%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n015.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 08:08:45 AM UTC 2026
% Result : Theorem 3.76s 2.79s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 33
% Syntax : Number of formulae : 68 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 192 ( 4 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 360 ( 21 ~; 2 |; 93 &; 215 @)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 0 ^; 50 !; 30 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(relation_non_empty_decl,type,
relation_non_empty: $i > $o ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(115,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(42,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(125,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8,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)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(38,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(65,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(53,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(96,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,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(44,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)],[5]) ).
thf(6,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(49,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(98,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
! [A: $i] :
~ ! [B: $i] :
( ( B @ ordinal )
=> ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_ordinal1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
~ ! [B: $i] :
( ( B @ ordinal )
=> ( A @ ( B @ in ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ! [A: $i] :
~ ! [B: $i] :
( ( B @ ordinal )
=> ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(112,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(67,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,axiom,
( ( empty_set @ ordinal )
& ( empty_set @ epsilon_connected )
& ( empty_set @ epsilon_transitive )
& ( empty_set @ empty )
& ( empty_set @ one_to_one )
& ( empty_set @ function )
& ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(154,plain,
( ( empty_set @ ordinal )
& ( empty_set @ epsilon_connected )
& ( empty_set @ epsilon_transitive )
& ( empty_set @ empty )
& ( empty_set @ one_to_one )
& ( empty_set @ function )
& ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(29,axiom,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(131,plain,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(16,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(83,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(69,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(138,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(88,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(34,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( A @ ( B @ in ) )
<=> ( B @ ordinal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).
thf(164,plain,
! [A: $i] :
~ ! [B: $i] :
( ( ( B @ ordinal )
=> ( A @ ( B @ in ) ) )
& ( ( A @ ( B @ in ) )
=> ( B @ ordinal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(121,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(32,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( ( C @ ordinal )
& ( A @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_43__ordinal1) ).
thf(147,plain,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ( ( C @ ordinal )
& ( A @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( ( C @ ordinal )
& ( A @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(61,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(30,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(133,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(14,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(74,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,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)],[9]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(117,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(21,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(103,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(91,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(107,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(79,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(171,plain,
$false,
inference(e,[status(thm)],[115,42,125,57,38,65,53,96,44,49,98,35,112,67,154,119,131,83,69,138,88,164,121,147,61,133,74,60,117,103,91,107,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.12/0.62 % Computer : n015.cluster.edu
% 0.12/0.62 % Model : x86_64 x86_64
% 0.12/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.62 % Memory : 8046.5625MB
% 0.12/0.62 % OS : Linux 6.8.0-71-generic
% 0.12/0.62 % CPULimit : 300
% 0.12/0.62 % WCLimit : 300
% 0.12/0.62 % DateTime : Sat Sep 26 02:42:13 UTC 2026
% 0.12/0.62 % CPUTime :
% 0.12/0.62 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
% 0.94/1.20 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.40 % [INFO] Parsing done (194ms).
% 1.31/1.42 % [INFO] Running in sequential loop mode.
% 1.93/1.82 % [INFO] eprover registered as external prover.
% 1.93/1.82 % [INFO] Scanning for conjecture ...
% 2.11/1.92 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 2.11/1.99 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 2.35/2.04 % [INFO] Problem is first-order (TPTP FOF).
% 2.35/2.05 % [INFO] Type checking passed.
% 2.35/2.05 % [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 ...
% 3.76/2.78 % External prover 'e' found a proof!
% 3.76/2.78 % [INFO] Killing All external provers ...
% 3.76/2.78 % Time passed: 2020ms (effective reasoning time: 1362ms)
% 3.76/2.78 % 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)>
% 3.76/2.79 % Axioms used in derivation (32): rc3_funct_1, cc1_relat_1, rc1_funct_1, cc2_ordinal1, rc4_funct_1, s1_xboole_0__e2_43__ordinal1, cc1_ordinal1, rc3_ordinal1, rc2_relat_1, t37_ordinal1, rc1_relat_1, rc2_ordinal1, fc2_ordinal1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, rc5_funct_1, t7_boole, cc1_funct_1, rc2_funct_1, cc3_ordinal1, cc2_funct_1, existence_m1_subset_1, rc1_ordinal1, t8_boole, rc1_xboole_0, t2_subset, fc12_relat_1
% 3.76/2.79 % No. of inferences in proof: 68
% 3.76/2.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2020 ms resp. 1362 ms w/o parsing
% 4.02/2.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.02/2.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------