%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG087+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 : n019.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 08:25:25 AM UTC 2026
% Result : Theorem 9.12s 3.97s
% Output : Refutation 9.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 98 ( 35 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 272 ( 26 ~; 14 |; 46 &; 186 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 12 !; 22 ?; 38 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sdtpldt1_decl,type,
sdtpldt1: $i > $i > $i ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(xI_decl,type,
xI: $i ).
thf(xJ_decl,type,
xJ: $i ).
thf(xy_decl,type,
xy: $i ).
thf(xx_decl,type,
xx: $i ).
thf(xz_decl,type,
xz: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ? [B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xx )
& ( xJ @ ( B @ aElementOf0 ) ) )
& ( xI @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( ( A @ ( sk1 @ sdtpldt0 ) )
= xx )
& ( xJ @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
( ? [B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xy )
& ( xJ @ ( B @ aElementOf0 ) ) )
& ( xI @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
( ( ( A @ ( sk3 @ sdtpldt0 ) )
= xy )
& ( xJ @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(17,axiom,
( ( xz @ aElement0 )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xy @ aElementOf0 ) )
& ? [A: $i,B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xy )
& ( xJ @ ( B @ aElementOf0 ) )
& ( xI @ ( A @ aElementOf0 ) ) )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xx @ aElementOf0 ) )
& ? [A: $i,B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xx )
& ( xJ @ ( B @ aElementOf0 ) )
& ( xI @ ( A @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
thf(78,plain,
( ( xz @ aElement0 )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xy @ aElementOf0 ) )
& ? [A: $i,B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xy )
& ( xJ @ ( B @ aElementOf0 ) )
& ( xI @ ( A @ aElementOf0 ) ) )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xx @ aElementOf0 ) )
& ? [A: $i,B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xx )
& ( xJ @ ( B @ aElementOf0 ) )
& ( xI @ ( A @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(79,plain,
( ( xz @ aElement0 )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xy @ aElementOf0 ) )
& ? [A: $i] :
( ? [B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xy )
& ( xJ @ ( B @ aElementOf0 ) ) )
& ( xI @ ( A @ aElementOf0 ) ) )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xx @ aElementOf0 ) )
& ? [A: $i] :
( ? [B: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
= xx )
& ( xJ @ ( B @ aElementOf0 ) ) )
& ( xI @ ( A @ aElementOf0 ) ) ) ),
inference(miniscope,[status(thm)],[78]) ).
thf(80,plain,
( ( xz @ aElement0 )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xy @ aElementOf0 ) )
& ( ( sk4 @ ( sk3 @ sdtpldt0 ) )
= xy )
& ( xJ @ ( sk4 @ aElementOf0 ) )
& ( xI @ ( sk3 @ aElementOf0 ) )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xx @ aElementOf0 ) )
& ( ( sk2 @ ( sk1 @ sdtpldt0 ) )
= xx )
& ( xJ @ ( sk2 @ aElementOf0 ) )
& ( xI @ ( sk1 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(83,plain,
( ( sk4 @ ( sk3 @ sdtpldt0 ) )
= xy ),
inference(cnfConj,[status(thm)],[80]) ).
thf(91,plain,
( ( sk4 @ ( sk3 @ sdtpldt0 ) )
= xy ),
inference(lifteq,[status(thm)],[83]) ).
thf(89,plain,
xJ @ ( sk4 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[80]) ).
thf(82,plain,
xI @ ( sk3 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[80]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
( ( xy
= ( B @ ( A @ sdtpldt0 ) ) )
& ( xJ @ ( B @ aElementOf0 ) )
& ( xI @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
( ( xy
= ( B @ ( A @ sdtpldt0 ) ) )
& ( xJ @ ( B @ aElementOf0 ) )
& ( xI @ ( A @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(30,plain,
~ ? [A: $i,B: $i] :
( ( xy
= ( B @ ( A @ sdtpldt0 ) ) )
& ( xJ @ ( B @ aElementOf0 ) )
& ( xI @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( xy
= ( B @ ( A @ sdtpldt0 ) ) )
& ( xJ @ ( B @ aElementOf0 ) ) )
& ( xI @ ( A @ aElementOf0 ) ) ),
inference(miniscope,[status(thm)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( xy
!= ( B @ ( A @ sdtpldt0 ) ) )
| ~ ( xJ @ ( B @ aElementOf0 ) )
| ~ ( xI @ ( A @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( xJ @ ( B @ aElementOf0 ) )
| ~ ( xI @ ( A @ aElementOf0 ) )
| ( ( B @ ( A @ sdtpldt0 ) )
!= xy ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( ( xI @ ( sk3 @ aElementOf0 ) )
!= ( xI @ ( A @ aElementOf0 ) ) )
| ~ ( xJ @ ( B @ aElementOf0 ) )
| ~ $true
| ( ( B @ ( A @ sdtpldt0 ) )
!= xy ) ),
inference(paramod_ordered,[status(thm)],[82,33]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( ( xI @ ( sk3 @ aElementOf0 ) )
!= ( xI @ ( A @ aElementOf0 ) ) )
| ~ ( xJ @ ( B @ aElementOf0 ) )
| ( ( B @ ( A @ sdtpldt0 ) )
!= xy ) ),
inference(simp,[status(thm)],[274]) ).
thf(276,plain,
! [A: $i] :
( ~ ( xJ @ ( A @ aElementOf0 ) )
| ( ( A @ ( sk3 @ sdtpldt0 ) )
!= xy ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( sk3 ))]]) ).
thf(286,plain,
! [A: $i] :
( ~ ( xJ @ ( A @ aElementOf0 ) )
| ( ( A @ ( sk3 @ sdtpldt0 ) )
!= xy ) ),
inference(simp,[status(thm)],[276]) ).
thf(332,plain,
! [A: $i] :
( ( ( xJ @ ( sk4 @ aElementOf0 ) )
!= ( xJ @ ( A @ aElementOf0 ) ) )
| ~ $true
| ( ( A @ ( sk3 @ sdtpldt0 ) )
!= xy ) ),
inference(paramod_ordered,[status(thm)],[89,286]) ).
thf(333,plain,
! [A: $i] :
( ( ( xJ @ ( sk4 @ aElementOf0 ) )
!= ( xJ @ ( A @ aElementOf0 ) ) )
| ( ( A @ ( sk3 @ sdtpldt0 ) )
!= xy ) ),
inference(simp,[status(thm)],[332]) ).
thf(334,plain,
( ( sk4 @ ( sk3 @ sdtpldt0 ) )
!= xy ),
inference(pattern_uni,[status(thm)],[333:[bind(A,$thf( sk4 ))]]) ).
thf(423,plain,
$false,
inference(simplifyReflect,[status(thm)],[91,334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG087+2 : 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
% 0.14/0.40 % Computer : n019.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 06:02:04 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 1.16/1.11 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.80/1.43 % [INFO] Parsing done (319ms).
% 1.80/1.45 % [INFO] Running in sequential loop mode.
% 2.66/1.89 % [INFO] eprover registered as external prover.
% 2.66/1.90 % [INFO] Scanning for conjecture ...
% 2.94/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.94/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.94/1.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.94/2.02 % [INFO] Found a conjecture (or negated_conjecture) and 27 axioms. Running axiom selection ...
% 3.32/2.09 % [INFO] Axiom selection finished. Selected 27 axioms (removed 0 axioms).
% 3.32/2.12 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.32/2.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.32/2.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.32/2.15 % [INFO] Problem is first-order (TPTP FOF).
% 3.61/2.16 % [INFO] Type checking passed.
% 3.61/2.16 % [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 ...
% 9.12/3.96 % [INFO] Killing All external provers ...
% 9.12/3.96 % Time passed: 3417ms (effective reasoning time: 2498ms)
% 9.12/3.96 % 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)>
% 9.12/3.97 % Axioms used in derivation (1): m__901
% 9.12/3.97 % No. of inferences in proof: 22
% 9.12/3.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3417 ms resp. 2498 ms w/o parsing
% 9.12/4.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.12/4.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------