetOf0(slbdtrb0(sz00),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS) ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS) ) ),
inference(unit_resolution,[status(thm)],[282,281,172]) ).
tff(284,plain,
~ ( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS) ),
inference(unit_resolution,[status(thm)],[283,85]) ).
tff(285,plain,
( ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00))
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),xS)
| aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00)) ),
inference(tautology,[status(thm)],]) ).
tff(286,plain,
aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00)),
inference(unit_resolution,[status(thm)],[285,284]) ).
tff(287,plain,
( ~ ! [W1: $i] : ~ aElementOf0(W1,slbdtrb0(sz00))
| ~ aElementOf0(tptp_fun_W2_1(slbdtrb0(sz00),xS),slbdtrb0(sz00)) ),
inference(quant_inst,[status(thm)],]) ).
tff(288,plain,
$false,
inference(unit_resolution,[status(thm)],[287,286,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM564+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 11:49:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.11/0.97 % SZS status Theorem
% 1.11/0.97 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------