%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU531^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : Wed Sep 30 08:28:25 AM UTC 2026
% Result : Theorem 4.36s 1.75s
% Output : Refutation 4.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 19 unt; 0 typ; 5 def)
% Number of atoms : 120 ( 60 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 367 ( 56 ~; 54 |; 7 &; 226 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 69 ( 0 ^; 66 !; 0 ?; 69 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setadjoinE_decl,type,
setadjoinE: $o ).
thf(uniqinunit_decl,type,
uniqinunit: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(setadjoinE_def,definition,
( setadjoinE
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ) ).
thf(uniqinunit_def,definition,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ( C = A )
| ( C = B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( in @ B @ ( setadjoin @ sk1 @ ( setadjoin @ A @ emptyset ) ) )
=> ( ( B = sk1 )
| ( B = A ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( in @ A @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) )
=> ( ( A = sk1 )
| ( A = sk2 ) ) ) ) ) ).
thf(1,conjecture,
( setadjoinE
=> ( uniqinunit
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ( C = A )
| ( C = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(2,negated_conjecture,
~ ( setadjoinE
=> ( uniqinunit
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ( C = A )
| ( C = B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ( C = A )
| ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [F: $i,E: $i,D: $o,C: $i,B: $i,A: $i] :
( ( ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( C = A )
| ( in @ C @ B )
| D )
& ( ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( C = A )
| ~ D
| D )
& ( ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ~ D
| ( in @ C @ B )
| D )
& ( ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ~ D
| ~ D
| D )
& ( ~ ( in @ E @ ( setadjoin @ F @ emptyset ) )
| ( E = F ) )
& ( in @ sk3 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) )
& ( sk3 != sk1 )
& ( sk3 != sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(11,plain,
in @ sk3 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
sk3 != sk1,
inference(cnfConj,[status(thm)],[4]) ).
thf(13,plain,
sk3 != sk1,
inference(lifteq,[status(thm)],[5]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B != sk1 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(55,plain,
! [A: $i] :
( ~ ( in @ sk3 @ ( setadjoin @ A @ emptyset ) )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( sk3 ))]]) ).
thf(69,plain,
~ ( in @ sk3 @ ( setadjoin @ sk1 @ emptyset ) ),
inference(simp,[status(thm)],[55]) ).
thf(78,plain,
( ~ $true
| ( ( in @ sk3 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) )
!= ( in @ sk3 @ ( setadjoin @ sk1 @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,69]) ).
thf(79,plain,
( ( in @ sk3 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) )
!= ( in @ sk3 @ ( setadjoin @ sk1 @ emptyset ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(96,plain,
( ( sk3 != sk3 )
| ( ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )
!= ( setadjoin @ sk1 @ emptyset ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(97,plain,
( ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )
!= ( setadjoin @ sk1 @ emptyset ) ),
inference(simp,[status(thm)],[96]) ).
thf(503,plain,
( ( sk1 != sk1 )
| ( ( setadjoin @ sk2 @ emptyset )
!= emptyset ) ),
inference(simp,[status(thm)],[97]) ).
thf(555,plain,
( ( setadjoin @ sk2 @ emptyset )
!= emptyset ),
inference(simp,[status(thm)],[503]) ).
thf(573,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B != emptyset )
| ( A
!= ( setadjoin @ sk2 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[19,555]) ).
thf(574,plain,
! [A: $i] :
( ~ ( in @ ( setadjoin @ sk2 @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
| ( A != emptyset ) ),
inference(pattern_uni,[status(thm)],[573:[bind(A,$thf( setadjoin @ sk2 @ emptyset )),bind(B,$thf( B ))]]) ).
thf(594,plain,
~ ( in @ ( setadjoin @ sk2 @ emptyset ) @ ( setadjoin @ emptyset @ emptyset ) ),
inference(simp,[status(thm)],[574]) ).
thf(7,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( C = A )
| ( in @ C @ B )
| D ),
inference(cnfConj,[status(thm)],[4]) ).
thf(17,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( in @ C @ B )
| D ),
inference(lifteq,[status(thm)],[7]) ).
thf(198,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ~ $true
| ( in @ C @ B )
| D
| ( ( in @ sk3 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) )
!= ( in @ C @ ( setadjoin @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,17]) ).
thf(199,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ( in @ C @ B )
| D
| ( ( in @ sk3 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) )
!= ( in @ C @ ( setadjoin @ A @ B ) ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(200,plain,
! [A: $o] :
( ( sk3 = sk1 )
| ( in @ sk3 @ ( setadjoin @ sk2 @ emptyset ) )
| A ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( sk1 )),bind(B,$thf( setadjoin @ sk2 @ emptyset )),bind(C,$thf( sk3 )),bind(D,$thf( D ))]]) ).
thf(261,plain,
! [A: $o] :
( ( sk3 = sk1 )
| ( in @ sk3 @ ( setadjoin @ sk2 @ emptyset ) )
| A ),
inference(simp,[status(thm)],[200]) ).
thf(9,plain,
sk3 != sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(15,plain,
sk3 != sk2,
inference(lifteq,[status(thm)],[9]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B != sk2 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[19,15]) ).
thf(59,plain,
! [A: $i] :
( ~ ( in @ sk3 @ ( setadjoin @ A @ emptyset ) )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( sk3 ))]]) ).
thf(73,plain,
~ ( in @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ),
inference(simp,[status(thm)],[59]) ).
thf(804,plain,
! [A: $o] :
( ( sk3 = sk1 )
| $false
| A ),
inference(rewrite,[status(thm)],[261,73]) ).
thf(805,plain,
! [A: $o] :
( ( sk3 = sk1 )
| A ),
inference(simp,[status(thm)],[804]) ).
thf(806,plain,
! [A: $o] : A,
inference(simplifyReflect,[status(thm)],[805,13]) ).
thf(813,plain,
~ $true,
inference(rewrite,[status(thm)],[594,806]) ).
thf(814,plain,
$false,
inference(simp,[status(thm)],[813]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU531^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.08/0.12 % Computer : n012.cluster.edu
% 0.08/0.12 % Model : x86_64 x86_64
% 0.08/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.12 % Memory : 8046.5625MB
% 0.08/0.12 % OS : Linux 6.8.0-71-generic
% 0.08/0.12 % CPULimit : 300
% 0.08/0.12 % WCLimit : 300
% 0.08/0.12 % DateTime : Tue Sep 29 13:48:03 UTC 2026
% 0.08/0.12 % CPUTime :
% 0.08/0.12 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
% 0.41/0.41 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.56/0.50 % [INFO] Parsing done (95ms).
% 0.56/0.51 % [INFO] Running in sequential loop mode.
% 0.87/0.70 % [INFO] eprover registered as external prover.
% 1.00/0.70 % [INFO] Scanning for conjecture ...
% 1.00/0.75 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.00/0.77 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.00/0.77 % [INFO] Problem is higher-order (TPTP THF).
% 1.00/0.77 % [INFO] Type checking passed.
% 1.00/0.77 % [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 ...
% 4.36/1.75 % [INFO] Killing All external provers ...
% 4.36/1.75 % Time passed: 1559ms (effective reasoning time: 1237ms)
% 4.36/1.75 % 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)>
% 4.36/1.75 % Axioms used in derivation (0):
% 4.36/1.75 % No. of inferences in proof: 38
% 4.36/1.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1559 ms resp. 1237 ms w/o parsing
% 4.36/1.78 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.36/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------