%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO518^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n009.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 08:46:03 AM UTC 2026
% Result : Theorem 4.30s 2.56s
% Output : Refutation 4.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 45 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 45 ( 13 ~; 2 |; 8 &; 18 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 ^; 12 !; 3 ?; 29 :)
% ( 0 !>; 0 ?*; 0 @-; 14 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ( @+[B: $i] : ( B = A ) )
!= A ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( @+[B: $i] : ( B = A ) )
!= A ) ) ) ).
thf(1,conjecture,
? [A: $o > $i > $i > $i] :
! [B: $i,C: $i] :
( ( ( A @ $true @ B @ C )
= B )
& ( ( A @ $false @ B @ C )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifi) ).
thf(2,negated_conjecture,
~ ? [A: $o > $i > $i > $i] :
! [B: $i,C: $i] :
( ( ( A @ $true @ B @ C )
= B )
& ( ( A @ $false @ B @ C )
= C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: $o > $i > $i > $i] :
! [B: $i,C: $i] :
( ( ( A @ $true @ B @ C )
= B )
& ( ( A @ $false @ B @ C )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: $i,B: $i] :
( ( ( @+[C: $i] :
( ( $true
=> ( C = A ) )
& ( ~ $true
=> ( C = B ) ) ) )
= A )
& ( ( @+[C: $i] :
( ( $false
=> ( C = A ) )
& ( ~ $false
=> ( C = B ) ) ) )
= B ) ),
inference(instance,[status(thm)],[3]) ).
thf(5,plain,
~ ! [A: $i,B: $i] :
( ( ( @+[C: $i] : ( C = A ) )
= A )
& ( ( @+[C: $i] : ( C = B ) )
= B ) ),
inference(simp,[status(thm)],[4]) ).
thf(6,plain,
~ ( ! [A: $i] :
( ( @+[B: $i] : ( B = A ) )
= A )
& ! [A: $i] :
( ( @+[B: $i] : ( B = A ) )
= A ) ),
inference(miniscope,[status(thm)],[5]) ).
thf(7,plain,
( ( ( @+[A: $i] : ( A = sk1 ) )
!= sk1 )
| ( ( @+[A: $i] : ( A = sk2 ) )
!= sk2 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(10,plain,
( ( ( @+[A: $i] : ( A = sk1 ) )
!= sk1 )
| ( ( @+[A: $i] : ( A = sk2 ) )
!= sk2 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[3,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO518^1 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.09/0.20 % Computer : n009.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:12:30 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 1.02/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/1.09 % [INFO] Parsing done (189ms).
% 1.42/1.10 % [INFO] Running in sequential loop mode.
% 2.11/1.56 % [INFO] eprover registered as external prover.
% 2.11/1.57 % [INFO] Scanning for conjecture ...
% 2.33/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.50/1.70 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.50/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 2.50/1.71 % [INFO] Type checking passed.
% 2.50/1.71 % [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 ...
% 4.30/2.56 % External prover 'e' found a proof!
% 4.30/2.56 % [INFO] Killing All external provers ...
% 4.30/2.56 % Time passed: 2207ms (effective reasoning time: 1449ms)
% 4.30/2.56 % 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)>
% 4.30/2.56 % Axioms used in derivation (0):
% 4.30/2.56 % No. of inferences in proof: 9
% 4.30/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2207 ms resp. 1449 ms w/o parsing
% 4.61/2.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.61/2.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------