%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO538^1 : 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 08:46:05 AM UTC 2026
% Result : Theorem 4.34s 2.52s
% Output : Refutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 7 ( 2 unt; 0 typ; 1 def)
% Number of atoms : 16 ( 11 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 32 ( 3 ~; 1 |; 5 &; 21 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-3 aty)
% Number of variables : 16 ( 6 ^; 8 !; 2 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(eps_decl,type,
eps: ( $i > $o ) > $i ).
thf(if_decl,type,
if: $o > $i > $i > $i ).
thf(if_def,definition,
( if
= ( ^ [A: $o,B: $i,C: $i] :
( eps
@ ^ [D: $i] :
( ( A
& ( D = B ) )
| ( ~ A
& ( D = C ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( if @ $true @ A @ B )
= A )
& ( ( if @ $false @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( if @ $true @ A @ B )
= A )
& ( ( if @ $false @ A @ B )
= B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i,B: $i] :
( ( ( eps
@ ^ [C: $i] : ( C = A ) )
= A )
& ( ( eps
@ ^ [C: $i] : ( C = B ) )
= B ) ),
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(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 : SYO538^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.09 % 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
% 0.10/0.25 % Computer : n018.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 17:15:56 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.26 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
% 1.14/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/1.22 % [INFO] Parsing done (239ms).
% 1.64/1.24 % [INFO] Running in sequential loop mode.
% 2.24/1.69 % [INFO] eprover registered as external prover.
% 2.24/1.70 % [INFO] Scanning for conjecture ...
% 2.67/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.67/1.84 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.67/1.85 % [INFO] Problem is higher-order (TPTP THF).
% 2.67/1.85 % [INFO] Type checking passed.
% 2.67/1.86 % [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 ...
% 4.34/2.51 % External prover 'e' found a proof!
% 4.34/2.52 % [INFO] Killing All external provers ...
% 4.34/2.52 % Time passed: 2046ms (effective reasoning time: 1275ms)
% 4.34/2.52 % 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)>
% 4.34/2.52 % Axioms used in derivation (1): choiceax
% 4.34/2.52 % No. of inferences in proof: 6
% 4.34/2.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2046 ms resp. 1275 ms w/o parsing
% 4.34/2.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.34/2.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------