%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG102+2 : 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 : n011.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 08:25:27 AM UTC 2026
% Result : Theorem 13.32s 5.63s
% Output : Refutation 13.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 51 ( 22 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 115 ( 12 ~; 5 |; 23 &; 75 @)
% ( 0 <=>; 0 =>; 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 : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 13 ( 0 ^; 4 !; 7 ?; 13 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(sdtasdt0_decl,type,
sdtasdt0: $i > $i > $i ).
thf(slsdtgt0_decl,type,
slsdtgt0: $i > $i ).
thf(xc_decl,type,
xc: $i ).
thf(xy_decl,type,
xy: $i ).
thf(xx_decl,type,
xx: $i ).
thf(xz_decl,type,
xz: $i ).
thf(sk19_decl,type,
sk19: $i ).
thf(sk20_decl,type,
sk20: $i ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i] :
( ( ( A @ ( xc @ sdtasdt0 ) )
= xx )
& ( A @ aElement0 ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
( ( ( A @ ( xc @ sdtasdt0 ) )
= xy )
& ( A @ aElement0 ) ) ) ) ).
thf(31,axiom,
( ( xz @ aElement0 )
& ( xc @ slsdtgt0 @ ( xy @ aElementOf0 ) )
& ? [A: $i] :
( ( ( A @ ( xc @ sdtasdt0 ) )
= xy )
& ( A @ aElement0 ) )
& ( xc @ slsdtgt0 @ ( xx @ aElementOf0 ) )
& ? [A: $i] :
( ( ( A @ ( xc @ sdtasdt0 ) )
= xx )
& ( A @ aElement0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1933) ).
thf(228,plain,
( ( xz @ aElement0 )
& ( xc @ slsdtgt0 @ ( xy @ aElementOf0 ) )
& ? [A: $i] :
( ( ( A @ ( xc @ sdtasdt0 ) )
= xy )
& ( A @ aElement0 ) )
& ( xc @ slsdtgt0 @ ( xx @ aElementOf0 ) )
& ? [A: $i] :
( ( ( A @ ( xc @ sdtasdt0 ) )
= xx )
& ( A @ aElement0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(229,plain,
( ( xz @ aElement0 )
& ( xc @ slsdtgt0 @ ( xy @ aElementOf0 ) )
& ( ( sk20 @ ( xc @ sdtasdt0 ) )
= xy )
& ( sk20 @ aElement0 )
& ( xc @ slsdtgt0 @ ( xx @ aElementOf0 ) )
& ( ( sk19 @ ( xc @ sdtasdt0 ) )
= xx )
& ( sk19 @ aElement0 ) ),
inference(cnf,[status(esa)],[228]) ).
thf(232,plain,
( ( sk20 @ ( xc @ sdtasdt0 ) )
= xy ),
inference(cnfConj,[status(thm)],[229]) ).
thf(238,plain,
( ( sk20 @ ( xc @ sdtasdt0 ) )
= xy ),
inference(lifteq,[status(thm)],[232]) ).
thf(236,plain,
sk20 @ aElement0,
inference(cnfConj,[status(thm)],[229]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( A @ ( xc @ sdtasdt0 ) )
= xy )
& ( A @ aElement0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( A @ ( xc @ sdtasdt0 ) )
= xy )
& ( A @ aElement0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
~ ? [A: $i] :
( ( ( A @ ( xc @ sdtasdt0 ) )
= xy )
& ( A @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,plain,
! [A: $i] :
( ( ( A @ ( xc @ sdtasdt0 ) )
!= xy )
| ~ ( A @ aElement0 ) ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [A: $i] :
( ~ ( A @ aElement0 )
| ( ( A @ ( xc @ sdtasdt0 ) )
!= xy ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(337,plain,
! [A: $i] :
( ( ( sk20 @ aElement0 )
!= ( A @ aElement0 ) )
| ~ $true
| ( ( A @ ( xc @ sdtasdt0 ) )
!= xy ) ),
inference(paramod_ordered,[status(thm)],[236,45]) ).
thf(338,plain,
! [A: $i] :
( ( ( sk20 @ aElement0 )
!= ( A @ aElement0 ) )
| ( ( A @ ( xc @ sdtasdt0 ) )
!= xy ) ),
inference(simp,[status(thm)],[337]) ).
thf(339,plain,
( ( sk20 @ ( xc @ sdtasdt0 ) )
!= xy ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( sk20 ))]]) ).
thf(404,plain,
$false,
inference(simplifyReflect,[status(thm)],[238,339]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG102+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.13 % 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
% 0.24/0.48 % Computer : n011.cluster.edu
% 0.24/0.48 % Model : x86_64 x86_64
% 0.24/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.48 % Memory : 8046.5625MB
% 0.24/0.48 % OS : Linux 6.8.0-71-generic
% 0.24/0.48 % CPULimit : 300
% 0.24/0.48 % WCLimit : 300
% 0.24/0.48 % DateTime : Sat Sep 26 06:05:43 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 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
% 1.43/1.37 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.22/1.72 % [INFO] Parsing done (347ms).
% 2.22/1.74 % [INFO] Running in sequential loop mode.
% 3.25/2.38 % [INFO] eprover registered as external prover.
% 3.25/2.39 % [INFO] Scanning for conjecture ...
% 3.67/2.53 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.67/2.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.67/2.56 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.67/2.56 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.67/2.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.67/2.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.67/2.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.67/2.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.91/2.60 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.91/2.64 % [INFO] Found a conjecture (or negated_conjecture) and 40 axioms. Running axiom selection ...
% 4.08/2.76 % [INFO] Axiom selection finished. Selected 40 axioms (removed 0 axioms).
% 4.08/2.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.08/2.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.31/2.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.31/2.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.31/2.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.31/2.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.31/2.85 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.31/2.85 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.31/2.86 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.31/2.86 % [INFO] Problem is first-order (TPTP FOF).
% 4.31/2.88 % [INFO] Type checking passed.
% 4.31/2.89 % [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 ...
% 13.32/5.62 % [INFO] Killing All external provers ...
% 13.32/5.63 % Time passed: 4930ms (effective reasoning time: 3874ms)
% 13.32/5.63 % 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)>
% 13.32/5.63 % Axioms used in derivation (1): m__1933
% 13.32/5.63 % No. of inferences in proof: 15
% 13.32/5.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4930 ms resp. 3874 ms w/o parsing
% 13.32/5.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.32/5.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------