%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM618+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 08:09:19 AM UTC 2026
% Result : Theorem 60.88s 19.78s
% Output : Refutation 61.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 69 ( 22 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 205 ( 28 ~; 17 |; 14 &; 144 @)
% ( 0 <=>; 2 =>; 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 : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 1 ^; 13 !; 5 ?; 20 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(szNzAzT0_decl,type,
szNzAzT0: $i ).
thf(sdtlbdtrb0_decl,type,
sdtlbdtrb0: $i > $i > $i ).
thf(sdtlpdtrp0_decl,type,
sdtlpdtrp0: $i > $i > $i ).
thf(xx_decl,type,
xx: $i ).
thf(xe_decl,type,
xe: $i ).
thf(xO_decl,type,
xO: $i ).
thf(xd_decl,type,
xd: $i ).
thf(szDzizrdt0_decl,type,
szDzizrdt0: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(49,axiom,
! [A: $i] :
( ( xO @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4982) ).
thf(272,plain,
! [A: $i] :
( ( xO @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( ( B @ ( xe @ sdtlpdtrp0 ) )
= A )
& ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( B @ aElementOf0 ) )
& ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(273,plain,
! [A: $i] :
( ( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A )
| ~ ( xO @ ( A @ aElementOf0 ) ) )
& ( ( xd @ szDzizrdt0 @ ( xd @ sdtlbdtrb0 ) @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( xO @ ( A @ aElementOf0 ) ) )
& ( ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( xO @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(276,plain,
! [A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A )
| ~ ( xO @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[273]) ).
thf(277,plain,
! [A: $i] :
( ~ ( xO @ ( A @ aElementOf0 ) )
| ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
= A ) ),
inference(lifteq,[status(thm)],[276]) ).
thf(58,axiom,
( ( xO @ ( xx @ aElementOf0 ) )
& ( szNzAzT0 @ ( xx @ aElementOf0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5365) ).
thf(309,plain,
( ( xO @ ( xx @ aElementOf0 ) )
& ( szNzAzT0 @ ( xx @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(310,plain,
( ( xO @ ( xx @ aElementOf0 ) )
& ( szNzAzT0 @ ( xx @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[309]) ).
thf(312,plain,
xO @ ( xx @ aElementOf0 ),
inference(cnfConj,[status(thm)],[310]) ).
thf(274,plain,
! [A: $i] :
( ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( xO @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[273]) ).
thf(25175,plain,
! [A: $i] :
( ( ( xO @ ( xx @ aElementOf0 ) )
!= ( xO @ ( A @ aElementOf0 ) ) )
| ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[312,274]) ).
thf(25176,plain,
! [A: $i] :
( ( ( xO @ ( xx @ aElementOf0 ) )
!= ( xO @ ( A @ aElementOf0 ) ) )
| ( szNzAzT0 @ ( A @ sk5 @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[25175]) ).
thf(25177,plain,
szNzAzT0 @ ( xx @ sk5 @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[25176:[bind(A,$thf( xx ))]]) ).
thf(1,conjecture,
? [A: $i] :
( ( xx
= ( A @ ( xe @ sdtlpdtrp0 ) ) )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( xx
= ( A @ ( xe @ sdtlpdtrp0 ) ) )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(117,plain,
~ ? [A: $i] :
( ( xx
= ( A @ ( xe @ sdtlpdtrp0 ) ) )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(118,plain,
! [A: $i] :
( ( xx
!= ( A @ ( xe @ sdtlpdtrp0 ) ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(119,plain,
! [A: $i] :
( ~ ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xx ) ),
inference(lifteq,[status(thm)],[118]) ).
thf(25527,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xx @ sk5 @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ~ $true
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xx ) ),
inference(paramod_ordered,[status(thm)],[25177,119]) ).
thf(25528,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xx @ sk5 @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( ( A @ ( xe @ sdtlpdtrp0 ) )
!= xx ) ),
inference(simp,[status(thm)],[25527]) ).
thf(25529,plain,
( ( xx @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= xx ),
inference(pattern_uni,[status(thm)],[25528:[bind(A,$thf( xx @ sk5 ))]]) ).
thf(27760,plain,
! [A: $i] :
( ( ( A @ sk5 @ ( xe @ sdtlpdtrp0 ) )
!= ( xx @ sk5 @ ( xe @ sdtlpdtrp0 ) ) )
| ( A != xx )
| ~ ( xO @ ( A @ aElementOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[277,25529]) ).
thf(27761,plain,
( ( xx != xx )
| ~ ( xO @ ( xx @ aElementOf0 ) ) ),
inference(pattern_uni,[status(thm)],[27760:[bind(A,$thf( xx ))]]) ).
thf(28017,plain,
~ ( xO @ ( xx @ aElementOf0 ) ),
inference(simp,[status(thm)],[27761]) ).
thf(28067,plain,
~ $true,
inference(rewrite,[status(thm)],[28017,312]) ).
thf(28068,plain,
$false,
inference(simp,[status(thm)],[28067]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM618+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.62 % Computer : n020.cluster.edu
% 0.13/0.62 % Model : x86_64 x86_64
% 0.13/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.62 % Memory : 8046.5625MB
% 0.13/0.62 % OS : Linux 6.8.0-71-generic
% 0.13/0.62 % CPULimit : 300
% 0.13/0.62 % WCLimit : 300
% 0.13/0.62 % DateTime : Sat Sep 26 03:28:50 UTC 2026
% 0.13/0.62 % CPUTime :
% 0.13/0.62 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.01/1.22 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/1.48 % [INFO] Parsing done (263ms).
% 1.78/1.50 % [INFO] Running in sequential loop mode.
% 2.20/1.87 % [INFO] eprover registered as external prover.
% 2.20/1.88 % [INFO] Scanning for conjecture ...
% 2.43/1.91 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.92 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.92 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/2.02 % [INFO] Found a conjecture (or negated_conjecture) and 114 axioms. Running axiom selection ...
% 2.98/2.15 % [INFO] Axiom selection finished. Selected 114 axioms (removed 0 axioms).
% 2.98/2.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.20/2.26 % [INFO] Problem is first-order (TPTP FOF).
% 3.20/2.28 % [INFO] Type checking passed.
% 3.20/2.28 % [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 ...
% 60.88/19.78 % [INFO] Killing All external provers ...
% 60.88/19.78 % Time passed: 19013ms (effective reasoning time: 18277ms)
% 60.88/19.78 % 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)>
% 60.88/19.78 % Axioms used in derivation (2): m__4982, m__5365
% 60.88/19.78 % No. of inferences in proof: 26
% 60.88/19.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19013 ms resp. 18277 ms w/o parsing
% 61.17/19.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 61.17/19.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------