%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM615+1 : 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 : n009.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 08:09:18 AM UTC 2026
% Result : Theorem 96.04s 29.06s
% Output : Refutation 96.04s
% 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 : 231 ( 28 ~; 17 |; 11 &; 173 @)
% ( 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(xd_decl,type,
xd: $i ).
thf(szDzizrdt0_decl,type,
szDzizrdt0: $i > $i ).
thf(xe_decl,type,
xe: $i ).
thf(xp_decl,type,
xp: $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(52,axiom,
! [A: $i] :
( ( xO @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4982) ).
thf(276,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)],[52]) ).
thf(277,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)],[276]) ).
thf(280,plain,
! [A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A )
| ~ ( xO @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(281,plain,
! [A: $i] :
( ~ ( xO @ ( A @ aElementOf0 ) )
| ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A ) ),
inference(lifteq,[status(thm)],[280]) ).
thf(76,axiom,
xO @ ( xp @ aElementOf0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5182) ).
thf(453,plain,
xO @ ( xp @ aElementOf0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(279,plain,
! [A: $i] :
( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( xO @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(28972,plain,
! [A: $i] :
( ( ( xO @ ( xp @ aElementOf0 ) )
!= ( xO @ ( A @ aElementOf0 ) ) )
| ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ sk5 @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[453,279]) ).
thf(28973,plain,
! [A: $i] :
( ( ( xO @ ( xp @ aElementOf0 ) )
!= ( xO @ ( A @ aElementOf0 ) ) )
| ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ sk5 @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[28972]) ).
thf(28974,plain,
xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( xp @ sk5 @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[28973:[bind(A,$thf( xp ))]]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xp )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xp )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xp )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(114,plain,
! [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xp )
| ~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(115,plain,
! [A: $i] :
( ~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xp ) ),
inference(lifteq,[status(thm)],[114]) ).
thf(29544,plain,
! [A: $i] :
( ( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( xp @ sk5 @ aElementOf0 ) )
!= ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
| ~ $true
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xp ) ),
inference(paramod_ordered,[status(thm)],[28974,115]) ).
thf(29545,plain,
! [A: $i] :
( ( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( xp @ sk5 @ aElementOf0 ) )
!= ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) )
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xp ) ),
inference(simp,[status(thm)],[29544]) ).
thf(29546,plain,
( ( xp @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= xp ),
inference(pattern_uni,[status(thm)],[29545:[bind(A,$thf( xp @ sk5 ))]]) ).
thf(30910,plain,
! [A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= ( xp @ sk5 @ ( xe @ sdtlpdtrp0 ) ) )
| ( A != xp )
| ~ ( xO @ ( A @ aElementOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[281,29546]) ).
thf(30911,plain,
( ( xp != xp )
| ~ ( xO @ ( xp @ aElementOf0 ) ) ),
inference(pattern_uni,[status(thm)],[30910:[bind(A,$thf( xp ))]]) ).
thf(31110,plain,
~ ( xO @ ( xp @ aElementOf0 ) ),
inference(simp,[status(thm)],[30911]) ).
thf(31132,plain,
~ $true,
inference(rewrite,[status(thm)],[31110,453]) ).
thf(31133,plain,
$false,
inference(simp,[status(thm)],[31132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM615+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.13 % 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
% 0.25/0.52 % Computer : n009.cluster.edu
% 0.25/0.52 % Model : x86_64 x86_64
% 0.25/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.52 % Memory : 8046.5625MB
% 0.25/0.52 % OS : Linux 6.8.0-71-generic
% 0.25/0.52 % CPULimit : 300
% 0.25/0.52 % WCLimit : 300
% 0.25/0.52 % DateTime : Sat Sep 26 03:27:15 UTC 2026
% 0.25/0.52 % CPUTime :
% 0.25/0.52 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
% 1.43/1.34 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.28/1.76 % [INFO] Parsing done (414ms).
% 2.28/1.78 % [INFO] Running in sequential loop mode.
% 3.73/2.39 % [INFO] eprover registered as external prover.
% 3.97/2.40 % [INFO] Scanning for conjecture ...
% 4.15/2.50 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.15/2.52 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.15/2.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.15/2.55 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.15/2.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.15/2.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.37/2.60 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.37/2.61 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.37/2.62 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.37/2.63 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.37/2.64 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.37/2.70 % [INFO] Found a conjecture (or negated_conjecture) and 110 axioms. Running axiom selection ...
% 4.85/2.87 % [INFO] Axiom selection finished. Selected 110 axioms (removed 0 axioms).
% 5.15/2.92 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/2.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/2.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/2.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/2.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/2.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/2.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/2.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/3.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/3.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/3.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 5.15/3.04 % [INFO] Problem is first-order (TPTP FOF).
% 5.58/3.07 % [INFO] Type checking passed.
% 5.58/3.07 % [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 ...
% 96.04/29.05 % [INFO] Killing All external provers ...
% 96.04/29.05 % Time passed: 28374ms (effective reasoning time: 27257ms)
% 96.04/29.05 % 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)>
% 96.04/29.06 % Axioms used in derivation (2): m__4982, m__5182
% 96.04/29.06 % No. of inferences in proof: 24
% 96.04/29.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 28374 ms resp. 27257 ms w/o parsing
% 96.04/29.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 96.04/29.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------