%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO530^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n026.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 08:46:04 AM UTC 2026
% Result : Theorem 3.67s 2.18s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 3 ( 2 equ; 0 cnn)
% Maximal formula atoms : 1 ( 0 avg)
% Number of connectives : 43 ( 2 ~; 0 |; 0 &; 36 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 21 ( 5 ^; 5 !; 11 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(eps_decl,type,
eps: ( $i > $o ) > $i ).
thf(epsa_decl,type,
epsa: ( $i > $i > $o ) > $i ).
thf(epsb_decl,type,
epsb: ( $i > $i > $o ) > $i ).
thf(epsa_def,definition,
( epsa
= ( ^ [A: $i > $i > $o] :
( eps
@ ^ [B: $i] :
? [C: $i] : ( A @ B @ C ) ) ) ) ).
thf(epsb_def,definition,
( epsb
= ( ^ [A: $i > $i > $o] : ( eps @ ( A @ ( epsa @ A ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ? [B: $i,C: $i] : ( A @ B @ C )
=> ( A @ ( epsa @ A ) @ ( epsb @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ? [B: $i,C: $i] : ( A @ B @ C )
=> ( A @ ( epsa @ A ) @ ( epsb @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i > $i > $o] :
( ? [B: $i,C: $i] : ( A @ B @ C )
=> ( A
@ ( eps
@ ^ [B: $i] :
? [C: $i] : ( A @ B @ C ) )
@ ( eps
@ ( A
@ ( eps
@ ^ [B: $i] :
? [C: $i] : ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i > $o] :
( ? [B: $i] : ( A @ B )
=> ( A @ ( eps @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax) ).
thf(8,plain,
! [A: $i > $o] :
( ? [B: $i] : ( A @ B )
=> ( A @ ( eps @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[4,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO530^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.10/0.22 % Computer : n026.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 17:15:42 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (185ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 2.03/1.42 % [INFO] eprover registered as external prover.
% 2.03/1.43 % [INFO] Scanning for conjecture ...
% 2.22/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.22/1.57 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.22/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.58 % [INFO] Type checking passed.
% 2.22/1.58 % [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 ...
% 3.67/2.18 % External prover 'e' found a proof!
% 3.67/2.18 % [INFO] Killing All external provers ...
% 3.67/2.18 % Time passed: 1817ms (effective reasoning time: 1171ms)
% 3.67/2.18 % 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)>
% 3.67/2.18 % Axioms used in derivation (1): choiceax
% 3.67/2.18 % No. of inferences in proof: 6
% 3.67/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1817 ms resp. 1171 ms w/o parsing
% 3.87/2.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.87/2.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------