%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU827^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n003.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 08:29:26 AM UTC 2026
% Result : Theorem 4.68s 2.55s
% Output : Refutation 4.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 151 ( 9 equ; 0 cnn)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 273 ( 45 ~; 55 |; 29 &; 141 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 25 ( 22 ^; 2 !; 0 ?; 25 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leibeq_decl,type,
leibeq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(u_decl,type,
u: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(n_decl,type,
n: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(a_decl,type,
a: $i > $o ).
thf(b_decl,type,
b: $i > $o ).
thf(c_decl,type,
c: $i > $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(leibeq_def,definition,
( leibeq
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: ( $i > $o ) > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(u_def,definition,
( u
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(n_def,definition,
( n
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( $i > $o ) > $o] :
~ ( ( A
@ ^ [B: $i] :
( ( a @ B )
| ( ( b @ B )
& ( c @ B ) ) ) )
=> ( A
@ ^ [B: $i] :
( ( ( a @ B )
| ( b @ B ) )
& ( ( a @ B )
| ( c @ B ) ) ) ) ) ) ) ).
thf(1,conjecture,
leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] :
( ( a @ B )
| ( ( b @ B )
& ( c @ B ) ) ) )
=> ( A
@ ^ [B: $i] :
( ( ( a @ B )
| ( b @ B ) )
& ( ( a @ B )
| ( c @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk1
@ ^ [A: $i] :
( ( a @ A )
| ( ( b @ A )
& ( c @ A ) ) ) )
& ~ ( sk1
@ ^ [A: $i] :
( ( ( a @ A )
| ( b @ A ) )
& ( ( a @ A )
| ( c @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( sk1
@ ^ [A: $i] :
( ( a @ A )
| ( ( b @ A )
& ( c @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
~ ( sk1
@ ^ [A: $i] :
( ( ( a @ A )
| ( b @ A ) )
& ( ( a @ A )
| ( c @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ~ $true
| ( ( sk1
@ ^ [A: $i] :
( ( ( a @ A )
| ( b @ A ) )
& ( ( a @ A )
| ( c @ A ) ) ) )
!= ( sk1
@ ^ [A: $i] :
( ( a @ A )
| ( ( b @ A )
& ( c @ A ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(8,plain,
( ( sk1
@ ^ [A: $i] :
( ( ( a @ A )
| ( b @ A ) )
& ( ( a @ A )
| ( c @ A ) ) ) )
!= ( sk1
@ ^ [A: $i] :
( ( a @ A )
| ( ( b @ A )
& ( c @ A ) ) ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(9,plain,
( ( ^ [A: $i] :
( ( ( a @ A )
| ( b @ A ) )
& ( ( a @ A )
| ( c @ A ) ) ) )
!= ( ^ [A: $i] :
( ( a @ A )
| ( ( b @ A )
& ( c @ A ) ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(10,plain,
( ( ( ( a @ sk2 )
| ( b @ sk2 ) )
& ( ( a @ sk2 )
| ( c @ sk2 ) ) )
!= ( ( a @ sk2 )
| ( ( b @ sk2 )
& ( c @ sk2 ) ) ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(11,plain,
( ~ ( ( ( a @ sk2 )
| ( b @ sk2 ) )
& ( ( a @ sk2 )
| ( c @ sk2 ) ) )
| ~ ( ( a @ sk2 )
| ( ( b @ sk2 )
& ( c @ sk2 ) ) ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( a @ sk2 )
| ~ ( a @ sk2 )
| ~ ( a @ sk2 ) )
& ( ~ ( a @ sk2 )
| ~ ( a @ sk2 )
| ~ ( b @ sk2 )
| ~ ( c @ sk2 ) )
& ( ~ ( a @ sk2 )
| ~ ( c @ sk2 )
| ~ ( a @ sk2 ) )
& ( ~ ( a @ sk2 )
| ~ ( c @ sk2 )
| ~ ( b @ sk2 )
| ~ ( c @ sk2 ) )
& ( ~ ( b @ sk2 )
| ~ ( a @ sk2 )
| ~ ( a @ sk2 ) )
& ( ~ ( b @ sk2 )
| ~ ( a @ sk2 )
| ~ ( b @ sk2 )
| ~ ( c @ sk2 ) )
& ( ~ ( b @ sk2 )
| ~ ( c @ sk2 )
| ~ ( a @ sk2 ) )
& ( ~ ( b @ sk2 )
| ~ ( c @ sk2 )
| ~ ( b @ sk2 )
| ~ ( c @ sk2 ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(14,plain,
( ~ ( a @ sk2 )
| ~ ( a @ sk2 )
| ~ ( a @ sk2 ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(22,plain,
~ ( a @ sk2 ),
inference(simp,[status(thm)],[14]) ).
thf(36,plain,
( ( ( $false
| ( b @ sk2 ) )
& ( $false
| ( c @ sk2 ) ) )
!= ( $false
| ( ( b @ sk2 )
& ( c @ sk2 ) ) ) ),
inference(rewrite,[status(thm)],[10,22]) ).
thf(37,plain,
$false,
inference(simp,[status(thm)],[36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU827^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.11 % 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
% 0.10/0.25 % Computer : n003.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 14:36:58 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 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
% 1.17/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.65/1.19 % [INFO] Parsing done (204ms).
% 1.75/1.20 % [INFO] Running in sequential loop mode.
% 2.36/1.67 % [INFO] eprover registered as external prover.
% 2.36/1.68 % [INFO] Scanning for conjecture ...
% 2.59/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.79/1.82 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.79/1.83 % [INFO] Problem is higher-order (TPTP THF).
% 2.79/1.83 % [INFO] Type checking passed.
% 2.79/1.83 % [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 ...
% 4.68/2.55 % [INFO] Killing All external provers ...
% 4.68/2.55 % Time passed: 2070ms (effective reasoning time: 1337ms)
% 4.68/2.55 % 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)>
% 4.68/2.55 % Axioms used in derivation (0):
% 4.68/2.55 % No. of inferences in proof: 16
% 4.68/2.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2070 ms resp. 1337 ms w/o parsing
% 4.99/2.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.99/2.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------