%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET984+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 : n010.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 08:31:28 AM UTC 2026
% Result : Theorem 3.62s 3.36s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 30 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 142 ( 4 ~; 10 |; 6 &; 112 @)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 50 !; 4 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(24,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ cartesian_product2 ) @ subset ) )
=> ( ( ( D @ ( B @ subset ) )
& ( C @ ( A @ subset ) ) )
| ( ( B @ ( A @ cartesian_product2 ) )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ cartesian_product2 ) @ subset ) )
=> ( ( ( D @ ( B @ subset ) )
& ( C @ ( A @ subset ) ) )
| ( ( B @ ( A @ cartesian_product2 ) )
= empty_set ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ cartesian_product2 ) @ subset ) )
=> ( ( ( D @ ( B @ subset ) )
& ( C @ ( A @ subset ) ) )
| ( ( B @ ( A @ cartesian_product2 ) )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(27,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(54,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ cartesian_product2 ) )
= ( D @ ( C @ cartesian_product2 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = empty_set )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(48,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ cartesian_product2 ) )
= ( D @ ( C @ cartesian_product2 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = empty_set )
| ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(23,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(29,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ set_intersection2 ) @ ( B @ ( A @ set_intersection2 ) @ cartesian_product2 ) )
= ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ set_intersection2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(45,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ set_intersection2 ) @ ( B @ ( A @ set_intersection2 ) @ cartesian_product2 ) )
= ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(32,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ cartesian_product2 ) )
= empty_set )
<=> ( ( B = empty_set )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( ( ( B = empty_set )
| ( A = empty_set ) )
=> ( ( B @ ( A @ cartesian_product2 ) )
= empty_set ) )
& ( ( ( B @ ( A @ cartesian_product2 ) )
= empty_set )
=> ( ( B = empty_set )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(59,plain,
$false,
inference(e,[status(thm)],[56,24,14,27,54,48,23,20,29,45,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET984+1 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.15/0.49 % Computer : n010.cluster.edu
% 0.15/0.49 % Model : x86_64 x86_64
% 0.15/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.49 % Memory : 8046.5625MB
% 0.15/0.49 % OS : Linux 6.8.0-71-generic
% 0.15/0.49 % CPULimit : 300
% 0.15/0.49 % WCLimit : 300
% 0.15/0.49 % DateTime : Sat Sep 26 08:29:01 UTC 2026
% 0.15/0.49 % CPUTime :
% 0.15/0.49 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
% 0.98/1.43 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.68 % [INFO] Parsing done (248ms).
% 1.41/1.70 % [INFO] Running in sequential loop mode.
% 2.06/2.22 % [INFO] eprover registered as external prover.
% 2.06/2.23 % [INFO] Scanning for conjecture ...
% 2.18/2.36 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.30/2.41 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.30/2.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.30/2.45 % [INFO] Type checking passed.
% 2.30/2.46 % [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 ...
% 3.62/3.35 % External prover 'e' found a proof!
% 3.62/3.35 % [INFO] Killing All external provers ...
% 3.62/3.35 % Time passed: 2597ms (effective reasoning time: 1640ms)
% 3.62/3.35 % 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)>
% 3.62/3.36 % Axioms used in derivation (11): t17_xboole_1, idempotence_k3_xboole_0, commutativity_k3_xboole_0, t123_zfmisc_1, rc1_xboole_0, t134_zfmisc_1, rc2_xboole_0, fc1_xboole_0, t113_zfmisc_1, t28_xboole_1, reflexivity_r1_tarski
% 3.62/3.36 % No. of inferences in proof: 26
% 3.62/3.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2597 ms resp. 1640 ms w/o parsing
% 3.83/3.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.83/3.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------