%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU267+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/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 08:38:16 AM UTC 2026
% Result : Theorem 5.45s 3.53s
% Output : Refutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 30 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 32 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 149 ( 14 ~; 2 |; 11 &; 98 @)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 54 !; 14 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(pair_first_decl,type,
pair_first: $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(pair_second_decl,type,
pair_second: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(5,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(24,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(41,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(32,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(35,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ordered_pair ) @ pair_second )
= B )
& ( ( B @ ( A @ ordered_pair ) @ pair_first )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mcart_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ ordered_pair ) @ pair_second )
= B )
& ( ( B @ ( A @ ordered_pair ) @ pair_first )
= A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ ordered_pair ) @ pair_second )
= B )
& ( ( B @ ( A @ ordered_pair ) @ pair_first )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(26,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ ordered_pair ) ) )
=> ! [B: $i] :
( ( B
= ( A @ pair_first ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mcart_1) ).
thf(47,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ ordered_pair ) ) )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = C ) )
=> ( B
= ( A @ pair_first ) ) )
& ( ( B
= ( A @ pair_first ) )
=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(44,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ ordered_pair ) ) )
=> ! [B: $i] :
( ( B
= ( A @ pair_second ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).
thf(59,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ ordered_pair ) ) )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = D ) )
=> ( B
= ( A @ pair_second ) ) )
& ( ( B
= ( A @ pair_second ) )
=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(36,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(30,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(74,plain,
$false,
inference(e,[status(thm)],[24,20,41,32,39,35,16,26,47,22,44,59,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU267+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.50 % Computer : n016.cluster.edu
% 0.23/0.50 % Model : x86_64 x86_64
% 0.23/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.50 % Memory : 8046.5625MB
% 0.23/0.50 % OS : Linux 6.8.0-71-generic
% 0.23/0.50 % CPULimit : 300
% 0.23/0.50 % WCLimit : 300
% 0.23/0.50 % DateTime : Sat Sep 26 09:06:32 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.41/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.93/1.60 % [INFO] Parsing done (273ms).
% 1.93/1.63 % [INFO] Running in sequential loop mode.
% 2.83/2.20 % [INFO] eprover registered as external prover.
% 2.83/2.22 % [INFO] Scanning for conjecture ...
% 3.01/2.36 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.16/2.44 % [INFO] Axiom selection finished. Selected 13 axioms (removed 5 axioms).
% 3.16/2.49 % [INFO] Problem is first-order (TPTP FOF).
% 3.16/2.49 % [INFO] Type checking passed.
% 3.36/2.50 % [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 ...
% 5.45/3.52 % External prover 'e' found a proof!
% 5.45/3.52 % [INFO] Killing All external provers ...
% 5.45/3.52 % Time passed: 2812ms (effective reasoning time: 1888ms)
% 5.45/3.52 % 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)>
% 5.45/3.53 % Axioms used in derivation (13): fc1_zfmisc_1, t6_boole, t7_boole, t2_subset, rc2_xboole_0, fc1_xboole_0, t1_subset, existence_m1_subset_1, d2_mcart_1, t8_boole, rc1_xboole_0, antisymmetry_r2_hidden, d1_mcart_1
% 5.45/3.53 % No. of inferences in proof: 30
% 5.45/3.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2812 ms resp. 1888 ms w/o parsing
% 5.66/3.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.66/3.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------