%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM605+3 : 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 : n005.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 08:09:17 AM UTC 2026
% Result : Theorem 25.06s 7.24s
% Output : Refutation 25.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 13 unt; 0 typ; 1 def)
% Number of atoms : 92 ( 45 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 184 ( 36 ~; 17 |; 28 &; 91 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 29 ( 1 ^; 18 !; 9 ?; 29 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_decl,type,
slcrc0: $i ).
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(slbdtsldtrb0_decl,type,
slbdtsldtrb0: $i > $i > $i ).
thf(sbrdtbr0_decl,type,
sbrdtbr0: $i > $i ).
thf(xQ_decl,type,
xQ: $i ).
thf(xK_decl,type,
xK: $i ).
thf(sz00_decl,type,
sz00: $i ).
thf(xO_decl,type,
xO: $i ).
thf(sk32_decl,type,
sk32: $i > $i ).
thf(sk32_def,definition,
( sk32
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ aElementOf0 ) ) ) ) ).
thf(32,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ( ( ( A @ sbrdtbr0 )
= sz00 )
<=> ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
thf(207,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ( ( ( A = slcrc0 )
=> ( ( A @ sbrdtbr0 )
= sz00 ) )
& ( ( ( A @ sbrdtbr0 )
= sz00 )
=> ( A = slcrc0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(208,plain,
! [A: $i] :
( ( ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 )
| ~ ( A @ aSet0 ) )
& ( ( A = slcrc0 )
| ( ( A @ sbrdtbr0 )
!= sz00 )
| ~ ( A @ aSet0 ) ) ),
inference(cnf,[status(esa)],[207]) ).
thf(210,plain,
! [A: $i] :
( ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[208]) ).
thf(212,plain,
! [A: $i] :
( ~ ( A @ aSet0 )
| ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(213,plain,
( ~ ( slcrc0 @ aSet0 )
| ( ( slcrc0 @ sbrdtbr0 )
= sz00 ) ),
inference(simp,[status(thm)],[212]) ).
thf(60,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
thf(500,plain,
! [A: $i] :
( ( ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) )
=> ( A = slcrc0 ) )
& ( ( A = slcrc0 )
=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(501,plain,
( ! [A: $i] :
( ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) )
=> ( A = slcrc0 ) )
& ! [A: $i] :
( ( A = slcrc0 )
=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ) ),
inference(miniscope,[status(thm)],[500]) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = slcrc0 )
| ( C @ ( C @ sk32 @ aElementOf0 ) )
| ~ ( C @ aSet0 ) )
& ( ~ ( A @ ( B @ aElementOf0 ) )
| ( A != slcrc0 ) )
& ( ( A @ aSet0 )
| ( A != slcrc0 ) ) ),
inference(cnf,[status(esa)],[501]) ).
thf(503,plain,
! [A: $i] :
( ( A @ aSet0 )
| ( A != slcrc0 ) ),
inference(cnfConj,[status(thm)],[502]) ).
thf(506,plain,
! [A: $i] :
( ( A @ aSet0 )
| ( A != slcrc0 ) ),
inference(lifteq,[status(thm)],[503]) ).
thf(507,plain,
slcrc0 @ aSet0,
inference(simp,[status(thm)],[506]) ).
thf(72,axiom,
( ( xK @ ( xO @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xK )
& ( xO @ ( xQ @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( xO @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
thf(678,plain,
( ( xK @ ( xO @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xK )
& ( xO @ ( xQ @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( xO @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(679,plain,
! [A: $i] :
( ( xK @ ( xO @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xK )
& ( xO @ ( xQ @ aSubsetOf0 ) )
& ( ( xO @ ( A @ aElementOf0 ) )
| ~ ( xQ @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 ) ),
inference(cnf,[status(esa)],[678]) ).
thf(681,plain,
( ( xQ @ sbrdtbr0 )
= xK ),
inference(cnfConj,[status(thm)],[679]) ).
thf(685,plain,
( ( xQ @ sbrdtbr0 )
= xK ),
inference(lifteq,[status(thm)],[681]) ).
thf(1,conjecture,
~ ( ( xQ = slcrc0 )
& ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ~ ( ( xQ = slcrc0 )
& ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(102,plain,
~ ~ ( ( xQ = slcrc0 )
& ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(103,plain,
( ( xQ = slcrc0 )
& ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
inference(polarity_switch,[status(thm)],[102]) ).
thf(104,plain,
! [A: $i] :
( ( xQ = slcrc0 )
& ~ ( xQ @ ( A @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(106,plain,
xQ = slcrc0,
inference(cnfConj,[status(thm)],[104]) ).
thf(107,plain,
xQ = slcrc0,
inference(lifteq,[status(thm)],[106]) ).
thf(1230,plain,
( ( slcrc0 @ sbrdtbr0 )
= xK ),
inference(rewrite,[status(thm)],[685,107]) ).
thf(4289,plain,
( ~ $true
| ( sz00 = xK ) ),
inference(rewrite,[status(thm)],[213,507,1230]) ).
thf(4290,plain,
sz00 = xK,
inference(simp,[status(thm)],[4289]) ).
thf(9,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
thf(119,plain,
xK != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(120,plain,
xK != sz00,
inference(polarity_switch,[status(thm)],[119]) ).
thf(121,plain,
sz00 != xK,
inference(lifteq,[status(thm)],[120]) ).
thf(4291,plain,
$false,
inference(simplifyReflect,[status(thm)],[4290,121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM605+3 : 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
% 0.14/0.39 % Computer : n005.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 03:25:16 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.99/1.30 % [INFO] Parsing done (319ms).
% 1.99/1.32 % [INFO] Running in sequential loop mode.
% 2.77/1.72 % [INFO] eprover registered as external prover.
% 2.77/1.72 % [INFO] Scanning for conjecture ...
% 2.77/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.84 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.84 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.85 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.85 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.86 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.21/1.92 % [INFO] Found a conjecture (or negated_conjecture) and 99 axioms. Running axiom selection ...
% 3.55/2.04 % [INFO] Axiom selection finished. Selected 99 axioms (removed 0 axioms).
% 3.55/2.08 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.55/2.12 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.55/2.12 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.90/2.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.90/2.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.90/2.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.90/2.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.90/2.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.90/2.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.90/2.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.90/2.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.05/2.20 % [INFO] Problem is first-order (TPTP FOF).
% 4.05/2.22 % [INFO] Type checking passed.
% 4.05/2.23 % [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 ...
% 25.06/7.24 % [INFO] Killing All external provers ...
% 25.06/7.24 % Time passed: 6702ms (effective reasoning time: 5918ms)
% 25.06/7.24 % 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)>
% 25.06/7.24 % Axioms used in derivation (4): mCardEmpty, mDefEmp, m__5078, m__3462
% 25.06/7.24 % No. of inferences in proof: 33
% 25.06/7.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6702 ms resp. 5918 ms w/o parsing
% 25.06/7.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.06/7.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------