%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM555+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 : 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 08:09:09 AM UTC 2026
% Result : Theorem 121.81s 58.05s
% Output : Refutation 121.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 184 ( 40 equ; 0 cnn)
% Maximal formula atoms : 64 ( 6 avg)
% Number of connectives : 524 ( 88 ~; 75 |; 55 &; 287 @)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 48 ( 6 ^; 40 !; 0 ?; 48 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(sdtmndt0_decl,type,
sdtmndt0: $i > $i > $i ).
thf(isFinite0_decl,type,
isFinite0: $i > $o ).
thf(sbrdtbr0_decl,type,
sbrdtbr0: $i > $i ).
thf(xx_decl,type,
xx: $i ).
thf(xQ_decl,type,
xQ: $i ).
thf(xy_decl,type,
xy: $i ).
thf(xk_decl,type,
xk: $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i > $o ).
thf(sk18_decl,type,
sk18: $i > $i > $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i > $i > $i ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ aElementOf0 ) )
=> ( ( D != B )
& ( C @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D != B )
& ( C @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) )
=> ( A @ ( D @ aElementOf0 ) ) ) ) ) ).
thf(1,conjecture,
~ ( xy @ ( xQ @ sdtmndt0 ) @ ( xx @ aElementOf0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ~ ( xy @ ( xQ @ sdtmndt0 ) @ ( xx @ aElementOf0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(73,plain,
~ ~ ( xy @ ( xQ @ sdtmndt0 ) @ ( xx @ aElementOf0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(74,plain,
xy @ ( xQ @ sdtmndt0 ) @ ( xx @ aElementOf0 ),
inference(polarity_switch,[status(thm)],[73]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( ( B @ aElement0 )
& ( A @ aSet0 ) )
=> ! [C: $i] :
( ( C
= ( B @ ( A @ sdtmndt0 ) ) )
<=> ( ! [D: $i] :
( ( C @ ( D @ aElementOf0 ) )
<=> ( ( D != B )
& ( A @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) ) )
& ( C @ aSet0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
thf(363,plain,
! [A: $i,B: $i] :
( ( ( B @ aElement0 )
& ( A @ aSet0 ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( ( ( D != B )
& ( A @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) )
=> ( C @ ( D @ aElementOf0 ) ) )
& ( ( C @ ( D @ aElementOf0 ) )
=> ( ( D != B )
& ( A @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) ) ) )
& ( C @ aSet0 ) )
=> ( C
= ( B @ ( A @ sdtmndt0 ) ) ) )
& ( ( C
= ( B @ ( A @ sdtmndt0 ) ) )
=> ( ! [D: $i] :
( ( ( ( D != B )
& ( A @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) )
=> ( C @ ( D @ aElementOf0 ) ) )
& ( ( C @ ( D @ aElementOf0 ) )
=> ( ( D != B )
& ( A @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) ) ) )
& ( C @ aSet0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(364,plain,
! [A: $i,B: $i] :
( ( ( B @ aElement0 )
& ( A @ aSet0 ) )
=> ( ! [C: $i] :
( ( ! [D: $i] :
( ( ( D != B )
& ( A @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) )
=> ( C @ ( D @ aElementOf0 ) ) )
& ! [D: $i] :
( ( C @ ( D @ aElementOf0 ) )
=> ( ( D != B )
& ( A @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) ) )
& ( C @ aSet0 ) )
=> ( C
= ( B @ ( A @ sdtmndt0 ) ) ) )
& ! [C: $i] :
( ( C
= ( B @ ( A @ sdtmndt0 ) ) )
=> ( ! [D: $i] :
( ( ( D != B )
& ( A @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) )
=> ( C @ ( D @ aElementOf0 ) ) )
& ! [D: $i] :
( ( C @ ( D @ aElementOf0 ) )
=> ( ( D != B )
& ( A @ ( D @ aElementOf0 ) )
& ( D @ aElement0 ) ) )
& ( C @ aSet0 ) ) ) ) ),
inference(miniscope,[status(thm)],[363]) ).
thf(365,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( B @ ( A @ sdtmndt0 ) ) )
| ~ ( F @ ( A @ ( B @ ( F @ sk19 ) ) @ aElementOf0 ) )
| ( F @ ( B @ ( A @ sk17 ) ) )
| ~ ( F @ aSet0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) )
& ( ( F
= ( B @ ( A @ sdtmndt0 ) ) )
| ( ( A @ ( B @ ( F @ sk19 ) ) )
!= B )
| ( F @ ( B @ ( A @ sk17 ) ) )
| ~ ( F @ aSet0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) )
& ( ( F
= ( B @ ( A @ sdtmndt0 ) ) )
| ( A @ ( A @ ( B @ ( F @ sk19 ) ) @ aElementOf0 ) )
| ( F @ ( B @ ( A @ sk17 ) ) )
| ~ ( F @ aSet0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) )
& ( ( F
= ( B @ ( A @ sdtmndt0 ) ) )
| ( A @ ( B @ ( F @ sk19 ) ) @ aElement0 )
| ( F @ ( B @ ( A @ sk17 ) ) )
| ~ ( F @ aSet0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) )
& ( ( F
= ( B @ ( A @ sdtmndt0 ) ) )
| ~ ( F @ ( B @ ( A @ sk17 ) ) )
| ( ( A @ ( B @ ( F @ sk18 ) ) )
= B )
| ~ ( A @ ( A @ ( B @ ( F @ sk18 ) ) @ aElementOf0 ) )
| ~ ( A @ ( B @ ( F @ sk18 ) ) @ aElement0 )
| ~ ( F @ aSet0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) )
& ( ( F
= ( B @ ( A @ sdtmndt0 ) ) )
| ~ ( F @ ( B @ ( A @ sk17 ) ) )
| ( F @ ( A @ ( B @ ( F @ sk18 ) ) @ aElementOf0 ) )
| ~ ( F @ aSet0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) )
& ( ( C @ ( E @ aElementOf0 ) )
| ( E = B )
| ~ ( A @ ( E @ aElementOf0 ) )
| ~ ( E @ aElement0 )
| ( C
!= ( B @ ( A @ sdtmndt0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) )
& ( ( D != B )
| ~ ( C @ ( D @ aElementOf0 ) )
| ( C
!= ( B @ ( A @ sdtmndt0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) )
& ( ( A @ ( D @ aElementOf0 ) )
| ~ ( C @ ( D @ aElementOf0 ) )
| ( C
!= ( B @ ( A @ sdtmndt0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) )
& ( ( D @ aElement0 )
| ~ ( C @ ( D @ aElementOf0 ) )
| ( C
!= ( B @ ( A @ sdtmndt0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) )
& ( ( C @ aSet0 )
| ( C
!= ( B @ ( A @ sdtmndt0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) ) ),
inference(cnf,[status(esa)],[364]) ).
thf(372,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ aElementOf0 ) )
| ~ ( C @ ( D @ aElementOf0 ) )
| ( C
!= ( B @ ( A @ sdtmndt0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[365]) ).
thf(377,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ aElementOf0 ) )
| ~ ( C @ ( D @ aElementOf0 ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 )
| ( C
!= ( B @ ( A @ sdtmndt0 ) ) ) ),
inference(lifteq,[status(thm)],[372]) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ aElementOf0 ) )
| ~ ( B @ ( A @ sdtmndt0 ) @ ( C @ aElementOf0 ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[377]) ).
thf(135853,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xy @ ( xQ @ sdtmndt0 ) @ ( xx @ aElementOf0 ) )
!= ( B @ ( A @ sdtmndt0 ) @ ( C @ aElementOf0 ) ) )
| ( A @ ( C @ aElementOf0 ) )
| ~ $true
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[74,378]) ).
thf(135854,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xy @ ( xQ @ sdtmndt0 ) @ ( xx @ aElementOf0 ) )
!= ( B @ ( A @ sdtmndt0 ) @ ( C @ aElementOf0 ) ) )
| ( A @ ( C @ aElementOf0 ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[135853]) ).
thf(135855,plain,
( ( xQ @ ( xx @ aElementOf0 ) )
| ~ ( xy @ aElement0 )
| ~ ( xQ @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[135854:[bind(A,$thf( xQ )),bind(B,$thf( xy )),bind(C,$thf( xx ))]]) ).
thf(26,axiom,
~ ( xQ @ ( xx @ aElementOf0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2323) ).
thf(160,plain,
~ ( xQ @ ( xx @ aElementOf0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(161,plain,
~ ( xQ @ ( xx @ aElementOf0 ) ),
inference(polarity_switch,[status(thm)],[160]) ).
thf(55,axiom,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
thf(306,plain,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(307,plain,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
inference(cnf,[status(esa)],[306]) ).
thf(308,plain,
xQ @ aSet0,
inference(cnfConj,[status(thm)],[307]) ).
thf(57,axiom,
( ( xQ @ ( xy @ aElementOf0 ) )
& ( xy @ aElement0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
thf(348,plain,
( ( xQ @ ( xy @ aElementOf0 ) )
& ( xy @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(349,plain,
( ( xQ @ ( xy @ aElementOf0 ) )
& ( xy @ aElement0 ) ),
inference(cnf,[status(esa)],[348]) ).
thf(350,plain,
xy @ aElement0,
inference(cnfConj,[status(thm)],[349]) ).
thf(136853,plain,
( $false
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[135855,161,308,350]) ).
thf(136854,plain,
$false,
inference(simp,[status(thm)],[136853]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM555+1 : 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
% 0.13/0.41 % Computer : n007.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 03:11:10 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.83/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/1.23 % [INFO] Parsing done (232ms).
% 1.34/1.25 % [INFO] Running in sequential loop mode.
% 2.09/1.64 % [INFO] eprover registered as external prover.
% 2.09/1.65 % [INFO] Scanning for conjecture ...
% 2.30/1.71 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.30/1.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.30/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.30/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.30/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.30/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.30/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.30/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.50/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 70 axioms. Running axiom selection ...
% 2.50/1.89 % [INFO] Axiom selection finished. Selected 70 axioms (removed 0 axioms).
% 2.70/1.92 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/1.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/1.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/1.96 % [INFO] Problem is first-order (TPTP FOF).
% 2.70/1.98 % [INFO] Type checking passed.
% 2.70/1.98 % [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 ...
% 121.81/58.04 % [INFO] Killing All external provers ...
% 121.81/58.05 % Time passed: 57489ms (effective reasoning time: 56793ms)
% 121.81/58.05 % 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)>
% 121.81/58.05 % Axioms used in derivation (4): mDefDiff, m__2323, m__2291, m__2304
% 121.81/58.05 % No. of inferences in proof: 27
% 121.81/58.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 57489 ms resp. 56793 ms w/o parsing
% 121.81/58.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 121.81/58.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------