%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM588+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:52:45 AM UTC 2026
% Result : Theorem 63.94s 64.25s
% Output : Proof 63.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 407 ( 46 equ)
% Maximal formula atoms : 48 ( 19 avg)
% Number of connectives : 523 ( 137 ~; 110 |; 252 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 13 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 86 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1)
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& sbrdtbr0(W2) = xk
& aSubsetOf0(W2,W1)
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSet0(W2) )
=> ( ( ! [W3] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ( ( ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ( aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(f_88_1,negated_conjecture,
~ ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1)
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& sbrdtbr0(W2) = xk
& aSubsetOf0(W2,W1)
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSet0(W2) )
=> ( ( ! [W3] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ( ( ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ( aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_88_2,negated_conjecture,
? [W0] :
( ? [W1] :
( ? [W2] :
( ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W3,W2) )
& ! [W3] :
( ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| W3 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ~ aElement0(W3) )
& ( ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) )
| ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& sbrdtbr0(W2) = xk
& aSubsetOf0(W2,W1)
& ! [W3] :
( aElementOf0(W3,W1)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
& isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1)
& ! [W2] :
( ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ~ aElement0(W2) )
& ( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) )
| ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
& aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[f_88_1]) ).
fof(f_88_3,negated_conjecture,
? [U_295] :
( ? [U_294] :
( ? [U_293] :
( ~ aElementOf0(U_293,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))),xk))
& ~ aSubsetOf0(U_293,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
& ? [U_292] :
( ~ aElementOf0(U_292,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
& aElementOf0(U_292,U_293) )
& ! [U_291] :
( ( aElementOf0(U_291,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
| U_291 = szmzizndt0(sdtlpdtrp0(xN,U_295))
| ~ aElementOf0(U_291,sdtlpdtrp0(xN,U_295))
| ~ aElement0(U_291) )
& ( ( U_291 != szmzizndt0(sdtlpdtrp0(xN,U_295))
& aElementOf0(U_291,sdtlpdtrp0(xN,U_295))
& aElement0(U_291) )
| ~ aElementOf0(U_291,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
& ! [U_290] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,U_295)),U_290)
| ~ aElementOf0(U_290,sdtlpdtrp0(xN,U_295)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,U_295)),sdtlpdtrp0(xN,U_295))
& aElementOf0(U_293,slbdtsldtrb0(U_294,xk))
& sbrdtbr0(U_293) = xk
& aSubsetOf0(U_293,U_294)
& ! [U_289] :
( aElementOf0(U_289,U_294)
| ~ aElementOf0(U_289,U_293) )
& aSet0(U_293) )
& isCountable0(U_294)
& aSubsetOf0(U_294,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
& ! [U_288] :
( aElementOf0(U_288,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
| ~ aElementOf0(U_288,U_294) )
& aSet0(U_294)
& ! [U_287] :
( ( aElementOf0(U_287,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
| U_287 = szmzizndt0(sdtlpdtrp0(xN,U_295))
| ~ aElementOf0(U_287,sdtlpdtrp0(xN,U_295))
| ~ aElement0(U_287) )
& ( ( U_287 != szmzizndt0(sdtlpdtrp0(xN,U_295))
& aElementOf0(U_287,sdtlpdtrp0(xN,U_295))
& aElement0(U_287) )
| ~ aElementOf0(U_287,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
& ! [U_286] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,U_295)),U_286)
| ~ aElementOf0(U_286,sdtlpdtrp0(xN,U_295)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,U_295)),sdtlpdtrp0(xN,U_295)) )
& aElementOf0(U_295,szNzAzT0) ),
inference(variable_rename,[status(thm)],[f_88_2]) ).
fof(f_88_4,negated_conjecture,
? [U_295] :
( ? [U_294] :
( ? [U_293] :
( ~ aElementOf0(U_293,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))),xk))
& ~ aSubsetOf0(U_293,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
& ? [U_292] :
( ~ aElementOf0(U_292,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
& aElementOf0(U_292,U_293) )
& ! [U_299] :
( aElementOf0(U_299,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
| U_299 = szmzizndt0(sdtlpdtrp0(xN,U_295))
| ~ aElementOf0(U_299,sdtlpdtrp0(xN,U_295))
| ~ aElement0(U_299) )
& ! [U_298] :
( ( U_298 != szmzizndt0(sdtlpdtrp0(xN,U_295))
& aElementOf0(U_298,sdtlpdtrp0(xN,U_295))
& aElement0(U_298) )
| ~ aElementOf0(U_298,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
& ! [U_290] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,U_295)),U_290)
| ~ aElementOf0(U_290,sdtlpdtrp0(xN,U_295)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,U_295)),sdtlpdtrp0(xN,U_295))
& aElementOf0(U_293,slbdtsldtrb0(U_294,xk))
& sbrdtbr0(U_293) = xk
& aSubsetOf0(U_293,U_294)
& ! [U_289] :
( aElementOf0(U_289,U_294)
| ~ aElementOf0(U_289,U_293) )
& aSet0(U_293) )
& isCountable0(U_294)
& aSubsetOf0(U_294,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
& ! [U_288] :
( aElementOf0(U_288,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
| ~ aElementOf0(U_288,U_294) )
& aSet0(U_294)
& ! [U_297] :
( aElementOf0(U_297,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
| U_297 = szmzizndt0(sdtlpdtrp0(xN,U_295))
| ~ aElementOf0(U_297,sdtlpdtrp0(xN,U_295))
| ~ aElement0(U_297) )
& ! [U_296] :
( ( U_296 != szmzizndt0(sdtlpdtrp0(xN,U_295))
& aElementOf0(U_296,sdtlpdtrp0(xN,U_295))
& aElement0(U_296) )
| ~ aElementOf0(U_296,sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,U_295),szmzizndt0(sdtlpdtrp0(xN,U_295))))
& ! [U_286] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,U_295)),U_286)
| ~ aElementOf0(U_286,sdtlpdtrp0(xN,U_295)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,U_295)),sdtlpdtrp0(xN,U_295)) )
& aElementOf0(U_295,szNzAzT0) ),
inference(miniscope,[status(thm)],[f_88_3]) ).
fof(f_88_5,negated_conjecture,
( ? [U_294] :
( ? [U_293] :
( ~ aElementOf0(U_293,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ~ aSubsetOf0(U_293,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ? [U_292] :
( ~ aElementOf0(U_292,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(U_292,U_293) )
& ! [U_299] :
( aElementOf0(U_299,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| U_299 = szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ aElementOf0(U_299,sdtlpdtrp0(xN,sK43))
| ~ aElement0(U_299) )
& ! [U_298] :
( ( U_298 != szmzizndt0(sdtlpdtrp0(xN,sK43))
& aElementOf0(U_298,sdtlpdtrp0(xN,sK43))
& aElement0(U_298) )
| ~ aElementOf0(U_298,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_290] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),U_290)
| ~ aElementOf0(U_290,sdtlpdtrp0(xN,sK43)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aElementOf0(U_293,slbdtsldtrb0(U_294,xk))
& sbrdtbr0(U_293) = xk
& aSubsetOf0(U_293,U_294)
& ! [U_289] :
( aElementOf0(U_289,U_294)
| ~ aElementOf0(U_289,U_293) )
& aSet0(U_293) )
& isCountable0(U_294)
& aSubsetOf0(U_294,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_288] :
( aElementOf0(U_288,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| ~ aElementOf0(U_288,U_294) )
& aSet0(U_294)
& ! [U_297] :
( aElementOf0(U_297,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| U_297 = szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ aElementOf0(U_297,sdtlpdtrp0(xN,sK43))
| ~ aElement0(U_297) )
& ! [U_296] :
( ( U_296 != szmzizndt0(sdtlpdtrp0(xN,sK43))
& aElementOf0(U_296,sdtlpdtrp0(xN,sK43))
& aElement0(U_296) )
| ~ aElementOf0(U_296,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_286] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),U_286)
| ~ aElementOf0(U_286,sdtlpdtrp0(xN,sK43)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43)) )
& aElementOf0(sK43,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_295,sK43)],[f_88_4]) ).
fof(f_88_6,negated_conjecture,
( ? [U_293] :
( ~ aElementOf0(U_293,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ~ aSubsetOf0(U_293,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ? [U_292] :
( ~ aElementOf0(U_292,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(U_292,U_293) )
& ! [U_299] :
( aElementOf0(U_299,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| U_299 = szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ aElementOf0(U_299,sdtlpdtrp0(xN,sK43))
| ~ aElement0(U_299) )
& ! [U_298] :
( ( U_298 != szmzizndt0(sdtlpdtrp0(xN,sK43))
& aElementOf0(U_298,sdtlpdtrp0(xN,sK43))
& aElement0(U_298) )
| ~ aElementOf0(U_298,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_290] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),U_290)
| ~ aElementOf0(U_290,sdtlpdtrp0(xN,sK43)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aElementOf0(U_293,slbdtsldtrb0(sK44,xk))
& sbrdtbr0(U_293) = xk
& aSubsetOf0(U_293,sK44)
& ! [U_289] :
( aElementOf0(U_289,sK44)
| ~ aElementOf0(U_289,U_293) )
& aSet0(U_293) )
& isCountable0(sK44)
& aSubsetOf0(sK44,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_288] :
( aElementOf0(U_288,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| ~ aElementOf0(U_288,sK44) )
& aSet0(sK44)
& ! [U_297] :
( aElementOf0(U_297,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| U_297 = szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ aElementOf0(U_297,sdtlpdtrp0(xN,sK43))
| ~ aElement0(U_297) )
& ! [U_296] :
( ( U_296 != szmzizndt0(sdtlpdtrp0(xN,sK43))
& aElementOf0(U_296,sdtlpdtrp0(xN,sK43))
& aElement0(U_296) )
| ~ aElementOf0(U_296,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_286] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),U_286)
| ~ aElementOf0(U_286,sdtlpdtrp0(xN,sK43)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aElementOf0(sK43,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_294,sK44)],[f_88_5]) ).
fof(f_88_7,negated_conjecture,
( ~ aElementOf0(sK45,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ~ aSubsetOf0(sK45,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ? [U_292] :
( ~ aElementOf0(U_292,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(U_292,sK45) )
& ! [U_299] :
( aElementOf0(U_299,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| U_299 = szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ aElementOf0(U_299,sdtlpdtrp0(xN,sK43))
| ~ aElement0(U_299) )
& ! [U_298] :
( ( U_298 != szmzizndt0(sdtlpdtrp0(xN,sK43))
& aElementOf0(U_298,sdtlpdtrp0(xN,sK43))
& aElement0(U_298) )
| ~ aElementOf0(U_298,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_290] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),U_290)
| ~ aElementOf0(U_290,sdtlpdtrp0(xN,sK43)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aElementOf0(sK45,slbdtsldtrb0(sK44,xk))
& sbrdtbr0(sK45) = xk
& aSubsetOf0(sK45,sK44)
& ! [U_289] :
( aElementOf0(U_289,sK44)
| ~ aElementOf0(U_289,sK45) )
& aSet0(sK45)
& isCountable0(sK44)
& aSubsetOf0(sK44,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_288] :
( aElementOf0(U_288,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| ~ aElementOf0(U_288,sK44) )
& aSet0(sK44)
& ! [U_297] :
( aElementOf0(U_297,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| U_297 = szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ aElementOf0(U_297,sdtlpdtrp0(xN,sK43))
| ~ aElement0(U_297) )
& ! [U_296] :
( ( U_296 != szmzizndt0(sdtlpdtrp0(xN,sK43))
& aElementOf0(U_296,sdtlpdtrp0(xN,sK43))
& aElement0(U_296) )
| ~ aElementOf0(U_296,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_286] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),U_286)
| ~ aElementOf0(U_286,sdtlpdtrp0(xN,sK43)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aElementOf0(sK43,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_293,sK45)],[f_88_6]) ).
fof(f_88_8,negated_conjecture,
( ~ aElementOf0(sK45,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ~ aSubsetOf0(sK45,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ~ aElementOf0(sK46,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(sK46,sK45)
& ! [U_299] :
( aElementOf0(U_299,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| U_299 = szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ aElementOf0(U_299,sdtlpdtrp0(xN,sK43))
| ~ aElement0(U_299) )
& ! [U_298] :
( ( U_298 != szmzizndt0(sdtlpdtrp0(xN,sK43))
& aElementOf0(U_298,sdtlpdtrp0(xN,sK43))
& aElement0(U_298) )
| ~ aElementOf0(U_298,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_290] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),U_290)
| ~ aElementOf0(U_290,sdtlpdtrp0(xN,sK43)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aElementOf0(sK45,slbdtsldtrb0(sK44,xk))
& sbrdtbr0(sK45) = xk
& aSubsetOf0(sK45,sK44)
& ! [U_289] :
( aElementOf0(U_289,sK44)
| ~ aElementOf0(U_289,sK45) )
& aSet0(sK45)
& isCountable0(sK44)
& aSubsetOf0(sK44,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_288] :
( aElementOf0(U_288,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| ~ aElementOf0(U_288,sK44) )
& aSet0(sK44)
& ! [U_297] :
( aElementOf0(U_297,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| U_297 = szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ aElementOf0(U_297,sdtlpdtrp0(xN,sK43))
| ~ aElement0(U_297) )
& ! [U_296] :
( ( U_296 != szmzizndt0(sdtlpdtrp0(xN,sK43))
& aElementOf0(U_296,sdtlpdtrp0(xN,sK43))
& aElement0(U_296) )
| ~ aElementOf0(U_296,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_286] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),U_286)
| ~ aElementOf0(U_286,sdtlpdtrp0(xN,sK43)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aElementOf0(sK43,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_292,sK46)],[f_88_7]) ).
fof(f_88_9,negated_conjecture,
( ! [U_298] :
( U_298 != szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ sP103(U_298) )
& ! [U_298] :
( aElementOf0(U_298,sdtlpdtrp0(xN,sK43))
| ~ sP103(U_298) )
& ! [U_298] :
( aElement0(U_298)
| ~ sP103(U_298) )
& ! [U_296] :
( U_296 != szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ sP102(U_296) )
& ! [U_296] :
( aElementOf0(U_296,sdtlpdtrp0(xN,sK43))
| ~ sP102(U_296) )
& ! [U_296] :
( aElement0(U_296)
| ~ sP102(U_296) )
& ~ aElementOf0(sK45,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ~ aSubsetOf0(sK45,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ~ aElementOf0(sK46,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(sK46,sK45)
& ! [U_299] :
( aElementOf0(U_299,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| U_299 = szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ aElementOf0(U_299,sdtlpdtrp0(xN,sK43))
| ~ aElement0(U_299) )
& ! [U_298] :
( sP103(U_298)
| ~ aElementOf0(U_298,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_290] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),U_290)
| ~ aElementOf0(U_290,sdtlpdtrp0(xN,sK43)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aElementOf0(sK45,slbdtsldtrb0(sK44,xk))
& sbrdtbr0(sK45) = xk
& aSubsetOf0(sK45,sK44)
& ! [U_289] :
( aElementOf0(U_289,sK44)
| ~ aElementOf0(U_289,sK45) )
& aSet0(sK45)
& isCountable0(sK44)
& aSubsetOf0(sK44,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_288] :
( aElementOf0(U_288,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| ~ aElementOf0(U_288,sK44) )
& aSet0(sK44)
& ! [U_297] :
( aElementOf0(U_297,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| U_297 = szmzizndt0(sdtlpdtrp0(xN,sK43))
| ~ aElementOf0(U_297,sdtlpdtrp0(xN,sK43))
| ~ aElement0(U_297) )
& ! [U_296] :
( sP102(U_296)
| ~ aElementOf0(U_296,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [U_286] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),U_286)
| ~ aElementOf0(U_286,sdtlpdtrp0(xN,sK43)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aElementOf0(sK43,szNzAzT0) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102,sP103])],[f_88_8]) ).
cnf(f_88_17,negated_conjecture,
( aElementOf0(U_288,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| ~ aElementOf0(U_288,sK44) ),
inference(clausify,[status(thm)],[f_88_9]) ).
cnf(f_88_21,negated_conjecture,
( aElementOf0(U_289,sK44)
| ~ aElementOf0(U_289,sK45) ),
inference(clausify,[status(thm)],[f_88_9]) ).
cnf(f_88_30,negated_conjecture,
aElementOf0(sK46,sK45),
inference(clausify,[status(thm)],[f_88_9]) ).
cnf(f_88_31,negated_conjecture,
~ aElementOf0(sK46,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))),
inference(clausify,[status(thm)],[f_88_9]) ).
cnf(t1,plain,
( aElementOf0(sK46,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| ~ aElementOf0(sK46,sK44) ),
inference(start,[status(thm),parent(0:0)],[f_88_17]) ).
cnf(t2,plain,
( ~ aElementOf0(sK46,sK45)
| aElementOf0(sK46,sK44) ),
inference(extension,[status(thm),parent(t1:1)],[f_88_21]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aElementOf0(sK46,sK45),
inference(extension,[status(thm),parent(t2:2)],[f_88_30]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ aElementOf0(sK46,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))),
inference(extension,[status(thm),parent(t1:2)],[f_88_31]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t1:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM588+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 18:53:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 63.94/64.25 % SZS status Theorem for theBenchmark
% 63.94/64.25 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------