%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM535+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 : 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 08:09:05 AM UTC 2026
% Result : Theorem 25.43s 6.97s
% Output : Refutation 25.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 6
% Syntax : Number of formulae : 81 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 477 ( 90 equ; 0 cnn)
% Maximal formula atoms : 78 ( 5 avg)
% Number of connectives : 1496 ( 188 ~; 215 |; 89 &; 950 @)
% ( 8 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 6 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 : 70 ( 0 ^; 68 !; 0 ?; 70 :)
% ( 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 @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(1,conjecture,
( ( ( ! [A: $i] :
( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtmndt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xS @ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) )
& ( ( ! [A: $i] :
( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtmndt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( xS @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
=> ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( ! [A: $i] :
( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtmndt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xS @ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) )
& ( ( ! [A: $i] :
( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtmndt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( xS @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
=> ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ( ( ( ! [A: $i] :
( ( ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) ) )
& ( xx @ ( xS @ sdtmndt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) ) )
& ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xS @ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) )
& ( ( ! [A: $i] :
( ( ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) ) )
& ( xx @ ( xS @ sdtmndt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) ) )
& ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( xS @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
=> ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
~ ( ( ( ! [A: $i] :
( ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtmndt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xS @ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) )
& ( ( ! [A: $i] :
( ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
=> ( ( A != xx )
& ( xS @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xS @ sdtmndt0 ) @ aSet0 ) )
=> ( ( ! [A: $i] :
( ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) )
=> ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( A @ aElement0 ) ) )
& ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSet0 ) )
=> ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( xS @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
=> ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( xS @ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSubsetOf0 ) )
| sk1 )
& ( ~ ( xS @ ( sk3 @ aElementOf0 ) )
| sk1 )
& ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( sk3 @ aElementOf0 ) )
| sk1 )
& ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( H @ aElementOf0 ) )
| ( H != xx )
| ~ ( H @ aElement0 )
| sk1 )
& ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( H @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( H @ aElementOf0 ) )
| ~ ( H @ aElement0 )
| sk1 )
& ( ( G = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( G @ aElementOf0 ) )
| ~ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( G @ aElementOf0 ) )
| sk1 )
& ( ( G @ aElement0 )
| ~ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( G @ aElementOf0 ) )
| sk1 )
& ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSet0 )
| sk1 )
& ( ( xx @ ( xS @ sdtmndt0 ) @ ( F @ aElementOf0 ) )
| ( F = xx )
| ~ ( xS @ ( F @ aElementOf0 ) )
| ~ ( F @ aElement0 )
| sk1 )
& ( ( E != xx )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( E @ aElementOf0 ) )
| sk1 )
& ( ( xS @ ( E @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( E @ aElementOf0 ) )
| sk1 )
& ( ( E @ aElement0 )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( E @ aElementOf0 ) )
| sk1 )
& ( ( xx @ ( xS @ sdtmndt0 ) @ aSet0 )
| sk1 )
& ( ~ sk1
| ~ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( xS @ aSubsetOf0 ) ) )
& ( ~ sk1
| ~ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) ) )
& ( ~ sk1
| ( xS @ ( sk2 @ aElementOf0 ) ) )
& ( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( D @ aElementOf0 ) )
| ( D != xx )
| ~ ( D @ aElement0 ) )
& ( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( D @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( D @ aElementOf0 ) )
| ~ ( D @ aElement0 ) )
& ( ~ sk1
| ( C = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( C @ aElementOf0 ) )
| ~ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( C @ aElementOf0 ) ) )
& ( ~ sk1
| ( C @ aElement0 )
| ~ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( C @ aElementOf0 ) ) )
& ( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ aSet0 ) )
& ( ~ sk1
| ( xx @ ( xS @ sdtmndt0 ) @ ( B @ aElementOf0 ) )
| ( B = xx )
| ~ ( xS @ ( B @ aElementOf0 ) )
| ~ ( B @ aElement0 ) )
& ( ~ sk1
| ( A != xx )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( ~ sk1
| ( xS @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( ~ sk1
| ( A @ aElement0 )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
& ( ~ sk1
| ( xx @ ( xS @ sdtmndt0 ) @ aSet0 ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(45,plain,
( ~ sk1
| ( xS @ ( sk2 @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(40,plain,
( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( sk3 @ aElementOf0 ) )
| sk1 ),
inference(cnfConj,[status(thm)],[23]) ).
thf(41,plain,
! [A: $i] :
( ( A = xx )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| sk1 ),
inference(cnfConj,[status(thm)],[23]) ).
thf(50,plain,
! [A: $i] :
( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| sk1
| ( A = xx ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(51,plain,
! [A: $i] :
( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| sk1
| ( A = xx ) ),
inference(simp,[status(thm)],[50]) ).
thf(462,plain,
! [A: $i] :
( ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( sk3 @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ $true
| sk1
| ( A = xx )
| sk1 ),
inference(paramod_ordered,[status(thm)],[40,51]) ).
thf(463,plain,
! [A: $i] :
( ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( sk3 @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) ) )
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ( A = xx )
| sk1 ),
inference(simp,[status(thm)],[462]) ).
thf(464,plain,
( ( xx @ ( xS @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
| ( sk3 = xx )
| sk1 ),
inference(pattern_uni,[status(thm)],[463:[bind(A,$thf( sk3 ))]]) ).
thf(11,axiom,
xS @ ( xx @ aElementOf0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617_02) ).
thf(86,plain,
xS @ ( xx @ aElementOf0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(29,plain,
( ~ ( xS @ ( sk3 @ aElementOf0 ) )
| sk1 ),
inference(cnfConj,[status(thm)],[23]) ).
thf(195,plain,
( ( ( xS @ ( sk3 @ aElementOf0 ) )
!= ( xS @ ( xx @ aElementOf0 ) ) )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[86,29]) ).
thf(196,plain,
( ( ( xS @ ( sk3 @ aElementOf0 ) )
!= ( xS @ ( xx @ aElementOf0 ) ) )
| sk1 ),
inference(simp,[status(thm)],[195]) ).
thf(197,plain,
( ( xS != xS )
| ( sk3 != xx )
| sk1 ),
inference(simp,[status(thm)],[196]) ).
thf(198,plain,
( ( sk3 != xx )
| sk1 ),
inference(simp,[status(thm)],[197]) ).
thf(521,plain,
( ( sk3 != sk3 )
| ( xx != xx )
| sk1
| ( xx @ ( xS @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
| sk1 ),
inference(paramod_ordered,[status(thm)],[464,198]) ).
thf(522,plain,
( ( sk3 != sk3 )
| ( xx @ ( xS @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
| sk1 ),
inference(simp,[status(thm)],[521]) ).
thf(523,plain,
( ( xx @ ( xS @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[522:[]]) ).
thf(33,plain,
! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| sk1 ),
inference(cnfConj,[status(thm)],[23]) ).
thf(63,plain,
! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| sk1 ),
inference(simp,[status(thm)],[33]) ).
thf(2743,plain,
! [A: $i] :
( ( ( xx @ ( xS @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
!= ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
| ( xS @ ( A @ aElementOf0 ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[523,63]) ).
thf(2744,plain,
! [A: $i] :
( ( ( xx @ ( xS @ sdtmndt0 ) @ ( sk3 @ aElementOf0 ) )
!= ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) ) )
| ( xS @ ( A @ aElementOf0 ) )
| sk1 ),
inference(simp,[status(thm)],[2743]) ).
thf(2745,plain,
( ( xS @ ( sk3 @ aElementOf0 ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[2744:[bind(A,$thf( sk3 ))]]) ).
thf(2794,plain,
( ( ( xS @ ( sk3 @ aElementOf0 ) )
!= ( xS @ ( sk3 @ aElementOf0 ) ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[2745,29]) ).
thf(2795,plain,
( ( ( xS @ ( sk3 @ aElementOf0 ) )
!= ( xS @ ( sk3 @ aElementOf0 ) ) )
| sk1 ),
inference(simp,[status(thm)],[2794]) ).
thf(2796,plain,
sk1,
inference(pattern_uni,[status(thm)],[2795:[]]) ).
thf(2856,plain,
( ~ $true
| ( xS @ ( sk2 @ aElementOf0 ) ) ),
inference(rewrite,[status(thm)],[45,2796]) ).
thf(2857,plain,
xS @ ( sk2 @ aElementOf0 ),
inference(simp,[status(thm)],[2856]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(146,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( B @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(cnf,[status(esa)],[146]) ).
thf(17950,plain,
! [B: $i,A: $i] :
( ( ( xS @ ( sk2 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ $true
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[2857,147]) ).
thf(17951,plain,
! [B: $i,A: $i] :
( ( ( xS @ ( sk2 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[17950]) ).
thf(17952,plain,
( ( sk2 @ aElement0 )
| ~ ( xS @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[17951:[bind(A,$thf( xS )),bind(B,$thf( sk2 ))]]) ).
thf(4,axiom,
xS @ aSet0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617) ).
thf(73,plain,
xS @ aSet0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18045,plain,
( ( sk2 @ aElement0 )
| ~ $true ),
inference(rewrite,[status(thm)],[17952,73]) ).
thf(18046,plain,
sk2 @ aElement0,
inference(simp,[status(thm)],[18045]) ).
thf(47,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ( A != xx )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(58,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A != xx ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(59,plain,
( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( xx @ aElementOf0 ) )
| ~ ( xx @ aElement0 ) ),
inference(simp,[status(thm)],[58]) ).
thf(38,plain,
( ~ sk1
| ~ ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(1589,plain,
( ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( xx @ aElementOf0 ) ) )
| ~ sk1
| ~ $true
| ~ sk1
| ~ ( xx @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[59,38]) ).
thf(1590,plain,
( ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( xx @ aElementOf0 ) ) )
| ~ sk1
| ~ ( xx @ aElement0 ) ),
inference(simp,[status(thm)],[1589]) ).
thf(1657,plain,
( ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) )
!= ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) ) )
| ( sk2 != xx )
| ~ sk1
| ~ ( xx @ aElement0 ) ),
inference(simp,[status(thm)],[1590]) ).
thf(1662,plain,
( ( sk2 != xx )
| ~ sk1
| ~ ( xx @ aElement0 ) ),
inference(simp,[status(thm)],[1657]) ).
thf(2896,plain,
( ( sk2 != xx )
| ~ $true
| ~ ( xx @ aElement0 ) ),
inference(rewrite,[status(thm)],[1662,2796]) ).
thf(2897,plain,
( ( sk2 != xx )
| ~ ( xx @ aElement0 ) ),
inference(simp,[status(thm)],[2896]) ).
thf(18098,plain,
( ( ( sk2 @ aElement0 )
!= ( xx @ aElement0 ) )
| ( sk2 != xx )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18046,2897]) ).
thf(18099,plain,
( ( ( sk2 @ aElement0 )
!= ( xx @ aElement0 ) )
| ( sk2 != xx ) ),
inference(simp,[status(thm)],[18098]) ).
thf(18205,plain,
( ( sk2 != xx )
| ( sk2 != xx ) ),
inference(simp,[status(thm)],[18099]) ).
thf(18214,plain,
sk2 != xx,
inference(simp,[status(thm)],[18205]) ).
thf(44,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ( A = xx )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(67,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(68,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(simp,[status(thm)],[67]) ).
thf(3004,plain,
! [A: $i] :
( ~ $true
| ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(rewrite,[status(thm)],[68,2796]) ).
thf(3005,plain,
! [A: $i] :
( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(simp,[status(thm)],[3004]) ).
thf(46,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(62,plain,
! [A: $i] :
( ~ sk1
| ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[46]) ).
thf(2327,plain,
! [A: $i] :
( ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) ) )
| ~ sk1
| ~ $true
| ~ sk1
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[62,38]) ).
thf(2328,plain,
! [A: $i] :
( ( ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( A @ aElementOf0 ) )
!= ( xx @ ( xx @ ( xS @ sdtmndt0 ) @ sdtpldt0 ) @ ( sk2 @ aElementOf0 ) ) )
| ~ sk1
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[2327]) ).
thf(2329,plain,
( ~ sk1
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) )
| ~ ( sk2 @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[2328:[bind(A,$thf( sk2 ))]]) ).
thf(2892,plain,
( ~ $true
| ~ ( xx @ ( xS @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) )
| ~ ( sk2 @ aElement0 ) ),
inference(rewrite,[status(thm)],[2329,2796]) ).
thf(2893,plain,
( ~ ( xx @ ( xS @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) )
| ~ ( sk2 @ aElement0 ) ),
inference(simp,[status(thm)],[2892]) ).
thf(3059,plain,
! [A: $i] :
( ( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
!= ( xx @ ( xS @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) ) )
| ~ $true
| ~ ( sk2 @ aElement0 )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(paramod_ordered,[status(thm)],[3005,2893]) ).
thf(3060,plain,
! [A: $i] :
( ( ( xx @ ( xS @ sdtmndt0 ) @ ( A @ aElementOf0 ) )
!= ( xx @ ( xS @ sdtmndt0 ) @ ( sk2 @ aElementOf0 ) ) )
| ~ ( sk2 @ aElement0 )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| ( A = xx ) ),
inference(simp,[status(thm)],[3059]) ).
thf(3061,plain,
( ~ ( sk2 @ aElement0 )
| ~ ( xS @ ( sk2 @ aElementOf0 ) )
| ~ ( sk2 @ aElement0 )
| ( sk2 = xx ) ),
inference(pattern_uni,[status(thm)],[3060:[bind(A,$thf( sk2 ))]]) ).
thf(3267,plain,
( ~ ( xS @ ( sk2 @ aElementOf0 ) )
| ~ ( sk2 @ aElement0 )
| ( sk2 = xx ) ),
inference(simp,[status(thm)],[3061]) ).
thf(3390,plain,
( ~ $true
| ~ ( sk2 @ aElement0 )
| ( sk2 = xx ) ),
inference(rewrite,[status(thm)],[3267,2857]) ).
thf(3391,plain,
( ~ ( sk2 @ aElement0 )
| ( sk2 = xx ) ),
inference(simp,[status(thm)],[3390]) ).
thf(18069,plain,
( ~ $true
| ( sk2 = xx ) ),
inference(rewrite,[status(thm)],[3391,18046]) ).
thf(18070,plain,
sk2 = xx,
inference(simp,[status(thm)],[18069]) ).
thf(18292,plain,
xx != xx,
inference(rewrite,[status(thm)],[18214,18070]) ).
thf(18293,plain,
$false,
inference(simp,[status(thm)],[18292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM535+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % 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
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Sat Sep 26 03:08:05 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 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
% 0.39/0.61 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.71 % [INFO] Parsing done (99ms).
% 0.66/0.72 % [INFO] Running in sequential loop mode.
% 1.07/0.90 % [INFO] eprover registered as external prover.
% 1.07/0.91 % [INFO] Scanning for conjecture ...
% 1.07/0.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.07/0.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.07/0.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.07/0.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.07/0.98 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 1.33/1.02 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.33/1.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.33/1.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.33/1.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.33/1.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.33/1.04 % [INFO] Problem is first-order (TPTP FOF).
% 1.33/1.04 % [INFO] Type checking passed.
% 1.33/1.04 % [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 ...
% 25.43/6.96 % [INFO] Killing All external provers ...
% 25.43/6.97 % Time passed: 6565ms (effective reasoning time: 6246ms)
% 25.43/6.97 % 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)>
% 25.43/6.97 % Axioms used in derivation (3): m__617_02, mEOfElem, m__617
% 25.43/6.97 % No. of inferences in proof: 79
% 25.43/6.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6565 ms resp. 6246 ms w/o parsing
% 25.43/7.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.43/7.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------