%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM549+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 : n016.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 91.56s 38.99s
% Output : Refutation 91.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 169 ( 60 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 346 ( 62 ~; 53 |; 32 &; 183 @)
% ( 2 <=>; 14 =>; 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 : 16 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 47 ( 1 ^; 37 !; 8 ?; 47 :)
% ( 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(aElement0_decl,type,
aElement0: $i > $o ).
thf(slbdtsldtrb0_decl,type,
slbdtsldtrb0: $i > $i > $i ).
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(20,axiom,
( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xk )
& ( xS @ ( xQ @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
thf(143,plain,
( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xk )
& ( xS @ ( xQ @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(144,plain,
! [A: $i] :
( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xk )
& ( xS @ ( xQ @ aSubsetOf0 ) )
& ( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xQ @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 ) ),
inference(cnf,[status(esa)],[143]) ).
thf(145,plain,
xQ @ aSet0,
inference(cnfConj,[status(thm)],[144]) ).
thf(35,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
thf(197,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(198,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)],[197]) ).
thf(199,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)],[198]) ).
thf(202,plain,
! [A: $i] :
( ( A = slcrc0 )
| ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[199]) ).
thf(207,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 )
| ( A = slcrc0 ) ),
inference(lifteq,[status(thm)],[202]) ).
thf(208,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 )
| ( A = slcrc0 ) ),
inference(simp,[status(thm)],[207]) ).
thf(33256,plain,
! [A: $i] :
( ( ( xQ @ aSet0 )
!= ( A @ aSet0 ) )
| ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ $true
| ( A = slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[145,208]) ).
thf(33257,plain,
! [A: $i] :
( ( ( xQ @ aSet0 )
!= ( A @ aSet0 ) )
| ( A @ ( A @ sk6 @ aElementOf0 ) )
| ( A = slcrc0 ) ),
inference(simp,[status(thm)],[33256]) ).
thf(33258,plain,
( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
| ( xQ = slcrc0 ) ),
inference(pattern_uni,[status(thm)],[33257:[bind(A,$thf( xQ ))]]) ).
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(200,plain,
! [A: $i] :
( ( A @ aSet0 )
| ( A != slcrc0 ) ),
inference(cnfConj,[status(thm)],[199]) ).
thf(203,plain,
! [A: $i] :
( ( A @ aSet0 )
| ( A != slcrc0 ) ),
inference(lifteq,[status(thm)],[200]) ).
thf(204,plain,
slcrc0 @ aSet0,
inference(simp,[status(thm)],[203]) ).
thf(570,plain,
( ~ $true
| ( ( slcrc0 @ sbrdtbr0 )
= sz00 ) ),
inference(rewrite,[status(thm)],[79,204]) ).
thf(571,plain,
( ( slcrc0 @ sbrdtbr0 )
= sz00 ),
inference(simp,[status(thm)],[570]) ).
thf(146,plain,
( ( xQ @ sbrdtbr0 )
= xk ),
inference(cnfConj,[status(thm)],[144]) ).
thf(150,plain,
( ( xQ @ sbrdtbr0 )
= xk ),
inference(lifteq,[status(thm)],[146]) ).
thf(572,plain,
( ( ( xQ @ sbrdtbr0 )
!= ( slcrc0 @ sbrdtbr0 ) )
| ( xk = sz00 ) ),
inference(paramod_ordered,[status(thm)],[571,150]) ).
thf(577,plain,
( ( xQ != slcrc0 )
| ( xk = sz00 ) ),
inference(simp,[status(thm)],[572]) ).
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(673,plain,
xQ != slcrc0,
inference(simplifyReflect,[status(thm)],[577,93]) ).
thf(36099,plain,
xQ @ ( xQ @ sk6 @ aElementOf0 ),
inference(simplifyReflect,[status(thm)],[33258,673]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(232,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( B @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(cnf,[status(esa)],[232]) ).
thf(46235,plain,
! [B: $i,A: $i] :
( ( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ $true
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[36099,233]) ).
thf(46236,plain,
! [B: $i,A: $i] :
( ( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[46235]) ).
thf(46237,plain,
( ( xQ @ sk6 @ aElement0 )
| ~ ( xQ @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[46236:[bind(A,$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(32595,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ aElementOf0 ) )
!= ( xQ @ ( B @ aElementOf0 ) ) )
| ~ $true
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 )
| ( A = slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[208,70]) ).
thf(32596,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ aElementOf0 ) )
!= ( xQ @ ( B @ aElementOf0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 )
| ( A = slcrc0 ) ),
inference(simp,[status(thm)],[32595]) ).
thf(32597,plain,
( ~ ( xQ @ sk6 @ aElement0 )
| ~ ( xQ @ aSet0 )
| ( xQ = slcrc0 ) ),
inference(pattern_uni,[status(thm)],[32596:[bind(A,$thf( xQ )),bind(B,$thf( xQ @ sk6 ))]]) ).
thf(34992,plain,
( ~ ( xQ @ sk6 @ aElement0 )
| ~ $true
| ( xQ = slcrc0 ) ),
inference(rewrite,[status(thm)],[32597,145]) ).
thf(34993,plain,
( ~ ( xQ @ sk6 @ aElement0 )
| ( xQ = slcrc0 ) ),
inference(simp,[status(thm)],[34992]) ).
thf(34994,plain,
~ ( xQ @ sk6 @ aElement0 ),
inference(simplifyReflect,[status(thm)],[34993,673]) ).
thf(80655,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[46237,145,34994]) ).
thf(80656,plain,
$false,
inference(simp,[status(thm)],[80655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM549+3 : 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
% 0.14/0.40 % Computer : n016.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 03:16:44 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/1.25 % [INFO] Parsing done (256ms).
% 1.44/1.26 % [INFO] Running in sequential loop mode.
% 2.43/1.67 % [INFO] eprover registered as external prover.
% 2.43/1.68 % [INFO] Scanning for conjecture ...
% 2.66/1.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.66/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.66/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.66/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.86/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.86/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.86/1.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.86/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.86/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 3.11/1.94 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 3.11/1.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/2.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/2.02 % [INFO] Problem is first-order (TPTP FOF).
% 3.43/2.03 % [INFO] Type checking passed.
% 3.43/2.04 % [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 ...
% 91.56/38.99 % [INFO] Killing All external provers ...
% 91.56/38.99 % Time passed: 38443ms (effective reasoning time: 37715ms)
% 91.56/38.99 % 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)>
% 91.56/38.99 % Axioms used in derivation (5): mCardEmpty, mDefEmp, mEOfElem, m__2270, m__2202_02
% 91.56/38.99 % No. of inferences in proof: 54
% 91.56/38.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 38443 ms resp. 37715 ms w/o parsing
% 91.77/39.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 91.77/39.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------