%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM604+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 : n002.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 08:09:16 AM UTC 2026
% Result : Theorem 264.34s 162.30s
% Output : Refutation 264.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 15 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 245 ( 15 ~; 13 |; 18 &; 193 @)
% ( 0 <=>; 6 =>; 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 : 16 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% 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(aFunction0_decl,type,
aFunction0: $i > $o ).
thf(szDzozmdt0_decl,type,
szDzozmdt0: $i > $i ).
thf(sdtlpdtrp0_decl,type,
sdtlpdtrp0: $i > $i > $i ).
thf(xx_decl,type,
xx: $i ).
thf(xS_decl,type,
xS: $i ).
thf(xe_decl,type,
xe: $i ).
thf(xN_decl,type,
xN: $i ).
thf(xi_decl,type,
xi: $i ).
thf(55,axiom,
( ( ( xi @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( szNzAzT0 @ ( xi @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5034) ).
thf(381,plain,
( ( ( xi @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( szNzAzT0 @ ( xi @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(382,plain,
( ( ( xi @ ( xe @ sdtlpdtrp0 ) )
= xx )
& ( szNzAzT0 @ ( xi @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[381]) ).
thf(383,plain,
szNzAzT0 @ ( xi @ aElementOf0 ),
inference(cnfConj,[status(thm)],[382]) ).
thf(61,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(467,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)],[61]) ).
thf(468,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)],[467]) ).
thf(471,plain,
! [A: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[468]) ).
thf(211884,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xi @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[383,471]) ).
thf(211885,plain,
! [A: $i] :
( ( ( szNzAzT0 @ ( xi @ aElementOf0 ) )
!= ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
| ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[211884]) ).
thf(211886,plain,
xi @ ( xN @ sdtlpdtrp0 ) @ ( xi @ ( xe @ sdtlpdtrp0 ) @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[211885:[bind(A,$thf( xi ))]]) ).
thf(384,plain,
( ( xi @ ( xe @ sdtlpdtrp0 ) )
= xx ),
inference(cnfConj,[status(thm)],[382]) ).
thf(385,plain,
( ( xi @ ( xe @ sdtlpdtrp0 ) )
= xx ),
inference(lifteq,[status(thm)],[384]) ).
thf(244988,plain,
xi @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ),
inference(rewrite,[status(thm)],[211886,385]) ).
thf(38,axiom,
( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5045) ).
thf(232,plain,
( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(233,plain,
! [A: $i] :
( ( xS @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[232]) ).
thf(234,plain,
! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(244999,plain,
! [A: $i] :
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) )
| ( xS @ ( A @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244988,234]) ).
thf(245000,plain,
! [A: $i] :
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( xx @ aElementOf0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) ) )
| ( xS @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[244999]) ).
thf(245001,plain,
xS @ ( xx @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[245000:[bind(A,$thf( xx ))]]) ).
thf(1,conjecture,
xS @ ( xx @ aElementOf0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( xS @ ( xx @ aElementOf0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(103,plain,
~ ( xS @ ( xx @ aElementOf0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(245951,plain,
$false,
inference(rewrite,[status(thm)],[245001,103]) ).
thf(245952,plain,
$false,
inference(simp,[status(thm)],[245951]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM604+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
% 0.14/0.39 % Computer : n002.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 03:28:05 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.71/0.70 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.95/0.89 % [INFO] Parsing done (182ms).
% 0.95/0.89 % [INFO] Running in sequential loop mode.
% 1.80/1.09 % [INFO] eprover registered as external prover.
% 1.80/1.10 % [INFO] Scanning for conjecture ...
% 2.10/1.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.10/1.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.10/1.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.10/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.10/1.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.10/1.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.25/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.25/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.25/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.25/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.25/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.25/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 100 axioms. Running axiom selection ...
% 2.42/1.38 % [INFO] Axiom selection finished. Selected 100 axioms (removed 0 axioms).
% 2.81/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/1.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/1.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.81/1.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/1.50 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/1.51 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/1.51 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/1.52 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/1.53 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.09/1.54 % [INFO] Problem is first-order (TPTP FOF).
% 3.09/1.55 % [INFO] Type checking passed.
% 3.09/1.56 % [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 ...
% 264.22/162.29 % [INFO] Killing All external provers ...
% 264.34/162.30 % Time passed: 161798ms (effective reasoning time: 161396ms)
% 264.34/162.30 % 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)>
% 264.34/162.30 % Axioms used in derivation (3): m__5034, m__4660, m__5045
% 264.34/162.30 % No. of inferences in proof: 26
% 264.34/162.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 161798 ms resp. 161396 ms w/o parsing
% 264.34/162.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 264.34/162.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------