%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET573+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n012.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 : Sun Sep 27 08:30:17 AM UTC 2026
% Result : Theorem 1.68s 1.21s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 8 ~; 0 |; 8 &; 56 @)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 21 !; 3 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_decl,type,
member: $i > $i > $o ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(intersect_decl,type,
intersect: $i > $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ member ) ) )
=> ~ ( C @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th12) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ member ) ) )
=> ~ ( C @ ( A @ member ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ member ) ) )
=> ~ ( C @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ intersect ) )
<=> ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
thf(11,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ intersect ) ) )
& ( ( B @ ( A @ intersect ) )
=> ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ~ ( B @ ( A @ intersect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ intersect ) )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ~ ( B @ ( A @ intersect ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ intersect ) )
=> ( A @ ( B @ intersect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ intersect ) )
=> ( A @ ( B @ intersect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,plain,
$false,
inference(e,[status(thm)],[6,11,18,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET573+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % 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
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sat Sep 26 07:56:19 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 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
% 0.39/0.60 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.53/0.69 % [INFO] Parsing done (85ms).
% 0.68/0.70 % [INFO] Running in sequential loop mode.
% 0.84/0.88 % [INFO] eprover registered as external prover.
% 0.84/0.88 % [INFO] Scanning for conjecture ...
% 1.01/0.92 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.01/0.94 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.01/0.94 % [INFO] Problem is first-order (TPTP FOF).
% 1.01/0.95 % [INFO] Type checking passed.
% 1.01/0.95 % [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 ...
% 1.68/1.21 % External prover 'e' found a proof!
% 1.68/1.21 % [INFO] Killing All external provers ...
% 1.68/1.21 % Time passed: 817ms (effective reasoning time: 510ms)
% 1.68/1.21 % 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)>
% 1.68/1.21 % Axioms used in derivation (3): intersect_defn, disjoint_defn, symmetry_of_intersect
% 1.68/1.21 % No. of inferences in proof: 10
% 1.68/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 817 ms resp. 510 ms w/o parsing
% 1.68/1.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.68/1.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------