%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM549+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 : n002.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 08:09:07 AM UTC 2026
% Result : Theorem 88.62s 35.59s
% Output : Refutation 88.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 158 ( 58 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 316 ( 65 ~; 53 |; 26 &; 158 @)
% ( 2 <=>; 12 =>; 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 : 15 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 44 ( 1 ^; 34 !; 8 ?; 44 :)
% ( 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(aElement0_decl,type,
aElement0: $i > $o ).
thf(isFinite0_decl,type,
isFinite0: $i > $o ).
thf(sbrdtbr0_decl,type,
sbrdtbr0: $i > $i ).
thf(xQ_decl,type,
xQ: $i ).
thf(sz00_decl,type,
sz00: $i ).
thf(xS_decl,type,
xS: $i ).
thf(xT_decl,type,
xT: $i ).
thf(xk_decl,type,
xk: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ aElementOf0 ) ) ) ) ).
thf(35,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
thf(194,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)],[35]) ).
thf(195,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)],[194]) ).
thf(196,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = slcrc0 )
| ( C @ ( C @ sk6 @ aElementOf0 ) )
| ~ ( C @ aSet0 ) )
& ( ~ ( A @ ( B @ aElementOf0 ) )
| ( A != slcrc0 ) )
& ( ( A @ aSet0 )
| ( A != slcrc0 ) ) ),
inference(cnf,[status(esa)],[195]) ).
thf(199,plain,
! [A: $i] :
( ( A = slcrc0 )
| ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[196]) ).
thf(204,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 )
| ( A = slcrc0 ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(205,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 )
| ( A = slcrc0 ) ),
inference(simp,[status(thm)],[204]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ( ( ( A @ sbrdtbr0 )
= sz00 )
<=> ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
thf(73,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ( ( ( A = slcrc0 )
=> ( ( A @ sbrdtbr0 )
= sz00 ) )
& ( ( ( A @ sbrdtbr0 )
= sz00 )
=> ( A = slcrc0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(74,plain,
! [A: $i] :
( ( ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 )
| ~ ( A @ aSet0 ) )
& ( ( A = slcrc0 )
| ( ( A @ sbrdtbr0 )
!= sz00 )
| ~ ( A @ aSet0 ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(76,plain,
! [A: $i] :
( ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[74]) ).
thf(78,plain,
! [A: $i] :
( ~ ( A @ aSet0 )
| ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(79,plain,
( ~ ( slcrc0 @ aSet0 )
| ( ( slcrc0 @ sbrdtbr0 )
= sz00 ) ),
inference(simp,[status(thm)],[78]) ).
thf(197,plain,
! [A: $i] :
( ( A @ aSet0 )
| ( A != slcrc0 ) ),
inference(cnfConj,[status(thm)],[196]) ).
thf(200,plain,
! [A: $i] :
( ( A @ aSet0 )
| ( A != slcrc0 ) ),
inference(lifteq,[status(thm)],[197]) ).
thf(201,plain,
slcrc0 @ aSet0,
inference(simp,[status(thm)],[200]) ).
thf(499,plain,
( ~ $true
| ( ( slcrc0 @ sbrdtbr0 )
= sz00 ) ),
inference(rewrite,[status(thm)],[79,201]) ).
thf(500,plain,
( ( slcrc0 @ sbrdtbr0 )
= sz00 ),
inference(simp,[status(thm)],[499]) ).
thf(52,axiom,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
thf(303,plain,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(304,plain,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
inference(cnf,[status(esa)],[303]) ).
thf(307,plain,
( ( xQ @ sbrdtbr0 )
= xk ),
inference(cnfConj,[status(thm)],[304]) ).
thf(308,plain,
( ( xQ @ sbrdtbr0 )
= xk ),
inference(lifteq,[status(thm)],[307]) ).
thf(501,plain,
( ( ( xQ @ sbrdtbr0 )
!= ( slcrc0 @ sbrdtbr0 ) )
| ( xk = sz00 ) ),
inference(paramod_ordered,[status(thm)],[500,308]) ).
thf(506,plain,
( ( xQ != slcrc0 )
| ( xk = sz00 ) ),
inference(simp,[status(thm)],[501]) ).
thf(9,axiom,
( ( xk != sz00 )
& ( xT @ aSet0 )
& ( xS @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
thf(88,plain,
( ( xk != sz00 )
& ( xT @ aSet0 )
& ( xS @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(89,plain,
( ( xk != sz00 )
& ( xT @ aSet0 )
& ( xS @ aSet0 ) ),
inference(cnf,[status(esa)],[88]) ).
thf(92,plain,
xk != sz00,
inference(cnfConj,[status(thm)],[89]) ).
thf(93,plain,
xk != sz00,
inference(lifteq,[status(thm)],[92]) ).
thf(526,plain,
xQ != slcrc0,
inference(simplifyReflect,[status(thm)],[506,93]) ).
thf(30458,plain,
! [A: $i] :
( ( A != xQ )
| ( slcrc0 != slcrc0 )
| ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[205,526]) ).
thf(30459,plain,
! [A: $i] :
( ( A != xQ )
| ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[30458]) ).
thf(30460,plain,
( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
| ~ ( xQ @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[30459:[bind(A,$thf( xQ ))]]) ).
thf(305,plain,
xQ @ aSet0,
inference(cnfConj,[status(thm)],[304]) ).
thf(34097,plain,
( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[30460,305]) ).
thf(34098,plain,
xQ @ ( xQ @ sk6 @ aElementOf0 ),
inference(simp,[status(thm)],[34097]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(229,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( B @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(cnf,[status(esa)],[229]) ).
thf(43481,plain,
! [B: $i,A: $i] :
( ( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ $true
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[34098,230]) ).
thf(43482,plain,
! [B: $i,A: $i] :
( ( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[43481]) ).
thf(43483,plain,
( ( xQ @ sk6 @ aElement0 )
| ~ ( xQ @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[43482:[bind(A,$thf( xQ )),bind(B,$thf( xQ @ sk6 ))]]) ).
thf(1,conjecture,
? [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ? [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,plain,
! [A: $i] :
( ~ ( xQ @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(cnf,[status(esa)],[69]) ).
thf(30209,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ aElementOf0 ) )
!= ( xQ @ ( B @ aElementOf0 ) ) )
| ~ $true
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 )
| ( A = slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[205,70]) ).
thf(30210,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ aElementOf0 ) )
!= ( xQ @ ( B @ aElementOf0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 )
| ( A = slcrc0 ) ),
inference(simp,[status(thm)],[30209]) ).
thf(30211,plain,
( ~ ( xQ @ sk6 @ aElement0 )
| ~ ( xQ @ aSet0 )
| ( xQ = slcrc0 ) ),
inference(pattern_uni,[status(thm)],[30210:[bind(A,$thf( xQ )),bind(B,$thf( xQ @ sk6 ))]]) ).
thf(32481,plain,
( ~ ( xQ @ sk6 @ aElement0 )
| ~ $true
| ( xQ = slcrc0 ) ),
inference(rewrite,[status(thm)],[30211,305]) ).
thf(32482,plain,
( ~ ( xQ @ sk6 @ aElement0 )
| ( xQ = slcrc0 ) ),
inference(simp,[status(thm)],[32481]) ).
thf(32483,plain,
~ ( xQ @ sk6 @ aElement0 ),
inference(simplifyReflect,[status(thm)],[32482,526]) ).
thf(72736,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[43483,305,32483]) ).
thf(72737,plain,
$false,
inference(simp,[status(thm)],[72736]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM549+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
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 03:14:05 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.86/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.46/1.23 % [INFO] Parsing done (251ms).
% 1.46/1.25 % [INFO] Running in sequential loop mode.
% 2.32/1.66 % [INFO] eprover registered as external prover.
% 2.32/1.67 % [INFO] Scanning for conjecture ...
% 2.56/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.56/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.56/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.56/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.56/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.56/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.79/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.79/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.79/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.99/1.93 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.99/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/1.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.99/2.01 % [INFO] Problem is first-order (TPTP FOF).
% 2.99/2.02 % [INFO] Type checking passed.
% 2.99/2.03 % [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 ...
% 88.62/35.58 % [INFO] Killing All external provers ...
% 88.62/35.59 % Time passed: 35045ms (effective reasoning time: 34326ms)
% 88.62/35.59 % 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)>
% 88.62/35.59 % Axioms used in derivation (5): mCardEmpty, mEOfElem, m__2202_02, mDefEmp, m__2291
% 88.62/35.59 % No. of inferences in proof: 55
% 88.62/35.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 35045 ms resp. 34326 ms w/o parsing
% 88.76/35.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 88.76/35.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------