%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU633_8 : TPTP v9.3.1. Released v8.0.0.
% 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 : n007.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 08:39:45 AM UTC 2026
% Result : Theorem 3.35s 1.64s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 77 ( 12 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 216 ( 28 ~; 18 |; 9 &; 135 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 46 ( 3 ^; 35 !; 5 ?; 46 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(setunionE_decl,type,
setunionE: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $o > $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( A @ setunion @ ( B @ in ) )
=> ? [C: $i] :
( ( C @ ( B @ in ) )
& ( A @ ( C @ in ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 @ setunion @ ( A @ in ) )
=> ? [B: $i] :
( ( B @ ( A @ in ) )
& ( sk1 @ ( B @ in ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $o,B: $i,C: $i] :
@+[D: $i] :
~ ( ( D @ ( B @ in ) )
=> ( ( C @ ( D @ in ) )
=> A ) ) ) ) ).
thf(1,conjecture,
( setunionE
=> ! [A: $i,B: $i] :
( ( A @ setunion @ ( B @ in ) )
=> ? [C: $i] :
( ( C @ ( B @ in ) )
& ( A @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(2,negated_conjecture,
~ ( setunionE
=> ! [A: $i,B: $i] :
( ( A @ setunion @ ( B @ in ) )
=> ? [C: $i] :
( ( C @ ( B @ in ) )
& ( A @ ( C @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( setunionE
=> ! [A: $i,B: $i] :
( ( A @ setunion @ ( B @ in ) )
=> ? [C: $i] :
( ( C @ ( B @ in ) )
& ( A @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [A: $i] :
( ( ~ ( A @ ( sk2 @ in ) )
| ~ ( sk1 @ ( A @ in ) ) )
& ( sk1 @ setunion @ ( sk2 @ in ) )
& setunionE ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
sk1 @ setunion @ ( sk2 @ in ),
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ in ) )
| ~ ( sk1 @ ( A @ in ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(18,plain,
! [A: $i] :
( ( ( sk1 @ setunion @ ( sk2 @ in ) )
!= ( A @ ( sk2 @ in ) ) )
| ~ $true
| ~ ( sk1 @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(19,plain,
! [A: $i] :
( ( ( sk1 @ setunion @ ( sk2 @ in ) )
!= ( A @ ( sk2 @ in ) ) )
| ~ ( sk1 @ ( A @ in ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(20,plain,
~ ( sk1 @ ( sk1 @ setunion @ in ) ),
inference(pattern_uni,[status(thm)],[19:[bind(A,$thf( sk1 @ setunion ))]]) ).
thf(6,plain,
setunionE,
inference(cnfConj,[status(thm)],[5]) ).
thf(3,axiom,
( setunionE
= ( ! [A: $i,B: $i] :
( ( A @ setunion @ ( B @ in ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( D @ ( B @ in ) )
=> ( ( A @ ( D @ in ) )
=> C ) )
=> C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(9,plain,
( setunionE
= ( ! [A: $i,B: $i] :
( ( A @ setunion @ ( B @ in ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( D @ ( B @ in ) )
=> ( ( A @ ( D @ in ) )
=> C ) )
=> C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
( setunionE
= ( ! [A: $i,B: $i] :
( ( A @ setunion @ ( B @ in ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( D @ ( B @ in ) )
=> ( ( A @ ( D @ in ) )
=> C ) )
=> C ) ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(11,plain,
! [A: $i,B: $i] :
( ( A @ setunion @ ( B @ in ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( D @ ( B @ in ) )
=> ( ( A @ ( D @ in ) )
=> C ) )
=> C ) ),
inference(rewrite,[status(thm)],[10,6]) ).
thf(12,plain,
! [C: $o,B: $i,A: $i] :
( ( C
| ~ C
| ~ ( A @ setunion @ ( B @ in ) ) )
& ( C
| ( A @ ( A @ ( B @ ( C @ sk3 ) ) @ in ) )
| ~ ( A @ setunion @ ( B @ in ) ) )
& ( C
| ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ in ) )
| ~ ( A @ setunion @ ( B @ in ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [C: $o,B: $i,A: $i] :
( C
| ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ in ) )
| ~ ( A @ setunion @ ( B @ in ) ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(21,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk2 @ in ) )
!= ( sk1 @ ( A @ in ) ) )
| ~ ( sk1 @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(24,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 != A )
| ~ ( sk1 @ ( A @ in ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(26,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(132,plain,
$false,
inference(e,[status(thm)],[20,6,9,13,7,26,8,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU633_8 : TPTP v9.3.1. Released v8.0.0.
% 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
% 0.14/0.40 % Computer : n007.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 10:12:39 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.70/0.71 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.93/0.81 % [INFO] Parsing done (93ms).
% 0.93/0.81 % [INFO] Running in sequential loop mode.
% 1.11/1.01 % [INFO] eprover registered as external prover.
% 1.11/1.01 % [INFO] Scanning for conjecture ...
% 1.41/1.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.41/1.07 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.41/1.10 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.41/1.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.41/1.10 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.41/1.10 % [INFO] Type checking passed.
% 1.41/1.10 % [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 ...
% 3.35/1.63 % External prover 'e' found a proof!
% 3.35/1.63 % [INFO] Killing All external provers ...
% 3.35/1.63 % Time passed: 1138ms (effective reasoning time: 819ms)
% 3.35/1.63 % 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)>
% 3.35/1.64 % Axioms used in derivation (1): setunionE
% 3.35/1.64 % No. of inferences in proof: 20
% 3.35/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1138 ms resp. 819 ms w/o parsing
% 3.35/1.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.35/1.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------