%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM409+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 : n019.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 08:08:46 AM UTC 2026
% Result : Theorem 7.23s 3.98s
% Output : Refutation 7.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 49
% Syntax : Number of formulae : 100 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 291 ( 13 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 605 ( 28 ~; 2 |; 127 &; 386 @)
% ( 6 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 2 con; 0-2 aty)
% Number of variables : 132 ( 0 ^; 95 !; 37 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
thf(transfinite_sequence_of_decl,type,
transfinite_sequence_of: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
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(transfinite_sequence_decl,type,
transfinite_sequence: $i > $o ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(relation_non_empty_decl,type,
relation_non_empty: $i > $o ).
thf(with_non_empty_elements_decl,type,
with_non_empty_elements: $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(47,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(228,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(144,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(130,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)],[27]) ).
thf(16,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(95,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(29,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(139,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1,conjecture,
! [A: $i] : ( A @ ( empty_set @ transfinite_sequence_of ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_ordinal1) ).
thf(2,negated_conjecture,
~ ! [A: $i] : ( A @ ( empty_set @ transfinite_sequence_of ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(51,plain,
~ ! [A: $i] : ( A @ ( empty_set @ transfinite_sequence_of ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(136,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(36,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(170,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)],[36]) ).
thf(22,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(115,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(39,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(202,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(21,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(110,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(125,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(43,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(216,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B
= ( A @ relation_dom ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(179,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_dom ) ) )
& ( ( B
= ( A @ relation_dom ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ transfinite_sequence_of ) )
=> ( ( B @ transfinite_sequence )
& ( B @ function )
& ( B @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
thf(211,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ transfinite_sequence_of ) )
=> ( ( B @ transfinite_sequence )
& ( B @ function )
& ( B @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(106,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( B @ transfinite_sequence )
& ( B @ function )
& ( B @ relation ) )
=> ( ( A @ ( B @ transfinite_sequence_of ) )
<=> ( A @ ( B @ relation_rng @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
thf(221,plain,
! [A: $i,B: $i] :
( ( ( B @ transfinite_sequence )
& ( B @ function )
& ( B @ relation ) )
=> ( ( ( A @ ( B @ relation_rng @ subset ) )
=> ( A @ ( B @ transfinite_sequence_of ) ) )
& ( ( A @ ( B @ transfinite_sequence_of ) )
=> ( A @ ( B @ relation_rng @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(40,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(206,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(44,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(220,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ transfinite_sequence )
<=> ( A @ relation_dom @ ordinal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
thf(102,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( ( A @ relation_dom @ ordinal )
=> ( A @ transfinite_sequence ) )
& ( ( A @ transfinite_sequence )
=> ( A @ relation_dom @ ordinal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(117,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(70,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(165,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(33,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(156,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(3,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(53,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(225,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(12,axiom,
? [A: $i] :
( ( A @ transfinite_sequence )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_ordinal1) ).
thf(77,plain,
? [A: $i] :
( ( A @ transfinite_sequence )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(31,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(148,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(161,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(8,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(64,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(48,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(230,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)],[48]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_dom )
= empty_set )
<=> ( ( A @ relation_rng )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(245,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( ( A @ relation_rng )
= empty_set )
=> ( ( A @ relation_dom )
= empty_set ) )
& ( ( ( A @ relation_dom )
= empty_set )
=> ( ( A @ relation_rng )
= empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(91,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(66,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(240,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(108,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(41,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ transfinite_sequence_of ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_ordinal1) ).
thf(209,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ transfinite_sequence_of ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(25,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) )
=> ( A @ relation_rng @ with_non_empty_elements ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_funct_1) ).
thf(123,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) )
=> ( A @ relation_rng @ with_non_empty_elements ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(154,plain,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(11,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(72,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)],[11]) ).
thf(17,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(99,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(87,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(82,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(119,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(38,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(200,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(7,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(62,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)],[7]) ).
thf(254,plain,
$false,
inference(e,[status(thm)],[56,228,144,130,95,139,51,136,170,115,202,110,125,216,179,211,106,221,206,220,102,60,117,70,165,156,53,225,77,148,161,64,230,245,91,66,240,108,209,123,154,72,99,87,82,119,58,200,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.14/0.39 % Computer : n019.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 02:39:18 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 1.32/1.20 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.52 % [INFO] Parsing done (323ms).
% 1.94/1.55 % [INFO] Running in sequential loop mode.
% 2.95/2.12 % [INFO] eprover registered as external prover.
% 2.95/2.13 % [INFO] Scanning for conjecture ...
% 3.33/2.28 % [INFO] Found a conjecture (or negated_conjecture) and 50 axioms. Running axiom selection ...
% 3.70/2.40 % [INFO] Axiom selection finished. Selected 48 axioms (removed 2 axioms).
% 3.93/2.51 % [INFO] Problem is first-order (TPTP FOF).
% 3.93/2.53 % [INFO] Type checking passed.
% 3.93/2.54 % [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 ...
% 7.23/3.98 % External prover 'e' found a proof!
% 7.23/3.98 % [INFO] Killing All external provers ...
% 7.23/3.98 % Time passed: 3382ms (effective reasoning time: 2425ms)
% 7.23/3.98 % 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)>
% 7.23/3.98 % Axioms used in derivation (48): fc1_zfmisc_1, d4_relat_1, rc4_funct_1, t4_subset, rc2_relat_1, rc2_ordinal1, fc2_ordinal1, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc4_ordinal1, rc3_funct_1, cc1_relat_1, d8_ordinal1, fc6_funct_1, rc1_funct_1, rc3_relat_1, t6_boole, cc2_ordinal1, t5_subset, existence_m1_ordinal1, cc1_ordinal1, rc5_funct_1, t7_boole, cc1_funct_1, rc2_funct_1, cc3_ordinal1, rc3_ordinal1, fc5_relat_1, cc2_funct_1, t3_subset, existence_m1_subset_1, rc1_ordinal1, rc1_relat_1, reflexivity_r1_tarski, t2_xboole_1, fc6_relat_1, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc8_relat_1, fc12_relat_1, t65_relat_1, dt_m1_ordinal1, d7_ordinal1, rc2_xboole_0
% 7.23/3.98 % No. of inferences in proof: 100
% 7.23/3.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3382 ms resp. 2425 ms w/o parsing
% 7.80/4.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.80/4.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------