%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO534^1 : 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 3.86s 2.14s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 9 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 4 ( 3 equ; 0 cnn)
% Maximal formula atoms : 1 ( 0 avg)
% Number of connectives : 78 ( 2 ~; 0 |; 0 &; 71 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 11 ^; 5 !; 24 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(eps_decl,type,
eps: ( $i > $o ) > $i ).
thf(epsa_decl,type,
epsa: ( $i > $i > $i > $o ) > $i ).
thf(epsb_decl,type,
epsb: ( $i > $i > $i > $o ) > $i ).
thf(epsc_decl,type,
epsc: ( $i > $i > $i > $o ) > $i ).
thf(epsa_def,definition,
( epsa
= ( ^ [A: $i > $i > $i > $o] :
( eps
@ ^ [B: $i] :
? [C: $i,D: $i] : ( A @ B @ C @ D ) ) ) ) ).
thf(epsb_def,definition,
( epsb
= ( ^ [A: $i > $i > $i > $o] :
( eps
@ ^ [B: $i] :
? [C: $i] : ( A @ ( epsa @ A ) @ B @ C ) ) ) ) ).
thf(epsc_def,definition,
( epsc
= ( ^ [A: $i > $i > $i > $o] : ( eps @ ( A @ ( epsa @ A ) @ ( epsb @ A ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $i > $o] :
( ? [B: $i,C: $i,D: $i] : ( A @ B @ C @ D )
=> ( A @ ( epsa @ A ) @ ( epsb @ A ) @ ( epsc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $i > $o] :
( ? [B: $i,C: $i,D: $i] : ( A @ B @ C @ D )
=> ( A @ ( epsa @ A ) @ ( epsb @ A ) @ ( epsc @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i > $i > $i > $o] :
( ? [B: $i,C: $i,D: $i] : ( A @ B @ C @ D )
=> ( A
@ ( eps
@ ^ [B: $i] :
? [C: $i,D: $i] : ( A @ B @ C @ D ) )
@ ( eps
@ ^ [B: $i] :
? [C: $i] :
( A
@ ( eps
@ ^ [D: $i] :
? [E: $i,F: $i] : ( A @ D @ E @ F ) )
@ B
@ C ) )
@ ( eps
@ ( A
@ ( eps
@ ^ [B: $i] :
? [C: $i,D: $i] : ( A @ B @ C @ D ) )
@ ( eps
@ ^ [B: $i] :
? [C: $i] :
( A
@ ( eps
@ ^ [D: $i] :
? [E: $i,F: $i] : ( A @ D @ E @ F ) )
@ 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(8,plain,
! [A: $i > $o] :
( ? [B: $i] : ( A @ B )
=> ( A @ ( eps @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
$false,
inference(e,[status(thm)],[4,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO534^1 : 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
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:13:15 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/0.97 % [INFO] Parsing done (192ms).
% 1.27/0.99 % [INFO] Running in sequential loop mode.
% 1.95/1.38 % [INFO] eprover registered as external prover.
% 1.95/1.39 % [INFO] Scanning for conjecture ...
% 2.33/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.33/1.54 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.33/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.33/1.55 % [INFO] Type checking passed.
% 2.33/1.55 % [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 ...
% 3.86/2.13 % External prover 'e' found a proof!
% 3.86/2.13 % [INFO] Killing All external provers ...
% 3.86/2.13 % Time passed: 1805ms (effective reasoning time: 1141ms)
% 3.86/2.13 % 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)>
% 3.86/2.14 % Axioms used in derivation (1): choiceax
% 3.86/2.14 % No. of inferences in proof: 6
% 3.86/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1805 ms resp. 1141 ms w/o parsing
% 3.86/2.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.86/2.19 % [INFO] Killing All external provers ...
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