%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET015-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n020.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 08:28:51 AM UTC 2026
% Result : Unsatisfiable 36.15s 8.19s
% Output : Refutation 32.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 192 ( 26 ~; 28 |; 0 &; 138 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(cs_decl,type,
cs: $i ).
thf(ds_decl,type,
ds: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(little_set_decl,type,
little_set: $i > $o ).
thf(f1_decl,type,
f1: $i > $i > $i ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(universal_set_decl,type,
universal_set: $i ).
thf(as_decl,type,
as: $i ).
thf(bs_decl,type,
bs: $i ).
thf(14,axiom,
( ( bs @ ( as @ union ) )
= cs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_union_b_is_c) ).
thf(46,plain,
( ( bs @ ( as @ union ) )
= cs ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
( ( as @ ( bs @ union ) )
= ds ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_union_a_is_d) ).
thf(48,plain,
( ( as @ ( bs @ union ) )
= ds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,negated_conjecture,
cs != ds,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
thf(16,plain,
cs != ds,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( B @ complement @ ( A @ complement @ intersection ) @ complement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( B @ complement @ ( A @ complement @ intersection ) @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(42,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( B @ ( A @ f1 ) @ member ) )
| ( A @ ( B @ ( A @ f1 ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( B @ ( A @ f1 ) @ member ) )
| ( A @ ( B @ ( A @ f1 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( A @ little_set )
| ( B @ complement @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( A @ little_set )
| ( B @ complement @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) )
| ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) )
| ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( A @ little_set )
| ( universal_set @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',universal_set) ).
thf(44,plain,
! [A: $i] :
( ~ ( A @ little_set )
| ( universal_set @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( B @ ( A @ f1 ) @ member ) )
| ~ ( A @ ( B @ ( A @ f1 ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( B @ ( A @ f1 ) @ member ) )
| ~ ( A @ ( B @ ( A @ f1 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( A @ little_set )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A @ little_set )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9725,plain,
$false,
inference(e,[status(thm)],[46,48,16,40,42,24,38,21,32,34,44,27,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET015-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.12/0.40 % Computer : n020.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 06:51:51 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.18 % [INFO] Parsing done (194ms).
% 1.25/1.19 % [INFO] Running in sequential loop mode.
% 1.90/1.59 % [INFO] eprover registered as external prover.
% 2.10/1.60 % [INFO] Scanning for conjecture ...
% 2.10/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.27/1.72 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.27/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.27/1.76 % [INFO] Type checking passed.
% 2.27/1.76 % [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 ...
% 36.15/8.19 % External prover 'e' found a proof!
% 36.15/8.19 % [INFO] Killing All external provers ...
% 36.15/8.19 % Time passed: 7640ms (effective reasoning time: 6987ms)
% 36.15/8.19 % Axioms used in derivation (14): complement1, union, empty_set, a_union_b_is_c, intersection3, extensionality1, complement2, universal_set, intersection2, a2, extensionality2, intersection1, extensionality3, b_union_a_is_d
% 36.15/8.19 % No. of inferences in proof: 31
% 36.15/8.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 7640 ms resp. 6987 ms w/o parsing
% 32.92/8.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.92/8.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------