%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM532+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 : n014.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 08:09:04 AM UTC 2026
% Result : Theorem 7.85s 3.94s
% Output : Refutation 7.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 104 ( 5 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 293 ( 45 ~; 45 |; 10 &; 179 @)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 2 ^; 32 !; 0 ?; 35 :)
% ( 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(xA_decl,type,
xA: $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ aElementOf0 ) )
=> ( B @ ( C @ aElementOf0 ) ) ) ) ) ).
thf(3,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
<=> ( ! [C: $i] :
( ( B @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ aElementOf0 ) ) )
& ( B @ aSet0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
thf(16,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( ( ! [C: $i] :
( ( B @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ aElementOf0 ) ) )
& ( B @ aSet0 ) )
=> ( A @ ( B @ aSubsetOf0 ) ) )
& ( ( A @ ( B @ aSubsetOf0 ) )
=> ( ! [C: $i] :
( ( B @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ aElementOf0 ) ) )
& ( B @ aSet0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ( ! [B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ aElementOf0 ) ) )
& ( B @ aSet0 ) )
=> ( A @ ( B @ aSubsetOf0 ) ) )
& ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
=> ( ! [C: $i] :
( ( B @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ aElementOf0 ) ) )
& ( B @ aSet0 ) ) ) ) ),
inference(miniscope,[status(thm)],[16]) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ aSubsetOf0 ) )
| ~ ( A @ ( A @ ( D @ sk1 ) @ aElementOf0 ) )
| ~ ( D @ aSet0 )
| ~ ( A @ aSet0 ) )
& ( ( A @ ( D @ aSubsetOf0 ) )
| ( D @ ( A @ ( D @ sk1 ) @ aElementOf0 ) )
| ~ ( D @ aSet0 )
| ~ ( A @ aSet0 ) )
& ( ( A @ ( C @ aElementOf0 ) )
| ~ ( B @ ( C @ aElementOf0 ) )
| ~ ( A @ ( B @ aSubsetOf0 ) )
| ~ ( A @ aSet0 ) )
& ( ( B @ aSet0 )
| ~ ( A @ ( B @ aSubsetOf0 ) )
| ~ ( A @ aSet0 ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
| ( B @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
| ( B @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[21]) ).
thf(1,conjecture,
xA @ ( xA @ aSubsetOf0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( xA @ ( xA @ aSubsetOf0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ( xA @ ( xA @ aSubsetOf0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ aSubsetOf0 ) )
!= ( xA @ ( xA @ aSubsetOf0 ) ) )
| ~ $true
| ( B @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[23,15]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ aSubsetOf0 ) )
!= ( xA @ ( xA @ aSubsetOf0 ) ) )
| ( B @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[302]) ).
thf(304,plain,
( ( xA @ ( xA @ ( xA @ sk1 ) @ aElementOf0 ) )
| ~ ( xA @ aSet0 )
| ~ ( xA @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[303:[bind(A,$thf( xA )),bind(B,$thf( xA ))]]) ).
thf(325,plain,
( ( xA @ ( xA @ ( xA @ sk1 ) @ aElementOf0 ) )
| ~ ( xA @ aSet0 ) ),
inference(simp,[status(thm)],[304]) ).
thf(14,axiom,
xA @ aSet0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__467) ).
thf(52,plain,
xA @ aSet0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(408,plain,
( ( xA @ ( xA @ ( xA @ sk1 ) @ aElementOf0 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[325,52]) ).
thf(409,plain,
xA @ ( xA @ ( xA @ sk1 ) @ aElementOf0 ),
inference(simp,[status(thm)],[408]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
| ~ ( A @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
| ~ ( A @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[22]) ).
thf(464,plain,
! [B: $i,A: $i] :
( ( ( xA @ ( xA @ ( xA @ sk1 ) @ aElementOf0 ) )
!= ( A @ ( A @ ( B @ sk1 ) @ aElementOf0 ) ) )
| ( A @ ( B @ aSubsetOf0 ) )
| ~ $true
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[409,24]) ).
thf(465,plain,
! [B: $i,A: $i] :
( ( ( xA @ ( xA @ ( xA @ sk1 ) @ aElementOf0 ) )
!= ( A @ ( A @ ( B @ sk1 ) @ aElementOf0 ) ) )
| ( A @ ( B @ aSubsetOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[464]) ).
thf(466,plain,
( ( xA @ ( xA @ aSubsetOf0 ) )
| ~ ( xA @ aSet0 )
| ~ ( xA @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[465:[bind(A,$thf( xA )),bind(B,$thf( xA ))]]) ).
thf(494,plain,
( ( xA @ ( xA @ aSubsetOf0 ) )
| ~ ( xA @ aSet0 ) ),
inference(simp,[status(thm)],[466]) ).
thf(520,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[494,52,15]) ).
thf(521,plain,
$false,
inference(simp,[status(thm)],[520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM532+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
% 0.14/0.41 % Computer : n014.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 03:07:47 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 1.29/1.28 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.75/1.57 % [INFO] Parsing done (289ms).
% 1.75/1.59 % [INFO] Running in sequential loop mode.
% 2.57/2.05 % [INFO] eprover registered as external prover.
% 2.57/2.06 % [INFO] Scanning for conjecture ...
% 2.75/2.13 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/2.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/2.16 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.75/2.19 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.75/2.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/2.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.85/2.21 % [INFO] Problem is first-order (TPTP FOF).
% 2.85/2.22 % [INFO] Type checking passed.
% 2.85/2.22 % [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 ...
% 7.85/3.94 % [INFO] Killing All external provers ...
% 7.85/3.94 % Time passed: 3316ms (effective reasoning time: 2337ms)
% 7.85/3.94 % 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)>
% 7.85/3.94 % Axioms used in derivation (2): mDefSub, m__467
% 7.85/3.94 % No. of inferences in proof: 25
% 7.85/3.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3316 ms resp. 2337 ms w/o parsing
% 7.85/3.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.85/3.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------