%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM550+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 : n020.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 08:09:08 AM UTC 2026
% Result : Theorem 12.42s 9.76s
% Output : Refutation 12.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 35 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 141 ( 26 ~; 11 |; 25 &; 72 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 13 ( 0 ^; 9 !; 4 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_decl,type,
slcrc0: $i ).
thf(aSet0_decl,type,
aSet0: $i > $o ).
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(xQ_decl,type,
xQ: $i ).
thf(xS_decl,type,
xS: $i ).
thf(xT_decl,type,
xT: $i ).
thf(xk_decl,type,
xk: $i ).
thf(sz00_decl,type,
sz00: $i ).
thf(24,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ( ( ( A @ sbrdtbr0 )
= sz00 )
<=> ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
thf(153,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ( ( ( A = slcrc0 )
=> ( ( A @ sbrdtbr0 )
= sz00 ) )
& ( ( ( A @ sbrdtbr0 )
= sz00 )
=> ( A = slcrc0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(154,plain,
! [A: $i] :
( ( ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 )
| ~ ( A @ aSet0 ) )
& ( ( A = slcrc0 )
| ( ( A @ sbrdtbr0 )
!= sz00 )
| ~ ( A @ aSet0 ) ) ),
inference(cnf,[status(esa)],[153]) ).
thf(156,plain,
! [A: $i] :
( ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[154]) ).
thf(158,plain,
! [A: $i] :
( ~ ( A @ aSet0 )
| ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 ) ),
inference(lifteq,[status(thm)],[156]) ).
thf(159,plain,
( ~ ( slcrc0 @ aSet0 )
| ( ( slcrc0 @ sbrdtbr0 )
= sz00 ) ),
inference(simp,[status(thm)],[158]) ).
thf(22,axiom,
( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xk )
& ( xS @ ( xQ @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
thf(144,plain,
( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xk )
& ( xS @ ( xQ @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(145,plain,
! [A: $i] :
( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( xQ @ aElementOf0 ) )
& ( ( xQ @ sbrdtbr0 )
= xk )
& ( xS @ ( xQ @ aSubsetOf0 ) )
& ( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xQ @ ( A @ aElementOf0 ) ) )
& ( xQ @ aSet0 ) ),
inference(cnf,[status(esa)],[144]) ).
thf(147,plain,
xQ @ aSet0,
inference(cnfConj,[status(thm)],[145]) ).
thf(1,conjecture,
~ ( ( xQ = slcrc0 )
& ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ~ ( ( xQ = slcrc0 )
& ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ~ ( ( xQ = slcrc0 )
& ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,plain,
( ( xQ = slcrc0 )
& ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
inference(polarity_switch,[status(thm)],[69]) ).
thf(71,plain,
! [A: $i] :
( ( xQ = slcrc0 )
& ~ ( xQ @ ( A @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(73,plain,
xQ = slcrc0,
inference(cnfConj,[status(thm)],[71]) ).
thf(74,plain,
xQ = slcrc0,
inference(lifteq,[status(thm)],[73]) ).
thf(508,plain,
slcrc0 @ aSet0,
inference(rewrite,[status(thm)],[147,74]) ).
thf(150,plain,
( ( xQ @ sbrdtbr0 )
= xk ),
inference(cnfConj,[status(thm)],[145]) ).
thf(151,plain,
( ( xQ @ sbrdtbr0 )
= xk ),
inference(lifteq,[status(thm)],[150]) ).
thf(524,plain,
( ( slcrc0 @ sbrdtbr0 )
= xk ),
inference(rewrite,[status(thm)],[151,74]) ).
thf(1368,plain,
( ~ $true
| ( sz00 = xk ) ),
inference(rewrite,[status(thm)],[159,508,524]) ).
thf(1369,plain,
sz00 = xk,
inference(simp,[status(thm)],[1368]) ).
thf(6,axiom,
( ( xk != sz00 )
& ( xT @ aSet0 )
& ( xS @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
thf(80,plain,
( ( xk != sz00 )
& ( xT @ aSet0 )
& ( xS @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(81,plain,
( ( xk != sz00 )
& ( xT @ aSet0 )
& ( xS @ aSet0 ) ),
inference(cnf,[status(esa)],[80]) ).
thf(84,plain,
xk != sz00,
inference(cnfConj,[status(thm)],[81]) ).
thf(85,plain,
sz00 != xk,
inference(lifteq,[status(thm)],[84]) ).
thf(1370,plain,
$false,
inference(simplifyReflect,[status(thm)],[1369,85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM550+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
% 0.16/5.42 % Computer : n020.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Sat Sep 26 03:13:09 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.42 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
% 0.18/6.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/6.26 % [INFO] Parsing done (242ms).
% 1.31/6.27 % [INFO] Running in sequential loop mode.
% 2.22/6.66 % [INFO] eprover registered as external prover.
% 2.22/6.67 % [INFO] Scanning for conjecture ...
% 2.41/6.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/6.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/6.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/6.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/6.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/6.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/6.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.61/6.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.61/6.83 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.80/6.93 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.80/6.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.80/6.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.80/6.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.80/6.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.80/6.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.80/6.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.80/6.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.80/7.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.80/7.02 % [INFO] Problem is first-order (TPTP FOF).
% 3.06/7.04 % [INFO] Type checking passed.
% 3.06/7.04 % [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 ...
% 12.42/9.75 % [INFO] Killing All external provers ...
% 12.42/9.76 % Time passed: 4181ms (effective reasoning time: 3476ms)
% 12.42/9.76 % 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)>
% 12.42/9.76 % Axioms used in derivation (3): mCardEmpty, m__2270, m__2202_02
% 12.42/9.76 % No. of inferences in proof: 29
% 12.42/9.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4181 ms resp. 3476 ms w/o parsing
% 12.42/9.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.42/9.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------