%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU527^2 : 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 : n002.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 08:28:24 AM UTC 2026
% Result : Theorem 6.74s 3.63s
% Output : Refutation 7.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 13 unt; 0 typ; 4 def)
% Number of atoms : 84 ( 30 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 237 ( 30 ~; 39 |; 6 &; 130 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 63 !; 1 ?; 66 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(setadjoinE_decl,type,
setadjoinE: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
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(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( in @ sk1 @ ( setadjoin @ A @ emptyset ) )
=> ( sk1 = A ) ) ) ) ).
thf(1,conjecture,
( emptysetE
=> ( setadjoinE
=> ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( setadjoinE
=> ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ( ! [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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ( ! [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 ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [F: $o,E: $i,D: $i,C: $i,B: $o,A: $i] :
( ( ~ ( in @ A @ emptyset )
| B )
& ( ~ ( in @ E @ ( setadjoin @ C @ D ) )
| ( E = C )
| ( in @ E @ D )
| F )
& ( ~ ( in @ E @ ( setadjoin @ C @ D ) )
| ( E = C )
| ~ F
| F )
& ( ~ ( in @ E @ ( setadjoin @ C @ D ) )
| ~ F
| ( in @ E @ D )
| F )
& ( ~ ( in @ E @ ( setadjoin @ C @ D ) )
| ~ F
| ~ F
| F )
& ( in @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )
& ( sk1 != sk2 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
in @ sk1 @ ( setadjoin @ sk2 @ emptyset ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( C = A )
| ( in @ C @ B )
| D ),
inference(cnfConj,[status(thm)],[5]) ).
thf(13,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( in @ C @ B )
| D ),
inference(lifteq,[status(thm)],[10]) ).
thf(14,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( in @ C @ B )
| D ),
inference(simp,[status(thm)],[13]) ).
thf(89,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ~ $true
| ( in @ C @ B )
| D
| ( ( in @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )
!= ( in @ C @ ( setadjoin @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,14]) ).
thf(90,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ( in @ C @ B )
| D
| ( ( in @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )
!= ( in @ C @ ( setadjoin @ A @ B ) ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
! [A: $o] :
( ( sk2 = sk1 )
| ( in @ sk1 @ emptyset )
| A ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( sk2 )),bind(B,$thf( emptyset )),bind(C,$thf( sk1 ))]]) ).
thf(118,plain,
! [A: $o] :
( ( sk2 = sk1 )
| ( in @ sk1 @ emptyset )
| A ),
inference(simp,[status(thm)],[91]) ).
thf(9,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnfConj,[status(thm)],[5]) ).
thf(25,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ( B
!= ( ~ ( in @ A @ emptyset ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9]) ).
thf(32,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( D )),bind(B,$thf( ~ ( in @ D @ emptyset ) ))]]) ).
thf(33,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(simp,[status(thm)],[32]) ).
thf(137,plain,
! [A: $o] :
( ( sk2 = sk1 )
| $false
| A ),
inference(rewrite,[status(thm)],[118,33]) ).
thf(138,plain,
! [A: $o] :
( ( sk2 = sk1 )
| A ),
inference(simp,[status(thm)],[137]) ).
thf(12,plain,
sk1 != sk2,
inference(cnfConj,[status(thm)],[5]) ).
thf(16,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[12]) ).
thf(139,plain,
! [A: $o] : A,
inference(simplifyReflect,[status(thm)],[138,16]) ).
thf(143,plain,
$false,
inference(prim_subst,[status(thm)],[139:[bind(A,$thf( $false ))]]) ).
thf(153,plain,
$false,
inference(simp,[status(thm)],[143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU527^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.11 % 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
% 0.29/0.31 % Computer : n002.cluster.edu
% 0.29/0.31 % Model : x86_64 x86_64
% 0.29/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.29/0.31 % Memory : 8046.5625MB
% 0.29/0.31 % OS : Linux 6.8.0-71-generic
% 0.29/0.31 % CPULimit : 300
% 0.29/0.31 % WCLimit : 300
% 0.29/0.31 % DateTime : Tue Sep 29 13:50:52 UTC 2026
% 0.29/0.31 % CPUTime :
% 0.29/0.31 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
% 1.40/1.10 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.36 % [INFO] Parsing done (253ms).
% 1.85/1.38 % [INFO] Running in sequential loop mode.
% 2.78/1.97 % [INFO] eprover registered as external prover.
% 2.78/1.98 % [INFO] Scanning for conjecture ...
% 3.08/2.14 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.27/2.18 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.27/2.18 % [INFO] Problem is higher-order (TPTP THF).
% 3.27/2.19 % [INFO] Type checking passed.
% 3.27/2.20 % [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 ...
% 6.74/3.62 % [INFO] Killing All external provers ...
% 6.74/3.63 % Time passed: 3113ms (effective reasoning time: 2238ms)
% 6.74/3.63 % 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)>
% 6.74/3.63 % Axioms used in derivation (0):
% 6.74/3.63 % No. of inferences in proof: 24
% 6.74/3.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3113 ms resp. 2238 ms w/o parsing
% 7.00/3.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.00/3.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------