%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU586^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n005.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 08:28:39 AM UTC 2026
% Result : Theorem 4.10s 2.37s
% Output : Refutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 9 unt; 0 typ; 4 def)
% Number of atoms : 73 ( 6 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 250 ( 23 ~; 35 |; 6 &; 160 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 0 ^; 47 !; 0 ?; 50 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(binunion_decl,type,
binunion: $i > $i > $i ).
thf(binunionEcases_decl,type,
binunionEcases: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(binunionEcases_def,definition,
( binunionEcases
= ( ! [A: $i,B: $i,C: $i,D: $o] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( ( in @ C @ A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( in @ C @ A )
| ( in @ C @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( in @ B @ ( binunion @ sk1 @ A ) )
=> ( ( in @ B @ sk1 )
| ( in @ B @ A ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( in @ A @ ( binunion @ sk1 @ sk2 ) )
=> ( ( in @ A @ sk1 )
| ( in @ A @ sk2 ) ) ) ) ) ).
thf(1,conjecture,
( binunionEcases
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( in @ C @ A )
| ( in @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(2,negated_conjecture,
~ ( binunionEcases
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( in @ C @ A )
| ( in @ C @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i,D: $o] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( ( in @ C @ A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( in @ C @ A )
| ( in @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ! [D: $o] :
( ( ( in @ C @ A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( in @ C @ A )
| ( in @ C @ B ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B )
| D )
& ( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ~ D
| D )
& ( ~ ( in @ C @ ( binunion @ A @ B ) )
| ~ D
| ( in @ C @ B )
| D )
& ( ~ ( in @ C @ ( binunion @ A @ B ) )
| ~ D
| ~ D
| D )
& ( in @ sk3 @ ( binunion @ sk1 @ sk2 ) )
& ~ ( in @ sk3 @ sk1 )
& ~ ( in @ sk3 @ sk2 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
~ ( in @ sk3 @ sk2 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
in @ sk3 @ ( binunion @ sk1 @ sk2 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(6,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B )
| D ),
inference(cnfConj,[status(thm)],[5]) ).
thf(31,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ $true
| ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( in @ sk3 @ ( binunion @ sk1 @ sk2 ) )
!= ( in @ C @ ( binunion @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,6]) ).
thf(32,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| D
| ( ( in @ sk3 @ ( binunion @ sk1 @ sk2 ) )
!= ( in @ C @ ( binunion @ A @ B ) ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(33,plain,
! [A: $o] :
( ( in @ sk3 @ sk1 )
| ( in @ sk3 @ sk2 )
| A ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(45,plain,
! [A: $o] :
( ( in @ sk3 @ sk1 )
| ( in @ sk3 @ sk2 )
| A ),
inference(simp,[status(thm)],[33]) ).
thf(9,plain,
~ ( in @ sk3 @ sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(56,plain,
! [A: $o] :
( $false
| $false
| A ),
inference(rewrite,[status(thm)],[45,7,9]) ).
thf(57,plain,
! [A: $o] : A,
inference(simp,[status(thm)],[56]) ).
thf(60,plain,
~ $true,
inference(rewrite,[status(thm)],[7,57]) ).
thf(61,plain,
$false,
inference(simp,[status(thm)],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU586^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.11/0.21 % Computer : n005.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 13:52:31 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (185ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 2.03/1.40 % [INFO] eprover registered as external prover.
% 2.03/1.41 % [INFO] Scanning for conjecture ...
% 2.23/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.55 % [INFO] Type checking passed.
% 2.23/1.55 % [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 ...
% 4.10/2.37 % [INFO] Killing All external provers ...
% 4.10/2.37 % Time passed: 2014ms (effective reasoning time: 1372ms)
% 4.10/2.37 % 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)>
% 4.10/2.37 % Axioms used in derivation (0):
% 4.10/2.37 % No. of inferences in proof: 17
% 4.10/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2014 ms resp. 1372 ms w/o parsing
% 4.43/2.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.43/2.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------