%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET911+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : 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 : Sun Sep 27 08:31:18 AM UTC 2026
% Result : Theorem 2.58s 1.52s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 9 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 67 ( 6 ~; 0 |; 0 &; 54 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 21 !; 4 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(7,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(24,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(14,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( A @ singleton @ ( B @ set_intersection2 ) )
= ( A @ singleton ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( A @ singleton @ ( B @ set_intersection2 ) )
= ( A @ singleton ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( A @ singleton @ ( B @ set_intersection2 ) )
= ( A @ singleton ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(22,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( A @ singleton @ ( B @ set_intersection2 ) )
= ( A @ singleton ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_zfmisc_1) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( A @ singleton @ ( B @ set_intersection2 ) )
= ( A @ singleton ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[24,14,20,9,17,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET911+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.13/0.40 % Computer : n001.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 08:30:57 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.69/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.93/0.80 % [INFO] Parsing done (87ms).
% 0.93/0.81 % [INFO] Running in sequential loop mode.
% 1.11/1.00 % [INFO] eprover registered as external prover.
% 1.11/1.01 % [INFO] Scanning for conjecture ...
% 1.39/1.06 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.39/1.07 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.39/1.08 % [INFO] Problem is first-order (TPTP FOF).
% 1.39/1.08 % [INFO] Type checking passed.
% 1.39/1.09 % [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 ...
% 2.58/1.51 % External prover 'e' found a proof!
% 2.58/1.52 % [INFO] Killing All external provers ...
% 2.58/1.52 % Time passed: 1010ms (effective reasoning time: 704ms)
% 2.58/1.52 % 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)>
% 2.58/1.52 % Axioms used in derivation (6): idempotence_k3_xboole_0, commutativity_k3_xboole_0, l32_zfmisc_1, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden
% 2.58/1.52 % No. of inferences in proof: 16
% 2.58/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1010 ms resp. 704 ms w/o parsing
% 2.58/1.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.58/1.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------