%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU506_8 : TPTP v9.3.1. Released v8.0.0.
% 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 : Sun Sep 27 08:39:10 AM UTC 2026
% Result : Theorem 4.99s 2.97s
% Output : Refutation 4.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 18 unt; 0 typ; 3 def)
% Number of atoms : 98 ( 29 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 210 ( 31 ~; 16 |; 6 &; 122 @)
% ( 0 <=>; 35 =>; 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 : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 57 ( 4 ^; 48 !; 2 ?; 57 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(setext_decl,type,
setext: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ~ ? [B: $i] : ( A @ ( B @ in ) )
=> ( A = emptyset ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ) ).
thf(1,conjecture,
( emptysetE
=> ( setext
=> ! [A: $i] :
( ! [B: $i] :
~ ( A @ ( B @ in ) )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( setext
=> ! [A: $i] :
( ! [B: $i] :
~ ( A @ ( B @ in ) )
=> ( A = emptyset ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( emptysetE
=> ( setext
=> ! [A: $i] :
( ! [B: $i] :
~ ( A @ ( B @ in ) )
=> ( A = emptyset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( emptysetE
=> ( setext
=> ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ in ) )
=> ( A = emptyset ) ) ) ),
inference(miniscope,[status(thm)],[5]) ).
thf(7,plain,
! [A: $i] :
( ( sk1 != emptyset )
& ~ ( sk1 @ ( A @ in ) )
& setext
& emptysetE ),
inference(cnf,[status(esa)],[6]) ).
thf(10,plain,
! [A: $i] :
~ ( sk1 @ ( A @ in ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(3,axiom,
( setext
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(13,plain,
( setext
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
( setext
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
=> ( A = B ) ) ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(9,plain,
setext,
inference(cnfConj,[status(thm)],[7]) ).
thf(44,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
=> ( A = B ) ) ),
inference(rewrite,[status(thm)],[14,9]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( ( A = B )
| ~ ( A @ ( A @ ( B @ sk3 ) @ in ) )
| ~ ( B @ ( A @ ( B @ sk2 ) @ in ) ) )
& ( ( A = B )
| ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ~ ( B @ ( A @ ( B @ sk2 ) @ in ) ) )
& ( ( A = B )
| ~ ( A @ ( A @ ( B @ sk3 ) @ in ) )
| ( A @ ( A @ ( B @ sk2 ) @ in ) ) )
& ( ( A = B )
| ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( A @ ( A @ ( B @ sk2 ) @ in ) ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk3 ) @ in ) )
| ~ ( B @ ( A @ ( B @ sk2 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk3 ) @ in ) )
| ~ ( B @ ( A @ ( B @ sk2 ) @ in ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(4,axiom,
( emptysetE
= ( ! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(15,plain,
( emptysetE
= ( ! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
( emptysetE
= ( ! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(8,plain,
emptysetE,
inference(cnfConj,[status(thm)],[7]) ).
thf(17,plain,
! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ),
inference(rewrite,[status(thm)],[16,8]) ).
thf(18,plain,
! [B: $o,A: $i] :
( B
| ~ ( emptyset @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [C: $i,B: $o,A: $i] :
( ( B
!= ( sk1 @ ( C @ in ) ) )
| ~ $true
| ~ ( emptyset @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[18,10]) ).
thf(20,plain,
! [C: $i,B: $o,A: $i] :
( ( B
!= ( sk1 @ ( C @ in ) ) )
| ~ ( emptyset @ ( A @ in ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(21,plain,
! [A: $i] :
~ ( emptyset @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ( D @ in ) )),bind(C,$thf( D ))]]) ).
thf(11,plain,
sk1 != emptyset,
inference(cnfConj,[status(thm)],[7]) ).
thf(12,plain,
sk1 != emptyset,
inference(lifteq,[status(thm)],[11]) ).
thf(154,plain,
$false,
inference(e,[status(thm)],[5,10,57,21,9,13,12,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU506_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % 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
% 0.15/0.53 % Computer : n005.cluster.edu
% 0.15/0.53 % Model : x86_64 x86_64
% 0.15/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.53 % Memory : 8046.5625MB
% 0.15/0.53 % OS : Linux 6.8.0-71-generic
% 0.15/0.53 % CPULimit : 300
% 0.15/0.53 % WCLimit : 300
% 0.15/0.53 % DateTime : Sat Sep 26 10:07:17 UTC 2026
% 0.15/0.53 % CPUTime :
% 0.15/0.53 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
% 0.85/1.12 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/1.29 % [INFO] Parsing done (172ms).
% 1.33/1.31 % [INFO] Running in sequential loop mode.
% 1.94/1.71 % [INFO] eprover registered as external prover.
% 1.94/1.72 % [INFO] Scanning for conjecture ...
% 1.94/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.12/1.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.12/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.12/1.87 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.12/1.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.12/1.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.12/1.88 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.12/1.88 % [INFO] Type checking passed.
% 2.12/1.89 % [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 ...
% 4.99/2.96 % External prover 'e' found a proof!
% 4.99/2.96 % [INFO] Killing All external provers ...
% 4.99/2.96 % Time passed: 2290ms (effective reasoning time: 1650ms)
% 4.99/2.96 % 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)>
% 4.99/2.97 % Axioms used in derivation (2): setext, emptysetE
% 4.99/2.97 % No. of inferences in proof: 26
% 4.99/2.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2290 ms resp. 1650 ms w/o parsing
% 4.99/3.02 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.99/3.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------