%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM602+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 : n010.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 48.92s 19.92s
% Output : Refutation 48.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 98 ( 35 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 300 ( 40 ~; 30 |; 26 &; 202 @)
% ( 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 : 33 ( 1 ^; 21 !; 9 ?; 33 :)
% ( 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(xe_decl,type,
xe: $i ).
thf(xx_decl,type,
xx: $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(34,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(209,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)],[34]) ).
thf(210,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)],[209]) ).
thf(212,plain,
! [A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A )
| ~ ( A @ sk4 ) ),
inference(cnfConj,[status(thm)],[210]) ).
thf(217,plain,
! [A: $i] :
( ~ ( A @ sk4 )
| ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A ) ),
inference(lifteq,[status(thm)],[212]) ).
thf(211,plain,
! [A: $i] :
( ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( A @ sk4 ) ),
inference(cnfConj,[status(thm)],[210]) ).
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(14882,plain,
! [B: $i,A: $i] :
( ( ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
!= ( szNzAzT0 @ ( B @ aElementOf0 ) ) )
| ~ $true
| ( ( B @ ( xe @ sdtlpdtrp0 ) )
!= xx )
| ~ ( A @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[211,103]) ).
thf(14883,plain,
! [B: $i,A: $i] :
( ( ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
!= ( szNzAzT0 @ ( B @ aElementOf0 ) ) )
| ( ( B @ ( xe @ sdtlpdtrp0 ) )
!= xx )
| ~ ( A @ sk4 ) ),
inference(simp,[status(thm)],[14882]) ).
thf(14884,plain,
! [A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= xx )
| ~ ( A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[14883:[bind(A,$thf( C )),bind(B,$thf( C @ sk5 ))]]) ).
thf(14939,plain,
! [A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= xx )
| ~ ( A @ sk4 ) ),
inference(simp,[status(thm)],[14884]) ).
thf(16744,plain,
! [B: $i,A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= ( B @ sk5 @ ( xe @ sdtlpdtrp0 ) ) )
| ( A != xx )
| ~ ( B @ sk4 )
| ~ ( A @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[217,14939]) ).
thf(16745,plain,
! [A: $i] :
( ( A != xx )
| ~ ( A @ sk4 )
| ~ ( A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[16744:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(16797,plain,
~ ( xx @ sk4 ),
inference(simp,[status(thm)],[16745]) ).
thf(83,axiom,
( ( xO @ ( xx @ aElementOf0 ) )
& ? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5009) ).
thf(792,plain,
( ( xO @ ( xx @ aElementOf0 ) )
& ? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(793,plain,
( ( xO @ ( xx @ aElementOf0 ) )
& ( ( sk56 @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( sk56 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[792]) ).
thf(796,plain,
xO @ ( xx @ aElementOf0 ),
inference(cnfConj,[status(thm)],[793]) ).
thf(213,plain,
! [A: $i] :
( ( A @ sk4 )
| ~ ( xO @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[210]) ).
thf(15385,plain,
! [A: $i] :
( ( ( xO @ ( xx @ aElementOf0 ) )
!= ( xO @ ( A @ aElementOf0 ) ) )
| ( A @ sk4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[796,213]) ).
thf(15386,plain,
! [A: $i] :
( ( ( xO @ ( xx @ aElementOf0 ) )
!= ( xO @ ( A @ aElementOf0 ) ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[15385]) ).
thf(15387,plain,
xx @ sk4,
inference(pattern_uni,[status(thm)],[15386:[bind(A,$thf( xx ))]]) ).
thf(16809,plain,
~ $true,
inference(rewrite,[status(thm)],[16797,15387]) ).
thf(16810,plain,
$false,
inference(simp,[status(thm)],[16809]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM602+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
% 0.12/5.62 % Computer : n010.cluster.edu
% 0.12/5.62 % Model : x86_64 x86_64
% 0.12/5.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.62 % Memory : 8046.5625MB
% 0.12/5.62 % OS : Linux 6.8.0-71-generic
% 0.12/5.62 % CPULimit : 300
% 0.12/5.62 % WCLimit : 300
% 0.12/5.62 % DateTime : Sat Sep 26 03:25:07 UTC 2026
% 0.12/5.63 % CPUTime :
% 0.12/5.63 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
% 0.98/6.22 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.72/6.53 % [INFO] Parsing done (305ms).
% 1.72/6.55 % [INFO] Running in sequential loop mode.
% 2.51/6.94 % [INFO] eprover registered as external prover.
% 2.51/6.95 % [INFO] Scanning for conjecture ...
% 2.51/7.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.51/7.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/7.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/7.05 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/7.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/7.07 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/7.07 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/7.08 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/7.09 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/7.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/7.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.96/7.15 % [INFO] Found a conjecture (or negated_conjecture) and 98 axioms. Running axiom selection ...
% 3.07/7.28 % [INFO] Axiom selection finished. Selected 98 axioms (removed 0 axioms).
% 3.41/7.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.41/7.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.41/7.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.41/7.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.41/7.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.41/7.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.41/7.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.65/7.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.65/7.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.65/7.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.65/7.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.65/7.44 % [INFO] Problem is first-order (TPTP FOF).
% 3.65/7.46 % [INFO] Type checking passed.
% 3.65/7.46 % [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 ...
% 48.92/19.91 % [INFO] Killing All external provers ...
% 48.92/19.92 % Time passed: 14131ms (effective reasoning time: 13359ms)
% 48.92/19.92 % 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)>
% 48.92/19.92 % Axioms used in derivation (2): m__4982, m__5009
% 48.92/19.92 % No. of inferences in proof: 28
% 48.92/19.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14131 ms resp. 13359 ms w/o parsing
% 48.92/19.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 48.92/19.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------