%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET935+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 : n016.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 08:31:23 AM UTC 2026
% Result : Theorem 4.05s 2.57s
% Output : Refutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 16 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 246 ( 14 ~; 8 |; 11 &; 180 @)
% ( 6 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 67 ( 0 ^; 63 !; 4 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(inclusion_comparable_decl,type,
inclusion_comparable: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(115,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(42,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i,B: $i] : ( A @ ( A @ inclusion_comparable ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_xboole_0) ).
thf(85,plain,
! [A: $i] : ( A @ ( A @ inclusion_comparable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(38,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(44,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( A @ ( C @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) )
=> ( B
= ( A @ powerset ) ) )
& ( ( B
= ( A @ powerset ) )
=> ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(112,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ powerset @ ( A @ powerset @ set_union2 ) )
= ( B @ ( A @ set_union2 ) @ powerset ) )
=> ( B @ ( A @ inclusion_comparable ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ powerset @ ( A @ powerset @ set_union2 ) )
= ( B @ ( A @ set_union2 ) @ powerset ) )
=> ( B @ ( A @ inclusion_comparable ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ powerset @ ( A @ powerset @ set_union2 ) )
= ( B @ ( A @ set_union2 ) @ powerset ) )
=> ( B @ ( A @ inclusion_comparable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ inclusion_comparable ) )
=> ( A @ ( B @ inclusion_comparable ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r3_xboole_0) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ inclusion_comparable ) )
=> ( A @ ( B @ inclusion_comparable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(82,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(47,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_union2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_union2 ) ) )
=> ! [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)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(89,plain,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ inclusion_comparable ) )
<=> ( ( A @ ( B @ subset ) )
| ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_xboole_0) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
| ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ inclusion_comparable ) ) )
& ( ( B @ ( A @ inclusion_comparable ) )
=> ( ( A @ ( B @ subset ) )
| ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(23,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(121,plain,
$false,
inference(e,[status(thm)],[115,42,85,38,44,91,112,18,87,82,47,89,74,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET935+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
% 0.15/0.40 % Computer : n016.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 08:31:15 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.90/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.44/1.20 % [INFO] Parsing done (207ms).
% 1.44/1.21 % [INFO] Running in sequential loop mode.
% 2.09/1.62 % [INFO] eprover registered as external prover.
% 2.09/1.63 % [INFO] Scanning for conjecture ...
% 2.25/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.25/1.79 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.39/1.81 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.82 % [INFO] Type checking passed.
% 2.39/1.83 % [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 ...
% 4.05/2.56 % External prover 'e' found a proof!
% 4.05/2.56 % [INFO] Killing All external provers ...
% 4.05/2.56 % Time passed: 2006ms (effective reasoning time: 1343ms)
% 4.05/2.56 % 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)>
% 4.05/2.57 % Axioms used in derivation (15): d9_xboole_0, reflexivity_r3_xboole_0, fc2_xboole_0, commutativity_k2_xboole_0, symmetry_r3_xboole_0, d1_zfmisc_1, reflexivity_r1_tarski, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, fc3_xboole_0, d2_xboole_0, idempotence_k2_xboole_0, d10_xboole_0, t7_xboole_1
% 4.05/2.57 % No. of inferences in proof: 34
% 4.05/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2006 ms resp. 1343 ms w/o parsing
% 4.42/2.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.42/2.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------