%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU373+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 : n026.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 08:38:36 AM UTC 2026
% Result : Theorem 5.47s 2.91s
% Output : Refutation 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 52
% Syntax : Number of formulae : 106 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 281 ( 9 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 766 ( 26 ~; 2 |; 84 &; 565 @)
% ( 4 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 2 con; 0-4 aty)
% Number of variables : 198 ( 0 ^; 162 !; 36 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(net_str_decl,type,
net_str: $i > $i > $o ).
thf(subnetstr_decl,type,
subnetstr: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(relation_dom_restriction_decl,type,
relation_dom_restriction: $i > $i > $i ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(relation_dom_restr_as_relation_of_decl,type,
relation_dom_restr_as_relation_of: $i > $i > $i > $i > $i ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(subrelstr_decl,type,
subrelstr: $i > $i > $o ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(the_mapping_decl,type,
the_mapping: $i > $i > $i ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(5,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(69,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(170,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(30,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(153,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(174,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(11,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(93,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ relation_dom_restr_as_relation_of ) ) ) @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_1) ).
thf(141,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ relation_dom_restr_as_relation_of ) ) ) @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(208,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)],[47]) ).
thf(6,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(72,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( A @ ( C @ net_str ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_6) ).
thf(227,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( A @ ( C @ net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
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(110,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(125,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(34,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(164,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)],[34]) ).
thf(15,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(106,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(221,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(23,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(132,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(45,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(201,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(3,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(60,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(117,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(42,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(192,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(137,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(229,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(97,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] : ( A @ ( B @ net_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(225,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] : ( A @ ( B @ net_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(7,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(77,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(166,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(28,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(148,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(4,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pboole) ).
thf(64,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(39,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(180,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( B @ the_carrier @ ( C @ the_carrier @ subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_yellow_6) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( B @ the_carrier @ ( C @ the_carrier @ subset ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(54,plain,
~ ! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( B @ the_carrier @ ( C @ the_carrier @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(144,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(32,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(159,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(103,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(91,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ relation_dom_restr_as_relation_of ) ) ) )
= ( D @ ( C @ relation_dom_restriction ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_relset_1) ).
thf(155,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ relation_dom_restr_as_relation_of ) ) ) )
= ( D @ ( C @ relation_dom_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(22,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(130,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(223,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( B @ rel_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
thf(162,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( B @ rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(112,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( B @ rel_str )
=> ( ( A @ ( B @ subrelstr ) )
<=> ( ( A @ the_InternalRel @ ( B @ the_InternalRel @ subset ) )
& ( A @ the_carrier @ ( B @ the_carrier @ subset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_0) ).
thf(194,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( B @ rel_str )
=> ( ( ( ( A @ the_InternalRel @ ( B @ the_InternalRel @ subset ) )
& ( A @ the_carrier @ ( B @ the_carrier @ subset ) ) )
=> ( A @ ( B @ subrelstr ) ) )
& ( ( A @ ( B @ subrelstr ) )
=> ( ( A @ the_InternalRel @ ( B @ the_InternalRel @ subset ) )
& ( A @ the_carrier @ ( B @ the_carrier @ subset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ subnetstr ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_6) ).
thf(199,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ subnetstr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(40,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(182,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(99,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(87,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
thf(203,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ function )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(186,plain,
! [A: $i,B: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ function )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_dom_restriction ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_dom_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( A @ relation_empty_yielding )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ relation_empty_yielding )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( ( A @ relation_empty_yielding )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ relation_empty_yielding )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,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(82,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)],[8]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( A @ ( C @ net_str ) )
=> ( ( B @ ( A @ ( C @ subnetstr ) ) )
<=> ( ( ( C @ ( A @ the_mapping ) )
= ( C @ the_carrier @ ( B @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( B @ the_carrier @ relation_dom_restr_as_relation_of ) ) ) ) )
& ( B @ ( C @ subrelstr ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_yellow_6) ).
thf(214,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( A @ ( C @ net_str ) )
=> ( ( ( ( ( C @ ( A @ the_mapping ) )
= ( C @ the_carrier @ ( B @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( B @ the_carrier @ relation_dom_restr_as_relation_of ) ) ) ) )
& ( B @ ( C @ subrelstr ) ) )
=> ( B @ ( A @ ( C @ subnetstr ) ) ) )
& ( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( ( ( C @ ( A @ the_mapping ) )
= ( C @ the_carrier @ ( B @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( B @ the_carrier @ relation_dom_restr_as_relation_of ) ) ) ) )
& ( B @ ( C @ subrelstr ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(168,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] : ( A @ ( B @ subrelstr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
thf(146,plain,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] : ( A @ ( B @ subrelstr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(231,plain,
$false,
inference(e,[status(thm)],[69,170,153,174,93,141,208,72,227,110,125,164,106,221,132,201,60,117,192,137,229,97,225,77,166,148,64,180,54,144,159,103,91,155,130,223,162,112,194,199,182,99,87,203,186,114,119,82,214,151,168,146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU373+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.14/0.40 % Computer : n026.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 09:24:25 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.84/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/1.22 % [INFO] Parsing done (220ms).
% 1.34/1.24 % [INFO] Running in sequential loop mode.
% 2.09/1.63 % [INFO] eprover registered as external prover.
% 2.09/1.64 % [INFO] Scanning for conjecture ...
% 2.30/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 58 axioms. Running axiom selection ...
% 2.46/1.84 % [INFO] Axiom selection finished. Selected 51 axioms (removed 7 axioms).
% 2.71/1.93 % [INFO] Problem is first-order (TPTP FOF).
% 2.71/1.94 % [INFO] Type checking passed.
% 2.71/1.94 % [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 ...
% 5.47/2.90 % External prover 'e' found a proof!
% 5.47/2.91 % [INFO] Killing All external provers ...
% 5.47/2.91 % Time passed: 2353ms (effective reasoning time: 1663ms)
% 5.47/2.91 % 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)>
% 5.47/2.91 % Axioms used in derivation (51): redefinition_m2_relset_1, dt_k8_relset_1, t5_subset, existence_m1_relset_1, dt_k7_relat_1, dt_l1_orders_2, rc1_pboole, t8_boole, antisymmetry_r2_hidden, fc4_relat_1, fc4_funct_1, t1_subset, fc4_subset_1, d13_yellow_0, rc3_funct_1, d8_yellow_6, dt_m2_relset_1, cc1_relat_1, rc1_funct_1, dt_u1_waybel_0, dt_u1_orders_2, rc3_relat_1, t6_boole, rc2_subset_1, rc4_funct_1, redefinition_k8_relset_1, dt_l1_waybel_0, existence_l1_waybel_0, fc13_relat_1, t4_subset, t7_boole, existence_l1_orders_2, cc1_funct_1, fc1_subset_1, rc2_funct_1, rc1_subset_1, cc2_funct_1, t3_subset, cc1_relset_1, existence_m1_subset_1, rc2_relat_1, existence_m2_relset_1, rc1_relat_1, reflexivity_r1_tarski, existence_m1_yellow_0, dt_m1_yellow_0, t2_subset, dt_m1_yellow_6, fc12_relat_1, existence_l1_struct_0, existence_m1_yellow_6
% 5.47/2.91 % No. of inferences in proof: 106
% 5.47/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2353 ms resp. 1663 ms w/o parsing
% 5.47/3.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.47/3.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------