%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET066^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n004.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 3.39s 1.66s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 79 ( 73 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 72 ( 27 ~; 34 |; 3 &; 8 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 13 ^; 7 !; 0 ?; 22 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(unord_pair_decl,type,
unord_pair: $i > $i > $i > $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(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ^ [C: $i] :
( ( C = A )
| ( C = B ) ) )
= ( ^ [C: $i] :
( ( C = B )
| ( C = A ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( ^ [B: $i] :
( ( B = sk1 )
| ( B = A ) ) )
!= ( ^ [B: $i] :
( ( B = A )
| ( B = sk1 ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( unord_pair @ A @ B )
= ( unord_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( 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: $i] :
( ( C = B )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i] :
( ( A = sk1 )
| ( A = sk2 ) ) )
!= ( ^ [A: $i] :
( ( A = sk2 )
| ( A = sk1 ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: $i] :
( ( A = sk1 )
| ( A = sk2 ) ) )
!= ( ^ [A: $i] :
( ( A = sk2 )
| ( A = sk1 ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk3 = sk1 )
| ( sk3 = sk2 ) )
!= ( ( sk3 = sk2 )
| ( sk3 = sk1 ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(30,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 )
| ( sk3 = sk2 )
| ( sk3 = sk1 ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(41,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 )
| ( sk3 = sk2 )
| ( sk3 = sk1 ) ),
inference(cnf,[status(esa)],[30]) ).
thf(42,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 )
| ( sk3 = sk2 )
| ( sk3 = sk1 ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(43,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 ) ),
inference(simp,[status(thm)],[42]) ).
thf(29,plain,
( ~ ( ( sk3 = sk1 )
| ( sk3 = sk2 ) )
| ~ ( ( sk3 = sk2 )
| ( sk3 = sk1 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(32,plain,
( ( ( sk3 != sk1 )
| ( sk3 != sk2 ) )
& ( ( sk3 != sk1 )
| ( sk3 != sk1 ) )
& ( ( sk3 != sk2 )
| ( sk3 != sk2 ) )
& ( ( sk3 != sk2 )
| ( sk3 != sk1 ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(34,plain,
( ( sk3 != sk1 )
| ( sk3 != sk1 ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(37,plain,
( ( sk3 != sk1 )
| ( sk3 != sk1 ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(38,plain,
sk3 != sk1,
inference(simp,[status(thm)],[37]) ).
thf(35,plain,
( ( sk3 != sk2 )
| ( sk3 != sk2 ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(39,plain,
( ( sk3 != sk2 )
| ( sk3 != sk2 ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(40,plain,
sk3 != sk2,
inference(simp,[status(thm)],[39]) ).
thf(50,plain,
$false,
inference(simplifyReflect,[status(thm)],[43,38,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET066^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n004.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:36:22 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.66/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.04/0.63 % [INFO] Parsing done (119ms).
% 1.04/0.64 % [INFO] Running in sequential loop mode.
% 1.42/0.85 % [INFO] eprover registered as external prover.
% 1.42/0.85 % [INFO] Scanning for conjecture ...
% 1.69/0.92 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.69/0.93 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.69/0.93 % [INFO] Problem is higher-order (TPTP THF).
% 1.69/0.94 % [INFO] Type checking passed.
% 1.69/0.94 % [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 ...
% 3.39/1.65 % [INFO] Killing All external provers ...
% 3.39/1.66 % Time passed: 1367ms (effective reasoning time: 1011ms)
% 3.39/1.66 % 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)>
% 3.39/1.66 % Axioms used in derivation (0):
% 3.39/1.66 % No. of inferences in proof: 19
% 3.39/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1367 ms resp. 1011 ms w/o parsing
% 3.69/1.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.69/1.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------