%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM560+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 : n003.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 08:09:10 AM UTC 2026
% Result : Theorem 7.47s 2.67s
% Output : Refutation 7.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 64 ( 11 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 257 ( 15 ~; 12 |; 18 &; 197 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 14 !; 0 ?; 15 :)
% ( 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(sdtlbdtrb0_decl,type,
sdtlbdtrb0: $i > $i > $i ).
thf(szDzozmdt0_decl,type,
szDzozmdt0: $i > $i ).
thf(sdtlpdtrp0_decl,type,
sdtlpdtrp0: $i > $i > $i ).
thf(xF_decl,type,
xF: $i ).
thf(xy_decl,type,
xy: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
=> ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A @ ( xF @ sdtlpdtrp0 ) )
= xy )
& ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) )
& ( xy @ ( xF @ sdtlbdtrb0 ) @ aSet0 ) )
=> ( ( xF @ szDzozmdt0 @ ( xy @ ( xF @ sdtlbdtrb0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
=> ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
<=> ( ( ( A @ ( xF @ sdtlpdtrp0 ) )
= xy )
& ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) )
& ( xy @ ( xF @ sdtlbdtrb0 ) @ aSet0 ) )
=> ( ( xF @ szDzozmdt0 @ ( xy @ ( xF @ sdtlbdtrb0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
=> ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(70,plain,
~ ( ( ! [A: $i] :
( ( ( ( ( A @ ( xF @ sdtlpdtrp0 ) )
= xy )
& ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) )
=> ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A @ ( xF @ sdtlpdtrp0 ) )
= xy )
& ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ) )
& ( xy @ ( xF @ sdtlbdtrb0 ) @ aSet0 ) )
=> ( ( xF @ szDzozmdt0 @ ( xy @ ( xF @ sdtlbdtrb0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
=> ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(71,plain,
~ ( ( ! [A: $i] :
( ( ( ( A @ ( xF @ sdtlpdtrp0 ) )
= xy )
& ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) )
=> ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
=> ( ( ( A @ ( xF @ sdtlpdtrp0 ) )
= xy )
& ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) )
& ( xy @ ( xF @ sdtlbdtrb0 ) @ aSet0 ) )
=> ( ( xF @ szDzozmdt0 @ ( xy @ ( xF @ sdtlbdtrb0 ) @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
=> ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ) ),
inference(miniscope,[status(thm)],[70]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( xF @ szDzozmdt0 @ ( xy @ ( xF @ sdtlbdtrb0 ) @ aSubsetOf0 ) )
& ~ ( xF @ szDzozmdt0 @ ( sk1 @ aElementOf0 ) )
& ( xy @ ( xF @ sdtlbdtrb0 ) @ ( sk1 @ aElementOf0 ) )
& ( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
| ( ( B @ ( xF @ sdtlpdtrp0 ) )
!= xy )
| ~ ( xF @ szDzozmdt0 @ ( B @ aElementOf0 ) ) )
& ( ( ( A @ ( xF @ sdtlpdtrp0 ) )
= xy )
| ~ ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
& ( ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) )
| ~ ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
& ( xy @ ( xF @ sdtlbdtrb0 ) @ aSet0 ) ),
inference(cnf,[status(esa)],[71]) ).
thf(76,plain,
xy @ ( xF @ sdtlbdtrb0 ) @ ( sk1 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[72]) ).
thf(77,plain,
! [A: $i] :
( ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) )
| ~ ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(607,plain,
! [A: $i] :
( ( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( sk1 @ aElementOf0 ) )
!= ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
| ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,77]) ).
thf(608,plain,
! [A: $i] :
( ( ( xy @ ( xF @ sdtlbdtrb0 ) @ ( sk1 @ aElementOf0 ) )
!= ( xy @ ( xF @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
| ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[607]) ).
thf(609,plain,
xF @ szDzozmdt0 @ ( sk1 @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[608:[bind(A,$thf( sk1 ))]]) ).
thf(79,plain,
~ ( xF @ szDzozmdt0 @ ( sk1 @ aElementOf0 ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(619,plain,
$false,
inference(rewrite,[status(thm)],[609,79]) ).
thf(620,plain,
$false,
inference(simp,[status(thm)],[619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM560+2 : 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
% 0.14/0.60 % Computer : n003.cluster.edu
% 0.14/0.60 % Model : x86_64 x86_64
% 0.14/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.60 % Memory : 8046.5625MB
% 0.14/0.60 % OS : Linux 6.8.0-71-generic
% 0.14/0.60 % CPULimit : 300
% 0.14/0.60 % WCLimit : 300
% 0.14/0.60 % DateTime : Sat Sep 26 03:15:39 UTC 2026
% 0.14/0.60 % CPUTime :
% 0.14/0.60 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
% 0.17/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.07/1.04 % [INFO] Parsing done (139ms).
% 1.07/1.05 % [INFO] Running in sequential loop mode.
% 1.74/1.25 % [INFO] eprover registered as external prover.
% 1.74/1.26 % [INFO] Scanning for conjecture ...
% 1.74/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.35 % [INFO] Found a conjecture (or negated_conjecture) and 67 axioms. Running axiom selection ...
% 2.33/1.41 % [INFO] Axiom selection finished. Selected 67 axioms (removed 0 axioms).
% 2.33/1.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.45 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.46 % [INFO] Problem is first-order (TPTP FOF).
% 2.33/1.47 % [INFO] Type checking passed.
% 2.33/1.47 % [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 ...
% 7.47/2.66 % [INFO] Killing All external provers ...
% 7.47/2.67 % Time passed: 1967ms (effective reasoning time: 1607ms)
% 7.47/2.67 % 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)>
% 7.47/2.67 % Axioms used in derivation (0):
% 7.47/2.67 % No. of inferences in proof: 13
% 7.47/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1967 ms resp. 1607 ms w/o parsing
% 7.93/2.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.93/2.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------