%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM401+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n009.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 5.13s 8.02s
% Output : Refutation 5.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 54
% Syntax : Number of formulae : 110 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 326 ( 30 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 713 ( 40 ~; 9 |; 126 &; 457 @)
% ( 10 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 2 con; 0-2 aty)
% Number of variables : 161 ( 0 ^; 133 !; 28 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(succ_decl,type,
succ: $i > $i ).
thf(ordinal_subset_decl,type,
ordinal_subset: $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(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
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(powerset_decl,type,
powerset: $i > $i ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(52,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
thf(288,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(19,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(125,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(270,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(188,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(15,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(109,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(32,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(173,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(64,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(176,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(86,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(162,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(12,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(104,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(37,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(190,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(222,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)],[39]) ).
thf(22,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(138,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(249,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(170,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(17,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(115,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ succ )
= ( A @ singleton @ ( A @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
thf(308,plain,
! [A: $i] :
( ( A @ succ )
= ( A @ singleton @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(18,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(120,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(247,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( B @ succ @ ( A @ in ) )
<=> ( B @ ( A @ ordinal_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_ordinal1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( B @ succ @ ( A @ in ) )
<=> ( B @ ( A @ ordinal_subset ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(56,plain,
~ ! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( ( B @ ( A @ ordinal_subset ) )
=> ( B @ succ @ ( A @ in ) ) )
& ( ( B @ succ @ ( A @ in ) )
=> ( B @ ( A @ ordinal_subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(142,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(153,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(147,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(49,axiom,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(280,plain,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(132,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)],[21]) ).
thf(10,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(89,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_union2 ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_union2 ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(5,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(70,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(11,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( A @ ( A @ ordinal_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(285,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( A @ ( A @ ordinal_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(40,axiom,
! [A: $i] : ( A @ succ @ ( A @ in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(224,plain,
! [A: $i] : ( A @ succ @ ( A @ in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(128,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(105,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(113,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(48,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(274,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(41,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(226,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)],[41]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(167,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ~ ( ~ ( A @ ( B @ in ) )
& ( A != B )
& ~ ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(282,plain,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ~ ( ~ ( A @ ( B @ in ) )
& ( A != B )
& ~ ( B @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(150,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( B @ ( A @ ordinal_subset ) )
<=> ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(304,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( ( B @ ( A @ subset ) )
=> ( B @ ( A @ ordinal_subset ) ) )
& ( ( B @ ( A @ ordinal_subset ) )
=> ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(158,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( A @ ( B @ ordinal_subset ) )
| ( B @ ( A @ ordinal_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(186,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( A @ ( B @ ordinal_subset ) )
| ( B @ ( A @ ordinal_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(6,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(75,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,axiom,
! [A: $i] :
( A
!= ( A @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_ordinal1) ).
thf(235,plain,
! [A: $i] :
( A
!= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(8,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(82,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(107,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(294,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)],[53]) ).
thf(7,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(79,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(195,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_union2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_union2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [A: $i] :
~ ( A @ succ @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(239,plain,
! [A: $i] :
~ ( A @ succ @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(242,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(68,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ epsilon_transitive )
<=> ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(178,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) )
=> ( A @ epsilon_transitive ) )
& ( ( A @ epsilon_transitive )
=> ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(317,plain,
$false,
inference(e,[status(thm)],[288,125,270,188,109,173,64,176,86,162,104,190,222,138,249,170,115,308,120,247,56,142,153,147,280,132,89,160,70,92,285,224,128,105,113,274,226,167,282,150,304,158,186,75,235,82,107,294,79,195,239,242,68,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM401+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.11/5.40 % Computer : n009.cluster.edu
% 0.11/5.40 % Model : x86_64 x86_64
% 0.11/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.40 % Memory : 8046.5625MB
% 0.11/5.40 % OS : Linux 6.8.0-71-generic
% 0.11/5.40 % CPULimit : 300
% 0.11/5.40 % WCLimit : 300
% 0.11/5.40 % DateTime : Sat Sep 26 02:38:50 UTC 2026
% 0.11/5.40 % CPUTime :
% 0.11/5.40 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 ...
% 1.34/6.22 % [INFO] Parsing done (225ms).
% 1.34/6.24 % [INFO] Running in sequential loop mode.
% 2.00/6.63 % [INFO] eprover registered as external prover.
% 2.00/6.64 % [INFO] Scanning for conjecture ...
% 2.20/6.75 % [INFO] Found a conjecture (or negated_conjecture) and 53 axioms. Running axiom selection ...
% 2.36/6.84 % [INFO] Axiom selection finished. Selected 53 axioms (removed 0 axioms).
% 2.57/6.91 % [INFO] Problem is first-order (TPTP FOF).
% 2.57/6.92 % [INFO] Type checking passed.
% 2.57/6.93 % [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 ...
% 5.13/8.01 % External prover 'e' found a proof!
% 5.13/8.02 % [INFO] Killing All external provers ...
% 5.13/8.02 % Time passed: 2469ms (effective reasoning time: 1774ms)
% 5.13/8.02 % 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)>
% 5.13/8.02 % Axioms used in derivation (53): redefinition_r1_ordinal1, d1_tarski, t1_boole, rc3_funct_1, cc1_relat_1, cc1_ordinal1, rc3_ordinal1, reflexivity_r1_ordinal1, rc2_ordinal1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc1_funct_1, fc2_xboole_0, rc3_relat_1, t6_boole, cc2_ordinal1, commutativity_k2_xboole_0, t5_subset, d1_ordinal1, rc4_funct_1, t4_subset, fc3_xboole_0, d2_xboole_0, rc5_funct_1, t7_boole, cc1_funct_1, fc3_ordinal1, rc2_funct_1, cc3_ordinal1, connectedness_r1_ordinal1, cc2_funct_1, t3_subset, t24_ordinal1, existence_m1_subset_1, rc1_ordinal1, rc2_relat_1, t10_ordinal1, rc1_relat_1, t14_ordinal1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc2_relat_1, fc1_ordinal1, d2_ordinal1, fc12_relat_1, idempotence_k2_xboole_0, fc2_ordinal1, d10_xboole_0
% 5.13/8.02 % No. of inferences in proof: 110
% 5.13/8.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2469 ms resp. 1774 ms w/o parsing
% 5.73/8.13 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.73/8.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------