%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET945+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 : 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 : Sun Sep 27 08:31:24 AM UTC 2026
% Result : Theorem 6.79s 3.61s
% Output : Refutation 6.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 22 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 10 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 208 ( 14 ~; 0 |; 22 &; 146 @)
% ( 4 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 57 ( 0 ^; 46 !; 11 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(8,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(78,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(85,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(21,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_intersection2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_intersection2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ disjoint ) ) )
=> ( B @ ( A @ union @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ disjoint ) ) )
=> ( B @ ( A @ union @ disjoint ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ disjoint ) ) )
=> ( B @ ( A @ union @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(80,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(75,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ union ) ) )
& ( ( B
= ( A @ union ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,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(18,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(100,plain,
$false,
inference(e,[status(thm)],[78,85,21,12,80,16,75,83,48,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET945+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.13 % 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
% 0.24/0.49 % Computer : n004.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Sat Sep 26 08:27:06 UTC 2026
% 0.24/0.50 % CPUTime :
% 0.24/0.50 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
% 1.43/1.35 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.99/1.64 % [INFO] Parsing done (292ms).
% 1.99/1.66 % [INFO] Running in sequential loop mode.
% 3.16/2.31 % [INFO] eprover registered as external prover.
% 3.16/2.31 % [INFO] Scanning for conjecture ...
% 3.40/2.41 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.40/2.45 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.40/2.47 % [INFO] Problem is first-order (TPTP FOF).
% 3.40/2.48 % [INFO] Type checking passed.
% 3.40/2.48 % [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 ...
% 6.79/3.61 % External prover 'e' found a proof!
% 6.79/3.61 % [INFO] Killing All external provers ...
% 6.79/3.61 % Time passed: 2889ms (effective reasoning time: 1935ms)
% 6.79/3.61 % 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)>
% 6.79/3.61 % Axioms used in derivation (9): idempotence_k3_xboole_0, commutativity_k3_xboole_0, t4_xboole_0, d4_tarski, rc1_xboole_0, symmetry_r1_xboole_0, rc2_xboole_0, d3_xboole_0, antisymmetry_r2_hidden
% 6.79/3.61 % No. of inferences in proof: 22
% 6.79/3.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2889 ms resp. 1935 ms w/o parsing
% 6.79/3.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.79/3.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------