%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU395+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.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 5 05:12:10 PM UTC 2026
% Result : Theorem 4.03s 3.23s
% Output : CNFRefutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 18 unt; 0 def)
% Number of atoms : 449 ( 5 equ)
% Maximal formula atoms : 50 ( 6 avg)
% Number of connectives : 592 ( 212 ~; 234 |; 116 &)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 84 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',t18_yellow19) ).
fof(fc2_pre_topc,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(dt_l1_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
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/sandbox2/benchmark/theBenchmark.p',t13_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/sandbox2/benchmark/theBenchmark.p',t15_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/sandbox2/benchmark/theBenchmark.p',fc4_yellow19) ).
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/sandbox2/benchmark/theBenchmark.p',fc5_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/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
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/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow19) ).
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) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_pre_topc]) ).
fof(c_0_11,plain,
! [X290] :
( ~ top_str(X290)
| one_sorted_str(X290) ),
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] :
( ( ~ 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_14,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_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))
& 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_16,plain,
! [X320] :
( empty_carrier(X320)
| ~ one_sorted_str(X320)
| ~ empty(cast_as_carrier_subset(X320)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
cnf(c_0_17,plain,
( one_sorted_str(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
top_str(esk46_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X431,X432,X433] :
( ( ~ in(X433,lim_points_of_net(X431,X432))
| is_a_convergence_point_of_set(X431,filter_of_net_str(X431,X432),X433)
| ~ element(X433,the_carrier(X431))
| empty_carrier(X432)
| ~ transitive_relstr(X432)
| ~ directed_relstr(X432)
| ~ net_str(X432,X431)
| empty_carrier(X431)
| ~ topological_space(X431)
| ~ top_str(X431) )
& ( ~ is_a_convergence_point_of_set(X431,filter_of_net_str(X431,X432),X433)
| in(X433,lim_points_of_net(X431,X432))
| ~ element(X433,the_carrier(X431))
| empty_carrier(X432)
| ~ transitive_relstr(X432)
| ~ directed_relstr(X432)
| ~ net_str(X432,X431)
| empty_carrier(X431)
| ~ topological_space(X431)
| ~ top_str(X431) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_20,plain,
! [X434,X435] :
( empty_carrier(X434)
| ~ one_sorted_str(X434)
| empty(X435)
| ~ filtered_subset(X435,boole_POSet(cast_as_carrier_subset(X434)))
| ~ upper_relstr_subset(X435,boole_POSet(cast_as_carrier_subset(X434)))
| ~ proper_element(X435,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X434)))))
| ~ element(X435,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X434)))))
| X435 = filter_of_net_str(X434,net_of_bool_filter(X434,cast_as_carrier_subset(X434),X435)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_21,plain,
! [X332,X333,X334] :
( ( ~ empty_carrier(net_of_bool_filter(X332,X333,X334))
| empty_carrier(X332)
| ~ one_sorted_str(X332)
| empty(X333)
| ~ element(X333,powerset(the_carrier(X332)))
| empty(X334)
| ~ filtered_subset(X334,boole_POSet(X333))
| ~ upper_relstr_subset(X334,boole_POSet(X333))
| ~ element(X334,powerset(the_carrier(boole_POSet(X333)))) )
& ( reflexive_relstr(net_of_bool_filter(X332,X333,X334))
| empty_carrier(X332)
| ~ one_sorted_str(X332)
| empty(X333)
| ~ element(X333,powerset(the_carrier(X332)))
| empty(X334)
| ~ filtered_subset(X334,boole_POSet(X333))
| ~ upper_relstr_subset(X334,boole_POSet(X333))
| ~ element(X334,powerset(the_carrier(boole_POSet(X333)))) )
& ( transitive_relstr(net_of_bool_filter(X332,X333,X334))
| empty_carrier(X332)
| ~ one_sorted_str(X332)
| empty(X333)
| ~ element(X333,powerset(the_carrier(X332)))
| empty(X334)
| ~ filtered_subset(X334,boole_POSet(X333))
| ~ upper_relstr_subset(X334,boole_POSet(X333))
| ~ element(X334,powerset(the_carrier(boole_POSet(X333)))) )
& ( strict_net_str(net_of_bool_filter(X332,X333,X334),X332)
| empty_carrier(X332)
| ~ one_sorted_str(X332)
| empty(X333)
| ~ element(X333,powerset(the_carrier(X332)))
| empty(X334)
| ~ filtered_subset(X334,boole_POSet(X333))
| ~ upper_relstr_subset(X334,boole_POSet(X333))
| ~ element(X334,powerset(the_carrier(boole_POSet(X333)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_22,negated_conjecture,
~ empty_carrier(esk46_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(cast_as_carrier_subset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
one_sorted_str(esk46_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_25,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]) ).
cnf(c_0_26,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_19]) ).
cnf(c_0_27,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_28,negated_conjecture,
topological_space(esk46_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
element(esk48_0,the_carrier(esk46_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,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_20]) ).
cnf(c_0_31,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_32,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_33,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_34,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_35,negated_conjecture,
~ empty(esk47_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,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_37,negated_conjecture,
~ empty(cast_as_carrier_subset(esk46_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
fof(c_0_38,plain,
! [X282] :
( ~ one_sorted_str(X282)
| element(cast_as_carrier_subset(X282),powerset(the_carrier(X282))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_pre_topc])]) ).
fof(c_0_39,plain,
! [X337,X338,X339] :
( ( ~ empty_carrier(net_of_bool_filter(X337,X338,X339))
| empty_carrier(X337)
| ~ one_sorted_str(X337)
| empty(X338)
| ~ element(X338,powerset(the_carrier(X337)))
| empty(X339)
| ~ filtered_subset(X339,boole_POSet(X338))
| ~ upper_relstr_subset(X339,boole_POSet(X338))
| ~ proper_element(X339,powerset(the_carrier(boole_POSet(X338))))
| ~ element(X339,powerset(the_carrier(boole_POSet(X338)))) )
& ( reflexive_relstr(net_of_bool_filter(X337,X338,X339))
| empty_carrier(X337)
| ~ one_sorted_str(X337)
| empty(X338)
| ~ element(X338,powerset(the_carrier(X337)))
| empty(X339)
| ~ filtered_subset(X339,boole_POSet(X338))
| ~ upper_relstr_subset(X339,boole_POSet(X338))
| ~ proper_element(X339,powerset(the_carrier(boole_POSet(X338))))
| ~ element(X339,powerset(the_carrier(boole_POSet(X338)))) )
& ( transitive_relstr(net_of_bool_filter(X337,X338,X339))
| empty_carrier(X337)
| ~ one_sorted_str(X337)
| empty(X338)
| ~ element(X338,powerset(the_carrier(X337)))
| empty(X339)
| ~ filtered_subset(X339,boole_POSet(X338))
| ~ upper_relstr_subset(X339,boole_POSet(X338))
| ~ proper_element(X339,powerset(the_carrier(boole_POSet(X338))))
| ~ element(X339,powerset(the_carrier(boole_POSet(X338)))) )
& ( strict_net_str(net_of_bool_filter(X337,X338,X339),X337)
| empty_carrier(X337)
| ~ one_sorted_str(X337)
| empty(X338)
| ~ element(X338,powerset(the_carrier(X337)))
| empty(X339)
| ~ filtered_subset(X339,boole_POSet(X338))
| ~ upper_relstr_subset(X339,boole_POSet(X338))
| ~ proper_element(X339,powerset(the_carrier(boole_POSet(X338))))
| ~ element(X339,powerset(the_carrier(boole_POSet(X338)))) )
& ( directed_relstr(net_of_bool_filter(X337,X338,X339))
| empty_carrier(X337)
| ~ one_sorted_str(X337)
| empty(X338)
| ~ element(X338,powerset(the_carrier(X337)))
| empty(X339)
| ~ filtered_subset(X339,boole_POSet(X338))
| ~ upper_relstr_subset(X339,boole_POSet(X338))
| ~ proper_element(X339,powerset(the_carrier(boole_POSet(X338))))
| ~ element(X339,powerset(the_carrier(boole_POSet(X338)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_40,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]) ).
cnf(c_0_41,negated_conjecture,
( is_a_convergence_point_of_set(esk46_0,filter_of_net_str(esk46_0,net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)),esk48_0)
| 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(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_26,c_0_27]),c_0_18]),c_0_28]),c_0_29])]),c_0_22]) ).
cnf(c_0_42,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_30,c_0_31]),c_0_32]),c_0_33]),c_0_34]),c_0_24])]),c_0_35]),c_0_22]) ).
cnf(c_0_43,negated_conjecture,
( 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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_34]),c_0_32]),c_0_33])]),c_0_35]),c_0_37]) ).
cnf(c_0_44,plain,
( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,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_39]) ).
fof(c_0_46,plain,
! [X285,X286,X287] :
( ( ~ empty_carrier(net_of_bool_filter(X285,X286,X287))
| empty_carrier(X285)
| ~ one_sorted_str(X285)
| empty(X286)
| ~ element(X286,powerset(the_carrier(X285)))
| empty(X287)
| ~ filtered_subset(X287,boole_POSet(X286))
| ~ upper_relstr_subset(X287,boole_POSet(X286))
| ~ element(X287,powerset(the_carrier(boole_POSet(X286)))) )
& ( strict_net_str(net_of_bool_filter(X285,X286,X287),X285)
| empty_carrier(X285)
| ~ one_sorted_str(X285)
| empty(X286)
| ~ element(X286,powerset(the_carrier(X285)))
| empty(X287)
| ~ filtered_subset(X287,boole_POSet(X286))
| ~ upper_relstr_subset(X287,boole_POSet(X286))
| ~ element(X287,powerset(the_carrier(boole_POSet(X286)))) )
& ( net_str(net_of_bool_filter(X285,X286,X287),X285)
| empty_carrier(X285)
| ~ one_sorted_str(X285)
| empty(X286)
| ~ element(X286,powerset(the_carrier(X285)))
| empty(X287)
| ~ filtered_subset(X287,boole_POSet(X286))
| ~ upper_relstr_subset(X287,boole_POSet(X286))
| ~ element(X287,powerset(the_carrier(boole_POSet(X286)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
cnf(c_0_47,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)],[c_0_41,c_0_42])]) ).
cnf(c_0_48,negated_conjecture,
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_44]),c_0_24])]),c_0_22]) ).
cnf(c_0_49,negated_conjecture,
( directed_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(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_45,c_0_31]),c_0_32]),c_0_33]),c_0_34])]),c_0_35]),c_0_37]) ).
cnf(c_0_50,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_46]) ).
cnf(c_0_51,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))
| ~ 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)],[c_0_47,c_0_48])]) ).
cnf(c_0_52,negated_conjecture,
directed_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_49,c_0_44]),c_0_24])]),c_0_22]) ).
cnf(c_0_53,negated_conjecture,
( 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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_34]),c_0_32]),c_0_33])]),c_0_35]),c_0_37]) ).
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_19]) ).
cnf(c_0_55,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_46]) ).
cnf(c_0_56,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))
| ~ 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)],[c_0_51,c_0_52])]) ).
cnf(c_0_57,negated_conjecture,
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_53,c_0_44]),c_0_24])]),c_0_22]) ).
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)
| ~ element(X1,the_carrier(esk46_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(rw,[status(thm)],[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_42]),c_0_18]),c_0_28])]),c_0_22]),c_0_52]),c_0_48])]) ).
cnf(c_0_59,negated_conjecture,
( 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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_34]),c_0_32]),c_0_33])]),c_0_35]),c_0_37]) ).
cnf(c_0_60,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)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_61,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)
| ~ element(X1,the_carrier(esk46_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_57])]) ).
cnf(c_0_62,negated_conjecture,
( is_a_convergence_point_of_set(esk46_0,esk47_0,esk48_0)
| ~ element(cast_as_carrier_subset(esk46_0),powerset(the_carrier(esk46_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_24])]),c_0_22]) ).
cnf(c_0_63,negated_conjecture,
( empty_carrier(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0))
| in(esk48_0,lim_points_of_net(esk46_0,net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)))
| ~ element(cast_as_carrier_subset(esk46_0),powerset(the_carrier(esk46_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_29])]) ).
cnf(c_0_64,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_65,negated_conjecture,
( empty_carrier(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_44]),c_0_24])]) ).
cnf(c_0_66,negated_conjecture,
empty_carrier(net_of_bool_filter(esk46_0,cast_as_carrier_subset(esk46_0),esk47_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_60]) ).
cnf(c_0_67,negated_conjecture,
~ element(cast_as_carrier_subset(esk46_0),powerset(the_carrier(esk46_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_66]),c_0_24])]),c_0_22]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_44]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU395+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 03:03:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 4.03/3.23 % Version : CSE_E---1.7
% 4.03/3.23 % Problem : theBenchmark.p
% 4.03/3.23 % SZS status Theorem for theBenchmark.p
% 4.03/3.23 % SZS output start CNFRefutation
% See solution above
% 4.03/3.23 % Total time : 2.422s
%------------------------------------------------------------------------------