%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM561+2 : 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 : 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 08:09:10 AM UTC 2026
% Result : Theorem 5.84s 7.29s
% Output : Refutation 6.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 11 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 128 ( 15 ~; 9 |; 4 &; 100 @)
% ( 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 : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 5 !; 3 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(szDzozmdt0_decl,type,
szDzozmdt0: $i > $i ).
thf(sdtlpdtrp0_decl,type,
sdtlpdtrp0: $i > $i > $i ).
thf(sdtlcdtrc0_decl,type,
sdtlcdtrc0: $i > $i > $i ).
thf(xF_decl,type,
xF: $i ).
thf(xx_decl,type,
xx: $i ).
thf(57,axiom,
xF @ szDzozmdt0 @ ( xx @ aElementOf0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2911_02) ).
thf(370,plain,
xF @ szDzozmdt0 @ ( xx @ aElementOf0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1,conjecture,
( ( xF @ szDzozmdt0 @ ( xF @ sdtlcdtrc0 ) @ ( xx @ ( xF @ sdtlpdtrp0 ) @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xF @ sdtlpdtrp0 ) )
= ( xx @ ( xF @ sdtlpdtrp0 ) ) )
& ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xF @ szDzozmdt0 @ ( xF @ sdtlcdtrc0 ) @ ( xx @ ( xF @ sdtlpdtrp0 ) @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xF @ sdtlpdtrp0 ) )
= ( xx @ ( xF @ sdtlpdtrp0 ) ) )
& ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(73,plain,
~ ( ( xF @ szDzozmdt0 @ ( xF @ sdtlcdtrc0 ) @ ( xx @ ( xF @ sdtlpdtrp0 ) @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xF @ sdtlpdtrp0 ) )
= ( xx @ ( xF @ sdtlpdtrp0 ) ) )
& ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(74,plain,
! [A: $i] :
( ~ ( xF @ szDzozmdt0 @ ( xF @ sdtlcdtrc0 ) @ ( xx @ ( xF @ sdtlpdtrp0 ) @ aElementOf0 ) )
& ( ( ( A @ ( xF @ sdtlpdtrp0 ) )
!= ( xx @ ( xF @ sdtlpdtrp0 ) ) )
| ~ ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(75,plain,
! [A: $i] :
( ( ( A @ ( xF @ sdtlpdtrp0 ) )
!= ( xx @ ( xF @ sdtlpdtrp0 ) ) )
| ~ ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[74]) ).
thf(77,plain,
! [A: $i] :
( ~ ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) )
| ( ( A @ ( xF @ sdtlpdtrp0 ) )
!= ( xx @ ( xF @ sdtlpdtrp0 ) ) ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(510,plain,
! [A: $i] :
( ( ( xF @ szDzozmdt0 @ ( xx @ aElementOf0 ) )
!= ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) )
| ~ $true
| ( ( A @ ( xF @ sdtlpdtrp0 ) )
!= ( xx @ ( xF @ sdtlpdtrp0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[370,77]) ).
thf(511,plain,
! [A: $i] :
( ( ( xF @ szDzozmdt0 @ ( xx @ aElementOf0 ) )
!= ( xF @ szDzozmdt0 @ ( A @ aElementOf0 ) ) )
| ( ( A @ ( xF @ sdtlpdtrp0 ) )
!= ( xx @ ( xF @ sdtlpdtrp0 ) ) ) ),
inference(simp,[status(thm)],[510]) ).
thf(512,plain,
( ( xx @ ( xF @ sdtlpdtrp0 ) )
!= ( xx @ ( xF @ sdtlpdtrp0 ) ) ),
inference(pattern_uni,[status(thm)],[511:[bind(A,$thf( xx ))]]) ).
thf(516,plain,
$false,
inference(simp,[status(thm)],[512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM561+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.15/5.52 % Computer : n010.cluster.edu
% 0.15/5.52 % Model : x86_64 x86_64
% 0.15/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.52 % Memory : 8046.5625MB
% 0.15/5.52 % OS : Linux 6.8.0-71-generic
% 0.15/5.52 % CPULimit : 300
% 0.15/5.52 % WCLimit : 300
% 0.15/5.52 % DateTime : Sat Sep 26 03:14:38 UTC 2026
% 0.15/5.52 % CPUTime :
% 0.15/5.52 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
% 0.19/5.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/5.96 % [INFO] Parsing done (142ms).
% 0.19/5.97 % [INFO] Running in sequential loop mode.
% 1.71/6.17 % [INFO] eprover registered as external prover.
% 1.71/6.17 % [INFO] Scanning for conjecture ...
% 1.91/6.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/6.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/6.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/6.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/6.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/6.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/6.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/6.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/6.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/6.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/6.26 % [INFO] Found a conjecture (or negated_conjecture) and 70 axioms. Running axiom selection ...
% 2.21/6.32 % [INFO] Axiom selection finished. Selected 70 axioms (removed 0 axioms).
% 2.21/6.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/6.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/6.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/6.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/6.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/6.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/6.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/6.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/6.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/6.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/6.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.21/6.38 % [INFO] Type checking passed.
% 2.21/6.38 % [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 ...
% 5.84/7.29 % [INFO] Killing All external provers ...
% 5.84/7.29 % Time passed: 1670ms (effective reasoning time: 1314ms)
% 5.84/7.29 % 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)>
% 5.84/7.29 % Axioms used in derivation (1): m__2911_02
% 5.84/7.29 % No. of inferences in proof: 12
% 5.84/7.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1670 ms resp. 1314 ms w/o parsing
% 6.39/7.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.39/7.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------