%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET067^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n001.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 08:22:53 AM UTC 2026
% Result : Theorem 3.56s 2.05s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 44 ( 35 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 44 ( 11 ~; 12 |; 2 &; 14 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 19 ( 5 ^; 11 !; 0 ?; 19 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(unord_pair_decl,type,
unord_pair: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(unord_pair_def,definition,
( unord_pair
= ( ^ [A: $i,B: $i,C: $i] :
( ( C = A )
| ( C = B ) ) ) ) ).
thf(subset_def,definition,
( subset
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C = A )
| ( C = B ) )
=> ( ( C = B )
| ( C = A ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B = sk1 )
| ( B = A ) )
=> ( ( B = A )
| ( B = sk1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( A = sk1 )
| ( A = sk2 ) )
=> ( ( A = sk2 )
| ( A = sk1 ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] : ( subset @ ( unord_pair @ A @ B ) @ ( unord_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] : ( subset @ ( unord_pair @ A @ B ) @ ( unord_pair @ B @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C = A )
| ( C = B ) )
=> ( ( C = B )
| ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ( sk3 = sk1 )
| ( sk3 = sk2 ) )
& ( sk3 != sk2 )
& ( sk3 != sk1 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(6,plain,
sk3 != sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
sk3 != sk2,
inference(lifteq,[status(thm)],[6]) ).
thf(7,plain,
sk3 != sk1,
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
sk3 != sk1,
inference(lifteq,[status(thm)],[7]) ).
thf(11,plain,
$false,
inference(simplifyReflect,[status(thm)],[8,9,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET067^1 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.10/0.21 % Computer : n001.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:42:35 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.02 % [INFO] Parsing done (233ms).
% 1.27/1.03 % [INFO] Running in sequential loop mode.
% 2.15/1.44 % [INFO] eprover registered as external prover.
% 2.15/1.45 % [INFO] Scanning for conjecture ...
% 2.35/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.35/1.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.35/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.56/1.60 % [INFO] Type checking passed.
% 2.56/1.60 % [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 ...
% 3.14/2.04 % [INFO] Killing All external provers ...
% 3.56/2.05 % Time passed: 1691ms (effective reasoning time: 1006ms)
% 3.56/2.05 % 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)>
% 3.56/2.05 % Axioms used in derivation (0):
% 3.56/2.05 % No. of inferences in proof: 11
% 3.56/2.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1691 ms resp. 1006 ms w/o parsing
% 3.56/2.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.56/2.10 % [INFO] Killing All external provers ...
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