%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU243+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 : n011.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 08:38:11 AM UTC 2026
% Result : Theorem 7.00s 4.09s
% Output : Refutation 7.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 60 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 156 ( 18 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 396 ( 40 ~; 2 |; 52 &; 260 @)
% ( 5 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 2 con; 0-2 aty)
% Number of variables : 103 ( 0 ^; 91 !; 12 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(well_founded_relation_decl,type,
well_founded_relation: $i > $o ).
thf(is_well_founded_in_decl,type,
is_well_founded_in: $i > $i > $o ).
thf(relation_field_decl,type,
relation_field: $i > $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(fiber_decl,type,
fiber: $i > $i > $i ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(22,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(88,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(120,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(84,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(61,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(38,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(64,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(44,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(113,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ well_founded_relation )
<=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ ( A @ fiber ) @ disjoint ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set )
& ( A @ relation_field @ ( B @ subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
thf(130,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ ( A @ fiber ) @ disjoint ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set )
& ( A @ relation_field @ ( B @ subset ) ) )
=> ( A @ well_founded_relation ) )
& ( ( A @ well_founded_relation )
=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ ( A @ fiber ) @ disjoint ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set )
& ( A @ relation_field @ ( B @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ well_founded_relation )
<=> ( A @ relation_field @ ( A @ is_well_founded_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ relation )
=> ( ( A @ well_founded_relation )
<=> ( A @ relation_field @ ( A @ is_well_founded_in ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_well_founded_in ) )
=> ( A @ well_founded_relation ) )
& ( ( A @ well_founded_relation )
=> ( A @ relation_field @ ( A @ is_well_founded_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(72,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_well_founded_in ) )
<=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ ( A @ fiber ) @ disjoint ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set )
& ( B @ ( C @ subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
thf(99,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ ( A @ fiber ) @ disjoint ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set )
& ( B @ ( C @ subset ) ) )
=> ( B @ ( A @ is_well_founded_in ) ) )
& ( ( B @ ( A @ is_well_founded_in ) )
=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ ( A @ fiber ) @ disjoint ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set )
& ( B @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(40,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(125,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(57,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(60,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field )
= ( A @ relation_rng @ ( A @ relation_dom @ set_union2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(117,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field )
= ( A @ relation_rng @ ( A @ relation_dom @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(54,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(49,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(86,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(79,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(94,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(145,plain,
$false,
inference(e,[status(thm)],[88,120,84,61,38,77,64,44,113,130,31,72,99,40,52,125,46,57,60,117,54,49,86,91,66,75,82,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.13 % 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
% 0.26/0.59 % Computer : n011.cluster.edu
% 0.26/0.59 % Model : x86_64 x86_64
% 0.26/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.59 % Memory : 8046.5625MB
% 0.26/0.59 % OS : Linux 6.8.0-71-generic
% 0.26/0.59 % CPULimit : 300
% 0.26/0.59 % WCLimit : 300
% 0.26/0.59 % DateTime : Sat Sep 26 08:57:30 UTC 2026
% 0.26/0.59 % CPUTime :
% 0.26/0.59 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
% 1.45/1.44 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.78 % [INFO] Parsing done (328ms).
% 2.21/1.80 % [INFO] Running in sequential loop mode.
% 3.01/2.33 % [INFO] eprover registered as external prover.
% 3.01/2.34 % [INFO] Scanning for conjecture ...
% 3.19/2.50 % [INFO] Found a conjecture (or negated_conjecture) and 36 axioms. Running axiom selection ...
% 3.56/2.61 % [INFO] Axiom selection finished. Selected 28 axioms (removed 8 axioms).
% 3.78/2.70 % [INFO] Problem is first-order (TPTP FOF).
% 3.78/2.71 % [INFO] Type checking passed.
% 3.78/2.72 % [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 ...
% 7.00/4.08 % External prover 'e' found a proof!
% 7.00/4.08 % [INFO] Killing All external provers ...
% 7.00/4.08 % Time passed: 3270ms (effective reasoning time: 2280ms)
% 7.00/4.08 % 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)>
% 7.00/4.09 % Axioms used in derivation (28): t1_boole, rc3_funct_1, rc2_funct_1, reflexivity_r1_tarski, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, t1_subset, rc1_funct_1, fc2_xboole_0, d3_wellord1, t6_boole, commutativity_k2_xboole_0, t5_subset, t4_subset, fc3_xboole_0, t7_boole, cc1_funct_1, cc2_funct_1, d2_wellord1, t3_subset, existence_m1_subset_1, d6_relat_1, t8_boole, rc1_xboole_0, t2_subset, symmetry_r1_xboole_0
% 7.00/4.09 % No. of inferences in proof: 60
% 7.00/4.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3270 ms resp. 2280 ms w/o parsing
% 7.33/4.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.33/4.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------