%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO535^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n018.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 5.00s 2.60s
% Output : Refutation 5.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 3 ( 2 equ; 0 cnn)
% Maximal formula atoms : 1 ( 0 avg)
% Number of connectives : 51 ( 2 ~; 0 |; 0 &; 42 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 25 ( 5 ^; 7 !; 13 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(eps_decl,type,
eps: ( $i > $o ) > $i ).
thf(epsii_decl,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(epsa_decl,type,
epsa: ( $i > ( $i > $i ) > $o ) > $i ).
thf(epsb_decl,type,
epsb: ( $i > ( $i > $i ) > $o ) > $i > $i ).
thf(epsa_def,definition,
( epsa
= ( ^ [A: $i > ( $i > $i ) > $o] :
( eps
@ ^ [B: $i] :
? [C: $i > $i] : ( A @ B @ C ) ) ) ) ).
thf(epsb_def,definition,
( epsb
= ( ^ [A: $i > ( $i > $i ) > $o] : ( epsii @ ( A @ ( epsa @ A ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > ( $i > $i ) > $o] :
( ? [B: $i,C: $i > $i] : ( A @ B @ C )
=> ( A @ ( epsa @ A ) @ ( epsb @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > ( $i > $i ) > $o] :
( ? [B: $i,C: $i > $i] : ( A @ B @ C )
=> ( A @ ( epsa @ A ) @ ( epsb @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i > ( $i > $i ) > $o] :
( ? [B: $i,C: $i > $i] : ( A @ B @ C )
=> ( A
@ ( eps
@ ^ [B: $i] :
? [C: $i > $i] : ( A @ B @ C ) )
@ ( epsii
@ ( A
@ ( eps
@ ^ [B: $i] :
? [C: $i > $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/sandbox/benchmark/theBenchmark.p',choiceax) ).
thf(9,plain,
! [A: $i > $o] :
( ? [B: $i] : ( A @ B )
=> ( A @ ( eps @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: ( $i > $i ) > $o] :
( ? [B: $i > $i] : ( A @ B )
=> ( A @ ( epsii @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceaxii) ).
thf(11,plain,
! [A: ( $i > $i ) > $o] :
( ? [B: $i > $i] : ( A @ B )
=> ( A @ ( epsii @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[5,9,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO535^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.11/0.28 % Computer : n018.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 17:15:41 UTC 2026
% 0.25/0.29 % CPUTime :
% 0.25/0.29 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
% 1.24/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.72/1.15 % [INFO] Parsing done (238ms).
% 1.72/1.17 % [INFO] Running in sequential loop mode.
% 2.46/1.62 % [INFO] eprover registered as external prover.
% 2.46/1.63 % [INFO] Scanning for conjecture ...
% 2.64/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.64/1.78 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.64/1.78 % [INFO] Problem is higher-order (TPTP THF).
% 2.64/1.79 % [INFO] Type checking passed.
% 2.64/1.79 % [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 ...
% 4.51/2.60 % External prover 'e' found a proof!
% 4.51/2.60 % [INFO] Killing All external provers ...
% 4.51/2.60 % Time passed: 2133ms (effective reasoning time: 1423ms)
% 4.51/2.60 % 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)>
% 4.51/2.60 % Axioms used in derivation (2): choiceax, choiceaxii
% 4.51/2.60 % No. of inferences in proof: 8
% 5.00/2.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2133 ms resp. 1423 ms w/o parsing
% 5.00/2.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.00/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------