%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM602+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 : 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 08:09:16 AM UTC 2026
% Result : Theorem 53.72s 18.35s
% Output : Refutation 53.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 64 ( 22 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 192 ( 28 ~; 17 |; 11 &; 134 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 1 ^; 13 !; 5 ?; 20 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(szNzAzT0_decl,type,
szNzAzT0: $i ).
thf(sdtlbdtrb0_decl,type,
sdtlbdtrb0: $i > $i > $i ).
thf(sdtlpdtrp0_decl,type,
sdtlpdtrp0: $i > $i > $i ).
thf(xe_decl,type,
xe: $i ).
thf(xx_decl,type,
xx: $i ).
thf(xd_decl,type,
xd: $i ).
thf(szDzizrdt0_decl,type,
szDzizrdt0: $i > $i ).
thf(xO_decl,type,
xO: $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(40,axiom,
! [A: $i] :
( ( xO @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4982) ).
thf(235,plain,
! [A: $i] :
( ( xO @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(236,plain,
! [A: $i] :
( ( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A )
| ~ ( xO @ ( A @ aElementOf0 ) ) )
& ( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( xO @ ( A @ aElementOf0 ) ) )
& ( ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( xO @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[235]) ).
thf(239,plain,
! [A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A )
| ~ ( xO @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[236]) ).
thf(240,plain,
! [A: $i] :
( ~ ( xO @ ( A @ aElementOf0 ) )
| ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A ) ),
inference(lifteq,[status(thm)],[239]) ).
thf(70,axiom,
xO @ ( xx @ aElementOf0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5009) ).
thf(460,plain,
xO @ ( xx @ aElementOf0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(237,plain,
! [A: $i] :
( ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( xO @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[236]) ).
thf(23492,plain,
! [A: $i] :
( ( ( xO @ ( xx @ aElementOf0 ) )
!= ( xO @ ( A @ aElementOf0 ) ) )
| ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[460,237]) ).
thf(23493,plain,
! [A: $i] :
( ( ( xO @ ( xx @ aElementOf0 ) )
!= ( xO @ ( A @ aElementOf0 ) ) )
| ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[23492]) ).
thf(23494,plain,
szNzAzT0 @ ( xx @ sk5 @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[23493:[bind(A,$thf( xx ))]]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(101,plain,
~ ? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(102,plain,
! [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xx )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[101]) ).
thf(103,plain,
! [A: $i] :
( ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xx ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(23832,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xx @ sk5 @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ~ $true
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xx ) ),
inference(paramod_ordered,[status(thm)],[23494,103]) ).
thf(23833,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xx @ sk5 @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xx ) ),
inference(simp,[status(thm)],[23832]) ).
thf(23834,plain,
( ( xx @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= xx ),
inference(pattern_uni,[status(thm)],[23833:[bind(A,$thf( xx @ sk5 ))]]) ).
thf(25656,plain,
! [A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= ( xx @ sk5 @ ( xe @ sdtlpdtrp0 ) ) )
| ( A != xx )
| ~ ( xO @ ( A @ aElementOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[240,23834]) ).
thf(25657,plain,
( ( xx != xx )
| ~ ( xO @ ( xx @ aElementOf0 ) ) ),
inference(pattern_uni,[status(thm)],[25656:[bind(A,$thf( xx ))]]) ).
thf(25858,plain,
~ ( xO @ ( xx @ aElementOf0 ) ),
inference(simp,[status(thm)],[25657]) ).
thf(25941,plain,
~ $true,
inference(rewrite,[status(thm)],[25858,460]) ).
thf(25942,plain,
$false,
inference(simp,[status(thm)],[25941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM602+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
% 0.13/0.40 % Computer : n005.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 03:24:48 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/1.26 % [INFO] Parsing done (276ms).
% 1.38/1.28 % [INFO] Running in sequential loop mode.
% 2.19/1.66 % [INFO] eprover registered as external prover.
% 2.19/1.67 % [INFO] Scanning for conjecture ...
% 2.39/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.39/1.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.39/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.39/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.39/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.39/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.86 % [INFO] Found a conjecture (or negated_conjecture) and 98 axioms. Running axiom selection ...
% 2.75/1.97 % [INFO] Axiom selection finished. Selected 98 axioms (removed 0 axioms).
% 2.75/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/2.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/2.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/2.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/2.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/2.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/2.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/2.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/2.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/2.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/2.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/2.08 % [INFO] Problem is first-order (TPTP FOF).
% 3.05/2.09 % [INFO] Type checking passed.
% 3.05/2.10 % [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 ...
% 53.72/18.35 % [INFO] Killing All external provers ...
% 53.72/18.35 % Time passed: 17803ms (effective reasoning time: 17063ms)
% 53.72/18.35 % 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)>
% 53.72/18.35 % Axioms used in derivation (2): m__4982, m__5009
% 53.72/18.35 % No. of inferences in proof: 24
% 53.72/18.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17803 ms resp. 17063 ms w/o parsing
% 53.72/18.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.72/18.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------