%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU242+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n001.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 4.27s 7.76s
% Output : Refutation 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 27
% Syntax : Number of formulae : 56 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 23 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 415 ( 50 ~; 2 |; 55 &; 273 @)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 2 con; 0-2 aty)
% Number of variables : 94 ( 0 ^; 82 !; 12 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(connected_decl,type,
connected: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_field_decl,type,
relation_field: $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(function_decl,type,
function: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(is_connected_in_decl,type,
is_connected_in: $i > $i > $o ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(120,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(56,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(70,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(65,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field )
= ( A @ relation_rng @ ( A @ relation_dom @ set_union2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(109,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field )
= ( A @ relation_rng @ ( A @ relation_dom @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(49,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(112,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)],[22]) ).
thf(27,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(127,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(43,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(55,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,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(75,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(52,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(16,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(78,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ connected )
<=> ! [B: $i,C: $i] :
~ ( ~ ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
& ( B != C )
& ( A @ relation_field @ ( C @ in ) )
& ( A @ relation_field @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_wellord1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ relation )
=> ( ( A @ connected )
<=> ! [B: $i,C: $i] :
~ ( ~ ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
& ( B != C )
& ( A @ relation_field @ ( C @ in ) )
& ( A @ relation_field @ ( B @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i,C: $i] :
~ ( ~ ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
& ( B != C )
& ( A @ relation_field @ ( C @ in ) )
& ( A @ relation_field @ ( B @ in ) ) )
=> ( A @ connected ) )
& ( ( A @ connected )
=> ! [B: $i,C: $i] :
~ ( ~ ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
& ( B != C )
& ( A @ relation_field @ ( C @ in ) )
& ( A @ relation_field @ ( B @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(132,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_connected_in ) )
<=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( C != D )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
thf(89,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( C != D )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( A @ is_connected_in ) ) )
& ( ( B @ ( A @ is_connected_in ) )
=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( C != D )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(117,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ connected )
<=> ( A @ relation_field @ ( A @ is_connected_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
thf(85,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_connected_in ) )
=> ( A @ connected ) )
& ( ( A @ connected )
=> ( A @ relation_field @ ( A @ is_connected_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(73,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(105,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(47,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(68,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(62,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(122,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(141,plain,
$false,
inference(e,[status(thm)],[120,56,70,65,109,59,49,112,127,43,55,75,52,125,78,29,132,89,117,85,73,105,47,68,62,122,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU242+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.12/5.40 % Computer : n001.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Sat Sep 26 09:03:33 UTC 2026
% 0.12/5.40 % CPUTime :
% 0.12/5.40 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
% 0.17/5.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/6.21 % [INFO] Parsing done (210ms).
% 1.34/6.22 % [INFO] Running in sequential loop mode.
% 1.97/6.62 % [INFO] eprover registered as external prover.
% 1.97/6.63 % [INFO] Scanning for conjecture ...
% 2.15/6.74 % [INFO] Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ...
% 2.32/6.81 % [INFO] Axiom selection finished. Selected 26 axioms (removed 9 axioms).
% 2.32/6.85 % [INFO] Problem is first-order (TPTP FOF).
% 2.32/6.86 % [INFO] Type checking passed.
% 2.32/6.87 % [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 ...
% 4.27/7.75 % External prover 'e' found a proof!
% 4.27/7.76 % [INFO] Killing All external provers ...
% 4.27/7.76 % Time passed: 2207ms (effective reasoning time: 1529ms)
% 4.27/7.76 % 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)>
% 4.27/7.76 % Axioms used in derivation (26): fc1_zfmisc_1, rc3_funct_1, t6_boole, commutativity_k2_xboole_0, fc3_xboole_0, rc2_funct_1, d14_relat_2, t2_subset, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, d6_relat_2, t1_boole, fc1_xboole_0, d5_tarski, t1_subset, rc1_funct_1, fc2_xboole_0, t7_boole, cc1_funct_1, cc2_funct_1, existence_m1_subset_1, commutativity_k2_tarski, d6_relat_1, t8_boole, rc1_xboole_0
% 4.27/7.76 % No. of inferences in proof: 56
% 4.27/7.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2207 ms resp. 1529 ms w/o parsing
% 4.69/7.83 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.69/7.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------