%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM624+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:38 AM UTC 2025
% Result : Theorem 0.86s 1.06s
% Output : Proof 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 44
% Syntax : Number of formulae : 114 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 878 ( 65 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 1273 ( 565 ~; 456 |; 144 &)
% ( 72 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 56 ( 56 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 200 ( 184 !; 1 ?; 200 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xN_type,type,
xN: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xe_type,type,
xe: $i ).
tff(xx_type,type,
xx: $i ).
tff(xp_type,type,
xp: $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(xP_type,type,
xP: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(1,plain,
( aElementOf0(xm,szNzAzT0)
<=> aElementOf0(xm,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aElementOf0(xm,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5389) ).
tff(3,plain,
aElementOf0(xm,szNzAzT0),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aElementOf0(xm,szNzAzT0),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,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(6,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)],[5]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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(10,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)],[9]) ).
tff(11,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)],[10,8]) ).
tff(12,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(13,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)],[12]) ).
tff(14,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(15,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(16,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)],[15]) ).
tff(17,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(18,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)],[17,16]) ).
tff(19,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)],[18,14]) ).
tff(20,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)],[19]) ).
tff(21,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)],[20,13]) ).
tff(22,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)],[21,11]) ).
tff(23,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)],[22,6]) ).
tff(24,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(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) )
<=> ( ~ ! [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(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) ) ) )
<=> ( ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,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(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| 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(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,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(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| 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(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ) ),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,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(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,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(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ),
inference(unit_resolution,[status(thm)],[29,23,4]) ).
tff(31,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) ) ),
inference(tautology,[status(thm)],[]) ).
tff(32,plain,
! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) ),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ( xp = szmzizndt0(xQ) )
<=> ( xp = szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& ( xp = szmzizndt0(xQ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
tff(35,plain,
xp = szmzizndt0(xQ),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
xp = szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[35,33]) ).
tff(37,plain,
szmzizndt0(xQ) = xp,
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
<=> aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
<=> aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
<=> aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
& aElementOf0(xx,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5481) ).
tff(42,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[42,40]) ).
tff(44,plain,
aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| aElementOf0(szmzizndt0(xQ),szNzAzT0) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| aElementOf0(szmzizndt0(xQ),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| aElementOf0(szmzizndt0(xQ),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xm))
| aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| aElementOf0(szmzizndt0(xQ),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
aElementOf0(szmzizndt0(xQ),szNzAzT0),
inference(unit_resolution,[status(thm)],[47,44,32]) ).
tff(49,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
<=> ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,W0) )
<=> ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5401) ).
tff(55,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,szmzizndt0(xQ)) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(unit_resolution,[status(thm)],[61,58]) ).
tff(63,plain,
sdtlseqdt0(xx,szmzizndt0(xQ)),
inference(unit_resolution,[status(thm)],[62,44]) ).
tff(64,plain,
( aElementOf0(xx,xQ)
<=> aElementOf0(xx,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
( aElement0(xx)
& aElementOf0(xx,xQ)
& ( xx != szmzizndt0(xQ) )
& aElementOf0(xx,xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
tff(66,plain,
( aElement0(xx)
& aElementOf0(xx,xQ)
& ( xx != szmzizndt0(xQ) ) ),
inference(and_elim,[status(thm)],[65]) ).
tff(67,plain,
( aElement0(xx)
& aElementOf0(xx,xQ) ),
inference(and_elim,[status(thm)],[66]) ).
tff(68,plain,
aElementOf0(xx,xQ),
inference(and_elim,[status(thm)],[67]) ).
tff(69,plain,
aElementOf0(xx,xQ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
<=> ( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
<=> ( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,axiom,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != szmzizndt0(xQ) ) ) )
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
tff(76,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != szmzizndt0(xQ) ) ) ) ),
inference(and_elim,[status(thm)],[75]) ).
tff(77,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(and_elim,[status(thm)],[76]) ).
tff(78,plain,
! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ),
inference(and_elim,[status(thm)],[77]) ).
tff(79,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ),
inference(modus_ponens,[status(thm)],[81,71]) ).
tff(83,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
| ~ aElementOf0(xx,xQ)
| sdtlseqdt0(szmzizndt0(xQ),xx) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
| ~ aElementOf0(xx,xQ)
| sdtlseqdt0(szmzizndt0(xQ),xx) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
| ~ aElementOf0(xx,xQ)
| sdtlseqdt0(szmzizndt0(xQ),xx) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
| ~ aElementOf0(xx,xQ)
| sdtlseqdt0(szmzizndt0(xQ),xx) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
sdtlseqdt0(szmzizndt0(xQ),xx),
inference(unit_resolution,[status(thm)],[85,82,69]) ).
tff(87,plain,
( aElementOf0(xx,szNzAzT0)
<=> aElementOf0(xx,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
( aElementOf0(xx,szNzAzT0)
& ? [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5365) ).
tff(89,plain,
aElementOf0(xx,szNzAzT0),
inference(and_elim,[status(thm)],[88]) ).
tff(90,plain,
aElementOf0(xx,szNzAzT0),
inference(modus_ponens,[status(thm)],[89,87]) ).
tff(91,plain,
( ( xx != szmzizndt0(xQ) )
<=> ( xx != szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
xx != szmzizndt0(xQ),
inference(and_elim,[status(thm)],[66]) ).
tff(93,plain,
xx != szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,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) ) )),
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ~ ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ~ ~ ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) ) )),
rewrite(( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
tff(102,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[105,95]) ).
tff(107,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ( ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ aElementOf0(xx,szNzAzT0)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) )
<=> ( ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ aElementOf0(xx,szNzAzT0)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ aElementOf0(xx,szNzAzT0)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ) ),
inference(transitivity,[status(thm)],[109,107]) ).
tff(111,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ aElementOf0(xx,szNzAzT0)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(unit_resolution,[status(thm)],[112,106,93,90,86]) ).
tff(114,plain,
$false,
inference(unit_resolution,[status(thm)],[113,63,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM624+3 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.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 01:37:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.86/1.06 % SZS status Theorem
% 0.86/1.06 % SZS output start Proof
% See solution above
% 0.93/1.08 % E exiting
%------------------------------------------------------------------------------