%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM584+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 : Sun Sep 27 08:09:13 AM UTC 2026
% Result : Theorem 13.80s 4.00s
% Output : Refutation 14.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 205 ( 39 equ; 0 cnn)
% Maximal formula atoms : 22 ( 9 avg)
% Number of connectives : 1147 ( 38 ~; 55 |; 86 &; 926 @)
% ( 4 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 40 !; 0 ?; 41 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(szmzizndt0_decl,type,
szmzizndt0: $i > $i ).
thf(sdtlseqdt0_decl,type,
sdtlseqdt0: $i > $i > $o ).
thf(slbdtsldtrb0_decl,type,
slbdtsldtrb0: $i > $i > $i ).
thf(sbrdtbr0_decl,type,
sbrdtbr0: $i > $i ).
thf(sdtlpdtrp0_decl,type,
sdtlpdtrp0: $i > $i > $i ).
thf(xN_decl,type,
xN: $i ).
thf(xi_decl,type,
xi: $i ).
thf(xQ_decl,type,
xQ: $i ).
thf(xS_decl,type,
xS: $i ).
thf(xK_decl,type,
xK: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) )
=> ( ( ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xK @ ( xS @ slbdtsldtrb0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aElementOf0 ) )
| ( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
= xK )
& ( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) )
=> ( ( ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xK @ ( xS @ slbdtsldtrb0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aElementOf0 ) )
| ( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
= xK )
& ( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(91,plain,
~ ( ( ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) )
=> ( ( ! [A: $i] :
( ( ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xK @ ( xS @ slbdtsldtrb0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aElementOf0 ) )
| ( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
= xK )
& ( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(92,plain,
~ ( ( ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) )
=> ( ( ! [A: $i] :
( ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xK @ ( xS @ slbdtsldtrb0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aElementOf0 ) )
| ( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
= xK )
& ( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[91]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( xK @ ( xS @ slbdtsldtrb0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aElementOf0 ) )
& ( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
!= xK )
| ~ ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) ) )
& ( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
!= xK )
| ~ ( xS @ ( sk1 @ aElementOf0 ) ) )
& ( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
!= xK )
| ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( sk1 @ aElementOf0 ) ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( C @ aElementOf0 ) )
| ( C
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ~ ( C @ aElement0 ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( C @ aElementOf0 ) )
| ~ ( xQ @ ( C @ aElementOf0 ) )
| ~ ( C @ aElement0 ) )
& ( ( B
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( B @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( B @ aElementOf0 ) ) )
& ( ( B @ aElement0 )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( B @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 )
& ( ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[92]) ).
thf(104,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
!= xK )
| ~ ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) ) ),
inference(cnfConj,[status(thm)],[93]) ).
thf(113,plain,
( ~ ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
!= xK ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(77,axiom,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
= xK )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4007) ).
thf(682,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
= xK )
& ! [A: $i] :
( ( ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(683,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
= xK )
& ! [A: $i] :
( ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ),
inference(miniscope,[status(thm)],[682]) ).
thf(684,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
= xK )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( C @ aElementOf0 ) )
| ( C
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ~ ( C @ aElement0 ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( C @ aElementOf0 ) )
| ~ ( xQ @ ( C @ aElementOf0 ) )
| ~ ( C @ aElement0 ) )
& ( ( B
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( B @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( B @ aElementOf0 ) ) )
& ( ( B @ aElement0 )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( B @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 )
& ( ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[683]) ).
thf(692,plain,
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
= xK ),
inference(cnfConj,[status(thm)],[684]) ).
thf(699,plain,
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ sbrdtbr0 )
= xK ),
inference(lifteq,[status(thm)],[692]) ).
thf(75,axiom,
( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4024) ).
thf(627,plain,
( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(628,plain,
( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ),
inference(miniscope,[status(thm)],[627]) ).
thf(629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
& ( ( xS @ ( D @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( D @ aElementOf0 ) ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( C @ aElementOf0 ) )
| ( C
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ~ ( C @ aElement0 ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( C @ aElementOf0 ) )
| ~ ( xQ @ ( C @ aElementOf0 ) )
| ~ ( C @ aElement0 ) )
& ( ( B
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( B @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( B @ aElementOf0 ) ) )
& ( ( B @ aElement0 )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( B @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSet0 )
& ( ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[628]) ).
thf(638,plain,
xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ),
inference(cnfConj,[status(thm)],[629]) ).
thf(1796,plain,
( ~ $true
| ( xK != xK ) ),
inference(rewrite,[status(thm)],[113,699,638]) ).
thf(1797,plain,
$false,
inference(simp,[status(thm)],[1796]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM584+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.06/0.32 % Computer : n012.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.32 % CPULimit : 300
% 0.06/0.32 % WCLimit : 300
% 0.06/0.32 % DateTime : Sat Sep 26 03:19:50 UTC 2026
% 0.06/0.32 % CPUTime :
% 0.06/0.32 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.52/0.62 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.77 % [INFO] Parsing done (148ms).
% 0.68/0.78 % [INFO] Running in sequential loop mode.
% 1.30/0.99 % [INFO] eprover registered as external prover.
% 1.30/0.99 % [INFO] Scanning for conjecture ...
% 1.53/1.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.05 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.05 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.07 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.07 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.10 % [INFO] Found a conjecture (or negated_conjecture) and 88 axioms. Running axiom selection ...
% 1.75/1.17 % [INFO] Axiom selection finished. Selected 88 axioms (removed 0 axioms).
% 1.75/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.23 % [INFO] Problem is first-order (TPTP FOF).
% 2.01/1.24 % [INFO] Type checking passed.
% 2.01/1.24 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 13.80/4.00 % [INFO] Killing All external provers ...
% 13.80/4.00 % Time passed: 3603ms (effective reasoning time: 3217ms)
% 13.80/4.00 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 13.80/4.00 % Axioms used in derivation (2): m__4007, m__4024
% 13.80/4.00 % No. of inferences in proof: 20
% 13.80/4.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3603 ms resp. 3217 ms w/o parsing
% 14.33/4.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.33/4.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------