TSTP Solution File: SEU385+1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SEU385+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 08:10:03 EDT 2024
% Result : Theorem 6.01s 2.56s
% Output : Refutation 6.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 109
% Syntax : Number of formulae : 182 ( 19 unt; 38 typ; 0 def)
% Number of atoms : 584 ( 48 equ; 0 cnn)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 1872 ( 98 ~; 2 |; 278 &;1334 @)
% ( 4 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 38 usr; 2 con; 0-4 aty)
% Number of variables : 340 ( 0 ^ 299 !; 41 ?; 340 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(directed_relstr_type,type,
directed_relstr: $i > $o ).
thf(net_str_type,type,
net_str: $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(netstr_restr_to_element_type,type,
netstr_restr_to_element: $i > $i > $i > $i ).
thf(apply_netmap_type,type,
apply_netmap: $i > $i > $i > $i ).
thf(cup_closed_type,type,
cup_closed: $i > $o ).
thf(diff_closed_type,type,
diff_closed: $i > $o ).
thf(preboolean_type,type,
preboolean: $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(quasi_total_type,type,
quasi_total: $i > $i > $i > $o ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(partfun_dom_restriction_type,type,
partfun_dom_restriction: $i > $i > $i > $i > $i ).
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(relation_type,type,
relation: $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(finite_type,type,
finite: $i > $o ).
thf(rel_str_type,type,
rel_str: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(relation_restriction_type,type,
relation_restriction: $i > $i > $i ).
thf(relation_restriction_as_relation_of_type,type,
relation_restriction_as_relation_of: $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(relation_dom_restriction_type,type,
relation_dom_restriction: $i > $i > $i ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(net_str_of_type,type,
net_str_of: $i > $i > $i > $i > $i ).
thf(apply_on_structs_type,type,
apply_on_structs: $i > $i > $i > $i > $i ).
thf(the_mapping_type,type,
the_mapping: $i > $i > $i ).
thf(apply_on_set_and_struct2_type,type,
apply_on_set_and_struct2: $i > $i > $i > $i > $i ).
thf(strict_net_str_type,type,
strict_net_str: $i > $i > $o ).
thf(the_InternalRel_type,type,
the_InternalRel: $i > $i ).
thf(related_type,type,
related: $i > $i > $i > $o ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(142,plain,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(34,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(192,plain,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(37,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(199,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(186,plain,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(72,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(332,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( relation_of2 @ C @ A @ B ) )
=> ( ( function @ ( partfun_dom_restriction @ A @ B @ C @ D ) )
& ( relation_of2_as_subset @ ( partfun_dom_restriction @ A @ B @ C @ D ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( relation_of2 @ C @ A @ B ) )
=> ( ( function @ ( partfun_dom_restriction @ A @ B @ C @ D ) )
& ( relation_of2_as_subset @ ( partfun_dom_restriction @ A @ B @ C @ D ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ~ ( empty_carrier @ ( net_str_of @ A @ B @ C @ D ) )
& ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_waybel_0) ).
thf(234,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ~ ( empty_carrier @ ( net_str_of @ A @ B @ C @ D ) )
& ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(4,axiom,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(88,plain,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(170,plain,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(10,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(115,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(276,plain,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ~ ( empty_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc22_waybel_9) ).
thf(247,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ~ ( empty_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(202,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(174,plain,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(68,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(288,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(257,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(14,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(125,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( function @ C )
& ( quasi_total @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(196,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( function @ C )
& ( quasi_total @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(23,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(157,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(189,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( element @ ( apply_on_set_and_struct2 @ A @ B @ C @ D ) @ ( the_carrier @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_yellow_2) ).
thf(284,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( element @ ( apply_on_set_and_struct2 @ A @ B @ C @ D ) @ ( the_carrier @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A )
& ( net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_waybel_9) ).
thf(325,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A )
& ( net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(152,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation_of2_as_subset @ C @ A @ B )
=> ( relation_of2 @ C @ A @ B ) )
& ( ( relation_of2 @ C @ A @ B )
=> ( relation_of2_as_subset @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(45,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(228,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(57,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(261,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( relation_of2 @ C @ A @ B ) )
=> ( ( partfun_dom_restriction @ A @ B @ C @ D )
= ( relation_dom_restriction @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_partfun1) ).
thf(179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( relation_of2 @ C @ A @ B ) )
=> ( ( partfun_dom_restriction @ A @ B @ C @ D )
= ( relation_dom_restriction @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( empty @ ( powerset @ A ) )
& ( cup_closed @ ( powerset @ A ) )
& ( diff_closed @ ( powerset @ A ) )
& ( preboolean @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(106,plain,
! [A: $i] :
( ~ ( empty @ ( powerset @ A ) )
& ( cup_closed @ ( powerset @ A ) )
& ( diff_closed @ ( powerset @ A ) )
& ( preboolean @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(121,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(280,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(42,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( apply_netmap @ A @ B @ C )
= ( apply_on_structs @ B @ A @ ( the_mapping @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_waybel_0) ).
thf(221,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( apply_netmap @ A @ B @ C )
= ( apply_on_structs @ B @ A @ ( the_mapping @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(16,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(133,plain,
? [A: $i] : ( rel_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( strict_net_str @ B @ A )
=> ( B
= ( net_str_of @ A @ ( the_carrier @ B ) @ ( the_InternalRel @ B ) @ ( the_mapping @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v6_waybel_0) ).
thf(265,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( strict_net_str @ B @ A )
=> ( B
= ( net_str_of @ A @ ( the_carrier @ B ) @ ( the_InternalRel @ B ) @ ( the_mapping @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(69,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ! [D: $i] :
( ( ( strict_net_str @ D @ A )
& ( net_str @ D @ A ) )
=> ( ( D
= ( netstr_restr_to_element @ A @ B @ C ) )
<=> ( ! [E: $i] :
( ( in @ E @ ( the_carrier @ D ) )
<=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
& ( F = E )
& ( related @ B @ C @ F ) ) )
& ( ( the_InternalRel @ D )
= ( relation_restriction_as_relation_of @ ( the_InternalRel @ B ) @ ( the_carrier @ D ) ) )
& ( ( the_mapping @ A @ D )
= ( partfun_dom_restriction @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_waybel_9) ).
thf(292,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ! [D: $i] :
( ( ( strict_net_str @ D @ A )
& ( net_str @ D @ A ) )
=> ( ( ( D
= ( netstr_restr_to_element @ A @ B @ C ) )
=> ( ! [E: $i] :
( ( ( in @ E @ ( the_carrier @ D ) )
=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
& ( F = E )
& ( related @ B @ C @ F ) ) )
& ( ? [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
& ( F = E )
& ( related @ B @ C @ F ) )
=> ( in @ E @ ( the_carrier @ D ) ) ) )
& ( ( the_InternalRel @ D )
= ( relation_restriction_as_relation_of @ ( the_InternalRel @ B ) @ ( the_carrier @ D ) ) )
& ( ( the_mapping @ A @ D )
= ( partfun_dom_restriction @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ D ) ) ) ) )
& ( ( ! [E: $i] :
( ( ( in @ E @ ( the_carrier @ D ) )
=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
& ( F = E )
& ( related @ B @ C @ F ) ) )
& ( ? [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
& ( F = E )
& ( related @ B @ C @ F ) )
=> ( in @ E @ ( the_carrier @ D ) ) ) )
& ( ( the_InternalRel @ D )
= ( relation_restriction_as_relation_of @ ( the_InternalRel @ B ) @ ( the_carrier @ D ) ) )
& ( ( the_mapping @ A @ D )
= ( partfun_dom_restriction @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ D ) ) ) )
=> ( D
= ( netstr_restr_to_element @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(60,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(270,plain,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ A ) ) )
=> ( ( apply_on_structs @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_waybel_0) ).
thf(252,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ A ) ) )
=> ( ( apply_on_structs @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(224,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
thf(328,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( net_str_of @ A @ B @ C @ D )
= ( net_str_of @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_waybel_0) ).
thf(212,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( net_str_of @ A @ B @ C @ D )
= ( net_str_of @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ ( netstr_restr_to_element @ A @ B @ C ) ) )
=> ( ( D = E )
=> ( ( apply_netmap @ A @ B @ D )
= ( apply_netmap @ A @ ( netstr_restr_to_element @ A @ B @ C ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_waybel_9) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ ( netstr_restr_to_element @ A @ B @ C ) ) )
=> ( ( D = E )
=> ( ( apply_netmap @ A @ B @ D )
= ( apply_netmap @ A @ ( netstr_restr_to_element @ A @ B @ C ) @ E ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(73,plain,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ ( netstr_restr_to_element @ A @ B @ C ) ) )
=> ( ( D = E )
=> ( ( apply_netmap @ A @ B @ D )
= ( apply_netmap @ A @ ( netstr_restr_to_element @ A @ B @ C ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C )
& ( quasi_total @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(128,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C )
& ( quasi_total @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(48,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( net_str @ B @ A )
& ( strict_net_str @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_waybel_0) ).
thf(237,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( net_str @ B @ A )
& ( strict_net_str @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( ( relation_restriction_as_relation_of @ A @ B )
= ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_toler_1) ).
thf(166,plain,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( ( relation_restriction_as_relation_of @ A @ B )
= ( relation_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(148,plain,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(176,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(286,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(11,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(118,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(56,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(259,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(3,axiom,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(86,plain,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(159,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(91,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( element @ ( apply_netmap @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_waybel_0) ).
thf(240,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( element @ ( apply_netmap @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(63,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(278,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ~ ( empty @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ~ ( empty @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ A ) ) )
=> ( element @ ( apply_on_structs @ A @ B @ C @ D ) @ ( the_carrier @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_waybel_0) ).
thf(226,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ A ) ) )
=> ( element @ ( apply_on_structs @ A @ B @ C @ D ) @ ( the_carrier @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(54,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(255,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(209,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(35,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(194,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation_of2_as_subset @ ( relation_restriction_as_relation_of @ A @ B ) @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_toler_1) ).
thf(145,plain,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation_of2_as_subset @ ( relation_restriction_as_relation_of @ A @ B ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(65,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(282,plain,
? [A: $i] : ( one_sorted_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ B )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(95,plain,
! [A: $i,B: $i] :
( ~ ( empty @ B )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(99,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(52,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(250,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( ( apply_on_set_and_struct2 @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_yellow_2) ).
thf(231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( ( apply_on_set_and_struct2 @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(12,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(119,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(39,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(207,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ A )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
thf(183,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ A )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A )
& ( net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_waybel_0) ).
thf(273,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A )
& ( net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ~ ( empty @ ( the_mapping @ A @ B ) )
& ( relation @ ( the_mapping @ A @ B ) )
& ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_yellow_6) ).
thf(242,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ~ ( empty @ ( the_mapping @ A @ B ) )
& ( relation @ ( the_mapping @ A @ B ) )
& ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(59,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(268,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(350,plain,
$false,
inference(cvc4,[status(thm)],[142,192,199,186,332,101,234,88,170,115,276,247,202,174,288,257,125,196,157,189,284,325,152,228,261,179,106,121,280,221,133,265,292,270,252,224,328,212,73,128,237,166,148,161,176,286,118,259,86,159,140,91,240,278,135,226,255,209,194,145,282,95,99,250,231,119,207,183,273,242,268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU385+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n023.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 10:33:42 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.03/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.50/1.11 % [INFO] Parsing done (174ms).
% 1.50/1.12 % [INFO] Running in sequential loop mode.
% 2.05/1.32 % [INFO] eprover registered as external prover.
% 2.05/1.32 % [INFO] cvc4 registered as external prover.
% 2.05/1.32 % [INFO] Scanning for conjecture ...
% 2.23/1.40 % [INFO] Found a conjecture and 78 axioms. Running axiom selection ...
% 2.49/1.47 % [INFO] Axiom selection finished. Selected 70 axioms (removed 8 axioms).
% 2.75/1.55 % [INFO] Problem is first-order (TPTP FOF).
% 2.75/1.56 % [INFO] Type checking passed.
% 2.75/1.56 % [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 ...
% 6.01/2.56 % External prover 'cvc4' found a proof!
% 6.01/2.56 % [INFO] Killing All external provers ...
% 6.01/2.56 % Time passed: 2016ms (effective reasoning time: 1437ms)
% 6.01/2.56 % 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)>
% 6.01/2.56 % Axioms used in derivation (70): cc2_finset_1, dt_k1_waybel_0, rc3_funct_1, dt_g1_waybel_0, t6_boole, t5_subset, existence_m1_relset_1, dt_k7_yellow_2, dt_k7_relat_1, rc3_finset_1, antisymmetry_r2_hidden, dt_k5_waybel_9, redefinition_m2_relset_1, fc1_finsub_1, rc4_finset_1, d7_waybel_9, fc1_xboole_0, fc4_funct_1, t1_subset, dt_m2_relset_1, dt_k1_toler_1, rc1_funct_1, cc2_finsub_1, dt_u1_waybel_0, dt_u1_orders_2, dt_l1_waybel_0, abstractness_v6_waybel_0, existence_l1_waybel_0, t4_subset, cc1_funct_2, d8_waybel_0, t7_boole, existence_l1_orders_2, cc1_funct_1, rc3_struct_0, redefinition_k1_toler_1, dt_k2_partfun1, rc2_funct_1, rc1_funct_2, fc15_yellow_6, redefinition_k1_waybel_0, cc2_funct_1, rc4_waybel_0, t3_subset, cc1_relset_1, existence_m1_subset_1, fc6_waybel_0, existence_m2_relset_1, t72_funct_1, dt_l1_orders_2, cc1_finsub_1, fc1_struct_0, cc6_funct_2, reflexivity_r1_tarski, redefinition_k7_yellow_2, free_g1_waybel_0, rc1_finset_1, cc1_finset_1, dt_k2_wellord1, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, existence_l1_struct_0, dt_k3_waybel_0, cc5_funct_2, fc22_waybel_9, rc2_xboole_0, redefinition_k2_partfun1, fc14_finset_1
% 6.01/2.56 % No. of inferences in proof: 144
% 6.01/2.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2016 ms resp. 1437 ms w/o parsing
% 6.51/2.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.51/2.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------