%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET076^1 : 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 : n008.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 08:22:54 AM UTC 2026
% Result : Theorem 5.20s 3.00s
% Output : Refutation 5.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 6 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 13 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 29 ( 2 ~; 2 |; 3 &; 17 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 16 ( 5 ^; 11 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(unord_pair_decl,type,
unord_pair: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
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(1,conjecture,
! [A: $i,B: $i,C: $i > $o] :
( ( ( C @ A )
& ( C @ B ) )
=> ( subset @ ( unord_pair @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i > $o] :
( ( ( C @ A )
& ( C @ B ) )
=> ( subset @ ( unord_pair @ A @ B ) @ C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i,C: $i > $o] :
( ( ( C @ A )
& ( C @ B ) )
=> ! [D: $i] :
( ( ( D = A )
| ( D = B ) )
=> ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET076^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.12 % 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
% 0.27/0.31 % Computer : n008.cluster.edu
% 0.27/0.31 % Model : x86_64 x86_64
% 0.27/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.31 % Memory : 8046.5625MB
% 0.27/0.31 % OS : Linux 6.8.0-71-generic
% 0.27/0.32 % CPULimit : 300
% 0.27/0.32 % WCLimit : 300
% 0.27/0.32 % DateTime : Tue Sep 29 13:37:24 UTC 2026
% 0.27/0.32 % CPUTime :
% 0.27/0.32 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
% 1.52/1.16 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.97/1.48 % [INFO] Parsing done (319ms).
% 2.32/1.50 % [INFO] Running in sequential loop mode.
% 3.22/2.12 % [INFO] eprover registered as external prover.
% 3.22/2.13 % [INFO] Scanning for conjecture ...
% 3.73/2.30 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.73/2.35 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.73/2.36 % [INFO] Problem is higher-order (TPTP THF).
% 3.73/2.36 % [INFO] Type checking passed.
% 3.73/2.37 % [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 ...
% 5.20/3.00 % External prover 'e' found a proof!
% 5.20/3.00 % [INFO] Killing All external provers ...
% 5.20/3.00 % Time passed: 2473ms (effective reasoning time: 1488ms)
% 5.20/3.00 % 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)>
% 5.20/3.00 % Axioms used in derivation (0):
% 5.20/3.00 % No. of inferences in proof: 4
% 5.20/3.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2473 ms resp. 1488 ms w/o parsing
% 5.20/3.03 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.20/3.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------