%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM609+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 : n012.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 08:09:17 AM UTC 2026
% Result : Theorem 66.52s 32.61s
% Output : Refutation 66.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 79 ( 14 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 219 ( 27 ~; 15 |; 29 &; 136 @)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 17 !; 0 ?; 18 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(sdtmndt0_decl,type,
sdtmndt0: $i > $i > $i ).
thf(szmzizndt0_decl,type,
szmzizndt0: $i > $i ).
thf(sdtlseqdt0_decl,type,
sdtlseqdt0: $i > $i > $o ).
thf(xP_decl,type,
xP: $i ).
thf(xQ_decl,type,
xQ: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( xP @ ( A @ aElementOf0 ) )
=> ( xQ @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(51,axiom,
( ( xP
= ( xQ @ szmzizndt0 @ ( xQ @ sdtmndt0 ) ) )
& ! [A: $i] :
( ( xP @ ( A @ aElementOf0 ) )
<=> ( ( A
!= ( xQ @ szmzizndt0 ) )
& ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( A @ ( xQ @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xP @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
thf(367,plain,
( ( xP
= ( xQ @ szmzizndt0 @ ( xQ @ sdtmndt0 ) ) )
& ! [A: $i] :
( ( ( ( A
!= ( xQ @ szmzizndt0 ) )
& ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xP @ ( A @ aElementOf0 ) ) )
& ( ( xP @ ( A @ aElementOf0 ) )
=> ( ( A
!= ( xQ @ szmzizndt0 ) )
& ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( A @ ( xQ @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xP @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(368,plain,
( ( xP
= ( xQ @ szmzizndt0 @ ( xQ @ sdtmndt0 ) ) )
& ! [A: $i] :
( ( ( A
!= ( xQ @ szmzizndt0 ) )
& ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) )
=> ( xP @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xP @ ( A @ aElementOf0 ) )
=> ( ( A
!= ( xQ @ szmzizndt0 ) )
& ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ) )
& ! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
=> ( A @ ( xQ @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( xP @ aSet0 ) ),
inference(miniscope,[status(thm)],[367]) ).
thf(369,plain,
! [C: $i,B: $i,A: $i] :
( ( xP
= ( xQ @ szmzizndt0 @ ( xQ @ sdtmndt0 ) ) )
& ( ( xP @ ( C @ aElementOf0 ) )
| ( C
= ( xQ @ szmzizndt0 ) )
| ~ ( xQ @ ( C @ aElementOf0 ) )
| ~ ( C @ aElement0 ) )
& ( ( B
!= ( xQ @ szmzizndt0 ) )
| ~ ( xP @ ( B @ aElementOf0 ) ) )
& ( ( xQ @ ( B @ aElementOf0 ) )
| ~ ( xP @ ( B @ aElementOf0 ) ) )
& ( ( B @ aElement0 )
| ~ ( xP @ ( B @ aElementOf0 ) ) )
& ( ( A @ ( xQ @ szmzizndt0 @ sdtlseqdt0 ) )
| ~ ( xQ @ ( A @ aElementOf0 ) ) )
& ( xP @ aSet0 ) ),
inference(cnf,[status(esa)],[368]) ).
thf(376,plain,
! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
| ~ ( xP @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[369]) ).
thf(377,plain,
! [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
| ~ ( xP @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[376]) ).
thf(1,conjecture,
( ( xQ @ ( xP @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xP @ ( A @ aElementOf0 ) )
=> ( xQ @ ( A @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xQ @ ( xP @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xP @ ( A @ aElementOf0 ) )
=> ( xQ @ ( A @ aElementOf0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(109,plain,
~ ( ( xQ @ ( xP @ aSubsetOf0 ) )
| ! [A: $i] :
( ( xP @ ( A @ aElementOf0 ) )
=> ( xQ @ ( A @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(110,plain,
( ~ ( xQ @ ( xP @ aSubsetOf0 ) )
& ~ ( xQ @ ( sk1 @ aElementOf0 ) )
& ( xP @ ( sk1 @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(112,plain,
~ ( xQ @ ( sk1 @ aElementOf0 ) ),
inference(cnfConj,[status(thm)],[110]) ).
thf(110349,plain,
! [A: $i] :
( ( ( xQ @ ( A @ aElementOf0 ) )
!= ( xQ @ ( sk1 @ aElementOf0 ) ) )
| ~ $true
| ~ ( xP @ ( A @ aElementOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[377,112]) ).
thf(110350,plain,
! [A: $i] :
( ( ( xQ @ ( A @ aElementOf0 ) )
!= ( xQ @ ( sk1 @ aElementOf0 ) ) )
| ~ ( xP @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[110349]) ).
thf(110351,plain,
~ ( xP @ ( sk1 @ aElementOf0 ) ),
inference(pattern_uni,[status(thm)],[110350:[bind(A,$thf( sk1 ))]]) ).
thf(111,plain,
xP @ ( sk1 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[110]) ).
thf(110836,plain,
~ $true,
inference(rewrite,[status(thm)],[110351,111]) ).
thf(110837,plain,
$false,
inference(simp,[status(thm)],[110836]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM609+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % 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
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Sat Sep 26 03:26:05 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 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
% 0.39/0.60 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.76 % [INFO] Parsing done (159ms).
% 0.69/0.77 % [INFO] Running in sequential loop mode.
% 1.28/0.96 % [INFO] eprover registered as external prover.
% 1.28/0.96 % [INFO] Scanning for conjecture ...
% 1.28/1.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.28/1.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.28/1.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.02 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.03 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.04 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.53/1.07 % [INFO] Found a conjecture (or negated_conjecture) and 106 axioms. Running axiom selection ...
% 1.79/1.13 % [INFO] Axiom selection finished. Selected 106 axioms (removed 0 axioms).
% 1.79/1.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.09/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.09/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.09/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.09/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.09/1.21 % [INFO] Problem is first-order (TPTP FOF).
% 2.09/1.22 % [INFO] Type checking passed.
% 2.09/1.23 % [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 ...
% 66.52/32.60 % [INFO] Killing All external provers ...
% 66.52/32.61 % Time passed: 32209ms (effective reasoning time: 31833ms)
% 66.52/32.61 % 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)>
% 66.52/32.61 % Axioms used in derivation (1): m__5164
% 66.52/32.61 % No. of inferences in proof: 17
% 66.52/32.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 32209 ms resp. 31833 ms w/o parsing
% 66.52/32.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 66.52/32.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------