%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET096^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 : Wed Sep 30 08:22:54 AM UTC 2026
% Result : Theorem 4.35s 2.18s
% Output : Refutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 19 unt; 0 typ; 5 def)
% Number of atoms : 147 ( 75 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 162 ( 55 ~; 44 |; 2 &; 52 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 17 ^; 20 !; 0 ?; 39 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(emptyset_decl,type,
emptyset: $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i > $o ).
thf(subset_decl,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(emptyset_def,definition,
( emptyset
= ( ^ [A: $i] : $false ) ) ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i,B: $i] : ( B = A ) ) ) ).
thf(subset_def,definition,
( subset
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ! [B: $i] :
( ! [C: $i] :
( ( A @ C )
=> ( C = B ) )
=> ( ( A
= ( ^ [C: $i] : $false ) )
| ( A
= ( ^ [C: $i] : ( C = B ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ( sk1 @ B )
=> ( B = A ) )
=> ( ( sk1
= ( ^ [B: $i] : $false ) )
| ( sk1
= ( ^ [B: $i] : ( B = A ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
=> ( ( A = emptyset )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
=> ( ( A = emptyset )
| ( A
= ( singleton @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i] :
( ! [C: $i] :
( ( A @ C )
=> ( C = B ) )
=> ( ( A
= ( ^ [C: $i] : $false ) )
| ( A
= ( ^ [C: $i] : ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i] :
( ( ~ ( sk1 @ A )
| ( A = sk2 ) )
& ( sk1
!= ( ^ [B: $i] : $false ) )
& ( sk1
!= ( ^ [B: $i] : ( B = sk2 ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( A = sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [A: $i] :
( ( A = sk2 )
| ~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(7,plain,
( sk1
!= ( ^ [A: $i] : ( A = sk2 ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
( sk1
!= ( ^ [A: $i] : ( A = sk2 ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(12,plain,
( ( sk1 @ sk4 )
!= ( sk4 = sk2 ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(13,plain,
( ~ ( sk1 @ sk4 )
| ( sk4 != sk2 ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(16,plain,
( ( sk4 != sk2 )
| ~ ( sk1 @ sk4 ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(91,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( sk2 != sk2 )
| ~ ( sk1 @ sk4 )
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[8,16]) ).
thf(92,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ~ ( sk1 @ sk4 )
| ( A != sk4 ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk4 ))]]) ).
thf(102,plain,
~ ( sk1 @ sk4 ),
inference(simp,[status(thm)],[93]) ).
thf(14,plain,
( ( sk1 @ sk4 )
| ( sk4 = sk2 ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(17,plain,
( ( sk4 = sk2 )
| ( sk1 @ sk4 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(86,plain,
! [A: $i] :
( ( sk4 = sk2 )
| ( A = sk2 )
| ~ $true
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17,8]) ).
thf(87,plain,
! [A: $i] :
( ( sk4 = sk2 )
| ( A = sk2 )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(88,plain,
( ( sk4 = sk2 )
| ( sk4 = sk2 ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( sk4 ))]]) ).
thf(101,plain,
sk4 = sk2,
inference(simp,[status(thm)],[88]) ).
thf(119,plain,
~ ( sk1 @ sk2 ),
inference(rewrite,[status(thm)],[102,101]) ).
thf(6,plain,
( sk1
!= ( ^ [A: $i] : $false ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( sk1
!= ( ^ [A: $i] : $false ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
sk1 @ sk3,
inference(func_ext,[status(esa)],[9]) ).
thf(19,plain,
( ( sk4 != sk2 )
| ~ $true
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[11,16]) ).
thf(20,plain,
( ( sk4 != sk2 )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(21,plain,
( ( sk4 != sk2 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
( ( sk1 @ sk4 )
| ( sk2 != sk2 )
| ( sk4 != sk3 )
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[17,21]) ).
thf(23,plain,
( ( sk1 @ sk4 )
| ( sk4 != sk3 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
( ( sk1 @ sk4 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[23:[]]) ).
thf(44,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ( sk3 != sk2 )
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[17,24]) ).
thf(45,plain,
( ( sk1 @ sk4 )
| ( sk3 != sk2 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[44]) ).
thf(46,plain,
( ( sk1 @ sk4 )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[45:[]]) ).
thf(98,plain,
! [A: $i] :
( ( A = sk2 )
| ~ $true
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,8]) ).
thf(99,plain,
! [A: $i] :
( ( A = sk2 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
sk3 = sk2,
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( sk3 ))]]) ).
thf(104,plain,
( ( sk1 @ sk4 )
| ( sk2 != sk2 ) ),
inference(rewrite,[status(thm)],[46,100]) ).
thf(105,plain,
sk1 @ sk4,
inference(simp,[status(thm)],[104]) ).
thf(126,plain,
sk1 @ sk2,
inference(rewrite,[status(thm)],[105,101]) ).
thf(127,plain,
~ $true,
inference(rewrite,[status(thm)],[119,126]) ).
thf(128,plain,
$false,
inference(simp,[status(thm)],[127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET096^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:36:39 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (207ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 1.98/1.36 % [INFO] eprover registered as external prover.
% 1.98/1.37 % [INFO] Scanning for conjecture ...
% 2.24/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.45 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.45 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.45 % [INFO] Type checking passed.
% 2.24/1.45 % [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 ...
% 4.35/2.18 % [INFO] Killing All external provers ...
% 4.35/2.18 % Time passed: 1854ms (effective reasoning time: 1179ms)
% 4.35/2.18 % 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)>
% 4.35/2.18 % Axioms used in derivation (0):
% 4.35/2.18 % No. of inferences in proof: 42
% 4.35/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1854 ms resp. 1179 ms w/o parsing
% 4.63/2.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.63/2.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------