%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM550+1 : 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 10.53s 4.14s
% Output : Refutation 10.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 83 ( 44 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 140 ( 31 ~; 16 |; 23 &; 60 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 21 ( 1 ^; 14 !; 5 ?; 21 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_decl,type,
slcrc0: $i ).
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(isFinite0_decl,type,
isFinite0: $i > $o ).
thf(sbrdtbr0_decl,type,
sbrdtbr0: $i > $i ).
thf(xQ_decl,type,
xQ: $i ).
thf(xS_decl,type,
xS: $i ).
thf(sz00_decl,type,
sz00: $i ).
thf(xT_decl,type,
xT: $i ).
thf(xk_decl,type,
xk: $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ aElementOf0 ) ) ) ) ).
thf(59,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ( ( ( A @ sbrdtbr0 )
= sz00 )
<=> ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
thf(347,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ( ( ( A = slcrc0 )
=> ( ( A @ sbrdtbr0 )
= sz00 ) )
& ( ( ( A @ sbrdtbr0 )
= sz00 )
=> ( A = slcrc0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(348,plain,
! [A: $i] :
( ( ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 )
| ~ ( A @ aSet0 ) )
& ( ( A = slcrc0 )
| ( ( A @ sbrdtbr0 )
!= sz00 )
| ~ ( A @ aSet0 ) ) ),
inference(cnf,[status(esa)],[347]) ).
thf(350,plain,
! [A: $i] :
( ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[348]) ).
thf(352,plain,
! [A: $i] :
( ~ ( A @ aSet0 )
| ( ( A @ sbrdtbr0 )
= sz00 )
| ( A != slcrc0 ) ),
inference(lifteq,[status(thm)],[350]) ).
thf(353,plain,
( ~ ( slcrc0 @ aSet0 )
| ( ( slcrc0 @ sbrdtbr0 )
= sz00 ) ),
inference(simp,[status(thm)],[352]) ).
thf(66,axiom,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
thf(403,plain,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(404,plain,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
inference(cnf,[status(esa)],[403]) ).
thf(407,plain,
( ( xQ @ sbrdtbr0 )
= xk ),
inference(cnfConj,[status(thm)],[404]) ).
thf(408,plain,
( ( xQ @ sbrdtbr0 )
= xk ),
inference(lifteq,[status(thm)],[407]) ).
thf(1,conjecture,
xQ != slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xQ != slcrc0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ( ( xQ != slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,plain,
xQ = slcrc0,
inference(polarity_switch,[status(thm)],[69]) ).
thf(71,plain,
xQ = slcrc0,
inference(lifteq,[status(thm)],[70]) ).
thf(531,plain,
( ( slcrc0 @ sbrdtbr0 )
= xk ),
inference(rewrite,[status(thm)],[408,71]) ).
thf(62,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
thf(372,plain,
! [A: $i] :
( ( ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) )
=> ( A = slcrc0 ) )
& ( ( A = slcrc0 )
=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(373,plain,
( ! [A: $i] :
( ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) )
=> ( A = slcrc0 ) )
& ! [A: $i] :
( ( A = slcrc0 )
=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ) ),
inference(miniscope,[status(thm)],[372]) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = slcrc0 )
| ( C @ ( C @ sk18 @ aElementOf0 ) )
| ~ ( C @ aSet0 ) )
& ( ~ ( A @ ( B @ aElementOf0 ) )
| ( A != slcrc0 ) )
& ( ( A @ aSet0 )
| ( A != slcrc0 ) ) ),
inference(cnf,[status(esa)],[373]) ).
thf(375,plain,
! [A: $i] :
( ( A @ aSet0 )
| ( A != slcrc0 ) ),
inference(cnfConj,[status(thm)],[374]) ).
thf(378,plain,
! [A: $i] :
( ( A @ aSet0 )
| ( A != slcrc0 ) ),
inference(lifteq,[status(thm)],[375]) ).
thf(379,plain,
slcrc0 @ aSet0,
inference(simp,[status(thm)],[378]) ).
thf(728,plain,
( ~ $true
| ( xk = sz00 ) ),
inference(rewrite,[status(thm)],[353,531,379]) ).
thf(729,plain,
xk = sz00,
inference(simp,[status(thm)],[728]) ).
thf(42,axiom,
( ( xk != sz00 )
& ( xT @ aSet0 )
& ( xS @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
thf(271,plain,
( ( xk != sz00 )
& ( xT @ aSet0 )
& ( xS @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(272,plain,
( ( xk != sz00 )
& ( xT @ aSet0 )
& ( xS @ aSet0 ) ),
inference(cnf,[status(esa)],[271]) ).
thf(275,plain,
xk != sz00,
inference(cnfConj,[status(thm)],[272]) ).
thf(276,plain,
xk != sz00,
inference(lifteq,[status(thm)],[275]) ).
thf(730,plain,
$false,
inference(simplifyReflect,[status(thm)],[729,276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM550+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 03:12:48 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.24 % [INFO] Parsing done (245ms).
% 1.36/1.25 % [INFO] Running in sequential loop mode.
% 2.21/1.65 % [INFO] eprover registered as external prover.
% 2.21/1.66 % [INFO] Scanning for conjecture ...
% 2.42/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.63/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.81/1.92 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.81/1.92 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/1.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/2.00 % [INFO] Problem is first-order (TPTP FOF).
% 2.81/2.02 % [INFO] Type checking passed.
% 2.81/2.02 % [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 ...
% 10.53/4.14 % [INFO] Killing All external provers ...
% 10.53/4.14 % Time passed: 3595ms (effective reasoning time: 2879ms)
% 10.53/4.14 % 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)>
% 10.53/4.14 % Axioms used in derivation (4): mCardEmpty, m__2291, mDefEmp, m__2202_02
% 10.53/4.14 % No. of inferences in proof: 32
% 10.53/4.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3595 ms resp. 2879 ms w/o parsing
% 10.53/4.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.53/4.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------