%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM551+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 : n004.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 96.33s 46.67s
% Output : Refutation 96.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 73 ( 12 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 164 ( 27 ~; 17 |; 16 &; 98 @)
% ( 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 : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 0 ^; 16 !; 6 ?; 23 :)
% ( 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(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(aElement0_decl,type,
aElement0: $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(xk_decl,type,
xk: $i ).
thf(sk24_decl,type,
sk24: $i ).
thf(sk24_def,definition,
( sk24
= ( @+[A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ) ) ).
thf(64,axiom,
~ ( ( xQ = slcrc0 )
| ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2313) ).
thf(468,plain,
~ ( ( xQ = slcrc0 )
| ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(469,plain,
~ ( ( xQ = slcrc0 )
| ~ ? [A: $i] : ( xQ @ ( A @ aElementOf0 ) ) ),
inference(polarity_switch,[status(thm)],[468]) ).
thf(470,plain,
( ( xQ != slcrc0 )
& ( xQ @ ( sk24 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[469]) ).
thf(471,plain,
xQ @ ( sk24 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[470]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(233,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( B @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(cnf,[status(esa)],[233]) ).
thf(43433,plain,
! [B: $i,A: $i] :
( ( ( xQ @ ( sk24 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ $true
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[471,234]) ).
thf(43434,plain,
! [B: $i,A: $i] :
( ( ( xQ @ ( sk24 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[43433]) ).
thf(43435,plain,
( ( sk24 @ aElement0 )
| ~ ( xQ @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[43434:[bind(A,$thf( xQ )),bind(B,$thf( sk24 ))]]) ).
thf(20,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)],[20]) ).
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(146,plain,
xQ @ aSet0,
inference(cnfConj,[status(thm)],[145]) ).
thf(1,conjecture,
? [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(70,plain,
~ ? [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(71,plain,
! [A: $i] :
( ~ ( xQ @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(564,plain,
! [A: $i] :
( ( ( xQ @ ( sk24 @ aElementOf0 ) )
!= ( xQ @ ( A @ aElementOf0 ) ) )
| ~ $true
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[471,71]) ).
thf(565,plain,
! [A: $i] :
( ( ( xQ @ ( sk24 @ aElementOf0 ) )
!= ( xQ @ ( A @ aElementOf0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[564]) ).
thf(566,plain,
~ ( sk24 @ aElement0 ),
inference(pattern_uni,[status(thm)],[565:[bind(A,$thf( sk24 ))]]) ).
thf(73238,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[43435,146,566]) ).
thf(73239,plain,
$false,
inference(simp,[status(thm)],[73238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM551+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
% 0.15/0.41 % Computer : n004.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 03:12:08 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.68/0.72 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.92/0.86 % [INFO] Parsing done (140ms).
% 0.92/0.86 % [INFO] Running in sequential loop mode.
% 1.79/1.07 % [INFO] eprover registered as external prover.
% 1.79/1.08 % [INFO] Scanning for conjecture ...
% 1.79/1.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.12 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.12 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.13 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.25/1.20 % [INFO] Found a conjecture (or negated_conjecture) and 67 axioms. Running axiom selection ...
% 2.25/1.29 % [INFO] Axiom selection finished. Selected 67 axioms (removed 0 axioms).
% 2.48/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.48/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.48/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.48/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.48/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.48/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.48/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.48/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.48/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.72/1.40 % [INFO] Type checking passed.
% 2.72/1.40 % [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 ...
% 96.33/46.66 % [INFO] Killing All external provers ...
% 96.33/46.66 % Time passed: 46151ms (effective reasoning time: 45790ms)
% 96.33/46.66 % 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)>
% 96.33/46.67 % Axioms used in derivation (3): m__2313, mEOfElem, m__2270
% 96.33/46.67 % No. of inferences in proof: 24
% 96.33/46.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 46151 ms resp. 45790 ms w/o parsing
% 96.49/46.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 96.49/46.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------