%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM568+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 : n019.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 08:09:11 AM UTC 2026
% Result : Theorem 241.57s 154.37s
% Output : Refutation 241.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 82 ( 42 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 176 ( 32 ~; 32 |; 7 &; 103 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 1 ^; 14 !; 5 ?; 21 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(szNzAzT0_decl,type,
szNzAzT0: $i ).
thf(szszuzczcdt0_decl,type,
szszuzczcdt0: $i > $i ).
thf(xK_decl,type,
xK: $i ).
thf(sz00_decl,type,
sz00: $i ).
thf(sk39_decl,type,
sk39: $i > $i ).
thf(sk39_def,definition,
( sk39
= ( ^ [A: $i] :
@+[B: $i] :
( ( A
= ( B @ szszuzczcdt0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(68,axiom,
! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ? [B: $i] :
( ( A
= ( B @ szszuzczcdt0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) )
| ( A = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtra) ).
thf(504,plain,
! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ? [B: $i] :
( ( A
= ( B @ szszuzczcdt0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) )
| ( A = sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(505,plain,
! [A: $i] :
( ( ( A
= ( A @ sk39 @ szszuzczcdt0 ) )
| ( A = sz00 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( szNzAzT0 @ ( A @ sk39 @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[504]) ).
thf(507,plain,
! [A: $i] :
( ( A
= ( A @ sk39 @ szszuzczcdt0 ) )
| ( A = sz00 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[505]) ).
thf(509,plain,
! [A: $i] :
( ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( ( A @ sk39 @ szszuzczcdt0 )
= A )
| ( A = sz00 ) ),
inference(lifteq,[status(thm)],[507]) ).
thf(48,axiom,
szNzAzT0 @ ( xK @ aElementOf0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
thf(329,plain,
szNzAzT0 @ ( xK @ aElementOf0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(506,plain,
! [A: $i] :
( ( szNzAzT0 @ ( A @ sk39 @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[505]) ).
thf(508,plain,
! [A: $i] :
( ( szNzAzT0 @ ( A @ sk39 @ aElementOf0 ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( A = sz00 ) ),
inference(lifteq,[status(thm)],[506]) ).
thf(821,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xK @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( szNzAzT0 @ ( A @ sk39 @ aElementOf0 ) )
| ~ $true
| ( A = sz00 ) ),
inference(paramod_ordered,[status(thm)],[329,508]) ).
thf(822,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xK @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( szNzAzT0 @ ( A @ sk39 @ aElementOf0 ) )
| ( A = sz00 ) ),
inference(simp,[status(thm)],[821]) ).
thf(823,plain,
( ( szNzAzT0 @ ( xK @ sk39 @ aElementOf0 ) )
| ( sz00 = xK ) ),
inference(pattern_uni,[status(thm)],[822:[bind(A,$thf( xK ))]]) ).
thf(62,axiom,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
thf(447,plain,
xK != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(448,plain,
xK != sz00,
inference(polarity_switch,[status(thm)],[447]) ).
thf(449,plain,
sz00 != xK,
inference(lifteq,[status(thm)],[448]) ).
thf(915,plain,
szNzAzT0 @ ( xK @ sk39 @ aElementOf0 ),
inference(simplifyReflect,[status(thm)],[823,449]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( A @ szszuzczcdt0 )
= xK )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( A @ szszuzczcdt0 )
= xK )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(82,plain,
~ ? [A: $i] :
( ( ( A @ szszuzczcdt0 )
= xK )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(83,plain,
! [A: $i] :
( ( ( A @ szszuzczcdt0 )
!= xK )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [A: $i] :
( ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( ( A @ szszuzczcdt0 )
!= xK ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(926,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xK @ sk39 @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ~ $true
| ( ( A @ szszuzczcdt0 )
!= xK ) ),
inference(paramod_ordered,[status(thm)],[915,84]) ).
thf(927,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xK @ sk39 @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( ( A @ szszuzczcdt0 )
!= xK ) ),
inference(simp,[status(thm)],[926]) ).
thf(928,plain,
( ( xK @ sk39 @ szszuzczcdt0 )
!= xK ),
inference(pattern_uni,[status(thm)],[927:[bind(A,$thf( xK @ sk39 ))]]) ).
thf(311061,plain,
! [A: $i] :
( ( ( A @ sk39 @ szszuzczcdt0 )
!= ( xK @ sk39 @ szszuzczcdt0 ) )
| ( A != xK )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( A = sz00 ) ),
inference(paramod_ordered,[status(thm)],[509,928]) ).
thf(311062,plain,
( ( xK != xK )
| ~ ( szNzAzT0 @ ( xK @ aElementOf0 ) )
| ( sz00 = xK ) ),
inference(pattern_uni,[status(thm)],[311061:[bind(A,$thf( xK ))]]) ).
thf(311612,plain,
( ~ ( szNzAzT0 @ ( xK @ aElementOf0 ) )
| ( sz00 = xK ) ),
inference(simp,[status(thm)],[311062]) ).
thf(311643,plain,
( ~ $true
| ( sz00 = xK ) ),
inference(rewrite,[status(thm)],[311612,329]) ).
thf(311644,plain,
sz00 = xK,
inference(simp,[status(thm)],[311643]) ).
thf(311645,plain,
$false,
inference(simplifyReflect,[status(thm)],[311644,449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM568+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n019.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 03:15:48 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.44/1.26 % [INFO] Parsing done (269ms).
% 1.44/1.27 % [INFO] Running in sequential loop mode.
% 2.38/1.66 % [INFO] eprover registered as external prover.
% 2.38/1.67 % [INFO] Scanning for conjecture ...
% 2.59/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.79/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.79/1.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.79/1.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.79/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 79 axioms. Running axiom selection ...
% 2.99/1.94 % [INFO] Axiom selection finished. Selected 79 axioms (removed 0 axioms).
% 2.99/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/2.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/2.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/2.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/2.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/2.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/2.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/2.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/2.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.33/2.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.33/2.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.33/2.05 % [INFO] Problem is first-order (TPTP FOF).
% 3.33/2.06 % [INFO] Type checking passed.
% 3.33/2.07 % [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 ...
% 241.57/154.36 % [INFO] Killing All external provers ...
% 241.57/154.36 % Time passed: 153814ms (effective reasoning time: 153081ms)
% 241.57/154.36 % 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)>
% 241.57/154.36 % Axioms used in derivation (3): mNatExtra, m__3418, m__3462
% 241.57/154.36 % No. of inferences in proof: 31
% 241.57/154.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 153814 ms resp. 153081 ms w/o parsing
% 241.90/154.41 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 241.90/154.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------