%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET600^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n001.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 08:22:59 AM UTC 2026
% Result : Theorem 3.75s 2.27s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 139 ( 49 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 100 ( 20 ~; 27 |; 12 &; 41 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 53 ^; 17 !; 0 ?; 72 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ( A
= ( ^ [C: a] : $false ) )
& ( B
= ( ^ [C: a] : $false ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
| ( A @ B ) ) )
= ( ^ [B: a] : $false ) )
!= ( ( sk1
= ( ^ [B: a] : $false ) )
& ( A
= ( ^ [B: a] : $false ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ( A
= ( ^ [C: a] : $false ) )
& ( B
= ( ^ [C: a] : $false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_59_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ( A
= ( ^ [C: a] : $false ) )
& ( B
= ( ^ [C: a] : $false ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ( A
= ( ^ [C: a] : $false ) )
& ( B
= ( ^ [C: a] : $false ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
| ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
!= ( ( sk1
= ( ^ [A: a] : $false ) )
& ( sk2
= ( ^ [A: a] : $false ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ( sk1
= ( ^ [A: a] : $false ) )
& ( sk2
= ( ^ [A: a] : $false ) ) )
!= ( ( ^ [A: a] :
( ( sk1 @ A )
| ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk1
= ( ^ [A: a] : $false ) )
& ( sk2
= ( ^ [A: a] : $false ) ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
| ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
| ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ( ( sk1
= ( ^ [A: a] : $false ) )
& ( sk2
= ( ^ [A: a] : $false ) ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(12,plain,
( ( ( ( ^ [A: a] :
( ( sk1 @ A )
| ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ( sk1
= ( ^ [A: a] : $false ) ) )
& ( ( ( ^ [A: a] :
( ( sk1 @ A )
| ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ( sk2
= ( ^ [A: a] : $false ) ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(13,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
| ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ( sk1
= ( ^ [A: a] : $false ) ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(15,plain,
( ( sk1
= ( ^ [A: a] : $false ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
| ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(17,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ~ ( ( sk1 @ B )
| ( sk2 @ B ) ) ),
inference(func_ext,[status(esa)],[15]) ).
thf(18,plain,
! [B: a,A: a] :
( ( ~ ( sk1 @ A )
| ~ ( sk1 @ B ) )
& ( ~ ( sk1 @ A )
| ~ ( sk2 @ B ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk1 @ B ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(31,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( ( sk1 @ B )
!= ( sk1 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(32,plain,
! [A: a] :
~ ( sk1 @ A ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( B ))]]) ).
thf(33,plain,
! [A: a] :
~ ( sk1 @ A ),
inference(simp,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ( ^ [A: a] : $false )
= ( ^ [A: a] : $false ) )
& ( sk2
= ( ^ [A: a] : $false ) ) )
!= ( ( ^ [A: a] :
( $false
| ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(rewrite,[status(thm)],[5,33]) ).
thf(37,plain,
$false,
inference(simp,[status(thm)],[36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET600^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.13/0.22 % Computer : n001.cluster.edu
% 0.13/0.22 % Model : x86_64 x86_64
% 0.13/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.22 % Memory : 8046.5625MB
% 0.13/0.22 % OS : Linux 6.8.0-71-generic
% 0.13/0.22 % CPULimit : 300
% 0.13/0.22 % WCLimit : 300
% 0.13/0.22 % DateTime : Tue Sep 29 13:44:05 UTC 2026
% 0.13/0.22 % CPUTime :
% 0.13/0.22 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (185ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 2.01/1.40 % [INFO] eprover registered as external prover.
% 2.01/1.41 % [INFO] Scanning for conjecture ...
% 2.20/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.20/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.20/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.54 % [INFO] Type checking passed.
% 2.20/1.55 % [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 ...
% 3.75/2.26 % [INFO] Killing All external provers ...
% 3.75/2.27 % Time passed: 1901ms (effective reasoning time: 1261ms)
% 3.75/2.27 % 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)>
% 3.75/2.27 % Axioms used in derivation (0):
% 3.75/2.27 % No. of inferences in proof: 18
% 3.75/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1901 ms resp. 1261 ms w/o parsing
% 3.98/2.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.98/2.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------