%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM615+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 : n016.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 30.56s 23.99s
% Output : Refutation 30.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 41 ( 21 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 167 ( 17 ~; 11 |; 11 &; 128 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 11 ( 0 ^; 5 !; 5 ?; 11 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(sdtlbdtrb0_decl,type,
sdtlbdtrb0: $i > $i > $i ).
thf(szDzozmdt0_decl,type,
szDzozmdt0: $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(sk62_decl,type,
sk62: $i ).
thf(sk62_def,definition,
( sk62
= ( @+[A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xp )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(100,axiom,
? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xp )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5182) ).
thf(958,plain,
? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xp )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(959,plain,
( ( ( sk62 @ ( xe @ sdtlpdtrp0 ) )
= xp )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( sk62 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[958]) ).
thf(960,plain,
xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( sk62 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[959]) ).
thf(961,plain,
( ( sk62 @ ( xe @ sdtlpdtrp0 ) )
= xp ),
inference(cnfConj,[status(thm)],[959]) ).
thf(962,plain,
( ( sk62 @ ( xe @ sdtlpdtrp0 ) )
= xp ),
inference(lifteq,[status(thm)],[961]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xp )
& ( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
| ( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= ( xd @ szDzizrdt0 ) )
& ( xd @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xp )
& ( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
| ( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= ( xd @ szDzizrdt0 ) )
& ( xd @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ? [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= xp )
& ( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
| ( ( ( A @ ( xd @ sdtlpdtrp0 ) )
= ( xd @ szDzizrdt0 ) )
& ( xd @ szDzozmdt0 @ ( 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 ) ) )
& ( ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xp )
| ( ( A @ ( xd @ sdtlpdtrp0 ) )
!= ( xd @ szDzizrdt0 ) )
| ~ ( xd @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(116,plain,
! [A: $i] :
( ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xp )
| ~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(118,plain,
! [A: $i] :
( ~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xp ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(2915,plain,
! [A: $i] :
( ( ( sk62 @ ( xe @ sdtlpdtrp0 ) )
!= ( A @ ( xe @ sdtlpdtrp0 ) ) )
| ~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) )
| ( xp != xp ) ),
inference(paramod_ordered,[status(thm)],[962,118]) ).
thf(2916,plain,
! [A: $i] :
( ( ( sk62 @ ( xe @ sdtlpdtrp0 ) )
!= ( A @ ( xe @ sdtlpdtrp0 ) ) )
| ~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[2915]) ).
thf(2917,plain,
~ ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( sk62 @ aElementOf0 ) ),
inference(pattern_uni,[status(thm)],[2916:[bind(A,$thf( sk62 ))]]) ).
thf(4298,plain,
$false,
inference(rewrite,[status(thm)],[960,2917]) ).
thf(4299,plain,
$false,
inference(simp,[status(thm)],[4298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM615+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
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.14/15.68 % CPULimit : 300
% 0.14/15.68 % WCLimit : 300
% 0.14/15.68 % DateTime : Sat Sep 26 03:28:05 UTC 2026
% 0.14/15.69 % CPUTime :
% 0.14/15.69 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
% 1.06/16.28 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.64/16.55 % [INFO] Parsing done (262ms).
% 1.64/16.56 % [INFO] Running in sequential loop mode.
% 2.58/16.94 % [INFO] eprover registered as external prover.
% 2.58/16.95 % [INFO] Scanning for conjecture ...
% 2.58/17.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/17.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.84/17.05 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.84/17.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.84/17.08 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.84/17.08 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.84/17.09 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.84/17.09 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.84/17.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.84/17.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.84/17.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.08/17.17 % [INFO] Found a conjecture (or negated_conjecture) and 110 axioms. Running axiom selection ...
% 3.17/17.29 % [INFO] Axiom selection finished. Selected 110 axioms (removed 0 axioms).
% 3.53/17.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.53/17.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.53/17.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.53/17.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.53/17.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.53/17.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.53/17.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.86/17.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.86/17.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.86/17.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.86/17.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.86/17.43 % [INFO] Problem is first-order (TPTP FOF).
% 3.86/17.45 % [INFO] Type checking passed.
% 3.86/17.46 % [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 ...
% 30.56/23.98 % [INFO] Killing All external provers ...
% 30.56/23.99 % Time passed: 8152ms (effective reasoning time: 7419ms)
% 30.56/23.99 % 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)>
% 30.56/23.99 % Axioms used in derivation (1): m__5182
% 30.56/23.99 % No. of inferences in proof: 17
% 30.56/23.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8152 ms resp. 7419 ms w/o parsing
% 30.56/24.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.56/24.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------