%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO537^1 : 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 : n014.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 3.84s 2.24s
% Output : Refutation 3.84s
% 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 : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 21 ( 5 ^; 5 !; 11 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(epsii_decl,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(epsa_decl,type,
epsa: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
thf(epsb_decl,type,
epsb: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
thf(epsa_def,definition,
( epsa
= ( ^ [A: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [B: $i > $i] :
? [C: $i > $i] : ( A @ B @ C ) ) ) ) ).
thf(epsb_def,definition,
( epsb
= ( ^ [A: ( $i > $i ) > ( $i > $i ) > $o] : ( epsii @ ( A @ ( epsa @ A ) ) ) ) ) ).
thf(1,conjecture,
! [A: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [B: $i > $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 > $i ) > $o] :
( ? [B: $i > $i,C: $i > $i] : ( A @ B @ C )
=> ( A @ ( epsa @ A ) @ ( epsb @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [B: $i > $i,C: $i > $i] : ( A @ B @ C )
=> ( A
@ ( epsii
@ ^ [B: $i > $i] :
? [C: $i > $i] : ( A @ B @ C ) )
@ ( epsii
@ ( A
@ ( epsii
@ ^ [B: $i > $i] :
? [C: $i > $i] : ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: ( $i > $i ) > $o] :
( ? [B: $i > $i] : ( A @ B )
=> ( A @ ( epsii @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceaxii) ).
thf(8,plain,
! [A: ( $i > $i ) > $o] :
( ? [B: $i > $i] : ( A @ B )
=> ( A @ ( epsii @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
$false,
inference(e,[status(thm)],[4,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO537^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n014.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:13:30 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.98 % [INFO] Parsing done (191ms).
% 1.21/1.00 % [INFO] Running in sequential loop mode.
% 1.81/1.39 % [INFO] eprover registered as external prover.
% 2.02/1.40 % [INFO] Scanning for conjecture ...
% 2.20/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.20/1.54 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.20/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.55 % [INFO] Type checking passed.
% 2.20/1.56 % [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 ...
% 3.84/2.24 % External prover 'e' found a proof!
% 3.84/2.24 % [INFO] Killing All external provers ...
% 3.84/2.24 % Time passed: 1895ms (effective reasoning time: 1233ms)
% 3.84/2.24 % 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)>
% 3.84/2.24 % Axioms used in derivation (1): choiceaxii
% 3.84/2.24 % No. of inferences in proof: 6
% 3.84/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1895 ms resp. 1233 ms w/o parsing
% 3.84/2.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.84/2.29 % [INFO] Killing All external provers ...
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