%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM533+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 : 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 08:09:05 AM UTC 2026
% Result : Theorem 29.42s 8.23s
% Output : Refutation 29.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 196 ( 13 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 539 ( 95 ~; 82 |; 21 &; 324 @)
% ( 1 <=>; 16 =>; 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 : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 62 ( 2 ^; 59 !; 0 ?; 62 :)
% ( 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(xB_decl,type,
xB: $i ).
thf(xC_decl,type,
xC: $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(22,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(23,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)],[22]) ).
thf(24,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)],[23]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
| ( B @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
| ( B @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[27]) ).
thf(1,conjecture,
( ( ( xC @ ( xB @ aSubsetOf0 ) )
& ( xB @ ( xA @ aSubsetOf0 ) ) )
=> ( xC @ ( xA @ aSubsetOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( xC @ ( xB @ aSubsetOf0 ) )
& ( xB @ ( xA @ aSubsetOf0 ) ) )
=> ( xC @ ( xA @ aSubsetOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ( ( ( xC @ ( xB @ aSubsetOf0 ) )
& ( xB @ ( xA @ aSubsetOf0 ) ) )
=> ( xC @ ( xA @ aSubsetOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
( ~ ( xC @ ( xA @ aSubsetOf0 ) )
& ( xC @ ( xB @ aSubsetOf0 ) )
& ( xB @ ( xA @ aSubsetOf0 ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
xB @ ( xA @ aSubsetOf0 ),
inference(cnfConj,[status(thm)],[18]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ aElementOf0 ) )
| ~ ( B @ ( C @ aElementOf0 ) )
| ~ ( A @ ( B @ aSubsetOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(321,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xB @ ( xA @ aSubsetOf0 ) )
!= ( A @ ( B @ aSubsetOf0 ) ) )
| ( A @ ( C @ aElementOf0 ) )
| ~ ( B @ ( C @ aElementOf0 ) )
| ~ $true
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[19,26]) ).
thf(322,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xB @ ( xA @ aSubsetOf0 ) )
!= ( A @ ( B @ aSubsetOf0 ) ) )
| ( A @ ( C @ aElementOf0 ) )
| ~ ( B @ ( C @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[321]) ).
thf(323,plain,
! [A: $i] :
( ( xB @ ( A @ aElementOf0 ) )
| ~ ( xA @ ( A @ aElementOf0 ) )
| ~ ( xB @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( xB )),bind(B,$thf( xA ))]]) ).
thf(326,plain,
! [A: $i] :
( ( xB @ ( A @ aElementOf0 ) )
| ~ ( xA @ ( A @ aElementOf0 ) )
| ~ ( xB @ aSet0 ) ),
inference(simp,[status(thm)],[323]) ).
thf(16,axiom,
( ( xC @ aSet0 )
& ( xB @ aSet0 )
& ( xA @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__522) ).
thf(63,plain,
( ( xC @ aSet0 )
& ( xB @ aSet0 )
& ( xA @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(64,plain,
( ( xC @ aSet0 )
& ( xB @ aSet0 )
& ( xA @ aSet0 ) ),
inference(cnf,[status(esa)],[63]) ).
thf(66,plain,
xB @ aSet0,
inference(cnfConj,[status(thm)],[64]) ).
thf(7471,plain,
! [A: $i] :
( ( xB @ ( A @ aElementOf0 ) )
| ~ ( xA @ ( A @ aElementOf0 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[326,66]) ).
thf(7472,plain,
! [A: $i] :
( ( xB @ ( A @ aElementOf0 ) )
| ~ ( xA @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[7471]) ).
thf(20,plain,
xC @ ( xB @ aSubsetOf0 ),
inference(cnfConj,[status(thm)],[18]) ).
thf(279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xC @ ( xB @ aSubsetOf0 ) )
!= ( A @ ( B @ aSubsetOf0 ) ) )
| ( A @ ( C @ aElementOf0 ) )
| ~ ( B @ ( C @ aElementOf0 ) )
| ~ $true
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[20,26]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xC @ ( xB @ aSubsetOf0 ) )
!= ( A @ ( B @ aSubsetOf0 ) ) )
| ( A @ ( C @ aElementOf0 ) )
| ~ ( B @ ( C @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[279]) ).
thf(281,plain,
! [A: $i] :
( ( xC @ ( A @ aElementOf0 ) )
| ~ ( xB @ ( A @ aElementOf0 ) )
| ~ ( xC @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( xC )),bind(B,$thf( xB ))]]) ).
thf(329,plain,
! [A: $i] :
( ( xC @ ( A @ aElementOf0 ) )
| ~ ( xB @ ( A @ aElementOf0 ) )
| ~ ( xC @ aSet0 ) ),
inference(simp,[status(thm)],[281]) ).
thf(67,plain,
xC @ aSet0,
inference(cnfConj,[status(thm)],[64]) ).
thf(8907,plain,
! [A: $i] :
( ( xC @ ( A @ aElementOf0 ) )
| ~ ( xB @ ( A @ aElementOf0 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[329,67]) ).
thf(8908,plain,
! [A: $i] :
( ( xC @ ( A @ aElementOf0 ) )
| ~ ( xB @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[8907]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
| ~ ( A @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
| ~ ( A @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[28]) ).
thf(21,plain,
~ ( xC @ ( xA @ aSubsetOf0 ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(771,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ aSubsetOf0 ) )
!= ( xC @ ( xA @ aSubsetOf0 ) ) )
| ~ $true
| ~ ( A @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[30,21]) ).
thf(772,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ aSubsetOf0 ) )
!= ( xC @ ( xA @ aSubsetOf0 ) ) )
| ~ ( A @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[771]) ).
thf(773,plain,
( ~ ( xC @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) )
| ~ ( xA @ aSet0 )
| ~ ( xC @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[772:[bind(A,$thf( xC )),bind(B,$thf( xA ))]]) ).
thf(65,plain,
xA @ aSet0,
inference(cnfConj,[status(thm)],[64]) ).
thf(4643,plain,
( ~ ( xC @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[773,65,67]) ).
thf(4644,plain,
~ ( xC @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) ),
inference(simp,[status(thm)],[4643]) ).
thf(8971,plain,
! [A: $i] :
( ( ( xC @ ( A @ aElementOf0 ) )
!= ( xC @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) ) )
| ~ $true
| ~ ( xB @ ( A @ aElementOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[8908,4644]) ).
thf(8972,plain,
! [A: $i] :
( ( ( xC @ ( A @ aElementOf0 ) )
!= ( xC @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) ) )
| ~ ( xB @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[8971]) ).
thf(8973,plain,
~ ( xB @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) ),
inference(pattern_uni,[status(thm)],[8972:[bind(A,$thf( xC @ ( xA @ sk1 ) ))]]) ).
thf(9267,plain,
! [A: $i] :
( ( ( xB @ ( A @ aElementOf0 ) )
!= ( xB @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) ) )
| ~ $true
| ~ ( xA @ ( A @ aElementOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[7472,8973]) ).
thf(9268,plain,
! [A: $i] :
( ( ( xB @ ( A @ aElementOf0 ) )
!= ( xB @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) ) )
| ~ ( xA @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[9267]) ).
thf(9269,plain,
~ ( xA @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) ),
inference(pattern_uni,[status(thm)],[9268:[bind(A,$thf( xC @ ( xA @ sk1 ) ))]]) ).
thf(9419,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
!= ( xA @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) ) )
| ~ $true
| ( A @ ( B @ aSubsetOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[29,9269]) ).
thf(9420,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk1 ) @ aElementOf0 ) )
!= ( xA @ ( xC @ ( xA @ sk1 ) @ aElementOf0 ) ) )
| ( A @ ( B @ aSubsetOf0 ) )
| ~ ( B @ aSet0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[9419]) ).
thf(9421,plain,
( ( xC @ ( xA @ aSubsetOf0 ) )
| ~ ( xA @ aSet0 )
| ~ ( xC @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[9420:[bind(A,$thf( xC )),bind(B,$thf( xA ))]]) ).
thf(14678,plain,
( $false
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[9421,65,67,21]) ).
thf(14679,plain,
$false,
inference(simp,[status(thm)],[14678]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM533+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
% 0.14/0.58 % Computer : n016.cluster.edu
% 0.14/0.58 % Model : x86_64 x86_64
% 0.14/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.58 % Memory : 8046.5625MB
% 0.14/0.58 % OS : Linux 6.8.0-71-generic
% 0.14/0.58 % CPULimit : 300
% 0.14/0.58 % WCLimit : 300
% 0.14/0.58 % DateTime : Sat Sep 26 03:12:45 UTC 2026
% 0.14/0.59 % CPUTime :
% 0.14/0.59 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
% 0.93/1.18 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.38 % [INFO] Parsing done (196ms).
% 1.24/1.39 % [INFO] Running in sequential loop mode.
% 2.11/1.80 % [INFO] eprover registered as external prover.
% 2.11/1.81 % [INFO] Scanning for conjecture ...
% 2.11/1.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.11/1.89 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.32/1.91 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.32/1.95 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.32/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.32/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.32/1.98 % [INFO] Problem is first-order (TPTP FOF).
% 2.32/1.98 % [INFO] Type checking passed.
% 2.32/1.99 % [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 ...
% 29.42/8.23 % [INFO] Killing All external provers ...
% 29.42/8.23 % Time passed: 7495ms (effective reasoning time: 6830ms)
% 29.42/8.23 % 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)>
% 29.42/8.23 % Axioms used in derivation (2): mDefSub, m__522
% 29.42/8.23 % No. of inferences in proof: 50
% 29.42/8.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7495 ms resp. 6830 ms w/o parsing
% 29.42/8.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.42/8.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------