%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM533+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 : n005.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 08:09:05 AM UTC 2026
% Result : Theorem 6.17s 3.04s
% Output : Refutation 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 69 ( 5 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 183 ( 21 ~; 14 |; 15 &; 120 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 ^; 18 !; 0 ?; 19 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(xA_decl,type,
xA: $i ).
thf(xB_decl,type,
xB: $i ).
thf(xC_decl,type,
xC: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( xA @ ( A @ aElementOf0 ) )
=> ( xC @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(1,conjecture,
( ( ( xC @ ( xB @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xB @ ( A @ aElementOf0 ) )
=> ( xC @ ( A @ aElementOf0 ) ) )
& ( xB @ ( xA @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xA @ ( A @ aElementOf0 ) )
=> ( xB @ ( A @ aElementOf0 ) ) ) )
=> ( ( xC @ ( xA @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xA @ ( A @ aElementOf0 ) )
=> ( xC @ ( A @ aElementOf0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( xC @ ( xB @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xB @ ( A @ aElementOf0 ) )
=> ( xC @ ( A @ aElementOf0 ) ) )
& ( xB @ ( xA @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xA @ ( A @ aElementOf0 ) )
=> ( xB @ ( A @ aElementOf0 ) ) ) )
=> ( ( xC @ ( xA @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xA @ ( A @ aElementOf0 ) )
=> ( xC @ ( A @ aElementOf0 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ( ( ( xC @ ( xB @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xB @ ( A @ aElementOf0 ) )
=> ( xC @ ( A @ aElementOf0 ) ) )
& ( xB @ ( xA @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xA @ ( A @ aElementOf0 ) )
=> ( xB @ ( A @ aElementOf0 ) ) ) )
=> ( ( xC @ ( xA @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xA @ ( A @ aElementOf0 ) )
=> ( xC @ ( A @ aElementOf0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ ( xC @ ( xA @ aSubsetOf0 ) )
& ~ ( xC @ ( sk1 @ aElementOf0 ) )
& ( xA @ ( sk1 @ aElementOf0 ) )
& ( xC @ ( xB @ aSubsetOf0 ) )
& ( ( xC @ ( B @ aElementOf0 ) )
| ~ ( xB @ ( B @ aElementOf0 ) ) )
& ( xB @ ( xA @ aSubsetOf0 ) )
& ( ( xB @ ( A @ aElementOf0 ) )
| ~ ( xA @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(23,plain,
! [A: $i] :
( ( xC @ ( A @ aElementOf0 ) )
| ~ ( xB @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(26,plain,
! [A: $i] :
( ( xC @ ( A @ aElementOf0 ) )
| ~ ( xB @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
~ ( xC @ ( sk1 @ aElementOf0 ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(278,plain,
! [A: $i] :
( ( ( xC @ ( A @ aElementOf0 ) )
!= ( xC @ ( sk1 @ aElementOf0 ) ) )
| ~ $true
| ~ ( xB @ ( A @ aElementOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[26,25]) ).
thf(279,plain,
! [A: $i] :
( ( ( xC @ ( A @ aElementOf0 ) )
!= ( xC @ ( sk1 @ aElementOf0 ) ) )
| ~ ( xB @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(280,plain,
~ ( xB @ ( sk1 @ aElementOf0 ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( sk1 ))]]) ).
thf(24,plain,
xA @ ( sk1 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[18]) ).
thf(22,plain,
! [A: $i] :
( ( xB @ ( A @ aElementOf0 ) )
| ~ ( xA @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(189,plain,
! [A: $i] :
( ( ( xA @ ( sk1 @ aElementOf0 ) )
!= ( xA @ ( A @ aElementOf0 ) ) )
| ( xB @ ( A @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,22]) ).
thf(190,plain,
! [A: $i] :
( ( ( xA @ ( sk1 @ aElementOf0 ) )
!= ( xA @ ( A @ aElementOf0 ) ) )
| ( xB @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(191,plain,
xB @ ( sk1 @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( sk1 ))]]) ).
thf(308,plain,
~ $true,
inference(rewrite,[status(thm)],[280,191]) ).
thf(309,plain,
$false,
inference(simp,[status(thm)],[308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM533+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % 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
% 0.15/0.40 % Computer : n005.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % 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 03:08:02 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.20 % [INFO] Parsing done (202ms).
% 1.44/1.21 % [INFO] Running in sequential loop mode.
% 2.10/1.61 % [INFO] eprover registered as external prover.
% 2.10/1.62 % [INFO] Scanning for conjecture ...
% 2.10/1.69 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.70 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.27/1.78 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.27/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.45/1.81 % [INFO] Problem is first-order (TPTP FOF).
% 2.45/1.81 % [INFO] Type checking passed.
% 2.45/1.82 % [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 ...
% 6.17/3.04 % [INFO] Killing All external provers ...
% 6.17/3.04 % Time passed: 2499ms (effective reasoning time: 1824ms)
% 6.17/3.04 % 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)>
% 6.17/3.04 % Axioms used in derivation (0):
% 6.17/3.04 % No. of inferences in proof: 17
% 6.17/3.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2499 ms resp. 1824 ms w/o parsing
% 6.17/3.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.17/3.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------