%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM537+2 : 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 : n013.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 08:09:05 AM UTC 2026
% Result : Theorem 70.23s 31.19s
% Output : Refutation 70.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 6
% Syntax : Number of formulae : 79 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 460 ( 82 equ; 0 cnn)
% Maximal formula atoms : 78 ( 5 avg)
% Number of connectives : 1480 ( 168 ~; 197 |; 92 &; 969 @)
% ( 8 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 72 ( 0 ^; 70 !; 0 ?; 72 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% 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(xS_decl,type,
xS: $i ).
thf(xx_decl,type,
xx: $i ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( xS @ ( A @ aElementOf0 ) )
=> ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(1,conjecture,
( ( ( ! [A: $i] :
( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtpldt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSet0 ) )
=> ( ( xS @ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) )
& ( ( ! [A: $i] :
( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtpldt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSet0 ) )
=> ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( xS @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
=> ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( ! [A: $i] :
( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtpldt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSet0 ) )
=> ( ( xS @ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) )
& ( ( ! [A: $i] :
( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtpldt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSet0 ) )
=> ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( xS @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
=> ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ( ( ( ! [A: $i] :
( ( ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) ) )
& ( xx @ ( xS @ sdtpldt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) ) )
& ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSet0 ) )
=> ( ( xS @ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) )
& ( ( ! [A: $i] :
( ( ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) ) )
& ( xx @ ( xS @ sdtpldt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) ) )
& ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSet0 ) )
=> ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( xS @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
=> ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,plain,
~ ( ( ( ! [A: $i] :
( ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtpldt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSet0 ) )
=> ( ( xS @ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) )
& ( ( ! [A: $i] :
( ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtpldt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( ( A != xx )
& ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSet0 ) )
=> ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( xS @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
=> ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[22]) ).
thf(24,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( xS @ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSubsetOf0 ) )
| sk1 )
& ( ~ ( xS @ ( sk3 @ aElementOf0 ) )
| sk1 )
& ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
| sk1 )
& ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( H @ aElementOf0 ) )
| ( H = xx )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( H @ aElementOf0 ) )
| ~ ( H @ aElement0 )
| sk1 )
& ( ( G != xx )
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( G @ aElementOf0 ) )
| sk1 )
& ( ( xx @ ( xS @ sdtpldt0 ) @ ( G @ aElementOf0 ) )
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( G @ aElementOf0 ) )
| sk1 )
& ( ( G @ aElement0 )
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( G @ aElementOf0 ) )
| sk1 )
& ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSet0 )
| sk1 )
& ( ( xx @ ( xS @ sdtpldt0 ) @ ( F @ aElementOf0 ) )
| ( F != xx )
| ~ ( F @ aElement0 )
| sk1 )
& ( ( xx @ ( xS @ sdtpldt0 ) @ ( F @ aElementOf0 ) )
| ~ ( xS @ ( F @ aElementOf0 ) )
| ~ ( F @ aElement0 )
| sk1 )
& ( ( E = xx )
| ( xS @ ( E @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( E @ aElementOf0 ) )
| sk1 )
& ( ( E @ aElement0 )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( E @ aElementOf0 ) )
| sk1 )
& ( ( xx @ ( xS @ sdtpldt0 ) @ aSet0 )
| sk1 )
& ( ~ sk1
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( xS @ aSubsetOf0 ) ) )
& ( ~ sk1
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) ) )
& ( ~ sk1
| ( xS @ ( sk2 @ aElementOf0 ) ) )
& ( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( D @ aElementOf0 ) )
| ( D = xx )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( D @ aElementOf0 ) )
| ~ ( D @ aElement0 ) )
& ( ~ sk1
| ( C != xx )
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( C @ aElementOf0 ) ) )
& ( ~ sk1
| ( xx @ ( xS @ sdtpldt0 ) @ ( C @ aElementOf0 ) )
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( C @ aElementOf0 ) ) )
& ( ~ sk1
| ( C @ aElement0 )
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( C @ aElementOf0 ) ) )
& ( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ aSet0 ) )
& ( ~ sk1
| ( xx @ ( xS @ sdtpldt0 ) @ ( B @ aElementOf0 ) )
| ( B != xx )
| ~ ( B @ aElement0 ) )
& ( ~ sk1
| ( xx @ ( xS @ sdtpldt0 ) @ ( B @ aElementOf0 ) )
| ~ ( xS @ ( B @ aElementOf0 ) )
| ~ ( B @ aElement0 ) )
& ( ~ sk1
| ( A = xx )
| ( xS @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ( ~ sk1
| ( A @ aElement0 )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ( ~ sk1
| ( xx @ ( xS @ sdtpldt0 ) @ aSet0 ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(42,plain,
( ~ sk1
| ( xS @ ( sk2 @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(34,plain,
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
| sk1 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(41,plain,
! [A: $i] :
( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| sk1 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(51,plain,
! [A: $i] :
( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| sk1 ),
inference(simp,[status(thm)],[41]) ).
thf(548,plain,
! [A: $i] :
( ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
| ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[34,51]) ).
thf(549,plain,
! [A: $i] :
( ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
| ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| sk1 ),
inference(simp,[status(thm)],[548]) ).
thf(550,plain,
( ( xx @ ( xS @ sdtpldt0 ) @ ( sk3 @ aElementOf0 ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[549:[bind(A,$thf( sk3 ))]]) ).
thf(40,plain,
! [A: $i] :
( ( A = xx )
| ( xS @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| sk1 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(67,plain,
! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| sk1
| ( A = xx ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(68,plain,
! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| sk1
| ( A = xx ) ),
inference(simp,[status(thm)],[67]) ).
thf(559,plain,
! [A: $i] :
( ( ( xx @ ( xS @ sdtpldt0 ) @ ( sk3 @ aElementOf0 ) )
!= ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
| ( xS @ ( A @ aElementOf0 ) )
| ~ $true
| sk1
| ( A = xx )
| sk1 ),
inference(paramod_ordered,[status(thm)],[550,68]) ).
thf(560,plain,
! [A: $i] :
( ( ( xx @ ( xS @ sdtpldt0 ) @ ( sk3 @ aElementOf0 ) )
!= ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
| ( xS @ ( A @ aElementOf0 ) )
| ( A = xx )
| sk1 ),
inference(simp,[status(thm)],[559]) ).
thf(561,plain,
( ( xS @ ( sk3 @ aElementOf0 ) )
| ( sk3 = xx )
| sk1 ),
inference(pattern_uni,[status(thm)],[560:[bind(A,$thf( sk3 ))]]) ).
thf(46,plain,
( ~ ( xS @ ( sk3 @ aElementOf0 ) )
| sk1 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(689,plain,
( ( ( xS @ ( sk3 @ aElementOf0 ) )
!= ( xS @ ( sk3 @ aElementOf0 ) ) )
| ~ $true
| sk1
| ( sk3 = xx )
| sk1 ),
inference(paramod_ordered,[status(thm)],[561,46]) ).
thf(690,plain,
( ( ( xS @ ( sk3 @ aElementOf0 ) )
!= ( xS @ ( sk3 @ aElementOf0 ) ) )
| ( sk3 = xx )
| sk1 ),
inference(simp,[status(thm)],[689]) ).
thf(691,plain,
( ( sk3 = xx )
| sk1 ),
inference(pattern_uni,[status(thm)],[690:[]]) ).
thf(48,plain,
! [A: $i] :
( ( A != xx )
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| sk1 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(53,plain,
! [A: $i] :
( ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| sk1
| ( A != xx ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(54,plain,
( ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( xx @ aElementOf0 ) )
| sk1 ),
inference(simp,[status(thm)],[53]) ).
thf(519,plain,
( ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( xx @ aElementOf0 ) ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[34,54]) ).
thf(520,plain,
( ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( xx @ aElementOf0 ) ) )
| sk1 ),
inference(simp,[status(thm)],[519]) ).
thf(521,plain,
( ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) )
!= ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) ) )
| ( sk3 != xx )
| sk1 ),
inference(simp,[status(thm)],[520]) ).
thf(522,plain,
( ( sk3 != xx )
| sk1 ),
inference(simp,[status(thm)],[521]) ).
thf(732,plain,
( ( sk3 != sk3 )
| ( xx != xx )
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[691,522]) ).
thf(733,plain,
( ( sk3 != sk3 )
| sk1 ),
inference(simp,[status(thm)],[732]) ).
thf(734,plain,
sk1,
inference(pattern_uni,[status(thm)],[733:[]]) ).
thf(779,plain,
( ~ $true
| ( xS @ ( sk2 @ aElementOf0 ) ) ),
inference(rewrite,[status(thm)],[42,734]) ).
thf(780,plain,
xS @ ( sk2 @ aElementOf0 ),
inference(simp,[status(thm)],[779]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(148,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( B @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(cnf,[status(esa)],[148]) ).
thf(30939,plain,
! [B: $i,A: $i] :
( ( ( xS @ ( sk2 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ $true
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[780,149]) ).
thf(30940,plain,
! [B: $i,A: $i] :
( ( ( xS @ ( sk2 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[30939]) ).
thf(30941,plain,
( ( sk2 @ aElement0 )
| ~ ( xS @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[30940:[bind(A,$thf( xS )),bind(B,$thf( sk2 ))]]) ).
thf(20,axiom,
( ( xS @ aSet0 )
& ( xx @ aElement0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679) ).
thf(191,plain,
( ( xS @ aSet0 )
& ( xx @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(192,plain,
( ( xS @ aSet0 )
& ( xx @ aElement0 ) ),
inference(cnf,[status(esa)],[191]) ).
thf(194,plain,
xS @ aSet0,
inference(cnfConj,[status(thm)],[192]) ).
thf(32,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(62,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[32]) ).
thf(1239,plain,
! [A: $i] :
( ~ $true
| ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(rewrite,[status(thm)],[62,734]) ).
thf(1240,plain,
! [A: $i] :
( ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[1239]) ).
thf(1266,plain,
! [A: $i] :
( ( ( xS @ ( sk2 @ aElementOf0 ) )
!= ( xS @ ( A @ aElementOf0 ) ) )
| ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ $true
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[780,1240]) ).
thf(1267,plain,
! [A: $i] :
( ( ( xS @ ( sk2 @ aElementOf0 ) )
!= ( xS @ ( A @ aElementOf0 ) ) )
| ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[1266]) ).
thf(1268,plain,
( ( xx @ ( xS @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) )
| ~ ( sk2 @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[1267:[bind(A,$thf( sk2 ))]]) ).
thf(27,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ( A = xx )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(63,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(64,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(simp,[status(thm)],[63]) ).
thf(1341,plain,
! [A: $i] :
( ~ $true
| ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(rewrite,[status(thm)],[64,734]) ).
thf(1342,plain,
! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(simp,[status(thm)],[1341]) ).
thf(33,plain,
( ~ sk1
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(795,plain,
( ~ $true
| ~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) ) ),
inference(rewrite,[status(thm)],[33,734]) ).
thf(796,plain,
~ ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) ),
inference(simp,[status(thm)],[795]) ).
thf(1719,plain,
! [A: $i] :
( ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) ) )
| ~ $true
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(paramod_ordered,[status(thm)],[1342,796]) ).
thf(1720,plain,
! [A: $i] :
( ( ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtpldt0 ) @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) ) )
| ~ ( xx @ ( xS @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(simp,[status(thm)],[1719]) ).
thf(1721,plain,
( ~ ( xx @ ( xS @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) )
| ~ ( sk2 @ aElement0 )
| ( sk2 = xx ) ),
inference(pattern_uni,[status(thm)],[1720:[bind(A,$thf( sk2 ))]]) ).
thf(17,axiom,
~ ( xS @ ( xx @ aElementOf0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679_02) ).
thf(151,plain,
~ ( xS @ ( xx @ aElementOf0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(152,plain,
~ ( xS @ ( xx @ aElementOf0 ) ),
inference(polarity_switch,[status(thm)],[151]) ).
thf(199,plain,
( ( ( xS @ ( sk2 @ aElementOf0 ) )
!= ( xS @ ( xx @ aElementOf0 ) ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[42,152]) ).
thf(200,plain,
( ( ( xS @ ( sk2 @ aElementOf0 ) )
!= ( xS @ ( xx @ aElementOf0 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[199]) ).
thf(201,plain,
( ( xS != xS )
| ( sk2 != xx )
| ~ sk1 ),
inference(simp,[status(thm)],[200]) ).
thf(202,plain,
( ( sk2 != xx )
| ~ sk1 ),
inference(simp,[status(thm)],[201]) ).
thf(777,plain,
( ( sk2 != xx )
| ~ $true ),
inference(rewrite,[status(thm)],[202,734]) ).
thf(778,plain,
sk2 != xx,
inference(simp,[status(thm)],[777]) ).
thf(1765,plain,
( ~ ( xx @ ( xS @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) )
| ~ ( sk2 @ aElement0 ) ),
inference(simplifyReflect,[status(thm)],[1721,778]) ).
thf(1795,plain,
( ( ( xx @ ( xS @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) )
!= ( xx @ ( xS @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) ) )
| ~ $true
| ~ ( sk2 @ aElement0 )
| ~ ( sk2 @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[1268,1765]) ).
thf(1796,plain,
( ( ( xx @ ( xS @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) )
!= ( xx @ ( xS @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) ) )
| ~ ( sk2 @ aElement0 ) ),
inference(simp,[status(thm)],[1795]) ).
thf(1797,plain,
~ ( sk2 @ aElement0 ),
inference(pattern_uni,[status(thm)],[1796:[]]) ).
thf(33603,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[30941,194,1797]) ).
thf(33604,plain,
$false,
inference(simp,[status(thm)],[33603]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM537+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.13/0.38 % Computer : n013.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 03:08:21 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 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
% 0.90/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.18 % [INFO] Parsing done (207ms).
% 1.31/1.20 % [INFO] Running in sequential loop mode.
% 2.20/1.60 % [INFO] eprover registered as external prover.
% 2.20/1.61 % [INFO] Scanning for conjecture ...
% 2.20/1.68 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.20/1.69 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.40/1.71 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.40/1.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.40/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.65/1.85 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.65/1.86 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.86 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.86 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.87 % [INFO] Problem is first-order (TPTP FOF).
% 2.65/1.88 % [INFO] Type checking passed.
% 2.65/1.89 % [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 ...
% 70.23/31.18 % [INFO] Killing All external provers ...
% 70.23/31.19 % Time passed: 30657ms (effective reasoning time: 29981ms)
% 70.23/31.19 % 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)>
% 70.23/31.19 % Axioms used in derivation (3): mEOfElem, m__679, m__679_02
% 70.23/31.19 % No. of inferences in proof: 77
% 70.23/31.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 30657 ms resp. 29981 ms w/o parsing
% 70.41/31.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 70.41/31.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------