%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM583+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 216.44s 138.09s
% Output : Refutation 216.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 231 ( 42 equ; 0 cnn)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1236 ( 50 ~; 62 |; 75 &;1013 @)
% ( 3 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 50 ( 0 ^; 49 !; 0 ?; 50 :)
% ( 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(sdtmndt0_decl,type,
sdtmndt0: $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 ) )
=> ( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/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 ) )
=> ( ( 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 ) )
=> ( ( 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 ) )
=> ( ( 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] :
( ~ ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ aSubsetOf0 ) )
& ~ ( xS @ ( sk1 @ aElementOf0 ) )
& ( 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(97,plain,
xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( sk1 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[93]) ).
thf(99,plain,
! [A: $i] :
( ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xQ @ ( A @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[93]) ).
thf(105,plain,
! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(106,plain,
! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(840,plain,
! [A: $i] :
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( sk1 @ aElementOf0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
| ( xQ @ ( A @ aElementOf0 ) )
| ~ $true
| ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) ) ),
inference(paramod_ordered,[status(thm)],[97,106]) ).
thf(841,plain,
! [A: $i] :
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( sk1 @ aElementOf0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xQ @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
| ( xQ @ ( A @ aElementOf0 ) )
| ( A
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) ) ),
inference(simp,[status(thm)],[840]) ).
thf(842,plain,
( ( xQ @ ( sk1 @ aElementOf0 ) )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[841:[bind(A,$thf( sk1 ))]]) ).
thf(12,axiom,
( ( xk @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xk )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( xQ @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( A
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ 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/sandbox2/benchmark/theBenchmark.p',m__3989_02) ).
thf(161,plain,
( ( xk @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xk )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( xQ @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 )
& ! [A: $i] :
( ( ( ( A
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( ( A
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ 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)],[12]) ).
thf(162,plain,
( ( xk @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xk )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( xQ @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 )
& ! [A: $i] :
( ( ( A
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( ( A
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ 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)],[161]) ).
thf(163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( xk @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xk )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( xQ @ aSubsetOf0 ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( D @ aElementOf0 ) )
| ~ ( xQ @ ( D @ aElementOf0 ) ) )
& ( xQ @ aSet0 )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( C @ aElementOf0 ) )
| ( C
= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ ( C @ aElementOf0 ) )
| ~ ( C @ aElement0 ) )
& ( ( B
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) ) )
& ( ( B @ aElement0 )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ aSet0 )
& ( ( A @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[162]) ).
thf(172,plain,
! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xQ @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(181,plain,
! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xQ @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(13259,plain,
! [A: $i] :
( ( ( xQ @ ( sk1 @ aElementOf0 ) )
!= ( xQ @ ( A @ aElementOf0 ) ) )
| ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ $true
| ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 )
= sk1 ) ),
inference(paramod_ordered,[status(thm)],[842,181]) ).
thf(13260,plain,
! [A: $i] :
( ( ( xQ @ ( sk1 @ aElementOf0 ) )
!= ( xQ @ ( A @ aElementOf0 ) ) )
| ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 )
= sk1 ) ),
inference(simp,[status(thm)],[13259]) ).
thf(13261,plain,
( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( sk1 @ aElementOf0 ) )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[13260:[bind(A,$thf( sk1 ))]]) ).
thf(175,plain,
! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(183,plain,
! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(23834,plain,
! [A: $i] :
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( sk1 @ aElementOf0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
| ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
| ~ $true
| ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 )
= sk1 ) ),
inference(paramod_ordered,[status(thm)],[13261,183]) ).
thf(23835,plain,
! [A: $i] :
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( sk1 @ aElementOf0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
| ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 )
= sk1 ) ),
inference(simp,[status(thm)],[23834]) ).
thf(23836,plain,
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( sk1 @ aElementOf0 ) )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[23835:[bind(A,$thf( sk1 ))]]) ).
thf(102,plain,
xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[93]) ).
thf(25955,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 )
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xi @ ( xN @ sdtlpdtrp0 ) @ ( sk1 @ aElementOf0 ) )
| ( xi @ ( xN @ sdtlpdtrp0 ) @ ( sk1 @ aElementOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[23836,102]) ).
thf(25956,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 )
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ( xi @ ( xN @ sdtlpdtrp0 ) @ ( sk1 @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[25955]) ).
thf(25957,plain,
xi @ ( xN @ sdtlpdtrp0 ) @ ( sk1 @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[25956:[]]) ).
thf(51,axiom,
( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4037) ).
thf(462,plain,
( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(463,plain,
! [A: $i] :
( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[462]) ).
thf(464,plain,
! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[463]) ).
thf(241349,plain,
! [A: $i] :
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( sk1 @ aElementOf0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) )
| ( xS @ ( A @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25957,464]) ).
thf(241350,plain,
! [A: $i] :
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( sk1 @ aElementOf0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) )
| ( xS @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[241349]) ).
thf(241351,plain,
xS @ ( sk1 @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[241350:[bind(A,$thf( sk1 ))]]) ).
thf(103,plain,
~ ( xS @ ( sk1 @ aElementOf0 ) ),
inference(cnfConj,[status(thm)],[93]) ).
thf(241727,plain,
$false,
inference(rewrite,[status(thm)],[241351,103]) ).
thf(241728,plain,
$false,
inference(simp,[status(thm)],[241727]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM583+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/5.40 % Computer : n020.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.16/5.40 % CPULimit : 300
% 0.16/5.40 % WCLimit : 300
% 0.16/5.40 % DateTime : Sat Sep 26 03:20:57 UTC 2026
% 0.16/5.40 % CPUTime :
% 0.16/5.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/5.71 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/5.87 % [INFO] Parsing done (158ms).
% 0.16/5.88 % [INFO] Running in sequential loop mode.
% 1.75/6.10 % [INFO] eprover registered as external prover.
% 1.75/6.11 % [INFO] Scanning for conjecture ...
% 2.04/6.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/6.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/6.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/6.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/6.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/6.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/6.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/6.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/6.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/6.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/6.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/6.22 % [INFO] Found a conjecture (or negated_conjecture) and 88 axioms. Running axiom selection ...
% 2.54/6.30 % [INFO] Axiom selection finished. Selected 88 axioms (removed 0 axioms).
% 2.54/6.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.54/6.39 % [INFO] Type checking passed.
% 2.54/6.39 % [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 ...
% 216.44/138.08 % [INFO] Killing All external provers ...
% 216.44/138.08 % Time passed: 132594ms (effective reasoning time: 132196ms)
% 216.44/138.08 % 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)>
% 216.44/138.09 % Axioms used in derivation (2): m__3989_02, m__4037
% 216.44/138.09 % No. of inferences in proof: 40
% 216.44/138.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 132594 ms resp. 132196 ms w/o parsing
% 216.64/138.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 216.64/138.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------