%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG115+4 : 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 : n007.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 08:25:29 AM UTC 2026
% Result : Theorem 61.37s 17.40s
% Output : Refutation 61.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 122 ( 49 equ; 0 cnn)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 413 ( 55 ~; 42 |; 52 &; 261 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 0 ^; 20 !; 29 ?; 51 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(sdtasdt0_decl,type,
sdtasdt0: $i > $i > $i ).
thf(slsdtgt0_decl,type,
slsdtgt0: $i > $i ).
thf(xa_decl,type,
xa: $i ).
thf(xb_decl,type,
xb: $i ).
thf(xu_decl,type,
xu: $i ).
thf(iLess0_decl,type,
iLess0: $i > $i > $o ).
thf(sz00_decl,type,
sz00: $i ).
thf(xI_decl,type,
xI: $i ).
thf(sbrdtbr0_decl,type,
sbrdtbr0: $i > $i ).
thf(sk39_decl,type,
sk39: $i ).
thf(sk40_decl,type,
sk40: $i ).
thf(sk39_def,definition,
( sk39
= ( @+[A: $i] :
( ? [B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xu )
& ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) ) )
& ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(sk40_def,definition,
( sk40
= ( @+[A: $i] :
( ( ( A @ ( sk39 @ sdtpldt0 ) )
= xu )
& ( xb @ slsdtgt0 @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(44,axiom,
( ! [A: $i] :
( ( ( A != sz00 )
& ( ( xI @ ( A @ aElementOf0 ) )
| ? [B: $i,C: $i] :
( ( ( C @ ( B @ sdtpldt0 ) )
= A )
& ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) )
& ( xa @ slsdtgt0 @ ( B @ aElementOf0 ) ) ) ) )
=> ~ ( xu @ sbrdtbr0 @ ( A @ sbrdtbr0 @ iLess0 ) ) )
& ( xu != sz00 )
& ( xI @ ( xu @ aElementOf0 ) )
& ? [A: $i,B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xu )
& ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
& ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
thf(390,plain,
( ! [A: $i] :
( ( ( A != sz00 )
& ( ( xI @ ( A @ aElementOf0 ) )
| ? [B: $i,C: $i] :
( ( ( C @ ( B @ sdtpldt0 ) )
= A )
& ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) )
& ( xa @ slsdtgt0 @ ( B @ aElementOf0 ) ) ) ) )
=> ~ ( xu @ sbrdtbr0 @ ( A @ sbrdtbr0 @ iLess0 ) ) )
& ( xu != sz00 )
& ( xI @ ( xu @ aElementOf0 ) )
& ? [A: $i,B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xu )
& ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
& ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(391,plain,
( ! [A: $i] :
( ( ( A != sz00 )
& ( ( xI @ ( A @ aElementOf0 ) )
| ? [B: $i] :
( ? [C: $i] :
( ( ( C @ ( B @ sdtpldt0 ) )
= A )
& ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) ) )
& ( xa @ slsdtgt0 @ ( B @ aElementOf0 ) ) ) ) )
=> ~ ( xu @ sbrdtbr0 @ ( A @ sbrdtbr0 @ iLess0 ) ) )
& ( xu != sz00 )
& ( xI @ ( xu @ aElementOf0 ) )
& ? [A: $i] :
( ? [B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xu )
& ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) ) )
& ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) ) ) ),
inference(miniscope,[status(thm)],[390]) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( ~ ( xu @ sbrdtbr0 @ ( A @ sbrdtbr0 @ iLess0 ) )
| ( A = sz00 )
| ~ ( xI @ ( A @ aElementOf0 ) ) )
& ( ~ ( xu @ sbrdtbr0 @ ( A @ sbrdtbr0 @ iLess0 ) )
| ( A = sz00 )
| ( ( C @ ( B @ sdtpldt0 ) )
!= A )
| ~ ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) )
| ~ ( xa @ slsdtgt0 @ ( B @ aElementOf0 ) ) )
& ( xu != sz00 )
& ( xI @ ( xu @ aElementOf0 ) )
& ( ( sk40 @ ( sk39 @ sdtpldt0 ) )
= xu )
& ( xb @ slsdtgt0 @ ( sk40 @ aElementOf0 ) )
& ( xa @ slsdtgt0 @ ( sk39 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[391]) ).
thf(397,plain,
( ( sk40 @ ( sk39 @ sdtpldt0 ) )
= xu ),
inference(cnfConj,[status(thm)],[392]) ).
thf(401,plain,
( ( sk40 @ ( sk39 @ sdtpldt0 ) )
= xu ),
inference(lifteq,[status(thm)],[397]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
( ( xu
= ( B @ ( A @ sdtpldt0 ) ) )
& ( ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
| ? [C: $i] :
( ( ( C @ ( xb @ sdtasdt0 ) )
= B )
& ( C @ aElement0 ) ) )
& ( ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) )
| ? [C: $i] :
( ( ( C @ ( xa @ sdtasdt0 ) )
= A )
& ( C @ aElement0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
( ( xu
= ( B @ ( A @ sdtpldt0 ) ) )
& ( ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
| ? [C: $i] :
( ( ( C @ ( xb @ sdtasdt0 ) )
= B )
& ( C @ aElement0 ) ) )
& ( ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) )
| ? [C: $i] :
( ( ( C @ ( xa @ sdtasdt0 ) )
= A )
& ( C @ aElement0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(49,plain,
~ ? [A: $i,B: $i] :
( ( xu
= ( B @ ( A @ sdtpldt0 ) ) )
& ( ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
| ? [C: $i] :
( ( ( C @ ( xb @ sdtasdt0 ) )
= B )
& ( C @ aElement0 ) ) )
& ( ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) )
| ? [C: $i] :
( ( ( C @ ( xa @ sdtasdt0 ) )
= A )
& ( C @ aElement0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(50,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( xu
= ( B @ ( A @ sdtpldt0 ) ) )
& ( ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
| ? [C: $i] :
( ( ( C @ ( xb @ sdtasdt0 ) )
= B )
& ( C @ aElement0 ) ) ) )
& ( ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) )
| ? [B: $i] :
( ( ( B @ ( xa @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) ) ) ),
inference(miniscope,[status(thm)],[49]) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( xu
!= ( C @ ( A @ sdtpldt0 ) ) )
| ~ ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) )
| ~ ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) ) )
& ( ( xu
!= ( C @ ( A @ sdtpldt0 ) ) )
| ( ( D @ ( xb @ sdtasdt0 ) )
!= C )
| ~ ( D @ aElement0 )
| ~ ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) ) )
& ( ( xu
!= ( C @ ( A @ sdtpldt0 ) ) )
| ~ ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) )
| ( ( B @ ( xa @ sdtasdt0 ) )
!= A )
| ~ ( B @ aElement0 ) )
& ( ( xu
!= ( C @ ( A @ sdtpldt0 ) ) )
| ( ( D @ ( xb @ sdtasdt0 ) )
!= C )
| ~ ( D @ aElement0 )
| ( ( B @ ( xa @ sdtasdt0 ) )
!= A )
| ~ ( B @ aElement0 ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( xu
!= ( B @ ( A @ sdtpldt0 ) ) )
| ~ ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
| ~ ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
| ~ ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) )
| ( ( B @ ( A @ sdtpldt0 ) )
!= xu ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
| ~ ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) )
| ( ( B @ ( A @ sdtpldt0 ) )
!= xu ) ),
inference(simp,[status(thm)],[62]) ).
thf(1584,plain,
! [B: $i,A: $i] :
( ( ( sk40 @ ( sk39 @ sdtpldt0 ) )
!= ( B @ ( A @ sdtpldt0 ) ) )
| ~ ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
| ~ ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) )
| ( xu != xu ) ),
inference(paramod_ordered,[status(thm)],[401,63]) ).
thf(1585,plain,
! [B: $i,A: $i] :
( ( ( sk40 @ ( sk39 @ sdtpldt0 ) )
!= ( B @ ( A @ sdtpldt0 ) ) )
| ~ ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) )
| ~ ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[1584]) ).
thf(1586,plain,
( ~ ( xb @ slsdtgt0 @ ( sk40 @ aElementOf0 ) )
| ~ ( xa @ slsdtgt0 @ ( sk39 @ aElementOf0 ) ) ),
inference(pattern_uni,[status(thm)],[1585:[bind(A,$thf( sk39 )),bind(B,$thf( sk40 ))]]) ).
thf(395,plain,
xb @ slsdtgt0 @ ( sk40 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[392]) ).
thf(398,plain,
xa @ slsdtgt0 @ ( sk39 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[392]) ).
thf(27686,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[1586,395,398]) ).
thf(27687,plain,
$false,
inference(simp,[status(thm)],[27686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG115+4 : 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
% 0.16/0.42 % Computer : n007.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 06:07:10 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 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
% 0.86/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.25 % [INFO] Parsing done (246ms).
% 1.40/1.27 % [INFO] Running in sequential loop mode.
% 2.21/1.69 % [INFO] eprover registered as external prover.
% 2.21/1.69 % [INFO] Scanning for conjecture ...
% 2.43/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.65/1.86 % [INFO] Found a conjecture (or negated_conjecture) and 46 axioms. Running axiom selection ...
% 2.89/1.96 % [INFO] Axiom selection finished. Selected 46 axioms (removed 0 axioms).
% 2.89/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/2.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/2.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/2.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/2.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/2.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.29/2.05 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.29/2.05 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.29/2.05 % [INFO] Problem is first-order (TPTP FOF).
% 3.29/2.07 % [INFO] Type checking passed.
% 3.29/2.07 % [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 ...
% 61.37/17.40 % [INFO] Killing All external provers ...
% 61.37/17.40 % Time passed: 16837ms (effective reasoning time: 16120ms)
% 61.37/17.40 % 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)>
% 61.37/17.40 % Axioms used in derivation (1): m__2273
% 61.37/17.40 % No. of inferences in proof: 21
% 61.37/17.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 16837 ms resp. 16120 ms w/o parsing
% 61.37/17.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 61.37/17.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------