%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET613^5 : 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 : n017.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 08:23:01 AM UTC 2026
% Result : Theorem 3.77s 2.29s
% Output : Refutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 153 ( 13 equ; 0 cnn)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 401 ( 91 ~; 84 |; 58 &; 168 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 23 ( 14 ^; 7 !; 0 ?; 23 :)
% ( 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 )
& ( B @ C ) ) ) )
= ( ^ [C: a] :
( ( ( A @ C )
& ~ ( B @ C ) )
| ( ( B @ C )
& ~ ( A @ C ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
( ( ^ [B: a] :
( ( ( sk1 @ B )
| ( A @ B ) )
& ~ ( ( sk1 @ B )
& ( A @ B ) ) ) )
!= ( ^ [B: a] :
( ( ( sk1 @ B )
& ~ ( A @ B ) )
| ( ( A @ B )
& ~ ( sk1 @ B ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o] :
( ( ^ [C: a] :
( ( ( A @ C )
| ( B @ C ) )
& ~ ( ( A @ C )
& ( B @ C ) ) ) )
= ( ^ [C: a] :
( ( ( A @ C )
& ~ ( B @ C ) )
| ( ( B @ C )
& ~ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_87_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o] :
( ( ^ [C: a] :
( ( ( A @ C )
| ( B @ C ) )
& ~ ( ( A @ C )
& ( B @ C ) ) ) )
= ( ^ [C: a] :
( ( ( A @ C )
& ~ ( 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 )
& ( B @ C ) ) ) )
= ( ^ [C: a] :
( ( ( A @ C )
& ~ ( 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 @ A )
& ( sk2 @ A ) ) ) )
!= ( ^ [A: a] :
( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
| ( ( sk2 @ A )
& ~ ( sk1 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: a] :
( ( ( sk1 @ A )
| ( sk2 @ A ) )
& ~ ( ( sk1 @ A )
& ( sk2 @ A ) ) ) )
!= ( ^ [A: a] :
( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
| ( ( sk2 @ A )
& ~ ( sk1 @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ( sk1 @ sk3 )
| ( sk2 @ sk3 ) )
& ~ ( ( sk1 @ sk3 )
& ( sk2 @ sk3 ) ) )
!= ( ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) )
| ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(7,plain,
( ~ ( ( ( sk1 @ sk3 )
| ( sk2 @ sk3 ) )
& ~ ( ( sk1 @ sk3 )
& ( sk2 @ sk3 ) ) )
| ~ ( ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) )
| ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( sk1 @ sk3 )
| ( sk1 @ sk3 )
| ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 ) )
& ( ~ ( sk1 @ sk3 )
| ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 ) )
& ( ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 ) )
& ( ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 ) )
& ( ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 ) )
& ( ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 ) )
& ( ~ ( sk2 @ sk3 )
| ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 ) )
& ( ~ ( sk2 @ sk3 )
| ( sk2 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(16,plain,
( ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(20,plain,
( ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 ) ),
inference(simp,[status(thm)],[16]) ).
thf(8,plain,
( ( ( ( sk1 @ sk3 )
| ( sk2 @ sk3 ) )
& ~ ( ( sk1 @ sk3 )
& ( sk2 @ sk3 ) ) )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) )
| ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(23,plain,
( ( ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk2 @ sk3 ) )
& ( ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ~ ( sk1 @ sk3 ) )
& ( ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk2 @ sk3 ) )
& ( ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ~ ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 ) )
& ( ~ ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk2 @ sk3 ) )
& ( ~ ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ~ ( sk1 @ sk3 ) )
& ( ~ ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk2 @ sk3 ) )
& ( ~ ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 )
| ~ ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(25,plain,
( ~ ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 )
| ~ ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(36,plain,
( ~ ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 ) ),
inference(simp,[status(thm)],[25]) ).
thf(46,plain,
( ~ ( sk1 @ sk3 )
| ~ ( sk1 @ sk3 )
| ~ $true
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[20,36]) ).
thf(47,plain,
( ~ ( sk1 @ sk3 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(48,plain,
~ ( sk1 @ sk3 ),
inference(pattern_uni,[status(thm)],[47:[]]) ).
thf(51,plain,
( ( ( $false
| ( sk2 @ sk3 ) )
& ~ ( $false
& ( sk2 @ sk3 ) ) )
!= ( ( $false
& ~ ( sk2 @ sk3 ) )
| ( ( sk2 @ sk3 )
& ~ $false ) ) ),
inference(rewrite,[status(thm)],[6,48]) ).
thf(52,plain,
$false,
inference(simp,[status(thm)],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET613^5 : 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
% 0.09/0.22 % Computer : n017.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 13:34:36 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (180ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 2.03/1.41 % [INFO] eprover registered as external prover.
% 2.03/1.42 % [INFO] Scanning for conjecture ...
% 2.22/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.54 % [INFO] Type checking passed.
% 2.22/1.55 % [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 ...
% 3.77/2.29 % [INFO] Killing All external provers ...
% 3.77/2.29 % Time passed: 1925ms (effective reasoning time: 1284ms)
% 3.77/2.29 % 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)>
% 3.77/2.29 % Axioms used in derivation (0):
% 3.77/2.29 % No. of inferences in proof: 19
% 3.77/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1925 ms resp. 1284 ms w/o parsing
% 4.06/2.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.06/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------