TSTP Solution File: SEU395+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 : Thu Aug 31 16:25:25 EDT 2023
% Result : Theorem 2.26s 2.37s
% Output : CNFRefutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 127
% Syntax : Number of formulae : 181 ( 13 unt; 118 typ; 0 def)
% Number of atoms : 439 ( 5 equ)
% Maximal formula atoms : 50 ( 6 avg)
% Number of connectives : 581 ( 205 ~; 230 |; 116 &)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 139 ( 98 >; 41 *; 0 +; 0 <<)
% Number of predicates : 57 ( 55 usr; 1 prp; 0-3 aty)
% Number of functors : 63 ( 63 usr; 20 con; 0-4 aty)
% Number of variables : 83 ( 0 sgn; 55 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
rel_str: $i > $o ).
tff(decl_23,type,
strict_rel_str: $i > $o ).
tff(decl_24,type,
the_carrier: $i > $i ).
tff(decl_25,type,
the_InternalRel: $i > $i ).
tff(decl_26,type,
rel_str_of: ( $i * $i ) > $i ).
tff(decl_27,type,
one_sorted_str: $i > $o ).
tff(decl_28,type,
net_str: ( $i * $i ) > $o ).
tff(decl_29,type,
strict_net_str: ( $i * $i ) > $o ).
tff(decl_30,type,
the_mapping: ( $i * $i ) > $i ).
tff(decl_31,type,
net_str_of: ( $i * $i * $i * $i ) > $i ).
tff(decl_32,type,
in: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_carrier: $i > $o ).
tff(decl_34,type,
reflexive_relstr: $i > $o ).
tff(decl_35,type,
complete_relstr: $i > $o ).
tff(decl_36,type,
up_complete_relstr: $i > $o ).
tff(decl_37,type,
join_complete_relstr: $i > $o ).
tff(decl_38,type,
lower_bounded_relstr: $i > $o ).
tff(decl_39,type,
transitive_relstr: $i > $o ).
tff(decl_40,type,
antisymmetric_relstr: $i > $o ).
tff(decl_41,type,
with_suprema_relstr: $i > $o ).
tff(decl_42,type,
with_infima_relstr: $i > $o ).
tff(decl_43,type,
upper_bounded_relstr: $i > $o ).
tff(decl_44,type,
bounded_relstr: $i > $o ).
tff(decl_45,type,
empty: $i > $o ).
tff(decl_46,type,
finite: $i > $o ).
tff(decl_47,type,
relation: $i > $o ).
tff(decl_48,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_49,type,
powerset: $i > $i ).
tff(decl_50,type,
element: ( $i * $i ) > $o ).
tff(decl_51,type,
topological_space: $i > $o ).
tff(decl_52,type,
top_str: $i > $o ).
tff(decl_53,type,
open_subset: ( $i * $i ) > $o ).
tff(decl_54,type,
closed_subset: ( $i * $i ) > $o ).
tff(decl_55,type,
boundary_set: ( $i * $i ) > $o ).
tff(decl_56,type,
trivial_carrier: $i > $o ).
tff(decl_57,type,
nowhere_dense: ( $i * $i ) > $o ).
tff(decl_58,type,
connected_relstr: $i > $o ).
tff(decl_59,type,
v1_membered: $i > $o ).
tff(decl_60,type,
v2_membered: $i > $o ).
tff(decl_61,type,
v3_membered: $i > $o ).
tff(decl_62,type,
v4_membered: $i > $o ).
tff(decl_63,type,
v5_membered: $i > $o ).
tff(decl_64,type,
filter_of_net_str: ( $i * $i ) > $i ).
tff(decl_65,type,
a_2_1_yellow19: ( $i * $i ) > $i ).
tff(decl_66,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_67,type,
function: $i > $o ).
tff(decl_68,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_69,type,
directed_relstr: $i > $o ).
tff(decl_70,type,
lim_points_of_net: ( $i * $i ) > $i ).
tff(decl_71,type,
cast_as_carrier_subset: $i > $i ).
tff(decl_72,type,
boole_POSet: $i > $i ).
tff(decl_73,type,
filtered_subset: ( $i * $i ) > $o ).
tff(decl_74,type,
upper_relstr_subset: ( $i * $i ) > $o ).
tff(decl_75,type,
net_of_bool_filter: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_77,type,
empty_set: $i ).
tff(decl_78,type,
relation_empty_yielding: $i > $o ).
tff(decl_79,type,
lower_relstr_subset: ( $i * $i ) > $o ).
tff(decl_80,type,
v1_yellow_3: $i > $o ).
tff(decl_81,type,
distributive_relstr: $i > $o ).
tff(decl_82,type,
heyting_relstr: $i > $o ).
tff(decl_83,type,
complemented_relstr: $i > $o ).
tff(decl_84,type,
boolean_relstr: $i > $o ).
tff(decl_85,type,
directed_subset: ( $i * $i ) > $o ).
tff(decl_86,type,
proper_element: ( $i * $i ) > $o ).
tff(decl_87,type,
dense: ( $i * $i ) > $o ).
tff(decl_88,type,
is_eventually_in: ( $i * $i * $i ) > $o ).
tff(decl_89,type,
subset: ( $i * $i ) > $o ).
tff(decl_90,type,
is_a_convergence_point_of_set: ( $i * $i * $i ) > $o ).
tff(decl_91,type,
esk1_0: $i ).
tff(decl_92,type,
esk2_0: $i ).
tff(decl_93,type,
esk3_0: $i ).
tff(decl_94,type,
esk4_1: $i > $i ).
tff(decl_95,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_96,type,
esk6_1: $i > $i ).
tff(decl_97,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_98,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_99,type,
esk9_1: $i > $i ).
tff(decl_100,type,
esk10_1: $i > $i ).
tff(decl_101,type,
esk11_0: $i ).
tff(decl_102,type,
esk12_0: $i ).
tff(decl_103,type,
esk13_0: $i ).
tff(decl_104,type,
esk14_0: $i ).
tff(decl_105,type,
esk15_0: $i ).
tff(decl_106,type,
esk16_1: $i > $i ).
tff(decl_107,type,
esk17_1: $i > $i ).
tff(decl_108,type,
esk18_1: $i > $i ).
tff(decl_109,type,
esk19_0: $i ).
tff(decl_110,type,
esk20_0: $i ).
tff(decl_111,type,
esk21_0: $i ).
tff(decl_112,type,
esk22_0: $i ).
tff(decl_113,type,
esk23_1: $i > $i ).
tff(decl_114,type,
esk24_1: $i > $i ).
tff(decl_115,type,
esk25_1: $i > $i ).
tff(decl_116,type,
esk26_1: $i > $i ).
tff(decl_117,type,
esk27_0: $i ).
tff(decl_118,type,
esk28_1: $i > $i ).
tff(decl_119,type,
esk29_0: $i ).
tff(decl_120,type,
esk30_0: $i ).
tff(decl_121,type,
esk31_1: $i > $i ).
tff(decl_122,type,
esk32_1: $i > $i ).
tff(decl_123,type,
esk33_1: $i > $i ).
tff(decl_124,type,
esk34_1: $i > $i ).
tff(decl_125,type,
esk35_1: $i > $i ).
tff(decl_126,type,
esk36_1: $i > $i ).
tff(decl_127,type,
esk37_0: $i ).
tff(decl_128,type,
esk38_1: $i > $i ).
tff(decl_129,type,
esk39_1: $i > $i ).
tff(decl_130,type,
esk40_1: $i > $i ).
tff(decl_131,type,
esk41_1: $i > $i ).
tff(decl_132,type,
esk42_1: $i > $i ).
tff(decl_133,type,
esk43_1: $i > $i ).
tff(decl_134,type,
esk44_1: $i > $i ).
tff(decl_135,type,
esk45_1: $i > $i ).
tff(decl_136,type,
esk46_0: $i ).
tff(decl_137,type,
esk47_0: $i ).
tff(decl_138,type,
esk48_0: $i ).
tff(decl_139,type,
esk49_2: ( $i * $i ) > $i ).
fof(t18_yellow19,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,lim_points_of_net(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)))
<=> is_a_convergence_point_of_set(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_yellow19) ).
fof(t15_yellow19,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_yellow19) ).
fof(dt_l1_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(fc5_yellow19,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty(X2)
& element(X2,powerset(the_carrier(X1)))
& ~ empty(X3)
& filtered_subset(X3,boole_POSet(X2))
& upper_relstr_subset(X3,boole_POSet(X2))
& proper_element(X3,powerset(the_carrier(boole_POSet(X2))))
& element(X3,powerset(the_carrier(boole_POSet(X2)))) )
=> ( ~ empty_carrier(net_of_bool_filter(X1,X2,X3))
& reflexive_relstr(net_of_bool_filter(X1,X2,X3))
& transitive_relstr(net_of_bool_filter(X1,X2,X3))
& strict_net_str(net_of_bool_filter(X1,X2,X3),X1)
& directed_relstr(net_of_bool_filter(X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_yellow19) ).
fof(fc4_yellow19,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty(X2)
& element(X2,powerset(the_carrier(X1)))
& ~ empty(X3)
& filtered_subset(X3,boole_POSet(X2))
& upper_relstr_subset(X3,boole_POSet(X2))
& element(X3,powerset(the_carrier(boole_POSet(X2)))) )
=> ( ~ empty_carrier(net_of_bool_filter(X1,X2,X3))
& reflexive_relstr(net_of_bool_filter(X1,X2,X3))
& transitive_relstr(net_of_bool_filter(X1,X2,X3))
& strict_net_str(net_of_bool_filter(X1,X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_yellow19) ).
fof(dt_k3_yellow19,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty(X2)
& element(X2,powerset(the_carrier(X1)))
& ~ empty(X3)
& filtered_subset(X3,boole_POSet(X2))
& upper_relstr_subset(X3,boole_POSet(X2))
& element(X3,powerset(the_carrier(boole_POSet(X2)))) )
=> ( ~ empty_carrier(net_of_bool_filter(X1,X2,X3))
& strict_net_str(net_of_bool_filter(X1,X2,X3),X1)
& net_str(net_of_bool_filter(X1,X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow19) ).
fof(t13_yellow19,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X1) )
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,lim_points_of_net(X1,X2))
<=> is_a_convergence_point_of_set(X1,filter_of_net_str(X1,X2),X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_yellow19) ).
fof(dt_k2_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(fc2_pre_topc,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,lim_points_of_net(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)))
<=> is_a_convergence_point_of_set(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t18_yellow19])]) ).
fof(c_0_10,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
inference(fof_simplification,[status(thm)],[t15_yellow19]) ).
fof(c_0_11,plain,
! [X65] :
( ~ top_str(X65)
| one_sorted_str(X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_pre_topc])]) ).
fof(c_0_12,negated_conjecture,
( ~ empty_carrier(esk46_0)
& topological_space(esk46_0)
& top_str(esk46_0)
& ~ empty(esk47_0)
& filtered_subset(esk47_0,boole_POSet(cast_as_carrier_subset(esk46_0)))
& upper_relstr_subset(esk47_0,boole_POSet(cast_as_carrier_subset(esk46_0)))
& proper_element(esk47_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk46_0)))))
& element(esk47_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk46_0)))))
& element(esk48_0,the_carrier(esk46_0))
& ( ~ in(esk48_0,lim_points_of_net(esk46_0,net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)))
| ~ is_a_convergence_point_of_set(esk46_0,esk47_0,esk48_0) )
& ( in(esk48_0,lim_points_of_net(esk46_0,net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)))
| is_a_convergence_point_of_set(esk46_0,esk47_0,esk48_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty(X2)
& element(X2,powerset(the_carrier(X1)))
& ~ empty(X3)
& filtered_subset(X3,boole_POSet(X2))
& upper_relstr_subset(X3,boole_POSet(X2))
& proper_element(X3,powerset(the_carrier(boole_POSet(X2))))
& element(X3,powerset(the_carrier(boole_POSet(X2)))) )
=> ( ~ empty_carrier(net_of_bool_filter(X1,X2,X3))
& reflexive_relstr(net_of_bool_filter(X1,X2,X3))
& transitive_relstr(net_of_bool_filter(X1,X2,X3))
& strict_net_str(net_of_bool_filter(X1,X2,X3),X1)
& directed_relstr(net_of_bool_filter(X1,X2,X3)) ) ),
inference(fof_simplification,[status(thm)],[fc5_yellow19]) ).
fof(c_0_14,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty(X2)
& element(X2,powerset(the_carrier(X1)))
& ~ empty(X3)
& filtered_subset(X3,boole_POSet(X2))
& upper_relstr_subset(X3,boole_POSet(X2))
& element(X3,powerset(the_carrier(boole_POSet(X2)))) )
=> ( ~ empty_carrier(net_of_bool_filter(X1,X2,X3))
& reflexive_relstr(net_of_bool_filter(X1,X2,X3))
& transitive_relstr(net_of_bool_filter(X1,X2,X3))
& strict_net_str(net_of_bool_filter(X1,X2,X3),X1) ) ),
inference(fof_simplification,[status(thm)],[fc4_yellow19]) ).
fof(c_0_15,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty(X2)
& element(X2,powerset(the_carrier(X1)))
& ~ empty(X3)
& filtered_subset(X3,boole_POSet(X2))
& upper_relstr_subset(X3,boole_POSet(X2))
& element(X3,powerset(the_carrier(boole_POSet(X2)))) )
=> ( ~ empty_carrier(net_of_bool_filter(X1,X2,X3))
& strict_net_str(net_of_bool_filter(X1,X2,X3),X1)
& net_str(net_of_bool_filter(X1,X2,X3),X1) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_yellow19]) ).
fof(c_0_16,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X1) )
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,lim_points_of_net(X1,X2))
<=> is_a_convergence_point_of_set(X1,filter_of_net_str(X1,X2),X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t13_yellow19]) ).
fof(c_0_17,plain,
! [X209,X210] :
( empty_carrier(X209)
| ~ one_sorted_str(X209)
| empty(X210)
| ~ filtered_subset(X210,boole_POSet(cast_as_carrier_subset(X209)))
| ~ upper_relstr_subset(X210,boole_POSet(cast_as_carrier_subset(X209)))
| ~ proper_element(X210,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X209)))))
| ~ element(X210,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X209)))))
| X210 = filter_of_net_str(X209,net_of_bool_filter(X209,cast_as_carrier_subset(X209),X210)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_18,plain,
( one_sorted_str(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
top_str(esk46_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X112,X113,X114] :
( ( ~ empty_carrier(net_of_bool_filter(X112,X113,X114))
| empty_carrier(X112)
| ~ one_sorted_str(X112)
| empty(X113)
| ~ element(X113,powerset(the_carrier(X112)))
| empty(X114)
| ~ filtered_subset(X114,boole_POSet(X113))
| ~ upper_relstr_subset(X114,boole_POSet(X113))
| ~ proper_element(X114,powerset(the_carrier(boole_POSet(X113))))
| ~ element(X114,powerset(the_carrier(boole_POSet(X113)))) )
& ( reflexive_relstr(net_of_bool_filter(X112,X113,X114))
| empty_carrier(X112)
| ~ one_sorted_str(X112)
| empty(X113)
| ~ element(X113,powerset(the_carrier(X112)))
| empty(X114)
| ~ filtered_subset(X114,boole_POSet(X113))
| ~ upper_relstr_subset(X114,boole_POSet(X113))
| ~ proper_element(X114,powerset(the_carrier(boole_POSet(X113))))
| ~ element(X114,powerset(the_carrier(boole_POSet(X113)))) )
& ( transitive_relstr(net_of_bool_filter(X112,X113,X114))
| empty_carrier(X112)
| ~ one_sorted_str(X112)
| empty(X113)
| ~ element(X113,powerset(the_carrier(X112)))
| empty(X114)
| ~ filtered_subset(X114,boole_POSet(X113))
| ~ upper_relstr_subset(X114,boole_POSet(X113))
| ~ proper_element(X114,powerset(the_carrier(boole_POSet(X113))))
| ~ element(X114,powerset(the_carrier(boole_POSet(X113)))) )
& ( strict_net_str(net_of_bool_filter(X112,X113,X114),X112)
| empty_carrier(X112)
| ~ one_sorted_str(X112)
| empty(X113)
| ~ element(X113,powerset(the_carrier(X112)))
| empty(X114)
| ~ filtered_subset(X114,boole_POSet(X113))
| ~ upper_relstr_subset(X114,boole_POSet(X113))
| ~ proper_element(X114,powerset(the_carrier(boole_POSet(X113))))
| ~ element(X114,powerset(the_carrier(boole_POSet(X113)))) )
& ( directed_relstr(net_of_bool_filter(X112,X113,X114))
| empty_carrier(X112)
| ~ one_sorted_str(X112)
| empty(X113)
| ~ element(X113,powerset(the_carrier(X112)))
| empty(X114)
| ~ filtered_subset(X114,boole_POSet(X113))
| ~ upper_relstr_subset(X114,boole_POSet(X113))
| ~ proper_element(X114,powerset(the_carrier(boole_POSet(X113))))
| ~ element(X114,powerset(the_carrier(boole_POSet(X113)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_21,plain,
! [X107,X108,X109] :
( ( ~ empty_carrier(net_of_bool_filter(X107,X108,X109))
| empty_carrier(X107)
| ~ one_sorted_str(X107)
| empty(X108)
| ~ element(X108,powerset(the_carrier(X107)))
| empty(X109)
| ~ filtered_subset(X109,boole_POSet(X108))
| ~ upper_relstr_subset(X109,boole_POSet(X108))
| ~ element(X109,powerset(the_carrier(boole_POSet(X108)))) )
& ( reflexive_relstr(net_of_bool_filter(X107,X108,X109))
| empty_carrier(X107)
| ~ one_sorted_str(X107)
| empty(X108)
| ~ element(X108,powerset(the_carrier(X107)))
| empty(X109)
| ~ filtered_subset(X109,boole_POSet(X108))
| ~ upper_relstr_subset(X109,boole_POSet(X108))
| ~ element(X109,powerset(the_carrier(boole_POSet(X108)))) )
& ( transitive_relstr(net_of_bool_filter(X107,X108,X109))
| empty_carrier(X107)
| ~ one_sorted_str(X107)
| empty(X108)
| ~ element(X108,powerset(the_carrier(X107)))
| empty(X109)
| ~ filtered_subset(X109,boole_POSet(X108))
| ~ upper_relstr_subset(X109,boole_POSet(X108))
| ~ element(X109,powerset(the_carrier(boole_POSet(X108)))) )
& ( strict_net_str(net_of_bool_filter(X107,X108,X109),X107)
| empty_carrier(X107)
| ~ one_sorted_str(X107)
| empty(X108)
| ~ element(X108,powerset(the_carrier(X107)))
| empty(X109)
| ~ filtered_subset(X109,boole_POSet(X108))
| ~ upper_relstr_subset(X109,boole_POSet(X108))
| ~ element(X109,powerset(the_carrier(boole_POSet(X108)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_22,plain,
! [X60,X61,X62] :
( ( ~ empty_carrier(net_of_bool_filter(X60,X61,X62))
| empty_carrier(X60)
| ~ one_sorted_str(X60)
| empty(X61)
| ~ element(X61,powerset(the_carrier(X60)))
| empty(X62)
| ~ filtered_subset(X62,boole_POSet(X61))
| ~ upper_relstr_subset(X62,boole_POSet(X61))
| ~ element(X62,powerset(the_carrier(boole_POSet(X61)))) )
& ( strict_net_str(net_of_bool_filter(X60,X61,X62),X60)
| empty_carrier(X60)
| ~ one_sorted_str(X60)
| empty(X61)
| ~ element(X61,powerset(the_carrier(X60)))
| empty(X62)
| ~ filtered_subset(X62,boole_POSet(X61))
| ~ upper_relstr_subset(X62,boole_POSet(X61))
| ~ element(X62,powerset(the_carrier(boole_POSet(X61)))) )
& ( net_str(net_of_bool_filter(X60,X61,X62),X60)
| empty_carrier(X60)
| ~ one_sorted_str(X60)
| empty(X61)
| ~ element(X61,powerset(the_carrier(X60)))
| empty(X62)
| ~ filtered_subset(X62,boole_POSet(X61))
| ~ upper_relstr_subset(X62,boole_POSet(X61))
| ~ element(X62,powerset(the_carrier(boole_POSet(X61)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_23,plain,
! [X206,X207,X208] :
( ( ~ in(X208,lim_points_of_net(X206,X207))
| is_a_convergence_point_of_set(X206,filter_of_net_str(X206,X207),X208)
| ~ element(X208,the_carrier(X206))
| empty_carrier(X207)
| ~ transitive_relstr(X207)
| ~ directed_relstr(X207)
| ~ net_str(X207,X206)
| empty_carrier(X206)
| ~ topological_space(X206)
| ~ top_str(X206) )
& ( ~ is_a_convergence_point_of_set(X206,filter_of_net_str(X206,X207),X208)
| in(X208,lim_points_of_net(X206,X207))
| ~ element(X208,the_carrier(X206))
| empty_carrier(X207)
| ~ transitive_relstr(X207)
| ~ directed_relstr(X207)
| ~ net_str(X207,X206)
| empty_carrier(X206)
| ~ topological_space(X206)
| ~ top_str(X206) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_24,plain,
( empty_carrier(X1)
| empty(X2)
| X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2))
| ~ one_sorted_str(X1)
| ~ filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
| ~ upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
| ~ element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
proper_element(esk47_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk46_0))))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,negated_conjecture,
upper_relstr_subset(esk47_0,boole_POSet(cast_as_carrier_subset(esk46_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
filtered_subset(esk47_0,boole_POSet(cast_as_carrier_subset(esk46_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_28,negated_conjecture,
element(esk47_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk46_0))))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
one_sorted_str(esk46_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_30,negated_conjecture,
~ empty(esk47_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_31,negated_conjecture,
~ empty_carrier(esk46_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_32,plain,
( directed_relstr(net_of_bool_filter(X1,X2,X3))
| empty_carrier(X1)
| empty(X2)
| empty(X3)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ filtered_subset(X3,boole_POSet(X2))
| ~ upper_relstr_subset(X3,boole_POSet(X2))
| ~ proper_element(X3,powerset(the_carrier(boole_POSet(X2))))
| ~ element(X3,powerset(the_carrier(boole_POSet(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_33,plain,
! [X57] :
( ~ one_sorted_str(X57)
| element(cast_as_carrier_subset(X57),powerset(the_carrier(X57))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_pre_topc])]) ).
cnf(c_0_34,plain,
( transitive_relstr(net_of_bool_filter(X1,X2,X3))
| empty_carrier(X1)
| empty(X2)
| empty(X3)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ filtered_subset(X3,boole_POSet(X2))
| ~ upper_relstr_subset(X3,boole_POSet(X2))
| ~ element(X3,powerset(the_carrier(boole_POSet(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_35,plain,
( empty_carrier(X1)
| empty(X2)
| empty(X3)
| ~ empty_carrier(net_of_bool_filter(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ filtered_subset(X3,boole_POSet(X2))
| ~ upper_relstr_subset(X3,boole_POSet(X2))
| ~ element(X3,powerset(the_carrier(boole_POSet(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_36,plain,
( is_a_convergence_point_of_set(X2,filter_of_net_str(X2,X3),X1)
| empty_carrier(X3)
| empty_carrier(X2)
| ~ in(X1,lim_points_of_net(X2,X3))
| ~ element(X1,the_carrier(X2))
| ~ transitive_relstr(X3)
| ~ directed_relstr(X3)
| ~ net_str(X3,X2)
| ~ topological_space(X2)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_37,negated_conjecture,
( in(esk48_0,lim_points_of_net(esk46_0,net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)))
| is_a_convergence_point_of_set(esk46_0,esk47_0,esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,negated_conjecture,
topological_space(esk46_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_39,negated_conjecture,
element(esk48_0,the_carrier(esk46_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_40,negated_conjecture,
filter_of_net_str(esk46_0,net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)) = esk47_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]),c_0_31]) ).
cnf(c_0_41,negated_conjecture,
( directed_relstr(net_of_bool_filter(X1,cast_as_carrier_subset(esk46_0),esk47_0))
| empty(cast_as_carrier_subset(esk46_0))
| empty_carrier(X1)
| ~ element(cast_as_carrier_subset(esk46_0),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_30]) ).
cnf(c_0_42,plain,
( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,negated_conjecture,
( empty(cast_as_carrier_subset(esk46_0))
| transitive_relstr(net_of_bool_filter(X1,cast_as_carrier_subset(esk46_0),esk47_0))
| empty_carrier(X1)
| ~ element(cast_as_carrier_subset(esk46_0),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_27]),c_0_28])]),c_0_30]) ).
cnf(c_0_44,negated_conjecture,
( empty(cast_as_carrier_subset(esk46_0))
| empty_carrier(X1)
| ~ element(cast_as_carrier_subset(esk46_0),powerset(the_carrier(X1)))
| ~ empty_carrier(net_of_bool_filter(X1,cast_as_carrier_subset(esk46_0),esk47_0))
| ~ one_sorted_str(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_26]),c_0_27]),c_0_28])]),c_0_30]) ).
cnf(c_0_45,plain,
( net_str(net_of_bool_filter(X1,X2,X3),X1)
| empty_carrier(X1)
| empty(X2)
| empty(X3)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ filtered_subset(X3,boole_POSet(X2))
| ~ upper_relstr_subset(X3,boole_POSet(X2))
| ~ element(X3,powerset(the_carrier(boole_POSet(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_46,negated_conjecture,
( is_a_convergence_point_of_set(esk46_0,esk47_0,esk48_0)
| empty_carrier(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0))
| ~ directed_relstr(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0))
| ~ transitive_relstr(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0))
| ~ net_str(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0),esk46_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_19]),c_0_38]),c_0_39])]),c_0_31]),c_0_40])]) ).
cnf(c_0_47,negated_conjecture,
( directed_relstr(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0))
| empty(cast_as_carrier_subset(esk46_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_29])]),c_0_31]) ).
cnf(c_0_48,negated_conjecture,
( empty(cast_as_carrier_subset(esk46_0))
| transitive_relstr(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_29])]),c_0_31]) ).
cnf(c_0_49,negated_conjecture,
( empty(cast_as_carrier_subset(esk46_0))
| ~ empty_carrier(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_42]),c_0_29])]),c_0_31]) ).
cnf(c_0_50,negated_conjecture,
( empty(cast_as_carrier_subset(esk46_0))
| empty_carrier(X1)
| net_str(net_of_bool_filter(X1,cast_as_carrier_subset(esk46_0),esk47_0),X1)
| ~ element(cast_as_carrier_subset(esk46_0),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_26]),c_0_27]),c_0_28])]),c_0_30]) ).
cnf(c_0_51,negated_conjecture,
( is_a_convergence_point_of_set(esk46_0,esk47_0,esk48_0)
| empty(cast_as_carrier_subset(esk46_0))
| ~ net_str(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0),esk46_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49]) ).
cnf(c_0_52,negated_conjecture,
( empty(cast_as_carrier_subset(esk46_0))
| net_str(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0),esk46_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_42]),c_0_29])]),c_0_31]) ).
fof(c_0_53,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_pre_topc]) ).
cnf(c_0_54,plain,
( in(X3,lim_points_of_net(X1,X2))
| empty_carrier(X2)
| empty_carrier(X1)
| ~ is_a_convergence_point_of_set(X1,filter_of_net_str(X1,X2),X3)
| ~ element(X3,the_carrier(X1))
| ~ transitive_relstr(X2)
| ~ directed_relstr(X2)
| ~ net_str(X2,X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_55,negated_conjecture,
( ~ in(esk48_0,lim_points_of_net(esk46_0,net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)))
| ~ is_a_convergence_point_of_set(esk46_0,esk47_0,esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_56,negated_conjecture,
( is_a_convergence_point_of_set(esk46_0,esk47_0,esk48_0)
| empty(cast_as_carrier_subset(esk46_0)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_57,plain,
! [X95] :
( empty_carrier(X95)
| ~ one_sorted_str(X95)
| ~ empty(cast_as_carrier_subset(X95)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])]) ).
cnf(c_0_58,negated_conjecture,
( empty_carrier(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0))
| in(X1,lim_points_of_net(esk46_0,net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)))
| ~ is_a_convergence_point_of_set(esk46_0,esk47_0,X1)
| ~ directed_relstr(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0))
| ~ element(X1,the_carrier(esk46_0))
| ~ transitive_relstr(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0))
| ~ net_str(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0),esk46_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_19]),c_0_38])]),c_0_31]) ).
cnf(c_0_59,negated_conjecture,
( empty(cast_as_carrier_subset(esk46_0))
| ~ in(esk48_0,lim_points_of_net(esk46_0,net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0))) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(cast_as_carrier_subset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_61,negated_conjecture,
empty(cast_as_carrier_subset(esk46_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_56]),c_0_39])]),c_0_52]),c_0_48]),c_0_47]),c_0_59]),c_0_49]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_29])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 20:50:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 2.26/2.37 % Version : CSE_E---1.5
% 2.26/2.37 % Problem : theBenchmark.p
% 2.26/2.37 % Proof found
% 2.26/2.37 % SZS status Theorem for theBenchmark.p
% 2.26/2.37 % SZS output start Proof
% See solution above
% 2.26/2.38 % Total time : 1.794000 s
% 2.26/2.38 % SZS output end Proof
% 2.26/2.38 % Total time : 1.801000 s
%------------------------------------------------------------------------------