%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM580+3 : 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 0.62s 0.84s
% Output : Proof 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 68
% Syntax : Number of formulae : 182 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 1438 ( 165 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 1963 ( 791 ~; 717 |; 192 &)
% ( 189 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 84 ( 84 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 359 ( 337 !; 0 ?; 359 :)
% Comments :
%------------------------------------------------------------------------------
tff(xK_type,type,
xK: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xi_type,type,
xi: $i ).
tff(xN_type,type,
xN: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xk_type,type,
xk: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(1,plain,
( ( szszuzczcdt0(xk) = xK )
<=> ( szszuzczcdt0(xk) = xK ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aElementOf0(xk,szNzAzT0)
& ( szszuzczcdt0(xk) = xK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
tff(3,plain,
szszuzczcdt0(xk) = xK,
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
szszuzczcdt0(xk) = xK,
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( ( sbrdtbr0(xQ) = xk )
<=> ( sbrdtbr0(xQ) = xk ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sbrdtbr0(xQ) = xk )
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989_02) ).
tff(7,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sbrdtbr0(xQ) = xk ) ),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
sbrdtbr0(xQ) = xk,
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
sbrdtbr0(xQ) = xk,
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
szszuzczcdt0(sbrdtbr0(xQ)) = szszuzczcdt0(xk),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( aElementOf0(xi,szNzAzT0)
<=> aElementOf0(xi,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989) ).
tff(13,plain,
aElementOf0(xi,szNzAzT0),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )),
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) )),
rewrite(( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) )),
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) )),
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )),
rewrite(( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )),
( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) )
<=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
tff(27,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) ),
inference(modus_ponens,[status(thm)],[31,15]) ).
tff(33,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) ) ) )
<=> ( ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,W0))
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
~ ( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(unit_resolution,[status(thm)],[38,32,13]) ).
tff(40,plain,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) ) ),
inference(tautology,[status(thm)],[]) ).
tff(41,plain,
! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) ),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
<=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(and_elim,[status(thm)],[7]) ).
tff(44,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(and_elim,[status(thm)],[43]) ).
tff(45,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aSet0(xQ) ),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ),
inference(and_elim,[status(thm)],[45]) ).
tff(47,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(and_elim,[status(thm)],[46]) ).
tff(48,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ) ),
inference(and_elim,[status(thm)],[47]) ).
tff(49,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(and_elim,[status(thm)],[48]) ).
tff(50,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0),
inference(unit_resolution,[status(thm)],[53,50,41]) ).
tff(55,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(57,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[56]) ).
tff(58,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[57,55]) ).
tff(59,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(68,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) ),
inference(unit_resolution,[status(thm)],[74,71,58]) ).
tff(76,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) )
| aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) )
| aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) )
| aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) )
| aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(unit_resolution,[status(thm)],[78,75,54]) ).
tff(80,plain,
^ [W0: $i] :
refl(( ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
^ [W0: $i] :
trans(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )),
( ( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
<=> ( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )),
rewrite(( ( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
<=> ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )),
( ( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
<=> ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )),
rewrite(( ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )),
( ( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
<=> ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
<=> ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
<=> ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
<=> ( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
<=> ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ),
inference(and_elim,[status(thm)],[46]) ).
tff(88,plain,
! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [W0: $i] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(modus_ponens,[status(thm)],[91,81]) ).
tff(93,plain,
( ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ( ( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
<=> ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
<=> ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ ( ( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
<=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(unit_resolution,[status(thm)],[98,92]) ).
tff(100,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )),
inference(bind,[status(th)],[]) ).
tff(101,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,xQ)
=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(and_elim,[status(thm)],[44]) ).
tff(106,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ),
inference(unit_resolution,[status(thm)],[112,109,99]) ).
tff(114,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[45]) ).
tff(116,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,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(118,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)],[117]) ).
tff(119,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(120,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(121,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)],[120]) ).
tff(122,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
tff(123,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[125,118]) ).
tff(127,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ),
inference(unit_resolution,[status(thm)],[129,126,116]) ).
tff(131,plain,
( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> aElementOf0(xk,szNzAzT0) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(132,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(sbrdtbr0(xQ),szNzAzT0) ),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(xk,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
aElementOf0(xk,szNzAzT0),
inference(and_elim,[status(thm)],[2]) ).
tff(135,plain,
aElementOf0(xk,szNzAzT0),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
aElementOf0(sbrdtbr0(xQ),szNzAzT0),
inference(modus_ponens,[status(thm)],[135,132]) ).
tff(137,plain,
( ~ ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) )
| ~ aElementOf0(sbrdtbr0(xQ),szNzAzT0)
| isFinite0(xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(138,plain,
isFinite0(xQ),
inference(unit_resolution,[status(thm)],[137,136,130]) ).
tff(139,plain,
^ [W0: $i] :
refl(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(140,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
^ [W0: $i] :
rewrite(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& isFinite0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ~ ( aSet0(W0)
& isFinite0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ~ ( aSet0(W0)
& isFinite0(W0) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
rewrite(( ( ~ aSet0(W0)
| ~ isFinite0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
( ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
trans(monotonicity(rewrite(( ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) )
<=> ( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) )),
( ( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) )
<=> ( aElement0(W1)
=> ( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) )),
rewrite(( ( aElement0(W1)
=> ( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) )
<=> ( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )),
( ( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) )
<=> ( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ))),
( ! [W1: $i] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) )
<=> ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )),
( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) )
<=> ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
rewrite(( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) )
<=> ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardCons) ).
tff(150,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[152,145]) ).
tff(154,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[153,143]) ).
tff(155,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
( ( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) )
<=> ( ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
^ [W1: $i] :
rewrite(( ( aElementOf0(W1,xQ)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) )
| ~ aElement0(W1) )
<=> ( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(158,plain,
( ! [W1: $i] :
( aElementOf0(W1,xQ)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) )
| ~ aElement0(W1) )
<=> ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) )
| ~ aElement0(W1) ) )
<=> ( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ) ),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
( ( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) )
| ~ aElement0(W1) ) )
<=> ( ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ) ),
inference(transitivity,[status(thm)],[159,156]) ).
tff(161,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) )
| ~ aElement0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) )
| ~ aElement0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ) ),
inference(transitivity,[status(thm)],[161,155]) ).
tff(163,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) )
| ~ aElement0(W1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
( ~ isFinite0(xQ)
| ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ),
inference(unit_resolution,[status(thm)],[164,154,116]) ).
tff(166,plain,
! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) ),
inference(unit_resolution,[status(thm)],[165,138]) ).
tff(167,plain,
( ( ~ ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
<=> ( ~ ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,plain,
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
<=> ( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ( ~ ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
<=> ( ~ ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ( ~ ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
<=> ( ~ ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) ) ),
inference(transitivity,[status(thm)],[169,167]) ).
tff(171,plain,
( ~ ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
( ~ ! [W1: $i] :
( aElementOf0(W1,xQ)
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(xQ,W1)) = szszuzczcdt0(sbrdtbr0(xQ)) ) )
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)) ) ),
inference(unit_resolution,[status(thm)],[172,166,113]) ).
tff(174,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ)),
inference(unit_resolution,[status(thm)],[173,79]) ).
tff(175,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
inference(transitivity,[status(thm)],[174,10,4]) ).
tff(176,plain,
( ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK )
<=> ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,plain,
( ~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0: $i] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xQ)
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ) )
=> ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ) )
<=> ~ ( ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )
| ~ ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0: $i] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xQ)
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,axiom,
~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0: $i] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xQ)
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ) )
=> ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(179,plain,
~ ( ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )
| ~ ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0: $i] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xQ)
| ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ) )
| ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ) ) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK,
inference(or_elim,[status(thm)],[179]) ).
tff(181,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK,
inference(modus_ponens,[status(thm)],[180,176]) ).
tff(182,plain,
$false,
inference(unit_resolution,[status(thm)],[181,175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM580+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:32:31 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.62/0.84 % SZS status Theorem
% 0.62/0.84 % SZS output start Proof
% See solution above
% 0.71/0.87 % E exiting
%------------------------------------------------------------------------------