%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU845^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n020.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 08:29:27 AM UTC 2026
% Result : Theorem 3.46s 2.25s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 79 ( 15 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 170 ( 43 ~; 17 |; 24 &; 76 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 8 ^; 16 !; 0 ?; 26 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( A
= ( ^ [C: a] :
( ( B @ C )
& ~ ( ( B @ C )
& ~ ( A @ C ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
~ ( ! [B: a] :
( ( sk1 @ B )
=> ( A @ B ) )
=> ( sk1
= ( ^ [B: a] :
( ( A @ B )
& ~ ( ( A @ B )
& ~ ( sk1 @ B ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( A
= ( ^ [C: a] :
( ( B @ C )
& ~ ( ( B @ C )
& ~ ( A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM12_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( A
= ( ^ [C: a] :
( ( B @ C )
& ~ ( ( B @ C )
& ~ ( A @ C ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( A
= ( ^ [C: a] :
( ( B @ C )
& ~ ( ( B @ C )
& ~ ( A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: a] :
( ( ~ ( sk1 @ A )
| ( sk2 @ A ) )
& ( sk1
!= ( ^ [B: a] :
( ( sk2 @ B )
& ~ ( ( sk2 @ B )
& ~ ( sk1 @ B ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( sk1
!= ( ^ [A: a] :
( ( sk2 @ A )
& ~ ( ( sk2 @ A )
& ~ ( sk1 @ A ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ( ^ [A: a] :
( ( sk2 @ A )
& ~ ( ( sk2 @ A )
& ~ ( sk1 @ A ) ) ) )
!= sk1 ),
inference(lifteq,[status(thm)],[6]) ).
thf(8,plain,
( ( ( sk2 @ sk3 )
& ~ ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) ) )
!= ( sk1 @ sk3 ) ),
inference(func_ext,[status(esa)],[7]) ).
thf(10,plain,
( ( ( sk2 @ sk3 )
& ~ ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) ) )
| ( sk1 @ sk3 ) ),
inference(bool_ext,[status(thm)],[8]) ).
thf(15,plain,
( ( ( sk2 @ sk3 )
| ( sk1 @ sk3 ) )
& ( ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk3 ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(16,plain,
( ( sk2 @ sk3 )
| ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(17,plain,
( ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(18,plain,
( ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 ) ),
inference(simp,[status(thm)],[17]) ).
thf(28,plain,
( ( sk1 @ sk3 )
| ~ $true
| ( sk1 @ sk3 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[16,18]) ).
thf(29,plain,
( ( sk1 @ sk3 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(30,plain,
sk1 @ sk3,
inference(pattern_uni,[status(thm)],[29:[]]) ).
thf(5,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(47,plain,
! [A: a] :
( ~ $true
| ( sk2 @ A )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,5]) ).
thf(48,plain,
! [A: a] :
( ( sk2 @ A )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
sk2 @ sk3,
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( sk3 ))]]) ).
thf(41,plain,
~ ( ( sk2 @ sk3 )
& ~ ( ( sk2 @ sk3 )
& ~ $true ) ),
inference(rewrite,[status(thm)],[8,30]) ).
thf(42,plain,
~ ( sk2 @ sk3 ),
inference(simp,[status(thm)],[41]) ).
thf(54,plain,
$false,
inference(rewrite,[status(thm)],[49,42]) ).
thf(55,plain,
$false,
inference(simp,[status(thm)],[54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU845^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.11/0.23 % Computer : n020.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 14:40:34 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 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
% 0.98/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/0.98 % [INFO] Parsing done (177ms).
% 1.15/1.00 % [INFO] Running in sequential loop mode.
% 1.88/1.40 % [INFO] eprover registered as external prover.
% 1.88/1.41 % [INFO] Scanning for conjecture ...
% 1.88/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.03/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.03/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.03/1.53 % [INFO] Type checking passed.
% 2.03/1.53 % [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 ...
% 3.46/2.24 % [INFO] Killing All external provers ...
% 3.46/2.25 % Time passed: 1865ms (effective reasoning time: 1239ms)
% 3.46/2.25 % 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)>
% 3.46/2.25 % Axioms used in derivation (0):
% 3.46/2.25 % No. of inferences in proof: 23
% 3.46/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1865 ms resp. 1239 ms w/o parsing
% 3.69/2.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.69/2.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------