%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM594+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 08:09:15 AM UTC 2026
% Result : Theorem 14.30s 5.11s
% Output : Refutation 14.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 80 ( 32 equ; 0 cnn)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 295 ( 28 ~; 24 |; 23 &; 213 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 9 con; 0-2 aty)
% Number of variables : 21 ( 2 ^; 12 !; 5 ?; 21 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(szNzAzT0_decl,type,
szNzAzT0: $i ).
thf(szszuzczcdt0_decl,type,
szszuzczcdt0: $i > $i ).
thf(slbdtsldtrb0_decl,type,
slbdtsldtrb0: $i > $i > $i ).
thf(sbrdtbr0_decl,type,
sbrdtbr0: $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(sdtlcdtrc0_decl,type,
sdtlcdtrc0: $i > $i > $i ).
thf(xd_decl,type,
xd: $i ).
thf(xx_decl,type,
xx: $i ).
thf(xN_decl,type,
xN: $i ).
thf(xk_decl,type,
xk: $i ).
thf(xC_decl,type,
xC: $i ).
thf(sk53_decl,type,
sk53: $i ).
thf(sk66_decl,type,
sk66: $i > $i > $i ).
thf(sk53_def,definition,
( sk53
= ( @+[A: $i] :
( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(sk66_def,definition,
( sk66
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ aElementOf0 ) )
=> ( B @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( C @ aElementOf0 ) ) ) ) ) ).
thf(79,axiom,
( ( xd @ szDzozmdt0 @ ( xd @ sdtlcdtrc0 ) @ ( xx @ aElementOf0 ) )
& ? [A: $i] :
( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4781) ).
thf(745,plain,
( ( xd @ szDzozmdt0 @ ( xd @ sdtlcdtrc0 ) @ ( xx @ aElementOf0 ) )
& ? [A: $i] :
( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(746,plain,
( ( xd @ szDzozmdt0 @ ( xd @ sdtlcdtrc0 ) @ ( xx @ aElementOf0 ) )
& ( ( sk53 @ ( xd @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzozmdt0 @ ( sk53 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[745]) ).
thf(748,plain,
( ( sk53 @ ( xd @ sdtlpdtrp0 ) )
= xx ),
inference(cnfConj,[status(thm)],[746]) ).
thf(750,plain,
( ( sk53 @ ( xd @ sdtlpdtrp0 ) )
= xx ),
inference(lifteq,[status(thm)],[748]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= xx )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= xx )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(97,plain,
~ ? [A: $i] :
( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= xx )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(98,plain,
! [A: $i] :
( ( ( A @ ( xd @ sdtlpdtrp0 ) )
!= xx )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[97]) ).
thf(99,plain,
! [A: $i] :
( ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( ( A @ ( xd @ sdtlpdtrp0 ) )
!= xx ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(1124,plain,
! [A: $i] :
( ( ( sk53 @ ( xd @ sdtlpdtrp0 ) )
!= ( A @ ( xd @ sdtlpdtrp0 ) ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( xx != xx ) ),
inference(paramod_ordered,[status(thm)],[750,99]) ).
thf(1125,plain,
! [A: $i] :
( ( ( sk53 @ ( xd @ sdtlpdtrp0 ) )
!= ( A @ ( xd @ sdtlpdtrp0 ) ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[1124]) ).
thf(1126,plain,
~ ( szNzAzT0 @ ( sk53 @ aElementOf0 ) ),
inference(pattern_uni,[status(thm)],[1125:[bind(A,$thf( sk53 ))]]) ).
thf(747,plain,
xd @ szDzozmdt0 @ ( sk53 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[746]) ).
thf(92,axiom,
( ! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ! [B: $i] :
( ( ( ( xk @ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ slbdtsldtrb0 ) @ ( B @ aElementOf0 ) )
| ( ( ( B @ sbrdtbr0 )
= xk )
& ( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( B @ aSubsetOf0 ) )
| ! [C: $i] :
( ( B @ ( C @ aElementOf0 ) )
=> ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( C @ aElementOf0 ) ) ) ) ) )
& ( B @ aSet0 ) )
=> ( ( A @ ( xd @ sdtlpdtrp0 ) )
= ( B @ ( A @ ( xC @ sdtlpdtrp0 ) @ sdtlpdtrp0 ) ) ) ) )
& ( ( xd @ szDzozmdt0 )
= szNzAzT0 )
& ( xd @ aFunction0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
thf(938,plain,
( ! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ! [B: $i] :
( ( ( ( xk @ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ slbdtsldtrb0 ) @ ( B @ aElementOf0 ) )
| ( ( ( B @ sbrdtbr0 )
= xk )
& ( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( B @ aSubsetOf0 ) )
| ! [C: $i] :
( ( B @ ( C @ aElementOf0 ) )
=> ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( C @ aElementOf0 ) ) ) ) ) )
& ( B @ aSet0 ) )
=> ( ( A @ ( xd @ sdtlpdtrp0 ) )
= ( B @ ( A @ ( xC @ sdtlpdtrp0 ) @ sdtlpdtrp0 ) ) ) ) )
& ( ( xd @ szDzozmdt0 )
= szNzAzT0 )
& ( xd @ aFunction0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(939,plain,
! [B: $i,A: $i] :
( ( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= ( B @ ( A @ ( xC @ sdtlpdtrp0 ) @ sdtlpdtrp0 ) ) )
| ~ ( xk @ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ slbdtsldtrb0 ) @ ( B @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= ( B @ ( A @ ( xC @ sdtlpdtrp0 ) @ sdtlpdtrp0 ) ) )
| ( ( B @ sbrdtbr0 )
!= xk )
| ~ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( B @ aSubsetOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= ( B @ ( A @ ( xC @ sdtlpdtrp0 ) @ sdtlpdtrp0 ) ) )
| ( ( B @ sbrdtbr0 )
!= xk )
| ~ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( B @ sk66 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= ( B @ ( A @ ( xC @ sdtlpdtrp0 ) @ sdtlpdtrp0 ) ) )
| ( ( B @ sbrdtbr0 )
!= xk )
| ( B @ ( A @ ( B @ sk66 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( xd @ szDzozmdt0 )
= szNzAzT0 )
& ( xd @ aFunction0 ) ),
inference(cnf,[status(esa)],[938]) ).
thf(941,plain,
( ( xd @ szDzozmdt0 )
= szNzAzT0 ),
inference(cnfConj,[status(thm)],[939]) ).
thf(946,plain,
( ( xd @ szDzozmdt0 )
= szNzAzT0 ),
inference(lifteq,[status(thm)],[941]) ).
thf(1120,plain,
szNzAzT0 @ ( sk53 @ aElementOf0 ),
inference(rewrite,[status(thm)],[747,946]) ).
thf(1147,plain,
~ $true,
inference(rewrite,[status(thm)],[1126,1120]) ).
thf(1148,plain,
$false,
inference(simp,[status(thm)],[1147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM594+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n014.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 03:22:32 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.29 % [INFO] Parsing done (301ms).
% 1.89/1.31 % [INFO] Running in sequential loop mode.
% 2.69/1.71 % [INFO] eprover registered as external prover.
% 2.69/1.72 % [INFO] Scanning for conjecture ...
% 2.69/1.79 % [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] Definitions in FOF are currently treated as axioms.
% 2.86/1.84 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.86/1.85 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.86/1.85 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.86/1.86 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.86/1.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.86/1.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.08/1.92 % [INFO] Found a conjecture (or negated_conjecture) and 94 axioms. Running axiom selection ...
% 3.43/2.04 % [INFO] Axiom selection finished. Selected 94 axioms (removed 0 axioms).
% 3.43/2.07 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.43/2.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.43/2.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.43/2.12 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.43/2.12 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.43/2.12 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.77/2.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.77/2.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.77/2.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.77/2.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.77/2.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.77/2.17 % [INFO] Problem is first-order (TPTP FOF).
% 3.77/2.19 % [INFO] Type checking passed.
% 3.77/2.20 % [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 ...
% 14.30/5.10 % [INFO] Killing All external provers ...
% 14.30/5.10 % Time passed: 4553ms (effective reasoning time: 3785ms)
% 14.30/5.10 % 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)>
% 14.30/5.10 % Axioms used in derivation (2): m__4781, m__4730
% 14.30/5.10 % No. of inferences in proof: 22
% 14.30/5.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4553 ms resp. 3785 ms w/o parsing
% 14.81/5.15 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.81/5.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------