%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET597+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n014.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 08:30:23 AM UTC 2026
% Result : Theorem 6.71s 3.85s
% Output : Refutation 6.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 12 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 217 ( 2 ~; 3 |; 24 &; 158 @)
% ( 7 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 53 ( 0 ^; 53 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( B @ ( A @ union ) @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).
thf(24,plain,
! [A: $i,B: $i] : ( B @ ( A @ union ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
<=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i] :
( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ union ) @ ( C @ member ) )
<=> ( ( B @ ( C @ member ) )
| ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(28,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( C @ member ) )
| ( A @ ( C @ member ) ) )
=> ( B @ ( A @ union ) @ ( C @ member ) ) )
& ( ( B @ ( A @ union ) @ ( C @ member ) )
=> ( ( B @ ( C @ member ) )
| ( A @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( A
= ( C @ ( B @ union ) ) )
<=> ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( D @ ( B @ subset ) ) )
=> ( D @ ( A @ subset ) ) )
& ( A @ ( C @ subset ) )
& ( A @ ( B @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th56) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( A
= ( C @ ( B @ union ) ) )
<=> ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( D @ ( B @ subset ) ) )
=> ( D @ ( A @ subset ) ) )
& ( A @ ( C @ subset ) )
& ( A @ ( B @ subset ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( D @ ( B @ subset ) ) )
=> ( D @ ( A @ subset ) ) )
& ( A @ ( C @ subset ) )
& ( A @ ( B @ subset ) ) )
=> ( A
= ( C @ ( B @ union ) ) ) )
& ( ( A
= ( C @ ( B @ union ) ) )
=> ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( D @ ( B @ subset ) ) )
=> ( D @ ( A @ subset ) ) )
& ( A @ ( C @ subset ) )
& ( A @ ( B @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ union ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_subset) ).
thf(26,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ union ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(44,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)],[7]) ).
thf(9,axiom,
! [A: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(59,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(113,plain,
$false,
inference(e,[status(thm)],[56,24,61,28,11,26,36,44,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET597+3 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.22/0.49 % Computer : n014.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sat Sep 26 07:58:18 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.42/1.35 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.95/1.64 % [INFO] Parsing done (283ms).
% 1.95/1.66 % [INFO] Running in sequential loop mode.
% 2.92/2.29 % [INFO] eprover registered as external prover.
% 3.13/2.30 % [INFO] Scanning for conjecture ...
% 3.34/2.45 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 3.50/2.51 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 3.50/2.54 % [INFO] Problem is first-order (TPTP FOF).
% 3.50/2.55 % [INFO] Type checking passed.
% 3.50/2.55 % [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 ...
% 6.71/3.84 % External prover 'e' found a proof!
% 6.71/3.84 % [INFO] Killing All external provers ...
% 6.71/3.84 % Time passed: 3137ms (effective reasoning time: 2171ms)
% 6.71/3.84 % 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)>
% 6.71/3.85 % Axioms used in derivation (8): reflexivity_of_subset, equal_member_defn, union_subset, subset_of_union, commutativity_of_union, equal_defn, union_defn, subset_defn
% 6.71/3.85 % No. of inferences in proof: 20
% 6.71/3.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3137 ms resp. 2171 ms w/o parsing
% 6.94/3.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.94/3.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------