%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM557+3 : 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 : n012.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 08:09:09 AM UTC 2026
% Result : Theorem 5.38s 7.28s
% Output : Refutation 5.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 48 ( 16 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 131 ( 17 ~; 13 |; 12 &; 83 @)
% ( 0 <=>; 6 =>; 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 : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 7 ( 0 ^; 6 !; 0 ?; 7 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(slbdtsldtrb0_decl,type,
slbdtsldtrb0: $i > $i > $i ).
thf(sbrdtbr0_decl,type,
sbrdtbr0: $i > $i ).
thf(xP_decl,type,
xP: $i ).
thf(xS_decl,type,
xS: $i ).
thf(xk_decl,type,
xk: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( xP @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(55,axiom,
( ( ( xP @ sbrdtbr0 )
= xk )
& ( xS @ ( xP @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xP @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2431) ).
thf(350,plain,
( ( ( xP @ sbrdtbr0 )
= xk )
& ( xS @ ( xP @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xP @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(351,plain,
! [A: $i] :
( ( ( xP @ sbrdtbr0 )
= xk )
& ( xS @ ( xP @ aSubsetOf0 ) )
& ( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xP @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[350]) ).
thf(354,plain,
( ( xP @ sbrdtbr0 )
= xk ),
inference(cnfConj,[status(thm)],[351]) ).
thf(355,plain,
( ( xP @ sbrdtbr0 )
= xk ),
inference(lifteq,[status(thm)],[354]) ).
thf(1,conjecture,
( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( xP @ aElementOf0 ) )
| ( ( ( xP @ sbrdtbr0 )
= xk )
& ( ( xS @ ( xP @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xP @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( xP @ aElementOf0 ) )
| ( ( ( xP @ sbrdtbr0 )
= xk )
& ( ( xS @ ( xP @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xP @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(75,plain,
~ ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( xP @ aElementOf0 ) )
| ( ( ( xP @ sbrdtbr0 )
= xk )
& ( ( xS @ ( xP @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xP @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(76,plain,
( ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( xP @ aElementOf0 ) )
& ( ( ( xP @ sbrdtbr0 )
!= xk )
| ~ ( xS @ ( xP @ aSubsetOf0 ) ) )
& ( ( ( xP @ sbrdtbr0 )
!= xk )
| ~ ( xS @ ( sk1 @ aElementOf0 ) ) )
& ( ( ( xP @ sbrdtbr0 )
!= xk )
| ( xP @ ( sk1 @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(79,plain,
( ( ( xP @ sbrdtbr0 )
!= xk )
| ~ ( xS @ ( xP @ aSubsetOf0 ) ) ),
inference(cnfConj,[status(thm)],[76]) ).
thf(83,plain,
( ~ ( xS @ ( xP @ aSubsetOf0 ) )
| ( ( xP @ sbrdtbr0 )
!= xk ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(353,plain,
xS @ ( xP @ aSubsetOf0 ),
inference(cnfConj,[status(thm)],[351]) ).
thf(674,plain,
( ~ $true
| ( ( xP @ sbrdtbr0 )
!= xk ) ),
inference(rewrite,[status(thm)],[83,353]) ).
thf(675,plain,
( ( xP @ sbrdtbr0 )
!= xk ),
inference(simp,[status(thm)],[674]) ).
thf(719,plain,
$false,
inference(simplifyReflect,[status(thm)],[355,675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM557+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % 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
% 0.06/5.33 % Computer : n012.cluster.edu
% 0.06/5.33 % Model : x86_64 x86_64
% 0.06/5.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/5.33 % Memory : 8046.5625MB
% 0.06/5.33 % OS : Linux 6.8.0-71-generic
% 0.06/5.33 % CPULimit : 300
% 0.06/5.33 % WCLimit : 300
% 0.06/5.33 % DateTime : Sat Sep 26 03:13:27 UTC 2026
% 0.06/5.33 % CPUTime :
% 0.06/5.33 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
% 0.09/5.61 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.09/5.73 % [INFO] Parsing done (118ms).
% 0.09/5.74 % [INFO] Running in sequential loop mode.
% 0.09/5.93 % [INFO] eprover registered as external prover.
% 0.09/5.93 % [INFO] Scanning for conjecture ...
% 0.09/5.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 0.09/5.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 0.09/5.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 0.09/5.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 0.09/5.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 0.09/6.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 0.09/6.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 0.09/6.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.42/6.02 % [INFO] Found a conjecture (or negated_conjecture) and 72 axioms. Running axiom selection ...
% 1.42/6.07 % [INFO] Axiom selection finished. Selected 72 axioms (removed 0 axioms).
% 1.42/6.08 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.42/6.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.42/6.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.42/6.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.42/6.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.42/6.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.42/6.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.66/6.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.66/6.12 % [INFO] Problem is first-order (TPTP FOF).
% 1.66/6.13 % [INFO] Type checking passed.
% 1.66/6.13 % [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 ...
% 5.38/7.27 % [INFO] Killing All external provers ...
% 5.38/7.27 % Time passed: 1865ms (effective reasoning time: 1530ms)
% 5.38/7.28 % 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)>
% 5.38/7.28 % Axioms used in derivation (1): m__2431
% 5.38/7.28 % No. of inferences in proof: 15
% 5.38/7.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1865 ms resp. 1530 ms w/o parsing
% 5.90/7.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.90/7.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------