%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO248^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n007.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 08:45:28 AM UTC 2026
% Result : Theorem 4.35s 2.34s
% Output : Refutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 96 equ; 0 cnn)
% Maximal formula atoms : 32 ( 24 avg)
% Number of connectives : 323 ( 38 ~; 15 |; 57 &; 192 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 13 con; 0-2 aty)
% Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
thf(hh_decl,type,
hh: $i ).
thf(h_decl,type,
h: $i ).
thf(ee_decl,type,
ee: $i ).
thf(e_decl,type,
e: $i ).
thf(dd_decl,type,
dd: $i ).
thf(d_decl,type,
d: $i ).
thf(cc_decl,type,
cc: $i ).
thf(c_decl,type,
c: $i ).
thf(bb_decl,type,
bb: $i ).
thf(b_decl,type,
b: $i ).
thf(aa_decl,type,
aa: $i ).
thf(a_decl,type,
a: $i ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( ( ( ( ( A @ a )
= ( A @ aa ) )
& ( ( A @ b )
= ( A @ bb ) )
& ( ( A @ e )
= ( A @ hh ) ) )
=> ( ( A @ c )
= ( A @ dd ) ) )
& ( ( ( ( A @ a )
= ( A @ aa ) )
& ( ( A @ h )
= ( A @ hh ) )
& ( ( A @ b )
= ( A @ cc ) ) )
=> ( ( A @ d )
!= ( A @ ee ) ) )
& ( ( ( ( A @ c )
= ( A @ cc ) )
& ( ( A @ cc )
= ( A @ d ) )
& ( ( A @ d )
= ( A @ dd ) )
& ( ( A @ a )
!= ( A @ bb ) ) )
=> ( ( A @ e )
!= ( A @ hh ) ) )
& ( ( ( ( A @ a )
= ( A @ aa ) )
& ( ( A @ d )
= ( A @ dd ) )
& ( ( A @ b )
!= ( A @ cc ) ) )
=> ( ( A @ e )
= ( A @ hh ) ) )
& ( ( ( ( A @ e )
= ( A @ ee ) )
& ( ( A @ h )
= ( A @ hh ) )
& ( ( A @ c )
= ( A @ dd ) ) )
=> ( ( A @ a )
!= ( A @ bb ) ) )
& ( ( ( ( A @ b )
= ( A @ bb ) )
& ( ( A @ bb )
= ( A @ c ) )
& ( ( A @ c )
= ( A @ cc ) )
& ( ( A @ e )
!= ( A @ hh ) ) )
=> ( ( A @ d )
= ( A @ ee ) ) ) )
=> ( ( ( A @ a )
!= ( A @ aa ) )
| ( ( A @ b )
!= ( A @ bb ) )
| ( ( A @ c )
!= ( A @ cc ) )
| ( ( A @ d )
!= ( A @ dd ) )
| ( ( A @ e )
!= ( A @ ee ) )
| ( ( A @ h )
!= ( A @ hh ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSIXFRIENDS_AGAIN) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( ( ( ( ( A @ a )
= ( A @ aa ) )
& ( ( A @ b )
= ( A @ bb ) )
& ( ( A @ e )
= ( A @ hh ) ) )
=> ( ( A @ c )
= ( A @ dd ) ) )
& ( ( ( ( A @ a )
= ( A @ aa ) )
& ( ( A @ h )
= ( A @ hh ) )
& ( ( A @ b )
= ( A @ cc ) ) )
=> ( ( A @ d )
!= ( A @ ee ) ) )
& ( ( ( ( A @ c )
= ( A @ cc ) )
& ( ( A @ cc )
= ( A @ d ) )
& ( ( A @ d )
= ( A @ dd ) )
& ( ( A @ a )
!= ( A @ bb ) ) )
=> ( ( A @ e )
!= ( A @ hh ) ) )
& ( ( ( ( A @ a )
= ( A @ aa ) )
& ( ( A @ d )
= ( A @ dd ) )
& ( ( A @ b )
!= ( A @ cc ) ) )
=> ( ( A @ e )
= ( A @ hh ) ) )
& ( ( ( ( A @ e )
= ( A @ ee ) )
& ( ( A @ h )
= ( A @ hh ) )
& ( ( A @ c )
= ( A @ dd ) ) )
=> ( ( A @ a )
!= ( A @ bb ) ) )
& ( ( ( ( A @ b )
= ( A @ bb ) )
& ( ( A @ bb )
= ( A @ c ) )
& ( ( A @ c )
= ( A @ cc ) )
& ( ( A @ e )
!= ( A @ hh ) ) )
=> ( ( A @ d )
= ( A @ ee ) ) ) )
=> ( ( ( A @ a )
!= ( A @ aa ) )
| ( ( A @ b )
!= ( A @ bb ) )
| ( ( A @ c )
!= ( A @ cc ) )
| ( ( A @ d )
!= ( A @ dd ) )
| ( ( A @ e )
!= ( A @ ee ) )
| ( ( A @ h )
!= ( A @ hh ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ( ( ( ( ( A @ a )
= ( A @ aa ) )
& ( ( A @ b )
= ( A @ bb ) )
& ( ( A @ e )
= ( A @ hh ) ) )
=> ( ( A @ c )
= ( A @ dd ) ) )
& ( ( ( ( A @ a )
= ( A @ aa ) )
& ( ( A @ h )
= ( A @ hh ) )
& ( ( A @ b )
= ( A @ cc ) ) )
=> ( ( A @ d )
!= ( A @ ee ) ) )
& ( ( ( ( A @ c )
= ( A @ cc ) )
& ( ( A @ cc )
= ( A @ d ) )
& ( ( A @ d )
= ( A @ dd ) )
& ( ( A @ a )
!= ( A @ bb ) ) )
=> ( ( A @ e )
!= ( A @ hh ) ) )
& ( ( ( ( A @ a )
= ( A @ aa ) )
& ( ( A @ d )
= ( A @ dd ) )
& ( ( A @ b )
!= ( A @ cc ) ) )
=> ( ( A @ e )
= ( A @ hh ) ) )
& ( ( ( ( A @ e )
= ( A @ ee ) )
& ( ( A @ h )
= ( A @ hh ) )
& ( ( A @ c )
= ( A @ dd ) ) )
=> ( ( A @ a )
!= ( A @ bb ) ) )
& ( ( ( ( A @ b )
= ( A @ bb ) )
& ( ( A @ bb )
= ( A @ c ) )
& ( ( A @ c )
= ( A @ cc ) )
& ( ( A @ e )
!= ( A @ hh ) ) )
=> ( ( A @ d )
= ( A @ ee ) ) ) )
=> ( ( ( A @ a )
!= ( A @ aa ) )
| ( ( A @ b )
!= ( A @ bb ) )
| ( ( A @ c )
!= ( A @ cc ) )
| ( ( A @ d )
!= ( A @ dd ) )
| ( ( A @ e )
!= ( A @ ee ) )
| ( ( A @ h )
!= ( A @ hh ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO248^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.09/0.21 % Computer : n007.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:39:10 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (191ms).
% 1.25/1.00 % [INFO] Running in sequential loop mode.
% 1.99/1.38 % [INFO] eprover registered as external prover.
% 1.99/1.39 % [INFO] Scanning for conjecture ...
% 2.41/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.41/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.41/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.41/1.58 % [INFO] Type checking passed.
% 2.41/1.58 % [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 ...
% 4.35/2.34 % External prover 'e' found a proof!
% 4.35/2.34 % [INFO] Killing All external provers ...
% 4.35/2.34 % Time passed: 1974ms (effective reasoning time: 1337ms)
% 4.35/2.34 % 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)>
% 4.35/2.34 % Axioms used in derivation (0):
% 4.35/2.34 % No. of inferences in proof: 4
% 4.35/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1974 ms resp. 1337 ms w/o parsing
% 4.64/2.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.64/2.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------