%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM618+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 : n018.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 08:09:19 AM UTC 2026
% Result : Theorem 60.85s 19.11s
% Output : Refutation 61.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 110 ( 40 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 353 ( 37 ~; 31 |; 26 &; 257 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 34 ( 1 ^; 22 !; 9 ?; 34 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% 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(xx_decl,type,
xx: $i ).
thf(xe_decl,type,
xe: $i ).
thf(szDzizrdt0_decl,type,
szDzizrdt0: $i > $i ).
thf(xO_decl,type,
xO: $i ).
thf(xd_decl,type,
xd: $i ).
thf(sk4_decl,type,
sk4: $i > $o ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk56_decl,type,
sk56: $i ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
& ( ( B @ ( xd @ sdtlpdtrp0 ) )
= ( xd @ szDzizrdt0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(sk56_def,definition,
( sk56
= ( @+[A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(95,axiom,
( ? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
& ( szNzAzT0 @ ( xx @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5365) ).
thf(876,plain,
( ? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
& ( szNzAzT0 @ ( xx @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(877,plain,
( ( ( sk56 @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( sk56 @ aElementOf0 ) )
& ( szNzAzT0 @ ( xx @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[876]) ).
thf(879,plain,
xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( sk56 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[877]) ).
thf(37,axiom,
! [A: $i] :
( ( ( xO @ ( A @ aElementOf0 ) )
| ? [B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) ) ) )
=> ? [B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
& ( ( B @ ( xd @ sdtlpdtrp0 ) )
= ( xd @ szDzizrdt0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4982) ).
thf(233,plain,
! [A: $i] :
( ( ( xO @ ( A @ aElementOf0 ) )
| ? [B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) ) ) )
=> ? [B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
& ( ( B @ ( xd @ sdtlpdtrp0 ) )
= ( xd @ szDzizrdt0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A )
| ~ ( A @ sk4 ) )
& ( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( A @ sk4 ) )
& ( ( ( A @ sk5 @ ( xd @ sdtlpdtrp0 ) )
= ( xd @ szDzizrdt0 ) )
| ~ ( A @ sk4 ) )
& ( ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( A @ sk4 ) )
& ( ( A @ sk4 )
| ~ ( xO @ ( A @ aElementOf0 ) ) )
& ( ( A @ sk4 )
| ( ( B @ ( xe @ sdtlpdtrp0 ) )
!= A )
| ~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[233]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( A @ sk4 )
| ( ( B @ ( xe @ sdtlpdtrp0 ) )
!= A )
| ~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[234]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( A @ sk4 )
| ~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
| ( ( B @ ( xe @ sdtlpdtrp0 ) )
!= A ) ),
inference(lifteq,[status(thm)],[238]) ).
thf(242,plain,
! [A: $i] :
( ( A @ ( xe @ sdtlpdtrp0 ) @ sk4 )
| ~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(16102,plain,
! [A: $i] :
( ( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( sk56 @ aElementOf0 ) )
!= ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
| ( A @ ( xe @ sdtlpdtrp0 ) @ sk4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,242]) ).
thf(16103,plain,
! [A: $i] :
( ( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( sk56 @ aElementOf0 ) )
!= ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
| ( A @ ( xe @ sdtlpdtrp0 ) @ sk4 ) ),
inference(simp,[status(thm)],[16102]) ).
thf(16104,plain,
sk56 @ ( xe @ sdtlpdtrp0 ) @ sk4,
inference(pattern_uni,[status(thm)],[16103:[bind(A,$thf( sk56 ))]]) ).
thf(880,plain,
( ( sk56 @ ( xe @ sdtlpdtrp0 ) )
= xx ),
inference(cnfConj,[status(thm)],[877]) ).
thf(881,plain,
( ( sk56 @ ( xe @ sdtlpdtrp0 ) )
= xx ),
inference(lifteq,[status(thm)],[880]) ).
thf(16324,plain,
xx @ sk4,
inference(rewrite,[status(thm)],[16104,881]) ).
thf(236,plain,
! [A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A )
| ~ ( A @ sk4 ) ),
inference(cnfConj,[status(thm)],[234]) ).
thf(243,plain,
! [A: $i] :
( ~ ( A @ sk4 )
| ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A ) ),
inference(lifteq,[status(thm)],[236]) ).
thf(16771,plain,
! [A: $i] :
( ( ( xx @ sk4 )
!= ( A @ sk4 ) )
| ~ $true
| ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[16324,243]) ).
thf(16772,plain,
! [A: $i] :
( ( ( xx @ sk4 )
!= ( A @ sk4 ) )
| ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A ) ),
inference(simp,[status(thm)],[16771]) ).
thf(16773,plain,
( ( xx @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= xx ),
inference(pattern_uni,[status(thm)],[16772:[bind(A,$thf( xx ))]]) ).
thf(1,conjecture,
? [A: $i] :
( ( xx
= ( A @ ( xe @ sdtlpdtrp0 ) ) )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( xx
= ( A @ ( xe @ sdtlpdtrp0 ) ) )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(117,plain,
~ ? [A: $i] :
( ( xx
= ( A @ ( xe @ sdtlpdtrp0 ) ) )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(118,plain,
! [A: $i] :
( ( xx
!= ( A @ ( xe @ sdtlpdtrp0 ) ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(119,plain,
! [A: $i] :
( ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xx ) ),
inference(lifteq,[status(thm)],[118]) ).
thf(17388,plain,
! [A: $i] :
( ( ( xx @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= ( A @ ( xe @ sdtlpdtrp0 ) ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( xx != xx ) ),
inference(paramod_ordered,[status(thm)],[16773,119]) ).
thf(17389,plain,
! [A: $i] :
( ( ( xx @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= ( A @ ( xe @ sdtlpdtrp0 ) ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[17388]) ).
thf(17390,plain,
~ ( szNzAzT0 @ ( xx @ sk5 @ aElementOf0 ) ),
inference(pattern_uni,[status(thm)],[17389:[bind(A,$thf( xx @ sk5 ))]]) ).
thf(237,plain,
! [A: $i] :
( ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( A @ sk4 ) ),
inference(cnfConj,[status(thm)],[234]) ).
thf(16327,plain,
! [A: $i] :
( ( ( xx @ sk4 )
!= ( A @ sk4 ) )
| ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16324,237]) ).
thf(16328,plain,
! [A: $i] :
( ( ( xx @ sk4 )
!= ( A @ sk4 ) )
| ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[16327]) ).
thf(16329,plain,
szNzAzT0 @ ( xx @ sk5 @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[16328:[bind(A,$thf( xx ))]]) ).
thf(17694,plain,
~ $true,
inference(rewrite,[status(thm)],[17390,16329]) ).
thf(17695,plain,
$false,
inference(simp,[status(thm)],[17694]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM618+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.15/0.39 % Computer : n018.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8046.5625MB
% 0.15/0.39 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 03:30:21 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 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
% 1.29/1.26 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.43/1.69 % [INFO] Parsing done (419ms).
% 2.88/1.71 % [INFO] Running in sequential loop mode.
% 4.08/2.34 % [INFO] eprover registered as external prover.
% 4.08/2.35 % [INFO] Scanning for conjecture ...
% 4.27/2.45 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.27/2.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.27/2.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.27/2.49 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.46/2.52 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.46/2.53 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.46/2.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.46/2.55 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.46/2.56 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.46/2.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.46/2.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.70/2.66 % [INFO] Found a conjecture (or negated_conjecture) and 114 axioms. Running axiom selection ...
% 5.18/2.87 % [INFO] Axiom selection finished. Selected 114 axioms (removed 0 axioms).
% 5.56/2.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.56/3.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.56/3.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.56/3.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.56/3.05 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.56/3.05 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.97/3.08 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.97/3.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.97/3.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.97/3.12 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.97/3.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 6.13/3.15 % [INFO] Problem is first-order (TPTP FOF).
% 6.13/3.19 % [INFO] Type checking passed.
% 6.22/3.20 % [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 ...
% 60.85/19.10 % [INFO] Killing All external provers ...
% 60.85/19.11 % Time passed: 18493ms (effective reasoning time: 17386ms)
% 60.85/19.11 % 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)>
% 60.85/19.11 % Axioms used in derivation (2): m__5365, m__4982
% 60.85/19.11 % No. of inferences in proof: 35
% 60.85/19.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18493 ms resp. 17386 ms w/o parsing
% 61.01/19.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 61.01/19.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------