%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM620+3 : 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 : n016.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 204.86s 129.07s
% Output : Refutation 204.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 15 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 323 ( 21 ~; 13 |; 20 &; 259 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(szNzAzT0_decl,type,
szNzAzT0: $i ).
thf(szmzizndt0_decl,type,
szmzizndt0: $i > $i ).
thf(sdtlseqdt0_decl,type,
sdtlseqdt0: $i > $i > $o ).
thf(szszuzczcdt0_decl,type,
szszuzczcdt0: $i > $i ).
thf(aFunction0_decl,type,
aFunction0: $i > $o ).
thf(szDzozmdt0_decl,type,
szDzozmdt0: $i > $i ).
thf(sdtlpdtrp0_decl,type,
sdtlpdtrp0: $i > $i > $i ).
thf(xN_decl,type,
xN: $i ).
thf(xm_decl,type,
xm: $i ).
thf(xn_decl,type,
xn: $i ).
thf(xx_decl,type,
xx: $i ).
thf(xe_decl,type,
xe: $i ).
thf(1,conjecture,
( ( ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xm @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xm @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ) )
=> ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xm @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xm @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ) )
=> ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(119,plain,
~ ( ( ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xm @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xm @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ) )
=> ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(120,plain,
! [A: $i] :
( ~ ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ) )
& ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xm @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ( ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
| ~ ( xm @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(121,plain,
! [A: $i] :
( ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
| ~ ( xm @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(123,plain,
~ ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(1133,plain,
! [A: $i] :
( ( ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
!= ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ) ) )
| ~ $true
| ~ ( xm @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[121,123]) ).
thf(1134,plain,
! [A: $i] :
( ( ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
!= ( xn @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ) ) )
| ~ ( xm @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[1133]) ).
thf(1135,plain,
~ ( xm @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ) ),
inference(pattern_uni,[status(thm)],[1134:[bind(A,$thf( xx ))]]) ).
thf(110,axiom,
( ( xx
= ( xm @ ( xe @ sdtlpdtrp0 ) ) )
& ( szNzAzT0 @ ( xm @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5389) ).
thf(1057,plain,
( ( xx
= ( xm @ ( xe @ sdtlpdtrp0 ) ) )
& ( szNzAzT0 @ ( xm @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1058,plain,
( ( xx
= ( xm @ ( xe @ sdtlpdtrp0 ) ) )
& ( szNzAzT0 @ ( xm @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[1057]) ).
thf(1059,plain,
szNzAzT0 @ ( xm @ aElementOf0 ),
inference(cnfConj,[status(thm)],[1058]) ).
thf(65,axiom,
( ! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ! [B: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( B @ ( A @ ( xe @ sdtlpdtrp0 ) @ sdtlseqdt0 ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ) ) ) )
& ( ( xe @ szDzozmdt0 )
= szNzAzT0 )
& ( xe @ aFunction0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
thf(515,plain,
( ! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ! [B: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( B @ ( A @ ( xe @ sdtlpdtrp0 ) @ sdtlseqdt0 ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ) ) ) )
& ( ( xe @ szDzozmdt0 )
= szNzAzT0 )
& ( xe @ aFunction0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(516,plain,
! [B: $i,A: $i] :
( ( ( ( A @ ( xe @ sdtlpdtrp0 ) )
= ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( B @ ( A @ ( xe @ sdtlpdtrp0 ) @ sdtlseqdt0 ) )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( xe @ szDzozmdt0 )
= szNzAzT0 )
& ( xe @ aFunction0 ) ),
inference(cnf,[status(esa)],[515]) ).
thf(517,plain,
! [A: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[516]) ).
thf(189129,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xm @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1059,517]) ).
thf(189130,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xm @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[189129]) ).
thf(189131,plain,
xm @ ( xN @ sdtlpdtrp0 ) @ ( xm @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[189130:[bind(A,$thf( xm ))]]) ).
thf(1060,plain,
( xx
= ( xm @ ( xe @ sdtlpdtrp0 ) ) ),
inference(cnfConj,[status(thm)],[1058]) ).
thf(1061,plain,
( ( xm @ ( xe @ sdtlpdtrp0 ) )
= xx ),
inference(lifteq,[status(thm)],[1060]) ).
thf(190270,plain,
xm @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ),
inference(rewrite,[status(thm)],[189131,1061]) ).
thf(190271,plain,
~ $true,
inference(rewrite,[status(thm)],[1135,190270]) ).
thf(190272,plain,
$false,
inference(simp,[status(thm)],[190271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM620+3 : 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
% 0.16/5.43 % Computer : n016.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Sat Sep 26 03:33:20 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.44 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
% 0.99/6.03 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/6.29 % [INFO] Parsing done (259ms).
% 1.68/6.31 % [INFO] Running in sequential loop mode.
% 2.53/6.72 % [INFO] eprover registered as external prover.
% 2.53/6.72 % [INFO] Scanning for conjecture ...
% 2.53/6.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/6.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/6.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/6.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/6.84 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/6.84 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/6.85 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/6.86 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/6.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/6.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.70/6.88 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.96/6.94 % [INFO] Found a conjecture (or negated_conjecture) and 116 axioms. Running axiom selection ...
% 3.32/7.08 % [INFO] Axiom selection finished. Selected 116 axioms (removed 0 axioms).
% 3.32/7.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.74/7.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.74/7.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.74/7.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.74/7.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.74/7.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.74/7.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.91/7.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.91/7.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.91/7.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.91/7.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.91/7.23 % [INFO] Problem is first-order (TPTP FOF).
% 3.91/7.26 % [INFO] Type checking passed.
% 3.91/7.26 % [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 ...
% 204.86/129.06 % [INFO] Killing All external provers ...
% 204.86/129.06 % Time passed: 123477ms (effective reasoning time: 122747ms)
% 204.86/129.06 % 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)>
% 204.86/129.07 % Axioms used in derivation (2): m__5389, m__4660
% 204.86/129.07 % No. of inferences in proof: 25
% 204.86/129.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 123477 ms resp. 122747 ms w/o parsing
% 204.86/129.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 204.86/129.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------