%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM582+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:28 AM UTC 2025
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 53 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 301 ( 8 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 393 ( 168 ~; 149 |; 27 &)
% ( 33 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 60 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xN_type,type,
xN: $i ).
tff(xi_type,type,
xi: $i ).
tff(xS_type,type,
xS: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(1,plain,
( ( sdtlpdtrp0(xN,sz00) = xS )
<=> ( sdtlpdtrp0(xN,sz00) = xS ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aFunction0(xN)
& ( szDzozmdt0(xN) = szNzAzT0 )
& ( sdtlpdtrp0(xN,sz00) = xS )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
tff(3,plain,
( aFunction0(xN)
& ( szDzozmdt0(xN) = szNzAzT0 )
& ( sdtlpdtrp0(xN,sz00) = xS ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
<=> aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
<=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
<=> ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
<=> ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(11,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)),
inference(modus_ponens,[status(thm)],[11,8]) ).
tff(13,plain,
( aElementOf0(xi,szNzAzT0)
<=> aElementOf0(xi,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989) ).
tff(15,plain,
aElementOf0(xi,szNzAzT0),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
tff(22,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(xi,szNzAzT0)
| sdtlseqdt0(sz00,xi) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(xi,szNzAzT0)
| sdtlseqdt0(sz00,xi) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(xi,szNzAzT0)
| sdtlseqdt0(sz00,xi) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(xi,szNzAzT0)
| sdtlseqdt0(sz00,xi) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
sdtlseqdt0(sz00,xi),
inference(unit_resolution,[status(thm)],[28,25,15]) ).
tff(30,plain,
^ [W0: $i,W1: $i] :
refl(( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
rewrite(( ~ ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W1,W0) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
<=> ( ~ sdtlseqdt0(W1,W0)
| aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ sdtlseqdt0(W1,W0)
| aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
rewrite(( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ sdtlseqdt0(W1,W0)
| aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).
tff(38,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[41,31]) ).
tff(43,plain,
( aElementOf0(sz00,szNzAzT0)
<=> aElementOf0(sz00,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
tff(45,plain,
aElementOf0(sz00,szNzAzT0),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,szNzAzT0) )
<=> ( ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)),
inference(unit_resolution,[status(thm)],[51,45,42,15,29]) ).
tff(53,plain,
$false,
inference(unit_resolution,[status(thm)],[52,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM582+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:32:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start Proof
% See solution above
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------