%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM571+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 : n008.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 18.75s 17.03s
% Output : Refutation 19.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 112 ( 42 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 351 ( 37 ~; 28 |; 30 &; 250 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 3 !; 2 ?; 6 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(sdtmndt0_decl,type,
sdtmndt0: $i > $i > $i ).
thf(szNzAzT0_decl,type,
szNzAzT0: $i ).
thf(szmzizndt0_decl,type,
szmzizndt0: $i > $i ).
thf(szszuzczcdt0_decl,type,
szszuzczcdt0: $i > $i ).
thf(aFunction0_decl,type,
aFunction0: $i > $o ).
thf(szDzozmdt0_decl,type,
szDzozmdt0: $i > $i ).
thf(sdtlpdtrp0_decl,type,
sdtlpdtrp0: $i > $i > $i ).
thf(xN_decl,type,
xN: $i ).
thf(xi_decl,type,
xi: $i ).
thf(isCountable0_decl,type,
isCountable0: $i > $o ).
thf(sz00_decl,type,
sz00: $i ).
thf(xS_decl,type,
xS: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
( ( ( A @ szszuzczcdt0 )
= xi )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(46,axiom,
( ( xi != sz00 )
=> ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ? [A: $i] :
( ( ( A @ szszuzczcdt0 )
= xi )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3702_02) ).
thf(326,plain,
( ( xi != sz00 )
=> ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ? [A: $i] :
( ( ( A @ szszuzczcdt0 )
= xi )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(327,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ( xi = sz00 ) )
& ( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( xi = sz00 ) )
& ( ( ( sk14 @ szszuzczcdt0 )
= xi )
| ( xi = sz00 ) )
& ( ( szNzAzT0 @ ( sk14 @ aElementOf0 ) )
| ( xi = sz00 ) ) ),
inference(cnf,[status(esa)],[326]) ).
thf(330,plain,
( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( xi = sz00 ) ),
inference(cnfConj,[status(thm)],[327]) ).
thf(334,plain,
( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( sz00 = xi ) ),
inference(lifteq,[status(thm)],[330]) ).
thf(1,conjecture,
( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(87,plain,
~ ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(88,plain,
( ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(331,plain,
( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ( xi = sz00 ) ),
inference(cnfConj,[status(thm)],[327]) ).
thf(335,plain,
( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ( sz00 = xi ) ),
inference(lifteq,[status(thm)],[331]) ).
thf(82,axiom,
( ! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ( ( A @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( szNzAzT0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) )
=> ( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ) ) )
& ( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS )
& ( ( xN @ szDzozmdt0 )
= szNzAzT0 )
& ( xN @ aFunction0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
thf(561,plain,
( ! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ( ( A @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( szNzAzT0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) )
=> ( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ) ) )
& ( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS )
& ( ( xN @ szDzozmdt0 )
= szNzAzT0 )
& ( xN @ aFunction0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(562,plain,
! [A: $i] :
( ( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ~ ( szNzAzT0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ~ ( szNzAzT0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS )
& ( ( xN @ szDzozmdt0 )
= szNzAzT0 )
& ( xN @ aFunction0 ) ),
inference(cnf,[status(esa)],[561]) ).
thf(565,plain,
( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS ),
inference(cnfConj,[status(thm)],[562]) ).
thf(568,plain,
( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS ),
inference(lifteq,[status(thm)],[565]) ).
thf(62,axiom,
( ( xS @ isCountable0 )
& ( szNzAzT0 @ ( xS @ aSubsetOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
thf(448,plain,
( ( xS @ isCountable0 )
& ( szNzAzT0 @ ( xS @ aSubsetOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(449,plain,
( ( xS @ isCountable0 )
& ( szNzAzT0 @ ( xS @ aSubsetOf0 ) ) ),
inference(cnf,[status(esa)],[448]) ).
thf(450,plain,
szNzAzT0 @ ( xS @ aSubsetOf0 ),
inference(cnfConj,[status(thm)],[449]) ).
thf(451,plain,
xS @ isCountable0,
inference(cnfConj,[status(thm)],[449]) ).
thf(597,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
!= ( xS @ isCountable0 ) )
| ~ $true
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[451,88]) ).
thf(598,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
!= ( xS @ isCountable0 ) )
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(simp,[status(thm)],[597]) ).
thf(599,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS )
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(simp,[status(thm)],[598]) ).
thf(658,plain,
( ( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
!= ( szNzAzT0 @ ( xS @ aSubsetOf0 ) ) )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[450,599]) ).
thf(659,plain,
( ( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
!= ( szNzAzT0 @ ( xS @ aSubsetOf0 ) ) )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS ) ),
inference(simp,[status(thm)],[658]) ).
thf(662,plain,
( ( szNzAzT0 != szNzAzT0 )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS ) ),
inference(simp,[status(thm)],[659]) ).
thf(665,plain,
( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS ),
inference(simp,[status(thm)],[662]) ).
thf(709,plain,
( ( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) ) )
| ( xS != xS ) ),
inference(paramod_ordered,[status(thm)],[568,665]) ).
thf(710,plain,
( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) ) ),
inference(simp,[status(thm)],[709]) ).
thf(711,plain,
( ( sz00 != xi )
| ( xN != xN ) ),
inference(simp,[status(thm)],[710]) ).
thf(716,plain,
sz00 != xi,
inference(simp,[status(thm)],[711]) ).
thf(791,plain,
xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0,
inference(simplifyReflect,[status(thm)],[335,716]) ).
thf(792,plain,
( ~ $true
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(rewrite,[status(thm)],[88,791]) ).
thf(793,plain,
~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ),
inference(simp,[status(thm)],[792]) ).
thf(976,plain,
( $false
| ( sz00 = xi ) ),
inference(rewrite,[status(thm)],[334,793]) ).
thf(977,plain,
sz00 = xi,
inference(simp,[status(thm)],[976]) ).
thf(978,plain,
$false,
inference(simplifyReflect,[status(thm)],[977,716]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM571+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.25/10.49 % Computer : n008.cluster.edu
% 0.25/10.49 % Model : x86_64 x86_64
% 0.25/10.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/10.49 % Memory : 8046.5625MB
% 0.25/10.49 % OS : Linux 6.8.0-71-generic
% 0.25/10.49 % CPULimit : 300
% 0.25/10.49 % WCLimit : 300
% 0.25/10.49 % DateTime : Sat Sep 26 03:17:24 UTC 2026
% 0.28/10.50 % CPUTime :
% 0.28/10.50 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
% 1.26/11.21 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.82/11.58 % [INFO] Parsing done (375ms).
% 2.30/11.61 % [INFO] Running in sequential loop mode.
% 3.32/12.19 % [INFO] eprover registered as external prover.
% 3.41/12.20 % [INFO] Scanning for conjecture ...
% 3.41/12.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.60/12.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.60/12.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.60/12.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.60/12.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.60/12.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.60/12.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.60/12.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.60/12.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.60/12.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.60/12.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.83/12.44 % [INFO] Found a conjecture (or negated_conjecture) and 84 axioms. Running axiom selection ...
% 3.99/12.59 % [INFO] Axiom selection finished. Selected 84 axioms (removed 0 axioms).
% 4.20/12.61 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.20/12.63 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.20/12.63 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.20/12.64 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.20/12.67 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.20/12.67 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.20/12.68 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.20/12.69 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.20/12.69 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.44/12.70 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.44/12.71 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.44/12.74 % [INFO] Problem is first-order (TPTP FOF).
% 4.44/12.77 % [INFO] Type checking passed.
% 4.44/12.77 % [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 ...
% 18.75/17.02 % [INFO] Killing All external provers ...
% 18.75/17.03 % Time passed: 6364ms (effective reasoning time: 5409ms)
% 18.75/17.03 % 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)>
% 18.75/17.03 % Axioms used in derivation (3): m__3702_02, m__3623, m__3435
% 18.75/17.03 % No. of inferences in proof: 38
% 18.75/17.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6364 ms resp. 5409 ms w/o parsing
% 19.43/17.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.43/17.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------