%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET063^5 : 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 : n010.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 08:22:53 AM UTC 2026
% Result : Theorem 2.64s 1.32s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 29 ( 10 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 28 ( 13 ~; 0 |; 1 &; 7 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% Number of variables : 22 ( 10 ^; 9 !; 2 ?; 22 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ( ~ ? [B: a] : ( A @ B )
=> ( A
= ( ^ [B: a] : $false ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> $false )
=> ( A
= ( ^ [B: a] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_30_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> $false )
=> ( A
= ( ^ [B: a] : $false ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o] :
( ! [B: a] :
~ ( A @ B )
=> ( A
= ( ^ [B: a] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: a > $o] :
( ~ ? [B: a] : ( A @ B )
=> ( A
= ( ^ [B: a] : $false ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [A: a] :
( ~ ( sk1 @ A )
& ( sk1
!= ( ^ [B: a] : $false ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
( sk1
!= ( ^ [A: a] : $false ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
( sk1
!= ( ^ [A: a] : $false ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(6,plain,
! [A: a] :
~ ( sk1 @ A ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) ),
inference(rewrite,[status(thm)],[8,6]) ).
thf(11,plain,
$false,
inference(simp,[status(thm)],[10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET063^5 : 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
% 0.11/0.21 % Computer : n010.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 13:36:48 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.65/0.51 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.87/0.60 % [INFO] Parsing done (91ms).
% 0.87/0.61 % [INFO] Running in sequential loop mode.
% 1.15/0.79 % [INFO] eprover registered as external prover.
% 1.37/0.80 % [INFO] Scanning for conjecture ...
% 1.37/0.84 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.37/0.85 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.37/0.85 % [INFO] Problem is higher-order (TPTP THF).
% 1.37/0.86 % [INFO] Type checking passed.
% 1.37/0.86 % [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 ...
% 2.64/1.31 % [INFO] Killing All external provers ...
% 2.64/1.31 % Time passed: 1014ms (effective reasoning time: 702ms)
% 2.64/1.31 % 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)>
% 2.64/1.31 % Axioms used in derivation (0):
% 2.64/1.31 % No. of inferences in proof: 10
% 2.64/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1014 ms resp. 702 ms w/o parsing
% 2.64/1.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.64/1.36 % [INFO] Killing All external provers ...
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