TSTP Solution File: SEU395+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n018.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 Aug 22 10:58:37 EDT 2023
% Result : Theorem 87.98s 66.91s
% Output : CNFRefutation 88.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 129
% Syntax : Number of formulae : 260 ( 49 unt; 119 typ; 0 def)
% Number of atoms : 543 ( 19 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 638 ( 236 ~; 334 |; 50 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 141 ( 99 >; 42 *; 0 +; 0 <<)
% Number of predicates : 57 ( 55 usr; 1 prp; 0-3 aty)
% Number of functors : 64 ( 64 usr; 20 con; 0-4 aty)
% Number of variables : 93 (; 93 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > quasi_total > is_eventually_in > is_a_convergence_point_of_set > upper_relstr_subset > subset > strict_net_str > proper_element > open_subset > nowhere_dense > net_str > lower_relstr_subset > in > filtered_subset > element > directed_subset > dense > closed_subset > boundary_set > with_suprema_relstr > with_infima_relstr > v5_membered > v4_membered > v3_membered > v2_membered > v1_yellow_3 > v1_membered > upper_bounded_relstr > up_complete_relstr > trivial_carrier > transitive_relstr > topological_space > top_str > strict_rel_str > relation_empty_yielding > relation > rel_str > reflexive_relstr > one_sorted_str > lower_bounded_relstr > join_complete_relstr > heyting_relstr > function > finite > empty_carrier > empty > distributive_relstr > directed_relstr > connected_relstr > complete_relstr > complemented_relstr > bounded_relstr > boolean_relstr > antisymmetric_relstr > net_str_of > net_of_bool_filter > the_mapping > rel_str_of > lim_points_of_net > filter_of_net_str > cartesian_product2 > a_2_1_yellow19 > #nlpp > the_carrier > the_InternalRel > powerset > cast_as_carrier_subset > boole_POSet > empty_set > #skF_9 > #skF_36 > #skF_25 > #skF_44 > #skF_16 > #skF_20 > #skF_4 > #skF_18 > #skF_24 > #skF_35 > #skF_11 > #skF_15 > #skF_31 > #skF_40 > #skF_19 > #skF_48 > #skF_37 > #skF_47 > #skF_34 > #skF_32 > #skF_14 > #skF_28 > #skF_46 > #skF_10 > #skF_41 > #skF_13 > #skF_49 > #skF_2 > #skF_38 > #skF_43 > #skF_3 > #skF_1 > #skF_21 > #skF_39 > #skF_23 > #skF_33 > #skF_26 > #skF_30 > #skF_50 > #skF_17 > #skF_22 > #skF_29 > #skF_27 > #skF_8 > #skF_7 > #skF_42 > #skF_45 > #skF_5 > #skF_6 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_36',type,
'#skF_36': $i > $i ).
tff('#skF_25',type,
'#skF_25': $i > $i ).
tff(empty_carrier,type,
empty_carrier: $i > $o ).
tff(directed_relstr,type,
directed_relstr: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_44',type,
'#skF_44': $i > $i ).
tff(filter_of_net_str,type,
filter_of_net_str: ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff(the_InternalRel,type,
the_InternalRel: $i > $i ).
tff(complete_relstr,type,
complete_relstr: $i > $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff('#skF_24',type,
'#skF_24': $i > $i ).
tff(boundary_set,type,
boundary_set: ( $i * $i ) > $o ).
tff(with_suprema_relstr,type,
with_suprema_relstr: $i > $o ).
tff('#skF_35',type,
'#skF_35': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(upper_relstr_subset,type,
upper_relstr_subset: ( $i * $i ) > $o ).
tff(quasi_total,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_31',type,
'#skF_31': $i > $i ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(net_of_bool_filter,type,
net_of_bool_filter: ( $i * $i * $i ) > $i ).
tff(filtered_subset,type,
filtered_subset: ( $i * $i ) > $o ).
tff(directed_subset,type,
directed_subset: ( $i * $i ) > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(finite,type,
finite: $i > $o ).
tff(proper_element,type,
proper_element: ( $i * $i ) > $o ).
tff(heyting_relstr,type,
heyting_relstr: $i > $o ).
tff(nowhere_dense,type,
nowhere_dense: ( $i * $i ) > $o ).
tff(lower_relstr_subset,type,
lower_relstr_subset: ( $i * $i ) > $o ).
tff('#skF_40',type,
'#skF_40': $i > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_48',type,
'#skF_48': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_37',type,
'#skF_37': $i ).
tff(is_a_convergence_point_of_set,type,
is_a_convergence_point_of_set: ( $i * $i * $i ) > $o ).
tff(is_eventually_in,type,
is_eventually_in: ( $i * $i * $i ) > $o ).
tff(antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
tff(open_subset,type,
open_subset: ( $i * $i ) > $o ).
tff('#skF_47',type,
'#skF_47': $i ).
tff(up_complete_relstr,type,
up_complete_relstr: $i > $o ).
tff('#skF_34',type,
'#skF_34': $i > $i ).
tff(net_str,type,
net_str: ( $i * $i ) > $o ).
tff('#skF_32',type,
'#skF_32': $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(strict_rel_str,type,
strict_rel_str: $i > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(boole_POSet,type,
boole_POSet: $i > $i ).
tff(reflexive_relstr,type,
reflexive_relstr: $i > $o ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff('#skF_28',type,
'#skF_28': $i > $i ).
tff('#skF_46',type,
'#skF_46': $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(a_2_1_yellow19,type,
a_2_1_yellow19: ( $i * $i ) > $i ).
tff('#skF_41',type,
'#skF_41': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(v1_yellow_3,type,
v1_yellow_3: $i > $o ).
tff(dense,type,
dense: ( $i * $i ) > $o ).
tff(lower_bounded_relstr,type,
lower_bounded_relstr: $i > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_49',type,
'#skF_49': ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_38',type,
'#skF_38': $i > $i ).
tff(transitive_relstr,type,
transitive_relstr: $i > $o ).
tff(rel_str_of,type,
rel_str_of: ( $i * $i ) > $i ).
tff(v3_membered,type,
v3_membered: $i > $o ).
tff('#skF_43',type,
'#skF_43': $i > $i ).
tff(bounded_relstr,type,
bounded_relstr: $i > $o ).
tff(net_str_of,type,
net_str_of: ( $i * $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
tff(connected_relstr,type,
connected_relstr: $i > $o ).
tff(empty,type,
empty: $i > $o ).
tff(closed_subset,type,
closed_subset: ( $i * $i ) > $o ).
tff('#skF_21',type,
'#skF_21': $i ).
tff(strict_net_str,type,
strict_net_str: ( $i * $i ) > $o ).
tff(distributive_relstr,type,
distributive_relstr: $i > $o ).
tff(v5_membered,type,
v5_membered: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_39',type,
'#skF_39': $i > $i ).
tff('#skF_23',type,
'#skF_23': $i > $i ).
tff(relation_of2,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(v2_membered,type,
v2_membered: $i > $o ).
tff(v1_membered,type,
v1_membered: $i > $o ).
tff('#skF_33',type,
'#skF_33': $i > $i ).
tff('#skF_26',type,
'#skF_26': $i > $i ).
tff(with_infima_relstr,type,
with_infima_relstr: $i > $o ).
tff('#skF_30',type,
'#skF_30': $i ).
tff('#skF_50',type,
'#skF_50': ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(the_mapping,type,
the_mapping: ( $i * $i ) > $i ).
tff(boolean_relstr,type,
boolean_relstr: $i > $o ).
tff(rel_str,type,
rel_str: $i > $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff(lim_points_of_net,type,
lim_points_of_net: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff(v4_membered,type,
v4_membered: $i > $o ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(complemented_relstr,type,
complemented_relstr: $i > $o ).
tff(join_complete_relstr,type,
join_complete_relstr: $i > $o ).
tff('#skF_42',type,
'#skF_42': $i > $i ).
tff(trivial_carrier,type,
trivial_carrier: $i > $o ).
tff('#skF_45',type,
'#skF_45': $i > $i ).
tff(relation_of2_as_subset,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(topological_space,type,
topological_space: $i > $o ).
tff(upper_bounded_relstr,type,
upper_bounded_relstr: $i > $o ).
tff(top_str,type,
top_str: $i > $o ).
tff(f_1592,negated_conjecture,
~ ! [A] :
( ( ~ empty_carrier(A)
& topological_space(A)
& top_str(A) )
=> ! [B] :
( ( ~ empty(B)
& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) )
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(C,lim_points_of_net(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)))
<=> is_a_convergence_point_of_set(A,B,C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow19) ).
tff(f_485,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
tff(f_435,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
tff(f_789,axiom,
! [A,B,C] :
( ( ~ empty_carrier(A)
& one_sorted_str(A)
& ~ empty(B)
& element(B,powerset(the_carrier(A)))
& ~ empty(C)
& filtered_subset(C,boole_POSet(B))
& upper_relstr_subset(C,boole_POSet(B))
& element(C,powerset(the_carrier(boole_POSet(B)))) )
=> ( ~ empty_carrier(net_of_bool_filter(A,B,C))
& reflexive_relstr(net_of_bool_filter(A,B,C))
& transitive_relstr(net_of_bool_filter(A,B,C))
& strict_net_str(net_of_bool_filter(A,B,C),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_yellow19) ).
tff(f_629,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(cast_as_carrier_subset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
tff(f_1565,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ! [B] :
( ( ~ empty(B)
& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) )
=> ( B = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow19) ).
tff(f_473,axiom,
! [A,B,C] :
( ( ~ empty_carrier(A)
& one_sorted_str(A)
& ~ empty(B)
& element(B,powerset(the_carrier(A)))
& ~ empty(C)
& filtered_subset(C,boole_POSet(B))
& upper_relstr_subset(C,boole_POSet(B))
& element(C,powerset(the_carrier(boole_POSet(B)))) )
=> ( ~ empty_carrier(net_of_bool_filter(A,B,C))
& strict_net_str(net_of_bool_filter(A,B,C),A)
& net_str(net_of_bool_filter(A,B,C),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow19) ).
tff(f_392,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ! [B] :
( ( ~ empty_carrier(B)
& net_str(B,A) )
=> ( filter_of_net_str(A,B) = a_2_1_yellow19(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_yellow19) ).
tff(f_839,axiom,
! [A,B,C] :
( ( ~ empty_carrier(A)
& one_sorted_str(A)
& ~ empty(B)
& element(B,powerset(the_carrier(A)))
& ~ empty(C)
& filtered_subset(C,boole_POSet(B))
& upper_relstr_subset(C,boole_POSet(B))
& proper_element(C,powerset(the_carrier(boole_POSet(B))))
& element(C,powerset(the_carrier(boole_POSet(B)))) )
=> ( ~ empty_carrier(net_of_bool_filter(A,B,C))
& reflexive_relstr(net_of_bool_filter(A,B,C))
& transitive_relstr(net_of_bool_filter(A,B,C))
& strict_net_str(net_of_bool_filter(A,B,C),A)
& directed_relstr(net_of_bool_filter(A,B,C)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_yellow19) ).
tff(f_1546,axiom,
! [A] :
( ( ~ empty_carrier(A)
& topological_space(A)
& top_str(A) )
=> ! [B] :
( ( ~ empty_carrier(B)
& transitive_relstr(B)
& directed_relstr(B)
& net_str(B,A) )
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(C,lim_points_of_net(A,B))
<=> is_a_convergence_point_of_set(A,filter_of_net_str(A,B),C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_yellow19) ).
tff(c_868,plain,
( in('#skF_48',lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')))
| is_a_convergence_point_of_set('#skF_46','#skF_47','#skF_48') ),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_940,plain,
is_a_convergence_point_of_set('#skF_46','#skF_47','#skF_48'),
inference(splitLeft,[status(thm)],[c_868]) ).
tff(c_844,plain,
element('#skF_48',the_carrier('#skF_46')),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_856,plain,
top_str('#skF_46'),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_968,plain,
! [A_259] :
( one_sorted_str(A_259)
| ~ top_str(A_259) ),
inference(cnfTransformation,[status(thm)],[f_485]) ).
tff(c_976,plain,
one_sorted_str('#skF_46'),
inference(resolution,[status(thm)],[c_856,c_968]) ).
tff(c_162,plain,
! [A_57] :
( element(cast_as_carrier_subset(A_57),powerset(the_carrier(A_57)))
| ~ one_sorted_str(A_57) ),
inference(cnfTransformation,[status(thm)],[f_435]) ).
tff(c_860,plain,
~ empty_carrier('#skF_46'),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_854,plain,
~ empty('#skF_47'),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_852,plain,
filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46'))),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_850,plain,
upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46'))),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_846,plain,
element('#skF_47',powerset(the_carrier(boole_POSet(cast_as_carrier_subset('#skF_46'))))),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_19774,plain,
! [A_1541,B_1542,C_1543] :
( transitive_relstr(net_of_bool_filter(A_1541,B_1542,C_1543))
| ~ element(C_1543,powerset(the_carrier(boole_POSet(B_1542))))
| ~ upper_relstr_subset(C_1543,boole_POSet(B_1542))
| ~ filtered_subset(C_1543,boole_POSet(B_1542))
| empty(C_1543)
| ~ element(B_1542,powerset(the_carrier(A_1541)))
| empty(B_1542)
| ~ one_sorted_str(A_1541)
| empty_carrier(A_1541) ),
inference(cnfTransformation,[status(thm)],[f_789]) ).
tff(c_19955,plain,
! [A_1541] :
( transitive_relstr(net_of_bool_filter(A_1541,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_1541)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_1541)
| empty_carrier(A_1541) ),
inference(resolution,[status(thm)],[c_846,c_19774]) ).
tff(c_20074,plain,
! [A_1541] :
( transitive_relstr(net_of_bool_filter(A_1541,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_1541)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_1541)
| empty_carrier(A_1541) ),
inference(demodulation,[status(thm),theory(equality)],[c_852,c_850,c_19955]) ).
tff(c_20075,plain,
! [A_1541] :
( transitive_relstr(net_of_bool_filter(A_1541,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_1541)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_1541)
| empty_carrier(A_1541) ),
inference(negUnitSimplification,[status(thm)],[c_854,c_20074]) ).
tff(c_20283,plain,
empty(cast_as_carrier_subset('#skF_46')),
inference(splitLeft,[status(thm)],[c_20075]) ).
tff(c_278,plain,
! [A_93] :
( ~ empty(cast_as_carrier_subset(A_93))
| ~ one_sorted_str(A_93)
| empty_carrier(A_93) ),
inference(cnfTransformation,[status(thm)],[f_629]) ).
tff(c_20300,plain,
( ~ one_sorted_str('#skF_46')
| empty_carrier('#skF_46') ),
inference(resolution,[status(thm)],[c_20283,c_278]) ).
tff(c_20317,plain,
empty_carrier('#skF_46'),
inference(demodulation,[status(thm),theory(equality)],[c_976,c_20300]) ).
tff(c_20319,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_860,c_20317]) ).
tff(c_20321,plain,
~ empty(cast_as_carrier_subset('#skF_46')),
inference(splitRight,[status(thm)],[c_20075]) ).
tff(c_848,plain,
proper_element('#skF_47',powerset(the_carrier(boole_POSet(cast_as_carrier_subset('#skF_46'))))),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_22835,plain,
! [A_1607,B_1608] :
( ( filter_of_net_str(A_1607,net_of_bool_filter(A_1607,cast_as_carrier_subset(A_1607),B_1608)) = B_1608 )
| ~ element(B_1608,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A_1607)))))
| ~ proper_element(B_1608,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A_1607)))))
| ~ upper_relstr_subset(B_1608,boole_POSet(cast_as_carrier_subset(A_1607)))
| ~ filtered_subset(B_1608,boole_POSet(cast_as_carrier_subset(A_1607)))
| empty(B_1608)
| ~ one_sorted_str(A_1607)
| empty_carrier(A_1607) ),
inference(cnfTransformation,[status(thm)],[f_1565]) ).
tff(c_22842,plain,
( ( filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = '#skF_47' )
| ~ element('#skF_47',powerset(the_carrier(boole_POSet(cast_as_carrier_subset('#skF_46')))))
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ one_sorted_str('#skF_46')
| empty_carrier('#skF_46') ),
inference(resolution,[status(thm)],[c_848,c_22835]) ).
tff(c_22850,plain,
( ( filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = '#skF_47' )
| empty('#skF_47')
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_976,c_852,c_850,c_846,c_22842]) ).
tff(c_22851,plain,
filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = '#skF_47',
inference(negUnitSimplification,[status(thm)],[c_860,c_854,c_22850]) ).
tff(c_22158,plain,
! [A_1592,B_1593,C_1594] :
( net_str(net_of_bool_filter(A_1592,B_1593,C_1594),A_1592)
| ~ element(C_1594,powerset(the_carrier(boole_POSet(B_1593))))
| ~ upper_relstr_subset(C_1594,boole_POSet(B_1593))
| ~ filtered_subset(C_1594,boole_POSet(B_1593))
| empty(C_1594)
| ~ element(B_1593,powerset(the_carrier(A_1592)))
| empty(B_1593)
| ~ one_sorted_str(A_1592)
| empty_carrier(A_1592) ),
inference(cnfTransformation,[status(thm)],[f_473]) ).
tff(c_22342,plain,
! [A_1592] :
( net_str(net_of_bool_filter(A_1592,cast_as_carrier_subset('#skF_46'),'#skF_47'),A_1592)
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_1592)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_1592)
| empty_carrier(A_1592) ),
inference(resolution,[status(thm)],[c_846,c_22158]) ).
tff(c_22462,plain,
! [A_1592] :
( net_str(net_of_bool_filter(A_1592,cast_as_carrier_subset('#skF_46'),'#skF_47'),A_1592)
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_1592)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_1592)
| empty_carrier(A_1592) ),
inference(demodulation,[status(thm),theory(equality)],[c_852,c_850,c_22342]) ).
tff(c_22518,plain,
! [A_1597] :
( net_str(net_of_bool_filter(A_1597,cast_as_carrier_subset('#skF_46'),'#skF_47'),A_1597)
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_1597)))
| ~ one_sorted_str(A_1597)
| empty_carrier(A_1597) ),
inference(negUnitSimplification,[status(thm)],[c_20321,c_854,c_22462]) ).
tff(c_22527,plain,
( net_str(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'),'#skF_46')
| empty_carrier('#skF_46')
| ~ one_sorted_str('#skF_46') ),
inference(resolution,[status(thm)],[c_162,c_22518]) ).
tff(c_22535,plain,
( net_str(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'),'#skF_46')
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_976,c_22527]) ).
tff(c_22536,plain,
net_str(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'),'#skF_46'),
inference(negUnitSimplification,[status(thm)],[c_860,c_22535]) ).
tff(c_146,plain,
! [A_46,B_48] :
( ( filter_of_net_str(A_46,B_48) = a_2_1_yellow19(A_46,B_48) )
| ~ net_str(B_48,A_46)
| empty_carrier(B_48)
| ~ one_sorted_str(A_46)
| empty_carrier(A_46) ),
inference(cnfTransformation,[status(thm)],[f_392]) ).
tff(c_22540,plain,
( ( filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = a_2_1_yellow19('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) )
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ one_sorted_str('#skF_46')
| empty_carrier('#skF_46') ),
inference(resolution,[status(thm)],[c_22536,c_146]) ).
tff(c_22546,plain,
( ( filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = a_2_1_yellow19('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) )
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_976,c_22540]) ).
tff(c_22547,plain,
( ( filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = a_2_1_yellow19('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) )
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) ),
inference(negUnitSimplification,[status(thm)],[c_860,c_22546]) ).
tff(c_23246,plain,
( ( a_2_1_yellow19('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = '#skF_47' )
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) ),
inference(demodulation,[status(thm),theory(equality)],[c_22851,c_22547]) ).
tff(c_23247,plain,
empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')),
inference(splitLeft,[status(thm)],[c_23246]) ).
tff(c_356,plain,
! [A_105,B_106,C_107] :
( ~ empty_carrier(net_of_bool_filter(A_105,B_106,C_107))
| ~ element(C_107,powerset(the_carrier(boole_POSet(B_106))))
| ~ upper_relstr_subset(C_107,boole_POSet(B_106))
| ~ filtered_subset(C_107,boole_POSet(B_106))
| empty(C_107)
| ~ element(B_106,powerset(the_carrier(A_105)))
| empty(B_106)
| ~ one_sorted_str(A_105)
| empty_carrier(A_105) ),
inference(cnfTransformation,[status(thm)],[f_789]) ).
tff(c_23249,plain,
( ~ element('#skF_47',powerset(the_carrier(boole_POSet(cast_as_carrier_subset('#skF_46')))))
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier('#skF_46')))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str('#skF_46')
| empty_carrier('#skF_46') ),
inference(resolution,[status(thm)],[c_23247,c_356]) ).
tff(c_23252,plain,
( empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier('#skF_46')))
| empty(cast_as_carrier_subset('#skF_46'))
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_976,c_852,c_850,c_846,c_23249]) ).
tff(c_23253,plain,
~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier('#skF_46'))),
inference(negUnitSimplification,[status(thm)],[c_860,c_20321,c_854,c_23252]) ).
tff(c_23262,plain,
~ one_sorted_str('#skF_46'),
inference(resolution,[status(thm)],[c_162,c_23253]) ).
tff(c_23273,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_976,c_23262]) ).
tff(c_23275,plain,
~ empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')),
inference(splitRight,[status(thm)],[c_23246]) ).
tff(c_71646,plain,
! [A_72648] :
( transitive_relstr(net_of_bool_filter(A_72648,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_72648)))
| ~ one_sorted_str(A_72648)
| empty_carrier(A_72648) ),
inference(splitRight,[status(thm)],[c_20075]) ).
tff(c_71667,plain,
( transitive_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46')
| ~ one_sorted_str('#skF_46') ),
inference(resolution,[status(thm)],[c_162,c_71646]) ).
tff(c_71679,plain,
( transitive_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_976,c_71667]) ).
tff(c_71680,plain,
transitive_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')),
inference(negUnitSimplification,[status(thm)],[c_860,c_71679]) ).
tff(c_858,plain,
topological_space('#skF_46'),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_22576,plain,
! [A_1598,B_1599,C_1600] :
( directed_relstr(net_of_bool_filter(A_1598,B_1599,C_1600))
| ~ element(C_1600,powerset(the_carrier(boole_POSet(B_1599))))
| ~ proper_element(C_1600,powerset(the_carrier(boole_POSet(B_1599))))
| ~ upper_relstr_subset(C_1600,boole_POSet(B_1599))
| ~ filtered_subset(C_1600,boole_POSet(B_1599))
| empty(C_1600)
| ~ element(B_1599,powerset(the_carrier(A_1598)))
| empty(B_1599)
| ~ one_sorted_str(A_1598)
| empty_carrier(A_1598) ),
inference(cnfTransformation,[status(thm)],[f_839]) ).
tff(c_22583,plain,
! [A_1598] :
( directed_relstr(net_of_bool_filter(A_1598,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ element('#skF_47',powerset(the_carrier(boole_POSet(cast_as_carrier_subset('#skF_46')))))
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_1598)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_1598)
| empty_carrier(A_1598) ),
inference(resolution,[status(thm)],[c_848,c_22576]) ).
tff(c_22591,plain,
! [A_1598] :
( directed_relstr(net_of_bool_filter(A_1598,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_1598)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_1598)
| empty_carrier(A_1598) ),
inference(demodulation,[status(thm),theory(equality)],[c_852,c_850,c_846,c_22583]) ).
tff(c_22593,plain,
! [A_1601] :
( directed_relstr(net_of_bool_filter(A_1601,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_1601)))
| ~ one_sorted_str(A_1601)
| empty_carrier(A_1601) ),
inference(negUnitSimplification,[status(thm)],[c_20321,c_854,c_22591]) ).
tff(c_22604,plain,
( directed_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46')
| ~ one_sorted_str('#skF_46') ),
inference(resolution,[status(thm)],[c_162,c_22593]) ).
tff(c_22612,plain,
( directed_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_976,c_22604]) ).
tff(c_22613,plain,
directed_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')),
inference(negUnitSimplification,[status(thm)],[c_860,c_22612]) ).
tff(c_838,plain,
! [C_205,A_199,B_203] :
( in(C_205,lim_points_of_net(A_199,B_203))
| ~ is_a_convergence_point_of_set(A_199,filter_of_net_str(A_199,B_203),C_205)
| ~ element(C_205,the_carrier(A_199))
| ~ net_str(B_203,A_199)
| ~ directed_relstr(B_203)
| ~ transitive_relstr(B_203)
| empty_carrier(B_203)
| ~ top_str(A_199)
| ~ topological_space(A_199)
| empty_carrier(A_199) ),
inference(cnfTransformation,[status(thm)],[f_1546]) ).
tff(c_22858,plain,
! [C_205] :
( in(C_205,lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')))
| ~ is_a_convergence_point_of_set('#skF_46','#skF_47',C_205)
| ~ element(C_205,the_carrier('#skF_46'))
| ~ net_str(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'),'#skF_46')
| ~ directed_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ transitive_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ top_str('#skF_46')
| ~ topological_space('#skF_46')
| empty_carrier('#skF_46') ),
inference(superposition,[status(thm),theory(equality)],[c_22851,c_838]) ).
tff(c_22880,plain,
! [C_205] :
( in(C_205,lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')))
| ~ is_a_convergence_point_of_set('#skF_46','#skF_47',C_205)
| ~ element(C_205,the_carrier('#skF_46'))
| ~ transitive_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_858,c_856,c_22613,c_22536,c_22858]) ).
tff(c_22881,plain,
! [C_205] :
( in(C_205,lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')))
| ~ is_a_convergence_point_of_set('#skF_46','#skF_47',C_205)
| ~ element(C_205,the_carrier('#skF_46'))
| ~ transitive_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) ),
inference(negUnitSimplification,[status(thm)],[c_860,c_22880]) ).
tff(c_112117,plain,
! [C_205] :
( in(C_205,lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')))
| ~ is_a_convergence_point_of_set('#skF_46','#skF_47',C_205)
| ~ element(C_205,the_carrier('#skF_46'))
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) ),
inference(demodulation,[status(thm),theory(equality)],[c_71680,c_22881]) ).
tff(c_112119,plain,
! [C_190981] :
( in(C_190981,lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')))
| ~ is_a_convergence_point_of_set('#skF_46','#skF_47',C_190981)
| ~ element(C_190981,the_carrier('#skF_46')) ),
inference(negUnitSimplification,[status(thm)],[c_23275,c_112117]) ).
tff(c_862,plain,
( ~ is_a_convergence_point_of_set('#skF_46','#skF_47','#skF_48')
| ~ in('#skF_48',lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))) ),
inference(cnfTransformation,[status(thm)],[f_1592]) ).
tff(c_941,plain,
~ in('#skF_48',lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))),
inference(splitLeft,[status(thm)],[c_862]) ).
tff(c_112167,plain,
( ~ is_a_convergence_point_of_set('#skF_46','#skF_47','#skF_48')
| ~ element('#skF_48',the_carrier('#skF_46')) ),
inference(resolution,[status(thm)],[c_112119,c_941]) ).
tff(c_112200,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_844,c_940,c_112167]) ).
tff(c_112201,plain,
~ is_a_convergence_point_of_set('#skF_46','#skF_47','#skF_48'),
inference(splitRight,[status(thm)],[c_862]) ).
tff(c_112204,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_940,c_112201]) ).
tff(c_112206,plain,
~ is_a_convergence_point_of_set('#skF_46','#skF_47','#skF_48'),
inference(splitRight,[status(thm)],[c_868]) ).
tff(c_112205,plain,
in('#skF_48',lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))),
inference(splitRight,[status(thm)],[c_868]) ).
tff(c_112207,plain,
~ in('#skF_48',lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))),
inference(splitLeft,[status(thm)],[c_862]) ).
tff(c_112210,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_112205,c_112207]) ).
tff(c_112212,plain,
in('#skF_48',lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))),
inference(splitRight,[status(thm)],[c_862]) ).
tff(c_112307,plain,
! [A_191135] :
( one_sorted_str(A_191135)
| ~ top_str(A_191135) ),
inference(cnfTransformation,[status(thm)],[f_485]) ).
tff(c_112315,plain,
one_sorted_str('#skF_46'),
inference(resolution,[status(thm)],[c_856,c_112307]) ).
tff(c_133061,plain,
! [A_192568,B_192569,C_192570] :
( reflexive_relstr(net_of_bool_filter(A_192568,B_192569,C_192570))
| ~ element(C_192570,powerset(the_carrier(boole_POSet(B_192569))))
| ~ upper_relstr_subset(C_192570,boole_POSet(B_192569))
| ~ filtered_subset(C_192570,boole_POSet(B_192569))
| empty(C_192570)
| ~ element(B_192569,powerset(the_carrier(A_192568)))
| empty(B_192569)
| ~ one_sorted_str(A_192568)
| empty_carrier(A_192568) ),
inference(cnfTransformation,[status(thm)],[f_789]) ).
tff(c_133245,plain,
! [A_192568] :
( reflexive_relstr(net_of_bool_filter(A_192568,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192568)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_192568)
| empty_carrier(A_192568) ),
inference(resolution,[status(thm)],[c_846,c_133061]) ).
tff(c_133365,plain,
! [A_192568] :
( reflexive_relstr(net_of_bool_filter(A_192568,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192568)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_192568)
| empty_carrier(A_192568) ),
inference(demodulation,[status(thm),theory(equality)],[c_852,c_850,c_133245]) ).
tff(c_133366,plain,
! [A_192568] :
( reflexive_relstr(net_of_bool_filter(A_192568,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192568)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_192568)
| empty_carrier(A_192568) ),
inference(negUnitSimplification,[status(thm)],[c_854,c_133365]) ).
tff(c_133586,plain,
empty(cast_as_carrier_subset('#skF_46')),
inference(splitLeft,[status(thm)],[c_133366]) ).
tff(c_133597,plain,
( ~ one_sorted_str('#skF_46')
| empty_carrier('#skF_46') ),
inference(resolution,[status(thm)],[c_133586,c_278]) ).
tff(c_133618,plain,
empty_carrier('#skF_46'),
inference(demodulation,[status(thm),theory(equality)],[c_112315,c_133597]) ).
tff(c_133620,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_860,c_133618]) ).
tff(c_133622,plain,
~ empty(cast_as_carrier_subset('#skF_46')),
inference(splitRight,[status(thm)],[c_133366]) ).
tff(c_136246,plain,
! [A_192624,B_192625] :
( ( filter_of_net_str(A_192624,net_of_bool_filter(A_192624,cast_as_carrier_subset(A_192624),B_192625)) = B_192625 )
| ~ element(B_192625,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A_192624)))))
| ~ proper_element(B_192625,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A_192624)))))
| ~ upper_relstr_subset(B_192625,boole_POSet(cast_as_carrier_subset(A_192624)))
| ~ filtered_subset(B_192625,boole_POSet(cast_as_carrier_subset(A_192624)))
| empty(B_192625)
| ~ one_sorted_str(A_192624)
| empty_carrier(A_192624) ),
inference(cnfTransformation,[status(thm)],[f_1565]) ).
tff(c_136253,plain,
( ( filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = '#skF_47' )
| ~ element('#skF_47',powerset(the_carrier(boole_POSet(cast_as_carrier_subset('#skF_46')))))
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ one_sorted_str('#skF_46')
| empty_carrier('#skF_46') ),
inference(resolution,[status(thm)],[c_848,c_136246]) ).
tff(c_136261,plain,
( ( filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = '#skF_47' )
| empty('#skF_47')
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_112315,c_852,c_850,c_846,c_136253]) ).
tff(c_136262,plain,
filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = '#skF_47',
inference(negUnitSimplification,[status(thm)],[c_860,c_854,c_136261]) ).
tff(c_135410,plain,
! [A_192605,B_192606,C_192607] :
( net_str(net_of_bool_filter(A_192605,B_192606,C_192607),A_192605)
| ~ element(C_192607,powerset(the_carrier(boole_POSet(B_192606))))
| ~ upper_relstr_subset(C_192607,boole_POSet(B_192606))
| ~ filtered_subset(C_192607,boole_POSet(B_192606))
| empty(C_192607)
| ~ element(B_192606,powerset(the_carrier(A_192605)))
| empty(B_192606)
| ~ one_sorted_str(A_192605)
| empty_carrier(A_192605) ),
inference(cnfTransformation,[status(thm)],[f_473]) ).
tff(c_135594,plain,
! [A_192605] :
( net_str(net_of_bool_filter(A_192605,cast_as_carrier_subset('#skF_46'),'#skF_47'),A_192605)
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192605)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_192605)
| empty_carrier(A_192605) ),
inference(resolution,[status(thm)],[c_846,c_135410]) ).
tff(c_135714,plain,
! [A_192605] :
( net_str(net_of_bool_filter(A_192605,cast_as_carrier_subset('#skF_46'),'#skF_47'),A_192605)
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192605)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_192605)
| empty_carrier(A_192605) ),
inference(demodulation,[status(thm),theory(equality)],[c_852,c_850,c_135594]) ).
tff(c_135851,plain,
! [A_192611] :
( net_str(net_of_bool_filter(A_192611,cast_as_carrier_subset('#skF_46'),'#skF_47'),A_192611)
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192611)))
| ~ one_sorted_str(A_192611)
| empty_carrier(A_192611) ),
inference(negUnitSimplification,[status(thm)],[c_133622,c_854,c_135714]) ).
tff(c_135860,plain,
( net_str(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'),'#skF_46')
| empty_carrier('#skF_46')
| ~ one_sorted_str('#skF_46') ),
inference(resolution,[status(thm)],[c_162,c_135851]) ).
tff(c_135868,plain,
( net_str(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'),'#skF_46')
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_112315,c_135860]) ).
tff(c_135869,plain,
net_str(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'),'#skF_46'),
inference(negUnitSimplification,[status(thm)],[c_860,c_135868]) ).
tff(c_135873,plain,
( ( filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = a_2_1_yellow19('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) )
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ one_sorted_str('#skF_46')
| empty_carrier('#skF_46') ),
inference(resolution,[status(thm)],[c_135869,c_146]) ).
tff(c_135879,plain,
( ( filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = a_2_1_yellow19('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) )
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_112315,c_135873]) ).
tff(c_135880,plain,
( ( filter_of_net_str('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = a_2_1_yellow19('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) )
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) ),
inference(negUnitSimplification,[status(thm)],[c_860,c_135879]) ).
tff(c_136310,plain,
( ( a_2_1_yellow19('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) = '#skF_47' )
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) ),
inference(demodulation,[status(thm),theory(equality)],[c_136262,c_135880]) ).
tff(c_136311,plain,
empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')),
inference(splitLeft,[status(thm)],[c_136310]) ).
tff(c_136313,plain,
( ~ element('#skF_47',powerset(the_carrier(boole_POSet(cast_as_carrier_subset('#skF_46')))))
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier('#skF_46')))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str('#skF_46')
| empty_carrier('#skF_46') ),
inference(resolution,[status(thm)],[c_136311,c_356]) ).
tff(c_136316,plain,
( empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier('#skF_46')))
| empty(cast_as_carrier_subset('#skF_46'))
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_112315,c_852,c_850,c_846,c_136313]) ).
tff(c_136317,plain,
~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier('#skF_46'))),
inference(negUnitSimplification,[status(thm)],[c_860,c_133622,c_854,c_136316]) ).
tff(c_136326,plain,
~ one_sorted_str('#skF_46'),
inference(resolution,[status(thm)],[c_162,c_136317]) ).
tff(c_136337,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_112315,c_136326]) ).
tff(c_136339,plain,
~ empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')),
inference(splitRight,[status(thm)],[c_136310]) ).
tff(c_133624,plain,
! [A_192575,B_192576,C_192577] :
( transitive_relstr(net_of_bool_filter(A_192575,B_192576,C_192577))
| ~ element(C_192577,powerset(the_carrier(boole_POSet(B_192576))))
| ~ upper_relstr_subset(C_192577,boole_POSet(B_192576))
| ~ filtered_subset(C_192577,boole_POSet(B_192576))
| empty(C_192577)
| ~ element(B_192576,powerset(the_carrier(A_192575)))
| empty(B_192576)
| ~ one_sorted_str(A_192575)
| empty_carrier(A_192575) ),
inference(cnfTransformation,[status(thm)],[f_789]) ).
tff(c_133808,plain,
! [A_192575] :
( transitive_relstr(net_of_bool_filter(A_192575,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192575)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_192575)
| empty_carrier(A_192575) ),
inference(resolution,[status(thm)],[c_846,c_133624]) ).
tff(c_133928,plain,
! [A_192575] :
( transitive_relstr(net_of_bool_filter(A_192575,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192575)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_192575)
| empty_carrier(A_192575) ),
inference(demodulation,[status(thm),theory(equality)],[c_852,c_850,c_133808]) ).
tff(c_134192,plain,
! [A_192581] :
( transitive_relstr(net_of_bool_filter(A_192581,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192581)))
| ~ one_sorted_str(A_192581)
| empty_carrier(A_192581) ),
inference(negUnitSimplification,[status(thm)],[c_133622,c_854,c_133928]) ).
tff(c_134203,plain,
( transitive_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46')
| ~ one_sorted_str('#skF_46') ),
inference(resolution,[status(thm)],[c_162,c_134192]) ).
tff(c_134211,plain,
( transitive_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_112315,c_134203]) ).
tff(c_134212,plain,
transitive_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')),
inference(negUnitSimplification,[status(thm)],[c_860,c_134211]) ).
tff(c_135905,plain,
! [A_192612,B_192613,C_192614] :
( directed_relstr(net_of_bool_filter(A_192612,B_192613,C_192614))
| ~ element(C_192614,powerset(the_carrier(boole_POSet(B_192613))))
| ~ proper_element(C_192614,powerset(the_carrier(boole_POSet(B_192613))))
| ~ upper_relstr_subset(C_192614,boole_POSet(B_192613))
| ~ filtered_subset(C_192614,boole_POSet(B_192613))
| empty(C_192614)
| ~ element(B_192613,powerset(the_carrier(A_192612)))
| empty(B_192613)
| ~ one_sorted_str(A_192612)
| empty_carrier(A_192612) ),
inference(cnfTransformation,[status(thm)],[f_839]) ).
tff(c_135912,plain,
! [A_192612] :
( directed_relstr(net_of_bool_filter(A_192612,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ element('#skF_47',powerset(the_carrier(boole_POSet(cast_as_carrier_subset('#skF_46')))))
| ~ upper_relstr_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| ~ filtered_subset('#skF_47',boole_POSet(cast_as_carrier_subset('#skF_46')))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192612)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_192612)
| empty_carrier(A_192612) ),
inference(resolution,[status(thm)],[c_848,c_135905]) ).
tff(c_135920,plain,
! [A_192612] :
( directed_relstr(net_of_bool_filter(A_192612,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty('#skF_47')
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192612)))
| empty(cast_as_carrier_subset('#skF_46'))
| ~ one_sorted_str(A_192612)
| empty_carrier(A_192612) ),
inference(demodulation,[status(thm),theory(equality)],[c_852,c_850,c_846,c_135912]) ).
tff(c_136091,plain,
! [A_192620] :
( directed_relstr(net_of_bool_filter(A_192620,cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ element(cast_as_carrier_subset('#skF_46'),powerset(the_carrier(A_192620)))
| ~ one_sorted_str(A_192620)
| empty_carrier(A_192620) ),
inference(negUnitSimplification,[status(thm)],[c_133622,c_854,c_135920]) ).
tff(c_136102,plain,
( directed_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46')
| ~ one_sorted_str('#skF_46') ),
inference(resolution,[status(thm)],[c_162,c_136091]) ).
tff(c_136110,plain,
( directed_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_112315,c_136102]) ).
tff(c_136111,plain,
directed_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')),
inference(negUnitSimplification,[status(thm)],[c_860,c_136110]) ).
tff(c_840,plain,
! [A_199,B_203,C_205] :
( is_a_convergence_point_of_set(A_199,filter_of_net_str(A_199,B_203),C_205)
| ~ in(C_205,lim_points_of_net(A_199,B_203))
| ~ element(C_205,the_carrier(A_199))
| ~ net_str(B_203,A_199)
| ~ directed_relstr(B_203)
| ~ transitive_relstr(B_203)
| empty_carrier(B_203)
| ~ top_str(A_199)
| ~ topological_space(A_199)
| empty_carrier(A_199) ),
inference(cnfTransformation,[status(thm)],[f_1546]) ).
tff(c_136269,plain,
! [C_205] :
( is_a_convergence_point_of_set('#skF_46','#skF_47',C_205)
| ~ in(C_205,lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')))
| ~ element(C_205,the_carrier('#skF_46'))
| ~ net_str(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'),'#skF_46')
| ~ directed_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ transitive_relstr(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| ~ top_str('#skF_46')
| ~ topological_space('#skF_46')
| empty_carrier('#skF_46') ),
inference(superposition,[status(thm),theory(equality)],[c_136262,c_840]) ).
tff(c_136291,plain,
! [C_205] :
( is_a_convergence_point_of_set('#skF_46','#skF_47',C_205)
| ~ in(C_205,lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')))
| ~ element(C_205,the_carrier('#skF_46'))
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47'))
| empty_carrier('#skF_46') ),
inference(demodulation,[status(thm),theory(equality)],[c_858,c_856,c_134212,c_136111,c_135869,c_136269]) ).
tff(c_136292,plain,
! [C_205] :
( is_a_convergence_point_of_set('#skF_46','#skF_47',C_205)
| ~ in(C_205,lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')))
| ~ element(C_205,the_carrier('#skF_46'))
| empty_carrier(net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')) ),
inference(negUnitSimplification,[status(thm)],[c_860,c_136291]) ).
tff(c_256641,plain,
! [C_486687] :
( is_a_convergence_point_of_set('#skF_46','#skF_47',C_486687)
| ~ in(C_486687,lim_points_of_net('#skF_46',net_of_bool_filter('#skF_46',cast_as_carrier_subset('#skF_46'),'#skF_47')))
| ~ element(C_486687,the_carrier('#skF_46')) ),
inference(negUnitSimplification,[status(thm)],[c_136339,c_136292]) ).
tff(c_256729,plain,
( is_a_convergence_point_of_set('#skF_46','#skF_47','#skF_48')
| ~ element('#skF_48',the_carrier('#skF_46')) ),
inference(resolution,[status(thm)],[c_112212,c_256641]) ).
tff(c_256753,plain,
is_a_convergence_point_of_set('#skF_46','#skF_47','#skF_48'),
inference(demodulation,[status(thm),theory(equality)],[c_844,c_256729]) ).
tff(c_256755,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_112206,c_256753]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 12:12:20 EDT 2023
% 0.15/0.37 % CPUTime :
% 87.98/66.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 88.07/66.93
% 88.07/66.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 88.23/66.97
% 88.23/66.97 Inference rules
% 88.23/66.97 ----------------------
% 88.23/66.97 #Ref : 20
% 88.23/66.97 #Sup : 48712
% 88.23/66.97 #Fact : 0
% 88.23/66.97 #Define : 0
% 88.23/66.97 #Split : 500
% 88.23/66.97 #Chain : 0
% 88.23/66.97 #Close : 0
% 88.23/66.97
% 88.23/66.97 Ordering : KBO
% 88.23/66.97
% 88.23/66.97 Simplification rules
% 88.23/66.97 ----------------------
% 88.23/66.97 #Subsume : 12673
% 88.23/66.97 #Demod : 6265
% 88.23/66.97 #Tautology : 2041
% 88.23/66.97 #SimpNegUnit : 3946
% 88.23/66.97 #BackRed : 219
% 88.23/66.97
% 88.23/66.97 #Partial instantiations: 505600
% 88.23/66.97 #Strategies tried : 1
% 88.23/66.97
% 88.23/66.97 Timing (in seconds)
% 88.23/66.97 ----------------------
% 88.23/66.98 Preprocessing : 0.98
% 88.23/66.98 Parsing : 0.49
% 88.23/66.98 CNF conversion : 0.10
% 88.23/66.98 Main loop : 64.88
% 88.23/66.98 Inferencing : 11.71
% 88.23/66.98 Reduction : 24.57
% 88.23/66.98 Demodulation : 18.72
% 88.23/66.98 BG Simplification : 0.37
% 88.23/66.98 Subsumption : 22.69
% 88.23/66.98 Abstraction : 0.46
% 88.23/66.98 MUC search : 0.00
% 88.23/66.98 Cooper : 0.00
% 88.23/66.98 Total : 65.93
% 88.23/66.98 Index Insertion : 0.00
% 88.23/66.98 Index Deletion : 0.00
% 88.23/66.98 Index Matching : 0.00
% 88.23/66.98 BG Taut test : 0.00
%------------------------------------------------------------------------------