%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM568+1 : 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 : n001.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 161.48s 85.79s
% Output : Refutation 161.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 83 ( 42 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 175 ( 28 ~; 31 |; 7 &; 107 @)
% ( 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 : 22 ( 1 ^; 15 !; 5 ?; 22 :)
% ( 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(sk24_decl,type,
sk24: $i > $i ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: $i] :
@+[B: $i] :
( ( A
= ( B @ szszuzczcdt0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(42,axiom,
szNzAzT0 @ ( xK @ aElementOf0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
thf(233,plain,
szNzAzT0 @ ( xK @ aElementOf0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(65,axiom,
! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ? [B: $i] :
( ( A
= ( B @ szszuzczcdt0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) )
| ( A = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
thf(423,plain,
! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ? [B: $i] :
( ( A
= ( B @ szszuzczcdt0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) )
| ( A = sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(424,plain,
! [A: $i] :
( ( ( A
= ( A @ sk24 @ szszuzczcdt0 ) )
| ( A = sz00 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( szNzAzT0 @ ( A @ sk24 @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[423]) ).
thf(426,plain,
! [A: $i] :
( ( A
= ( A @ sk24 @ szszuzczcdt0 ) )
| ( A = sz00 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[424]) ).
thf(428,plain,
! [A: $i] :
( ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( ( A @ sk24 @ szszuzczcdt0 )
= A )
| ( A = sz00 ) ),
inference(lifteq,[status(thm)],[426]) ).
thf(183079,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xK @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ~ $true
| ( ( A @ sk24 @ szszuzczcdt0 )
= A )
| ( A = sz00 ) ),
inference(paramod_ordered,[status(thm)],[233,428]) ).
thf(183080,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xK @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( ( A @ sk24 @ szszuzczcdt0 )
= A )
| ( A = sz00 ) ),
inference(simp,[status(thm)],[183079]) ).
thf(183081,plain,
( ( ( xK @ sk24 @ szszuzczcdt0 )
= xK )
| ( sz00 = xK ) ),
inference(pattern_uni,[status(thm)],[183080:[bind(A,$thf( xK ))]]) ).
thf(59,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
thf(366,plain,
xK != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(367,plain,
xK != sz00,
inference(polarity_switch,[status(thm)],[366]) ).
thf(368,plain,
sz00 != xK,
inference(lifteq,[status(thm)],[367]) ).
thf(425,plain,
! [A: $i] :
( ( szNzAzT0 @ ( A @ sk24 @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[424]) ).
thf(427,plain,
! [A: $i] :
( ( szNzAzT0 @ ( A @ sk24 @ aElementOf0 ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( A = sz00 ) ),
inference(lifteq,[status(thm)],[425]) ).
thf(688,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xK @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( szNzAzT0 @ ( A @ sk24 @ aElementOf0 ) )
| ~ $true
| ( A = sz00 ) ),
inference(paramod_ordered,[status(thm)],[233,427]) ).
thf(689,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xK @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( szNzAzT0 @ ( A @ sk24 @ aElementOf0 ) )
| ( A = sz00 ) ),
inference(simp,[status(thm)],[688]) ).
thf(690,plain,
( ( szNzAzT0 @ ( xK @ sk24 @ aElementOf0 ) )
| ( sz00 = xK ) ),
inference(pattern_uni,[status(thm)],[689:[bind(A,$thf( xK ))]]) ).
thf(877,plain,
szNzAzT0 @ ( xK @ sk24 @ aElementOf0 ),
inference(simplifyReflect,[status(thm)],[690,368]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( A @ szszuzczcdt0 )
= xK )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/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(878,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xK @ sk24 @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ~ $true
| ( ( A @ szszuzczcdt0 )
!= xK ) ),
inference(paramod_ordered,[status(thm)],[877,84]) ).
thf(879,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xK @ sk24 @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( ( A @ szszuzczcdt0 )
!= xK ) ),
inference(simp,[status(thm)],[878]) ).
thf(880,plain,
( ( xK @ sk24 @ szszuzczcdt0 )
!= xK ),
inference(pattern_uni,[status(thm)],[879:[bind(A,$thf( xK @ sk24 ))]]) ).
thf(186095,plain,
$false,
inference(simplifyReflect,[status(thm)],[183081,368,880]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM568+1 : 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
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 03:21:11 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 0.91/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.55/1.24 % [INFO] Parsing done (264ms).
% 1.55/1.25 % [INFO] Running in sequential loop mode.
% 2.45/1.65 % [INFO] eprover registered as external prover.
% 2.45/1.66 % [INFO] Scanning for conjecture ...
% 2.68/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.90/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.90/1.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.90/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.90/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.90/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 79 axioms. Running axiom selection ...
% 3.09/1.95 % [INFO] Axiom selection finished. Selected 79 axioms (removed 0 axioms).
% 3.09/1.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/2.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/2.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/2.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/2.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/2.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/2.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/2.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.42/2.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.42/2.05 % [INFO] Problem is first-order (TPTP FOF).
% 3.42/2.07 % [INFO] Type checking passed.
% 3.42/2.07 % [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 ...
% 161.48/85.78 % [INFO] Killing All external provers ...
% 161.48/85.79 % Time passed: 85257ms (effective reasoning time: 84525ms)
% 161.48/85.79 % 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)>
% 161.48/85.79 % Axioms used in derivation (3): m__3418, mNatExtra, m__3462
% 161.48/85.79 % No. of inferences in proof: 29
% 161.48/85.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 85257 ms resp. 84525 ms w/o parsing
% 161.60/85.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 161.60/85.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------