%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU394+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:59:11 AM UTC 2026
% Result : Theorem 252.59s 252.90s
% Output : Proof 252.88s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(abstractness_v1_orders_2,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('theBenchmark.p',abstractness_v1_orders_2) ).
fof(abstractness_v6_waybel_0,axiom,
! [A,B] :
( ( net_str(B,A)
& one_sorted_str(A) )
=> ( strict_net_str(B,A)
=> B = net_str_of(A,the_carrier(B),the_InternalRel(B),the_mapping(A,B)) ) ),
file('theBenchmark.p',abstractness_v6_waybel_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc10_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( join_complete_relstr(A)
& up_complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc10_waybel_0) ).
fof(cc11_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( join_complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( lower_bounded_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc11_waybel_0) ).
fof(cc12_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( up_complete_relstr(A)
& lower_bounded_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc12_waybel_0) ).
fof(cc13_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( join_complete_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( with_infima_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc13_waybel_0) ).
fof(cc14_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( join_complete_relstr(A)
& upper_bounded_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( upper_bounded_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc14_waybel_0) ).
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
fof(cc1_lattice3,axiom,
! [A] :
( rel_str(A)
=> ( with_suprema_relstr(A)
=> ~ empty_carrier(A) ) ),
file('theBenchmark.p',cc1_lattice3) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(cc1_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( ( complete_relstr(A)
& ~ empty_carrier(A) )
=> ( with_infima_relstr(A)
& with_suprema_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc1_yellow_0) ).
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(cc2_lattice3,axiom,
! [A] :
( rel_str(A)
=> ( with_infima_relstr(A)
=> ~ empty_carrier(A) ) ),
file('theBenchmark.p',cc2_lattice3) ).
fof(cc2_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( ( trivial_carrier(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( complete_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc2_yellow_0) ).
fof(cc3_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( ( complete_relstr(A)
& ~ empty_carrier(A) )
=> ( bounded_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc3_yellow_0) ).
fof(cc4_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( bounded_relstr(A)
=> ( upper_bounded_relstr(A)
& lower_bounded_relstr(A) ) ) ),
file('theBenchmark.p',cc4_yellow_0) ).
fof(cc5_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( trivial_carrier(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( connected_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc5_waybel_0) ).
fof(cc5_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( ( upper_bounded_relstr(A)
& lower_bounded_relstr(A) )
=> bounded_relstr(A) ) ),
file('theBenchmark.p',cc5_yellow_0) ).
fof(cc9_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( up_complete_relstr(A)
& with_suprema_relstr(A)
& reflexive_relstr(A) )
=> ( upper_bounded_relstr(A)
& with_suprema_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc9_waybel_0) ).
fof(d3_yellow19,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& ~ empty_carrier(B) )
=> filter_of_net_str(A,B) = a_2_1_yellow19(A,B) ) ),
file('theBenchmark.p',d3_yellow19) ).
fof(dt_g1_orders_2,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ( rel_str(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) ) ),
file('theBenchmark.p',dt_g1_orders_2) ).
fof(dt_g1_waybel_0,axiom,
! [A,B,C,D] :
( ( relation_of2(D,B,the_carrier(A))
& quasi_total(D,B,the_carrier(A))
& function(D)
& relation_of2(C,B,B)
& one_sorted_str(A) )
=> ( net_str(net_str_of(A,B,C,D),A)
& strict_net_str(net_str_of(A,B,C,D),A) ) ),
file('theBenchmark.p',dt_g1_waybel_0) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('theBenchmark.p',dt_k2_pre_topc) ).
fof(dt_k2_yellow19,axiom,
! [A,B] :
( ( net_str(B,A)
& ~ empty_carrier(B)
& one_sorted_str(A)
& ~ empty_carrier(A) )
=> element(filter_of_net_str(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) ),
file('theBenchmark.p',dt_k2_yellow19) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_yellow19,axiom,
! [A,B,C] :
( ( element(C,powerset(the_carrier(boole_POSet(B))))
& upper_relstr_subset(C,boole_POSet(B))
& filtered_subset(C,boole_POSet(B))
& ~ empty(C)
& element(B,powerset(the_carrier(A)))
& ~ empty(B)
& one_sorted_str(A)
& ~ empty_carrier(A) )
=> ( net_str(net_of_bool_filter(A,B,C),A)
& strict_net_str(net_of_bool_filter(A,B,C),A)
& ~ empty_carrier(net_of_bool_filter(A,B,C)) ) ),
file('theBenchmark.p',dt_k3_yellow19) ).
fof(dt_k3_yellow_1,axiom,
! [A] :
( rel_str(boole_POSet(A))
& strict_rel_str(boole_POSet(A)) ),
file('theBenchmark.p',dt_k3_yellow_1) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_orders_2) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_l1_waybel_0,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> rel_str(B) ) ),
file('theBenchmark.p',dt_l1_waybel_0) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(dt_u1_orders_2,axiom,
! [A] :
( rel_str(A)
=> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) ),
file('theBenchmark.p',dt_u1_orders_2) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(dt_u1_waybel_0,axiom,
! [A,B] :
( ( net_str(B,A)
& one_sorted_str(A) )
=> ( relation_of2_as_subset(the_mapping(A,B),the_carrier(B),the_carrier(A))
& quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A))
& function(the_mapping(A,B)) ) ),
file('theBenchmark.p',dt_u1_waybel_0) ).
fof(existence_l1_orders_2,axiom,
? [A] : rel_str(A),
file('theBenchmark.p',existence_l1_orders_2) ).
fof(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l1_waybel_0,axiom,
! [A] :
( one_sorted_str(A)
=> ? [B] : net_str(B,A) ),
file('theBenchmark.p',existence_l1_waybel_0) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : relation_of2(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(fc12_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('theBenchmark.p',fc12_finset_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc14_finset_1,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc14_finset_1) ).
fof(fc15_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& ~ empty_carrier(A) )
=> ( upper_relstr_subset(cast_as_carrier_subset(A),A)
& lower_relstr_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) ) ),
file('theBenchmark.p',fc15_waybel_0) ).
fof(fc15_yellow_6,axiom,
! [A,B] :
( ( net_str(B,A)
& ~ empty_carrier(B)
& one_sorted_str(A)
& ~ empty_carrier(A) )
=> ( quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A))
& function(the_mapping(A,B))
& relation(the_mapping(A,B))
& ~ empty(the_mapping(A,B)) ) ),
file('theBenchmark.p',fc15_yellow_6) ).
fof(fc1_finset_1,axiom,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
file('theBenchmark.p',fc1_finset_1) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_waybel_7,axiom,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& boolean_relstr(boole_POSet(A))
& complemented_relstr(boole_POSet(A))
& heyting_relstr(boole_POSet(A))
& distributive_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('theBenchmark.p',fc1_waybel_7) ).
fof(fc1_yellow_0,axiom,
! [A,B] :
( relation_of2(B,singleton(A),singleton(A))
=> ( trivial_carrier(rel_str_of(singleton(A),B))
& strict_rel_str(rel_str_of(singleton(A),B))
& ~ empty_carrier(rel_str_of(singleton(A),B)) ) ),
file('theBenchmark.p',fc1_yellow_0) ).
fof(fc2_pre_topc,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(cast_as_carrier_subset(A)) ),
file('theBenchmark.p',fc2_pre_topc) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc2_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& with_suprema_relstr(A) )
=> ( directed_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) ) ),
file('theBenchmark.p',fc2_waybel_0) ).
fof(fc2_waybel_7,axiom,
! [A] :
( ~ empty(A)
=> ( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& boolean_relstr(boole_POSet(A))
& complemented_relstr(boole_POSet(A))
& heyting_relstr(boole_POSet(A))
& distributive_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ trivial_carrier(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ) ),
file('theBenchmark.p',fc2_waybel_7) ).
fof(fc2_yellow19,axiom,
! [A,B] :
( ( net_str(B,A)
& ~ empty_carrier(B)
& one_sorted_str(A)
& ~ empty_carrier(A) )
=> ( upper_relstr_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(filter_of_net_str(A,B)) ) ),
file('theBenchmark.p',fc2_yellow19) ).
fof(fc2_yellow_0,axiom,
! [A] :
( ( rel_str(A)
& ~ empty_carrier(A) )
=> ~ empty(cast_as_carrier_subset(A)) ),
file('theBenchmark.p',fc2_yellow_0) ).
fof(fc3_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_difference(A,B)) ),
file('theBenchmark.p',fc3_relat_1) ).
fof(fc3_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& upper_bounded_relstr(A)
& ~ empty_carrier(A) )
=> ( directed_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) ) ),
file('theBenchmark.p',fc3_waybel_0) ).
fof(fc3_yellow19,axiom,
! [A,B] :
( ( net_str(B,A)
& directed_relstr(B)
& transitive_relstr(B)
& ~ empty_carrier(B)
& one_sorted_str(A)
& ~ empty_carrier(A) )
=> ( proper_element(filter_of_net_str(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& upper_relstr_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A)))
& filtered_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(filter_of_net_str(A,B)) ) ),
file('theBenchmark.p',fc3_yellow19) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(fc4_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& with_infima_relstr(A) )
=> ( filtered_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) ) ),
file('theBenchmark.p',fc4_waybel_0) ).
fof(fc4_yellow19,axiom,
! [A,B,C] :
( ( element(C,powerset(the_carrier(boole_POSet(B))))
& upper_relstr_subset(C,boole_POSet(B))
& filtered_subset(C,boole_POSet(B))
& ~ empty(C)
& element(B,powerset(the_carrier(A)))
& ~ empty(B)
& one_sorted_str(A)
& ~ empty_carrier(A) )
=> ( strict_net_str(net_of_bool_filter(A,B,C),A)
& transitive_relstr(net_of_bool_filter(A,B,C))
& reflexive_relstr(net_of_bool_filter(A,B,C))
& ~ empty_carrier(net_of_bool_filter(A,B,C)) ) ),
file('theBenchmark.p',fc4_yellow19) ).
fof(fc5_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& ~ empty_carrier(A) )
=> ( filtered_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) ) ),
file('theBenchmark.p',fc5_waybel_0) ).
fof(fc5_yellow19,axiom,
! [A,B,C] :
( ( element(C,powerset(the_carrier(boole_POSet(B))))
& proper_element(C,powerset(the_carrier(boole_POSet(B))))
& upper_relstr_subset(C,boole_POSet(B))
& filtered_subset(C,boole_POSet(B))
& ~ empty(C)
& element(B,powerset(the_carrier(A)))
& ~ empty(B)
& one_sorted_str(A)
& ~ empty_carrier(A) )
=> ( directed_relstr(net_of_bool_filter(A,B,C))
& strict_net_str(net_of_bool_filter(A,B,C),A)
& transitive_relstr(net_of_bool_filter(A,B,C))
& reflexive_relstr(net_of_bool_filter(A,B,C))
& ~ empty_carrier(net_of_bool_filter(A,B,C)) ) ),
file('theBenchmark.p',fc5_yellow19) ).
fof(fc6_waybel_0,axiom,
! [A,B,C,D] :
( ( relation_of2(D,B,the_carrier(A))
& quasi_total(D,B,the_carrier(A))
& function(D)
& relation_of2(C,B,B)
& ~ empty(B)
& one_sorted_str(A) )
=> ( strict_net_str(net_str_of(A,B,C,D),A)
& ~ empty_carrier(net_str_of(A,B,C,D)) ) ),
file('theBenchmark.p',fc6_waybel_0) ).
fof(fc7_yellow_1,axiom,
! [A] :
( antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('theBenchmark.p',fc7_yellow_1) ).
fof(fc8_yellow_1,axiom,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('theBenchmark.p',fc8_yellow_1) ).
fof(fc8_yellow_6,axiom,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& directed_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('theBenchmark.p',fc8_yellow_6) ).
fof(fraenkel_a_2_1_yellow19,axiom,
! [A,B,C] :
( ( net_str(C,B)
& ~ empty_carrier(C)
& one_sorted_str(B)
& ~ empty_carrier(B) )
=> ( in(A,a_2_1_yellow19(B,C))
<=> ? [D] :
( is_eventually_in(B,C,D)
& A = D
& element(D,powerset(the_carrier(B))) ) ) ),
file('theBenchmark.p',fraenkel_a_2_1_yellow19) ).
fof(free_g1_orders_2,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ! [C,D] :
( rel_str_of(A,B) = rel_str_of(C,D)
=> ( B = D
& A = C ) ) ),
file('theBenchmark.p',free_g1_orders_2) ).
fof(free_g1_waybel_0,axiom,
! [A,B,C,D] :
( ( relation_of2(D,B,the_carrier(A))
& quasi_total(D,B,the_carrier(A))
& function(D)
& relation_of2(C,B,B)
& one_sorted_str(A) )
=> ! [E,F,G,H] :
( net_str_of(A,B,C,D) = net_str_of(E,F,G,H)
=> ( D = H
& C = G
& B = F
& A = E ) ) ),
file('theBenchmark.p',free_g1_waybel_0) ).
fof(rc10_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ? [B] :
( upper_relstr_subset(B,A)
& filtered_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc10_waybel_0) ).
fof(rc11_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A) )
=> ? [B] :
( upper_relstr_subset(B,A)
& lower_relstr_subset(B,A)
& filtered_subset(B,A)
& directed_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc11_waybel_0) ).
fof(rc12_waybel_0,axiom,
? [A] :
( connected_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc12_waybel_0) ).
fof(rc13_waybel_0,axiom,
? [A] :
( join_complete_relstr(A)
& up_complete_relstr(A)
& bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc13_waybel_0) ).
fof(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_1) ).
fof(rc1_lattice3,axiom,
? [A] :
( complete_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc1_lattice3) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ? [B] :
( filtered_subset(B,A)
& directed_subset(B,A)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc1_waybel_0) ).
fof(rc1_waybel_7,axiom,
? [A] :
( with_infima_relstr(A)
& with_suprema_relstr(A)
& boolean_relstr(A)
& complemented_relstr(A)
& heyting_relstr(A)
& distributive_relstr(A)
& ~ v1_yellow_3(A)
& bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ trivial_carrier(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc1_waybel_7) ).
fof(rc1_yellow_0,axiom,
? [A] :
( trivial_carrier(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc1_yellow_0) ).
fof(rc2_lattice3,axiom,
? [A] :
( complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc2_lattice3) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ? [B] :
( filtered_subset(B,A)
& directed_subset(B,A)
& finite(B)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc2_waybel_0) ).
fof(rc2_waybel_7,axiom,
! [A] :
? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(powerset(A))) ),
file('theBenchmark.p',rc2_waybel_7) ).
fof(rc2_yellow_0,axiom,
? [A] :
( bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc2_yellow_0) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc3_finset_1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc3_waybel_7,axiom,
! [A] :
( one_sorted_str(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(powerset(the_carrier(A)))) ) ),
file('theBenchmark.p',rc3_waybel_7) ).
fof(rc4_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc4_finset_1) ).
fof(rc4_waybel_0,axiom,
! [A] :
( one_sorted_str(A)
=> ? [B] :
( strict_net_str(B,A)
& net_str(B,A) ) ),
file('theBenchmark.p',rc4_waybel_0) ).
fof(rc4_waybel_7,axiom,
! [A] :
( ( rel_str(A)
& upper_bounded_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ trivial_carrier(A)
& ~ empty_carrier(A) )
=> ? [B] :
( upper_relstr_subset(B,A)
& filtered_subset(B,A)
& proper_element(B,powerset(the_carrier(A)))
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc4_waybel_7) ).
fof(rc4_yellow_6,axiom,
? [A] :
( directed_relstr(A)
& transitive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc4_yellow_6) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ? [B] :
( ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(rc5_waybel_0,axiom,
! [A] :
( one_sorted_str(A)
=> ? [B] :
( directed_relstr(B)
& strict_net_str(B,A)
& antisymmetric_relstr(B)
& transitive_relstr(B)
& reflexive_relstr(B)
& ~ empty_carrier(B)
& net_str(B,A) ) ),
file('theBenchmark.p',rc5_waybel_0) ).
fof(rc7_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ? [B] :
( upper_relstr_subset(B,A)
& lower_relstr_subset(B,A)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc7_waybel_0) ).
fof(rc8_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& ~ empty_carrier(A) )
=> ? [B] :
( upper_relstr_subset(B,A)
& lower_relstr_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc8_waybel_0) ).
fof(rc9_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ? [B] :
( lower_relstr_subset(B,A)
& directed_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc9_waybel_0) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t14_yellow19,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(B) )
=> set_difference(B,singleton(empty_set)) = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) ) ),
file('theBenchmark.p',t14_yellow19) ).
fof(t15_yellow19,conjecture,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(B) )
=> B = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) ) ),
file('theBenchmark.p',t15_yellow19) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t2_yellow19,axiom,
! [A] :
( ~ empty(A)
=> ! [B] :
( ( element(B,powerset(the_carrier(boole_POSet(A))))
& proper_element(B,powerset(the_carrier(boole_POSet(A))))
& upper_relstr_subset(B,boole_POSet(A))
& filtered_subset(B,boole_POSet(A))
& ~ empty(B) )
=> ! [C] :
~ ( empty(C)
& in(C,B) ) ) ),
file('theBenchmark.p',t2_yellow19) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t65_zfmisc_1,axiom,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A] :
( A = rel_str_of(the_carrier(A),the_InternalRel(A))
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2]) ).
fof(f_1_2,plain,
! [U_0] :
( U_0 = rel_str_of(the_carrier(U_0),the_InternalRel(U_0))
| ~ strict_rel_str(U_0)
| ~ rel_str(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( U_0 = rel_str_of(the_carrier(U_0),the_InternalRel(U_0))
| ~ strict_rel_str(U_0)
| ~ rel_str(U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( B = net_str_of(A,the_carrier(B),the_InternalRel(B),the_mapping(A,B))
| ~ strict_net_str(B,A)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[abstractness_v6_waybel_0]) ).
fof(f_2_2,plain,
! [U_2,U_1] :
( U_1 = net_str_of(U_2,the_carrier(U_1),the_InternalRel(U_1),the_mapping(U_2,U_1))
| ~ strict_net_str(U_1,U_2)
| ~ net_str(U_1,U_2)
| ~ one_sorted_str(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( U_1 = net_str_of(U_2,the_carrier(U_1),the_InternalRel(U_1),the_mapping(U_2,U_1))
| ~ strict_net_str(U_1,U_2)
| ~ net_str(U_1,U_2)
| ~ one_sorted_str(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_3_2,plain,
! [U_4,U_3] :
( ~ in(U_3,U_4)
| ~ in(U_4,U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ in(U_3,U_4)
| ~ in(U_4,U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ( join_complete_relstr(A)
& up_complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ complete_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc10_waybel_0]) ).
fof(f_4_2,plain,
! [U_5] :
( ( join_complete_relstr(U_5)
& up_complete_relstr(U_5)
& reflexive_relstr(U_5)
& ~ empty_carrier(U_5) )
| ~ complete_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( ~ empty_carrier(U_5)
| ~ complete_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( reflexive_relstr(U_5)
| ~ complete_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( up_complete_relstr(U_5)
| ~ complete_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_6,plain,
( join_complete_relstr(U_5)
| ~ complete_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( lower_bounded_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ join_complete_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc11_waybel_0]) ).
fof(f_5_2,plain,
! [U_6] :
( ( lower_bounded_relstr(U_6)
& reflexive_relstr(U_6)
& ~ empty_carrier(U_6) )
| ~ join_complete_relstr(U_6)
| ~ reflexive_relstr(U_6)
| empty_carrier(U_6)
| ~ rel_str(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( ~ empty_carrier(U_6)
| ~ join_complete_relstr(U_6)
| ~ reflexive_relstr(U_6)
| empty_carrier(U_6)
| ~ rel_str(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( reflexive_relstr(U_6)
| ~ join_complete_relstr(U_6)
| ~ reflexive_relstr(U_6)
| empty_carrier(U_6)
| ~ rel_str(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( lower_bounded_relstr(U_6)
| ~ join_complete_relstr(U_6)
| ~ reflexive_relstr(U_6)
| empty_carrier(U_6)
| ~ rel_str(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ( bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ up_complete_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ with_suprema_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc12_waybel_0]) ).
fof(f_6_2,plain,
! [U_7] :
( ( bounded_relstr(U_7)
& upper_bounded_relstr(U_7)
& lower_bounded_relstr(U_7)
& complete_relstr(U_7)
& with_infima_relstr(U_7)
& with_suprema_relstr(U_7)
& antisymmetric_relstr(U_7)
& transitive_relstr(U_7)
& reflexive_relstr(U_7)
& ~ empty_carrier(U_7) )
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ~ empty_carrier(U_7)
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( reflexive_relstr(U_7)
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( transitive_relstr(U_7)
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_6,plain,
( antisymmetric_relstr(U_7)
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_7,plain,
( with_suprema_relstr(U_7)
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_8,plain,
( with_infima_relstr(U_7)
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_9,plain,
( complete_relstr(U_7)
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_10,plain,
( lower_bounded_relstr(U_7)
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_11,plain,
( upper_bounded_relstr(U_7)
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_12,plain,
( bounded_relstr(U_7)
| ~ up_complete_relstr(U_7)
| ~ lower_bounded_relstr(U_7)
| ~ with_suprema_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ transitive_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ( with_infima_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ join_complete_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc13_waybel_0]) ).
fof(f_7_2,plain,
! [U_8] :
( ( with_infima_relstr(U_8)
& antisymmetric_relstr(U_8)
& reflexive_relstr(U_8)
& ~ empty_carrier(U_8) )
| ~ join_complete_relstr(U_8)
| ~ antisymmetric_relstr(U_8)
| ~ reflexive_relstr(U_8)
| empty_carrier(U_8)
| ~ rel_str(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ~ empty_carrier(U_8)
| ~ join_complete_relstr(U_8)
| ~ antisymmetric_relstr(U_8)
| ~ reflexive_relstr(U_8)
| empty_carrier(U_8)
| ~ rel_str(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( reflexive_relstr(U_8)
| ~ join_complete_relstr(U_8)
| ~ antisymmetric_relstr(U_8)
| ~ reflexive_relstr(U_8)
| empty_carrier(U_8)
| ~ rel_str(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_5,plain,
( antisymmetric_relstr(U_8)
| ~ join_complete_relstr(U_8)
| ~ antisymmetric_relstr(U_8)
| ~ reflexive_relstr(U_8)
| empty_carrier(U_8)
| ~ rel_str(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_6,plain,
( with_infima_relstr(U_8)
| ~ join_complete_relstr(U_8)
| ~ antisymmetric_relstr(U_8)
| ~ reflexive_relstr(U_8)
| empty_carrier(U_8)
| ~ rel_str(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ( upper_bounded_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ join_complete_relstr(A)
| ~ upper_bounded_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc14_waybel_0]) ).
fof(f_8_2,plain,
! [U_9] :
( ( upper_bounded_relstr(U_9)
& with_suprema_relstr(U_9)
& antisymmetric_relstr(U_9)
& reflexive_relstr(U_9)
& ~ empty_carrier(U_9) )
| ~ join_complete_relstr(U_9)
| ~ upper_bounded_relstr(U_9)
| ~ antisymmetric_relstr(U_9)
| ~ reflexive_relstr(U_9)
| empty_carrier(U_9)
| ~ rel_str(U_9) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( ~ empty_carrier(U_9)
| ~ join_complete_relstr(U_9)
| ~ upper_bounded_relstr(U_9)
| ~ antisymmetric_relstr(U_9)
| ~ reflexive_relstr(U_9)
| empty_carrier(U_9)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( reflexive_relstr(U_9)
| ~ join_complete_relstr(U_9)
| ~ upper_bounded_relstr(U_9)
| ~ antisymmetric_relstr(U_9)
| ~ reflexive_relstr(U_9)
| empty_carrier(U_9)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( antisymmetric_relstr(U_9)
| ~ join_complete_relstr(U_9)
| ~ upper_bounded_relstr(U_9)
| ~ antisymmetric_relstr(U_9)
| ~ reflexive_relstr(U_9)
| empty_carrier(U_9)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_6,plain,
( with_suprema_relstr(U_9)
| ~ join_complete_relstr(U_9)
| ~ upper_bounded_relstr(U_9)
| ~ antisymmetric_relstr(U_9)
| ~ reflexive_relstr(U_9)
| empty_carrier(U_9)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_7,plain,
( upper_bounded_relstr(U_9)
| ~ join_complete_relstr(U_9)
| ~ upper_bounded_relstr(U_9)
| ~ antisymmetric_relstr(U_9)
| ~ reflexive_relstr(U_9)
| empty_carrier(U_9)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_9_2,plain,
! [U_10] :
( finite(U_10)
| ~ empty(U_10) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( finite(U_10)
| ~ empty(U_10) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
( ~ empty_carrier(A)
| ~ with_suprema_relstr(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc1_lattice3]) ).
fof(f_10_2,plain,
! [U_11] :
( ~ empty_carrier(U_11)
| ~ with_suprema_relstr(U_11)
| ~ rel_str(U_11) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( ~ empty_carrier(U_11)
| ~ with_suprema_relstr(U_11)
| ~ rel_str(U_11) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_11_2,plain,
! [U_12] :
( relation(U_12)
| ~ empty(U_12) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( relation(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_12_2,plain,
! [U_15,U_14,U_13] :
( relation(U_13)
| ~ element(U_13,powerset(cartesian_product2(U_15,U_14))) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( relation(U_13)
| ~ element(U_13,powerset(cartesian_product2(U_15,U_14))) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A] :
( ( with_infima_relstr(A)
& with_suprema_relstr(A)
& ~ empty_carrier(A) )
| ~ complete_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc1_yellow_0]) ).
fof(f_13_2,plain,
! [U_16] :
( ( with_infima_relstr(U_16)
& with_suprema_relstr(U_16)
& ~ empty_carrier(U_16) )
| ~ complete_relstr(U_16)
| empty_carrier(U_16)
| ~ rel_str(U_16) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( ~ empty_carrier(U_16)
| ~ complete_relstr(U_16)
| empty_carrier(U_16)
| ~ rel_str(U_16) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( with_suprema_relstr(U_16)
| ~ complete_relstr(U_16)
| empty_carrier(U_16)
| ~ rel_str(U_16) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_5,plain,
( with_infima_relstr(U_16)
| ~ complete_relstr(U_16)
| empty_carrier(U_16)
| ~ rel_str(U_16) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_14_2,plain,
! [U_18] :
( ! [U_17] :
( finite(U_17)
| ~ element(U_17,powerset(U_18)) )
| ~ finite(U_18) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( finite(U_17)
| ~ element(U_17,powerset(U_18))
| ~ finite(U_18) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( ~ empty_carrier(A)
| ~ with_infima_relstr(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc2_lattice3]) ).
fof(f_15_2,plain,
! [U_19] :
( ~ empty_carrier(U_19)
| ~ with_infima_relstr(U_19)
| ~ rel_str(U_19) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( ~ empty_carrier(U_19)
| ~ with_infima_relstr(U_19)
| ~ rel_str(U_19) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( ( complete_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ trivial_carrier(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc2_yellow_0]) ).
fof(f_16_2,plain,
! [U_20] :
( ( complete_relstr(U_20)
& antisymmetric_relstr(U_20)
& transitive_relstr(U_20)
& reflexive_relstr(U_20)
& ~ empty_carrier(U_20) )
| ~ trivial_carrier(U_20)
| ~ reflexive_relstr(U_20)
| empty_carrier(U_20)
| ~ rel_str(U_20) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( ~ empty_carrier(U_20)
| ~ trivial_carrier(U_20)
| ~ reflexive_relstr(U_20)
| empty_carrier(U_20)
| ~ rel_str(U_20) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( reflexive_relstr(U_20)
| ~ trivial_carrier(U_20)
| ~ reflexive_relstr(U_20)
| empty_carrier(U_20)
| ~ rel_str(U_20) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_5,plain,
( transitive_relstr(U_20)
| ~ trivial_carrier(U_20)
| ~ reflexive_relstr(U_20)
| empty_carrier(U_20)
| ~ rel_str(U_20) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_6,plain,
( antisymmetric_relstr(U_20)
| ~ trivial_carrier(U_20)
| ~ reflexive_relstr(U_20)
| empty_carrier(U_20)
| ~ rel_str(U_20) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_7,plain,
( complete_relstr(U_20)
| ~ trivial_carrier(U_20)
| ~ reflexive_relstr(U_20)
| empty_carrier(U_20)
| ~ rel_str(U_20) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( ( bounded_relstr(A)
& ~ empty_carrier(A) )
| ~ complete_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc3_yellow_0]) ).
fof(f_17_2,plain,
! [U_21] :
( ( bounded_relstr(U_21)
& ~ empty_carrier(U_21) )
| ~ complete_relstr(U_21)
| empty_carrier(U_21)
| ~ rel_str(U_21) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( ~ empty_carrier(U_21)
| ~ complete_relstr(U_21)
| empty_carrier(U_21)
| ~ rel_str(U_21) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( bounded_relstr(U_21)
| ~ complete_relstr(U_21)
| empty_carrier(U_21)
| ~ rel_str(U_21) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A] :
( ( upper_bounded_relstr(A)
& lower_bounded_relstr(A) )
| ~ bounded_relstr(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc4_yellow_0]) ).
fof(f_18_2,plain,
! [U_22] :
( ( upper_bounded_relstr(U_22)
& lower_bounded_relstr(U_22) )
| ~ bounded_relstr(U_22)
| ~ rel_str(U_22) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( lower_bounded_relstr(U_22)
| ~ bounded_relstr(U_22)
| ~ rel_str(U_22) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( upper_bounded_relstr(U_22)
| ~ bounded_relstr(U_22)
| ~ rel_str(U_22) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( ( connected_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ trivial_carrier(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc5_waybel_0]) ).
fof(f_19_2,plain,
! [U_23] :
( ( connected_relstr(U_23)
& reflexive_relstr(U_23)
& ~ empty_carrier(U_23) )
| ~ trivial_carrier(U_23)
| ~ reflexive_relstr(U_23)
| empty_carrier(U_23)
| ~ rel_str(U_23) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( ~ empty_carrier(U_23)
| ~ trivial_carrier(U_23)
| ~ reflexive_relstr(U_23)
| empty_carrier(U_23)
| ~ rel_str(U_23) ),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( reflexive_relstr(U_23)
| ~ trivial_carrier(U_23)
| ~ reflexive_relstr(U_23)
| empty_carrier(U_23)
| ~ rel_str(U_23) ),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_5,plain,
( connected_relstr(U_23)
| ~ trivial_carrier(U_23)
| ~ reflexive_relstr(U_23)
| empty_carrier(U_23)
| ~ rel_str(U_23) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A] :
( bounded_relstr(A)
| ~ upper_bounded_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc5_yellow_0]) ).
fof(f_20_2,plain,
! [U_24] :
( bounded_relstr(U_24)
| ~ upper_bounded_relstr(U_24)
| ~ lower_bounded_relstr(U_24)
| ~ rel_str(U_24) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( bounded_relstr(U_24)
| ~ upper_bounded_relstr(U_24)
| ~ lower_bounded_relstr(U_24)
| ~ rel_str(U_24) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A] :
( ( upper_bounded_relstr(A)
& with_suprema_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ up_complete_relstr(A)
| ~ with_suprema_relstr(A)
| ~ reflexive_relstr(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc9_waybel_0]) ).
fof(f_21_2,plain,
! [U_25] :
( ( upper_bounded_relstr(U_25)
& with_suprema_relstr(U_25)
& reflexive_relstr(U_25)
& ~ empty_carrier(U_25) )
| ~ up_complete_relstr(U_25)
| ~ with_suprema_relstr(U_25)
| ~ reflexive_relstr(U_25)
| ~ rel_str(U_25) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( ~ empty_carrier(U_25)
| ~ up_complete_relstr(U_25)
| ~ with_suprema_relstr(U_25)
| ~ reflexive_relstr(U_25)
| ~ rel_str(U_25) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( reflexive_relstr(U_25)
| ~ up_complete_relstr(U_25)
| ~ with_suprema_relstr(U_25)
| ~ reflexive_relstr(U_25)
| ~ rel_str(U_25) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_5,plain,
( with_suprema_relstr(U_25)
| ~ up_complete_relstr(U_25)
| ~ with_suprema_relstr(U_25)
| ~ reflexive_relstr(U_25)
| ~ rel_str(U_25) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_6,plain,
( upper_bounded_relstr(U_25)
| ~ up_complete_relstr(U_25)
| ~ with_suprema_relstr(U_25)
| ~ reflexive_relstr(U_25)
| ~ rel_str(U_25) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A] :
( ! [B] :
( filter_of_net_str(A,B) = a_2_1_yellow19(A,B)
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d3_yellow19]) ).
fof(f_22_2,plain,
! [U_27] :
( ! [U_26] :
( filter_of_net_str(U_27,U_26) = a_2_1_yellow19(U_27,U_26)
| ~ net_str(U_26,U_27)
| empty_carrier(U_26) )
| ~ one_sorted_str(U_27)
| empty_carrier(U_27) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( filter_of_net_str(U_27,U_26) = a_2_1_yellow19(U_27,U_26)
| ~ net_str(U_26,U_27)
| empty_carrier(U_26)
| ~ one_sorted_str(U_27)
| empty_carrier(U_27) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,B] :
( ( rel_str(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) )
| ~ relation_of2(B,A,A) ),
inference(fof_nnf,[status(thm)],[dt_g1_orders_2]) ).
fof(f_23_2,plain,
! [U_29,U_28] :
( ( rel_str(rel_str_of(U_29,U_28))
& strict_rel_str(rel_str_of(U_29,U_28)) )
| ~ relation_of2(U_28,U_29,U_29) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( strict_rel_str(rel_str_of(U_29,U_28))
| ~ relation_of2(U_28,U_29,U_29) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( rel_str(rel_str_of(U_29,U_28))
| ~ relation_of2(U_28,U_29,U_29) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B,C,D] :
( ( net_str(net_str_of(A,B,C,D),A)
& strict_net_str(net_str_of(A,B,C,D),A) )
| ~ relation_of2(D,B,the_carrier(A))
| ~ quasi_total(D,B,the_carrier(A))
| ~ function(D)
| ~ relation_of2(C,B,B)
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[dt_g1_waybel_0]) ).
fof(f_24_2,plain,
! [U_33,U_32,U_31,U_30] :
( ( net_str(net_str_of(U_33,U_32,U_31,U_30),U_33)
& strict_net_str(net_str_of(U_33,U_32,U_31,U_30),U_33) )
| ~ relation_of2(U_30,U_32,the_carrier(U_33))
| ~ quasi_total(U_30,U_32,the_carrier(U_33))
| ~ function(U_30)
| ~ relation_of2(U_31,U_32,U_32)
| ~ one_sorted_str(U_33) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( strict_net_str(net_str_of(U_33,U_32,U_31,U_30),U_33)
| ~ relation_of2(U_30,U_32,the_carrier(U_33))
| ~ quasi_total(U_30,U_32,the_carrier(U_33))
| ~ function(U_30)
| ~ relation_of2(U_31,U_32,U_32)
| ~ one_sorted_str(U_33) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( net_str(net_str_of(U_33,U_32,U_31,U_30),U_33)
| ~ relation_of2(U_30,U_32,the_carrier(U_33))
| ~ quasi_total(U_30,U_32,the_carrier(U_33))
| ~ function(U_30)
| ~ relation_of2(U_31,U_32,U_32)
| ~ one_sorted_str(U_33) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_25_2,plain,
$true,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_26_2,plain,
$true,
inference(clausify,[status(thm)],[f_26_1]) ).
fof(f_27_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_27_2,plain,
$true,
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_1,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_pre_topc]) ).
fof(f_28_2,plain,
! [U_34] :
( element(cast_as_carrier_subset(U_34),powerset(the_carrier(U_34)))
| ~ one_sorted_str(U_34) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( element(cast_as_carrier_subset(U_34),powerset(the_carrier(U_34)))
| ~ one_sorted_str(U_34) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( element(filter_of_net_str(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
| ~ net_str(B,A)
| empty_carrier(B)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_yellow19]) ).
fof(f_29_2,plain,
! [U_36,U_35] :
( element(filter_of_net_str(U_36,U_35),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(U_36)))))
| ~ net_str(U_35,U_36)
| empty_carrier(U_35)
| ~ one_sorted_str(U_36)
| empty_carrier(U_36) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( element(filter_of_net_str(U_36,U_35),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(U_36)))))
| ~ net_str(U_35,U_36)
| empty_carrier(U_35)
| ~ one_sorted_str(U_36)
| empty_carrier(U_36) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_30_2,plain,
$true,
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_1,plain,
! [A,B,C] :
( ( net_str(net_of_bool_filter(A,B,C),A)
& strict_net_str(net_of_bool_filter(A,B,C),A)
& ~ empty_carrier(net_of_bool_filter(A,B,C)) )
| ~ element(C,powerset(the_carrier(boole_POSet(B))))
| ~ upper_relstr_subset(C,boole_POSet(B))
| ~ filtered_subset(C,boole_POSet(B))
| empty(C)
| ~ element(B,powerset(the_carrier(A)))
| empty(B)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k3_yellow19]) ).
fof(f_31_2,plain,
! [U_39,U_38,U_37] :
( ( net_str(net_of_bool_filter(U_39,U_38,U_37),U_39)
& strict_net_str(net_of_bool_filter(U_39,U_38,U_37),U_39)
& ~ empty_carrier(net_of_bool_filter(U_39,U_38,U_37)) )
| ~ element(U_37,powerset(the_carrier(boole_POSet(U_38))))
| ~ upper_relstr_subset(U_37,boole_POSet(U_38))
| ~ filtered_subset(U_37,boole_POSet(U_38))
| empty(U_37)
| ~ element(U_38,powerset(the_carrier(U_39)))
| empty(U_38)
| ~ one_sorted_str(U_39)
| empty_carrier(U_39) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( ~ empty_carrier(net_of_bool_filter(U_39,U_38,U_37))
| ~ element(U_37,powerset(the_carrier(boole_POSet(U_38))))
| ~ upper_relstr_subset(U_37,boole_POSet(U_38))
| ~ filtered_subset(U_37,boole_POSet(U_38))
| empty(U_37)
| ~ element(U_38,powerset(the_carrier(U_39)))
| empty(U_38)
| ~ one_sorted_str(U_39)
| empty_carrier(U_39) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( strict_net_str(net_of_bool_filter(U_39,U_38,U_37),U_39)
| ~ element(U_37,powerset(the_carrier(boole_POSet(U_38))))
| ~ upper_relstr_subset(U_37,boole_POSet(U_38))
| ~ filtered_subset(U_37,boole_POSet(U_38))
| empty(U_37)
| ~ element(U_38,powerset(the_carrier(U_39)))
| empty(U_38)
| ~ one_sorted_str(U_39)
| empty_carrier(U_39) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_5,plain,
( net_str(net_of_bool_filter(U_39,U_38,U_37),U_39)
| ~ element(U_37,powerset(the_carrier(boole_POSet(U_38))))
| ~ upper_relstr_subset(U_37,boole_POSet(U_38))
| ~ filtered_subset(U_37,boole_POSet(U_38))
| empty(U_37)
| ~ element(U_38,powerset(the_carrier(U_39)))
| empty(U_38)
| ~ one_sorted_str(U_39)
| empty_carrier(U_39) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A] :
( rel_str(boole_POSet(A))
& strict_rel_str(boole_POSet(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_yellow_1]) ).
fof(f_32_2,plain,
! [U_40] :
( rel_str(boole_POSet(U_40))
& strict_rel_str(boole_POSet(U_40)) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_42] : rel_str(boole_POSet(U_42))
& ! [U_41] : strict_rel_str(boole_POSet(U_41)) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
strict_rel_str(boole_POSet(U_41)),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
rel_str(boole_POSet(U_42)),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_33_2,plain,
$true,
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_1,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_orders_2]) ).
fof(f_34_2,plain,
! [U_43] :
( one_sorted_str(U_43)
| ~ rel_str(U_43) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( one_sorted_str(U_43)
| ~ rel_str(U_43) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_35_2,plain,
$true,
inference(clausify,[status(thm)],[f_35_1]) ).
fof(f_36_1,plain,
! [A] :
( ! [B] :
( rel_str(B)
| ~ net_str(B,A) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_waybel_0]) ).
fof(f_36_2,plain,
! [U_45] :
( ! [U_44] :
( rel_str(U_44)
| ~ net_str(U_44,U_45) )
| ~ one_sorted_str(U_45) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( rel_str(U_44)
| ~ net_str(U_44,U_45)
| ~ one_sorted_str(U_45) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_37_2,plain,
$true,
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_38_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_38_2,plain,
$true,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_1,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_39_2,plain,
! [U_48,U_47,U_46] :
( element(U_46,powerset(cartesian_product2(U_48,U_47)))
| ~ relation_of2_as_subset(U_46,U_48,U_47) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( element(U_46,powerset(cartesian_product2(U_48,U_47)))
| ~ relation_of2_as_subset(U_46,U_48,U_47) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A] :
( relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_orders_2]) ).
fof(f_40_2,plain,
! [U_49] :
( relation_of2_as_subset(the_InternalRel(U_49),the_carrier(U_49),the_carrier(U_49))
| ~ rel_str(U_49) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( relation_of2_as_subset(the_InternalRel(U_49),the_carrier(U_49),the_carrier(U_49))
| ~ rel_str(U_49) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_41_2,plain,
$true,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,plain,
! [A,B] :
( ( relation_of2_as_subset(the_mapping(A,B),the_carrier(B),the_carrier(A))
& quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A))
& function(the_mapping(A,B)) )
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_waybel_0]) ).
fof(f_42_2,plain,
! [U_51,U_50] :
( ( relation_of2_as_subset(the_mapping(U_51,U_50),the_carrier(U_50),the_carrier(U_51))
& quasi_total(the_mapping(U_51,U_50),the_carrier(U_50),the_carrier(U_51))
& function(the_mapping(U_51,U_50)) )
| ~ net_str(U_50,U_51)
| ~ one_sorted_str(U_51) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( function(the_mapping(U_51,U_50))
| ~ net_str(U_50,U_51)
| ~ one_sorted_str(U_51) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( quasi_total(the_mapping(U_51,U_50),the_carrier(U_50),the_carrier(U_51))
| ~ net_str(U_50,U_51)
| ~ one_sorted_str(U_51) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_5,plain,
( relation_of2_as_subset(the_mapping(U_51,U_50),the_carrier(U_50),the_carrier(U_51))
| ~ net_str(U_50,U_51)
| ~ one_sorted_str(U_51) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
? [A] : rel_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_orders_2]) ).
fof(f_43_2,plain,
? [U_52] : rel_str(U_52),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
rel_str(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_52,sK1)],[f_43_2]) ).
cnf(f_43_4,plain,
rel_str(sK1),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_44_2,plain,
? [U_53] : one_sorted_str(U_53),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
one_sorted_str(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_53,sK2)],[f_44_2]) ).
cnf(f_44_4,plain,
one_sorted_str(sK2),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A] :
( ? [B] : net_str(B,A)
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[existence_l1_waybel_0]) ).
fof(f_45_2,plain,
! [U_55] :
( ? [U_54] : net_str(U_54,U_55)
| ~ one_sorted_str(U_55) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_55] :
( net_str(sK3(U_55),U_55)
| ~ one_sorted_str(U_55) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_54,sK3(U_55))],[f_45_2]) ).
cnf(f_45_4,plain,
( net_str(sK3(U_55),U_55)
| ~ one_sorted_str(U_55) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_46_2,plain,
! [U_58,U_57] :
? [U_56] : relation_of2(U_56,U_58,U_57),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_58,U_57] : relation_of2(sK4(U_58,U_57),U_58,U_57),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_56,sK4(U_58,U_57))],[f_46_2]) ).
cnf(f_46_4,plain,
relation_of2(sK4(U_58,U_57),U_58,U_57),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_47_2,plain,
! [U_60] :
? [U_59] : element(U_59,U_60),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_60] : element(sK5(U_60),U_60),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_59,sK5(U_60))],[f_47_2]) ).
cnf(f_47_4,plain,
element(sK5(U_60),U_60),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_48_2,plain,
! [U_63,U_62] :
? [U_61] : relation_of2_as_subset(U_61,U_63,U_62),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_63,U_62] : relation_of2_as_subset(sK6(U_63,U_62),U_63,U_62),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_61,sK6(U_63,U_62))],[f_48_2]) ).
cnf(f_48_4,plain,
relation_of2_as_subset(sK6(U_63,U_62),U_63,U_62),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A,B] :
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc12_finset_1]) ).
fof(f_49_2,plain,
! [U_65,U_64] :
( finite(set_difference(U_65,U_64))
| ~ finite(U_65) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_65] :
( ! [U_64] : finite(set_difference(U_65,U_64))
| ~ finite(U_65) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
( finite(set_difference(U_65,U_64))
| ~ finite(U_65) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_50_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_50_1]) ).
cnf(f_50_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_50_1]) ).
fof(f_51_1,plain,
! [A,B] :
( finite(cartesian_product2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc14_finset_1]) ).
fof(f_51_2,plain,
! [U_67,U_66] :
( finite(cartesian_product2(U_67,U_66))
| ~ finite(U_66)
| ~ finite(U_67) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( finite(cartesian_product2(U_67,U_66))
| ~ finite(U_66)
| ~ finite(U_67) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
! [A] :
( ( upper_relstr_subset(cast_as_carrier_subset(A),A)
& lower_relstr_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) )
| ~ rel_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc15_waybel_0]) ).
fof(f_52_2,plain,
! [U_68] :
( ( upper_relstr_subset(cast_as_carrier_subset(U_68),U_68)
& lower_relstr_subset(cast_as_carrier_subset(U_68),U_68)
& ~ empty(cast_as_carrier_subset(U_68)) )
| ~ rel_str(U_68)
| empty_carrier(U_68) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( ~ empty(cast_as_carrier_subset(U_68))
| ~ rel_str(U_68)
| empty_carrier(U_68) ),
inference(clausify,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
( lower_relstr_subset(cast_as_carrier_subset(U_68),U_68)
| ~ rel_str(U_68)
| empty_carrier(U_68) ),
inference(clausify,[status(thm)],[f_52_2]) ).
cnf(f_52_5,plain,
( upper_relstr_subset(cast_as_carrier_subset(U_68),U_68)
| ~ rel_str(U_68)
| empty_carrier(U_68) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [A,B] :
( ( quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A))
& function(the_mapping(A,B))
& relation(the_mapping(A,B))
& ~ empty(the_mapping(A,B)) )
| ~ net_str(B,A)
| empty_carrier(B)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc15_yellow_6]) ).
fof(f_53_2,plain,
! [U_70,U_69] :
( ( quasi_total(the_mapping(U_70,U_69),the_carrier(U_69),the_carrier(U_70))
& function(the_mapping(U_70,U_69))
& relation(the_mapping(U_70,U_69))
& ~ empty(the_mapping(U_70,U_69)) )
| ~ net_str(U_69,U_70)
| empty_carrier(U_69)
| ~ one_sorted_str(U_70)
| empty_carrier(U_70) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( ~ empty(the_mapping(U_70,U_69))
| ~ net_str(U_69,U_70)
| empty_carrier(U_69)
| ~ one_sorted_str(U_70)
| empty_carrier(U_70) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
( relation(the_mapping(U_70,U_69))
| ~ net_str(U_69,U_70)
| empty_carrier(U_69)
| ~ one_sorted_str(U_70)
| empty_carrier(U_70) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_5,plain,
( function(the_mapping(U_70,U_69))
| ~ net_str(U_69,U_70)
| empty_carrier(U_69)
| ~ one_sorted_str(U_70)
| empty_carrier(U_70) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_6,plain,
( quasi_total(the_mapping(U_70,U_69),the_carrier(U_69),the_carrier(U_70))
| ~ net_str(U_69,U_70)
| empty_carrier(U_69)
| ~ one_sorted_str(U_70)
| empty_carrier(U_70) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
inference(fof_nnf,[status(thm)],[fc1_finset_1]) ).
fof(f_54_2,plain,
! [U_71] :
( finite(singleton(U_71))
& ~ empty(singleton(U_71)) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_73] : finite(singleton(U_73))
& ! [U_72] : ~ empty(singleton(U_72)) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
~ empty(singleton(U_72)),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_5,plain,
finite(singleton(U_73)),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_55_2,plain,
! [U_74] :
( ~ empty(the_carrier(U_74))
| ~ one_sorted_str(U_74)
| empty_carrier(U_74) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( ~ empty(the_carrier(U_74))
| ~ one_sorted_str(U_74)
| empty_carrier(U_74) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_56_2,plain,
! [U_75] : ~ empty(powerset(U_75)),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
~ empty(powerset(U_75)),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& boolean_relstr(boole_POSet(A))
& complemented_relstr(boole_POSet(A))
& heyting_relstr(boole_POSet(A))
& distributive_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(fof_nnf,[status(thm)],[fc1_waybel_7]) ).
fof(f_57_2,plain,
! [U_76] :
( complete_relstr(boole_POSet(U_76))
& with_infima_relstr(boole_POSet(U_76))
& with_suprema_relstr(boole_POSet(U_76))
& boolean_relstr(boole_POSet(U_76))
& complemented_relstr(boole_POSet(U_76))
& heyting_relstr(boole_POSet(U_76))
& distributive_relstr(boole_POSet(U_76))
& ~ v1_yellow_3(boole_POSet(U_76))
& join_complete_relstr(boole_POSet(U_76))
& up_complete_relstr(boole_POSet(U_76))
& bounded_relstr(boole_POSet(U_76))
& upper_bounded_relstr(boole_POSet(U_76))
& lower_bounded_relstr(boole_POSet(U_76))
& antisymmetric_relstr(boole_POSet(U_76))
& transitive_relstr(boole_POSet(U_76))
& reflexive_relstr(boole_POSet(U_76))
& strict_rel_str(boole_POSet(U_76))
& ~ empty_carrier(boole_POSet(U_76)) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_94] : complete_relstr(boole_POSet(U_94))
& ! [U_93] : with_infima_relstr(boole_POSet(U_93))
& ! [U_92] : with_suprema_relstr(boole_POSet(U_92))
& ! [U_91] : boolean_relstr(boole_POSet(U_91))
& ! [U_90] : complemented_relstr(boole_POSet(U_90))
& ! [U_89] : heyting_relstr(boole_POSet(U_89))
& ! [U_88] : distributive_relstr(boole_POSet(U_88))
& ! [U_87] : ~ v1_yellow_3(boole_POSet(U_87))
& ! [U_86] : join_complete_relstr(boole_POSet(U_86))
& ! [U_85] : up_complete_relstr(boole_POSet(U_85))
& ! [U_84] : bounded_relstr(boole_POSet(U_84))
& ! [U_83] : upper_bounded_relstr(boole_POSet(U_83))
& ! [U_82] : lower_bounded_relstr(boole_POSet(U_82))
& ! [U_81] : antisymmetric_relstr(boole_POSet(U_81))
& ! [U_80] : transitive_relstr(boole_POSet(U_80))
& ! [U_79] : reflexive_relstr(boole_POSet(U_79))
& ! [U_78] : strict_rel_str(boole_POSet(U_78))
& ! [U_77] : ~ empty_carrier(boole_POSet(U_77)) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
cnf(f_57_4,plain,
~ empty_carrier(boole_POSet(U_77)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
strict_rel_str(boole_POSet(U_78)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_6,plain,
reflexive_relstr(boole_POSet(U_79)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_7,plain,
transitive_relstr(boole_POSet(U_80)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_8,plain,
antisymmetric_relstr(boole_POSet(U_81)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_9,plain,
lower_bounded_relstr(boole_POSet(U_82)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_10,plain,
upper_bounded_relstr(boole_POSet(U_83)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_11,plain,
bounded_relstr(boole_POSet(U_84)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_12,plain,
up_complete_relstr(boole_POSet(U_85)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_13,plain,
join_complete_relstr(boole_POSet(U_86)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_14,plain,
~ v1_yellow_3(boole_POSet(U_87)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_15,plain,
distributive_relstr(boole_POSet(U_88)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_16,plain,
heyting_relstr(boole_POSet(U_89)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_17,plain,
complemented_relstr(boole_POSet(U_90)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_18,plain,
boolean_relstr(boole_POSet(U_91)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_19,plain,
with_suprema_relstr(boole_POSet(U_92)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_20,plain,
with_infima_relstr(boole_POSet(U_93)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_21,plain,
complete_relstr(boole_POSet(U_94)),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A,B] :
( ( trivial_carrier(rel_str_of(singleton(A),B))
& strict_rel_str(rel_str_of(singleton(A),B))
& ~ empty_carrier(rel_str_of(singleton(A),B)) )
| ~ relation_of2(B,singleton(A),singleton(A)) ),
inference(fof_nnf,[status(thm)],[fc1_yellow_0]) ).
fof(f_58_2,plain,
! [U_96,U_95] :
( ( trivial_carrier(rel_str_of(singleton(U_96),U_95))
& strict_rel_str(rel_str_of(singleton(U_96),U_95))
& ~ empty_carrier(rel_str_of(singleton(U_96),U_95)) )
| ~ relation_of2(U_95,singleton(U_96),singleton(U_96)) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( ~ empty_carrier(rel_str_of(singleton(U_96),U_95))
| ~ relation_of2(U_95,singleton(U_96),singleton(U_96)) ),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_4,plain,
( strict_rel_str(rel_str_of(singleton(U_96),U_95))
| ~ relation_of2(U_95,singleton(U_96),singleton(U_96)) ),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_5,plain,
( trivial_carrier(rel_str_of(singleton(U_96),U_95))
| ~ relation_of2(U_95,singleton(U_96),singleton(U_96)) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
! [A] :
( ~ empty(cast_as_carrier_subset(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc2_pre_topc]) ).
fof(f_59_2,plain,
! [U_97] :
( ~ empty(cast_as_carrier_subset(U_97))
| ~ one_sorted_str(U_97)
| empty_carrier(U_97) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( ~ empty(cast_as_carrier_subset(U_97))
| ~ one_sorted_str(U_97)
| empty_carrier(U_97) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_60_2,plain,
! [U_98] : ~ empty(singleton(U_98)),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
~ empty(singleton(U_98)),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
! [A] :
( ( directed_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) )
| ~ rel_str(A)
| ~ with_suprema_relstr(A) ),
inference(fof_nnf,[status(thm)],[fc2_waybel_0]) ).
fof(f_61_2,plain,
! [U_99] :
( ( directed_subset(cast_as_carrier_subset(U_99),U_99)
& ~ empty(cast_as_carrier_subset(U_99)) )
| ~ rel_str(U_99)
| ~ with_suprema_relstr(U_99) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( ~ empty(cast_as_carrier_subset(U_99))
| ~ rel_str(U_99)
| ~ with_suprema_relstr(U_99) ),
inference(clausify,[status(thm)],[f_61_2]) ).
cnf(f_61_4,plain,
( directed_subset(cast_as_carrier_subset(U_99),U_99)
| ~ rel_str(U_99)
| ~ with_suprema_relstr(U_99) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [A] :
( ( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& boolean_relstr(boole_POSet(A))
& complemented_relstr(boole_POSet(A))
& heyting_relstr(boole_POSet(A))
& distributive_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ trivial_carrier(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_waybel_7]) ).
fof(f_62_2,plain,
! [U_100] :
( ( complete_relstr(boole_POSet(U_100))
& with_infima_relstr(boole_POSet(U_100))
& with_suprema_relstr(boole_POSet(U_100))
& boolean_relstr(boole_POSet(U_100))
& complemented_relstr(boole_POSet(U_100))
& heyting_relstr(boole_POSet(U_100))
& distributive_relstr(boole_POSet(U_100))
& ~ v1_yellow_3(boole_POSet(U_100))
& join_complete_relstr(boole_POSet(U_100))
& up_complete_relstr(boole_POSet(U_100))
& bounded_relstr(boole_POSet(U_100))
& upper_bounded_relstr(boole_POSet(U_100))
& lower_bounded_relstr(boole_POSet(U_100))
& antisymmetric_relstr(boole_POSet(U_100))
& transitive_relstr(boole_POSet(U_100))
& reflexive_relstr(boole_POSet(U_100))
& strict_rel_str(boole_POSet(U_100))
& ~ trivial_carrier(boole_POSet(U_100))
& ~ empty_carrier(boole_POSet(U_100)) )
| empty(U_100) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( ~ empty_carrier(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_4,plain,
( ~ trivial_carrier(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_5,plain,
( strict_rel_str(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_6,plain,
( reflexive_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_7,plain,
( transitive_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_8,plain,
( antisymmetric_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_9,plain,
( lower_bounded_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_10,plain,
( upper_bounded_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_11,plain,
( bounded_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_12,plain,
( up_complete_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_13,plain,
( join_complete_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_14,plain,
( ~ v1_yellow_3(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_15,plain,
( distributive_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_16,plain,
( heyting_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_17,plain,
( complemented_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_18,plain,
( boolean_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_19,plain,
( with_suprema_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_20,plain,
( with_infima_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_21,plain,
( complete_relstr(boole_POSet(U_100))
| empty(U_100) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
! [A,B] :
( ( upper_relstr_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(filter_of_net_str(A,B)) )
| ~ net_str(B,A)
| empty_carrier(B)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc2_yellow19]) ).
fof(f_63_2,plain,
! [U_102,U_101] :
( ( upper_relstr_subset(filter_of_net_str(U_102,U_101),boole_POSet(cast_as_carrier_subset(U_102)))
& ~ empty(filter_of_net_str(U_102,U_101)) )
| ~ net_str(U_101,U_102)
| empty_carrier(U_101)
| ~ one_sorted_str(U_102)
| empty_carrier(U_102) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( ~ empty(filter_of_net_str(U_102,U_101))
| ~ net_str(U_101,U_102)
| empty_carrier(U_101)
| ~ one_sorted_str(U_102)
| empty_carrier(U_102) ),
inference(clausify,[status(thm)],[f_63_2]) ).
cnf(f_63_4,plain,
( upper_relstr_subset(filter_of_net_str(U_102,U_101),boole_POSet(cast_as_carrier_subset(U_102)))
| ~ net_str(U_101,U_102)
| empty_carrier(U_101)
| ~ one_sorted_str(U_102)
| empty_carrier(U_102) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_1,plain,
! [A] :
( ~ empty(cast_as_carrier_subset(A))
| ~ rel_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc2_yellow_0]) ).
fof(f_64_2,plain,
! [U_103] :
( ~ empty(cast_as_carrier_subset(U_103))
| ~ rel_str(U_103)
| empty_carrier(U_103) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( ~ empty(cast_as_carrier_subset(U_103))
| ~ rel_str(U_103)
| empty_carrier(U_103) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_65_2,plain,
! [U_105,U_104] :
( relation(set_difference(U_105,U_104))
| ~ relation(U_104)
| ~ relation(U_105) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( relation(set_difference(U_105,U_104))
| ~ relation(U_104)
| ~ relation(U_105) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [A] :
( ( directed_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) )
| ~ rel_str(A)
| ~ upper_bounded_relstr(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc3_waybel_0]) ).
fof(f_66_2,plain,
! [U_106] :
( ( directed_subset(cast_as_carrier_subset(U_106),U_106)
& ~ empty(cast_as_carrier_subset(U_106)) )
| ~ rel_str(U_106)
| ~ upper_bounded_relstr(U_106)
| empty_carrier(U_106) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( ~ empty(cast_as_carrier_subset(U_106))
| ~ rel_str(U_106)
| ~ upper_bounded_relstr(U_106)
| empty_carrier(U_106) ),
inference(clausify,[status(thm)],[f_66_2]) ).
cnf(f_66_4,plain,
( directed_subset(cast_as_carrier_subset(U_106),U_106)
| ~ rel_str(U_106)
| ~ upper_bounded_relstr(U_106)
| empty_carrier(U_106) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_1,plain,
! [A,B] :
( ( proper_element(filter_of_net_str(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& upper_relstr_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A)))
& filtered_subset(filter_of_net_str(A,B),boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(filter_of_net_str(A,B)) )
| ~ net_str(B,A)
| ~ directed_relstr(B)
| ~ transitive_relstr(B)
| empty_carrier(B)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc3_yellow19]) ).
fof(f_67_2,plain,
! [U_108,U_107] :
( ( proper_element(filter_of_net_str(U_108,U_107),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(U_108)))))
& upper_relstr_subset(filter_of_net_str(U_108,U_107),boole_POSet(cast_as_carrier_subset(U_108)))
& filtered_subset(filter_of_net_str(U_108,U_107),boole_POSet(cast_as_carrier_subset(U_108)))
& ~ empty(filter_of_net_str(U_108,U_107)) )
| ~ net_str(U_107,U_108)
| ~ directed_relstr(U_107)
| ~ transitive_relstr(U_107)
| empty_carrier(U_107)
| ~ one_sorted_str(U_108)
| empty_carrier(U_108) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( ~ empty(filter_of_net_str(U_108,U_107))
| ~ net_str(U_107,U_108)
| ~ directed_relstr(U_107)
| ~ transitive_relstr(U_107)
| empty_carrier(U_107)
| ~ one_sorted_str(U_108)
| empty_carrier(U_108) ),
inference(clausify,[status(thm)],[f_67_2]) ).
cnf(f_67_4,plain,
( filtered_subset(filter_of_net_str(U_108,U_107),boole_POSet(cast_as_carrier_subset(U_108)))
| ~ net_str(U_107,U_108)
| ~ directed_relstr(U_107)
| ~ transitive_relstr(U_107)
| empty_carrier(U_107)
| ~ one_sorted_str(U_108)
| empty_carrier(U_108) ),
inference(clausify,[status(thm)],[f_67_2]) ).
cnf(f_67_5,plain,
( upper_relstr_subset(filter_of_net_str(U_108,U_107),boole_POSet(cast_as_carrier_subset(U_108)))
| ~ net_str(U_107,U_108)
| ~ directed_relstr(U_107)
| ~ transitive_relstr(U_107)
| empty_carrier(U_107)
| ~ one_sorted_str(U_108)
| empty_carrier(U_108) ),
inference(clausify,[status(thm)],[f_67_2]) ).
cnf(f_67_6,plain,
( proper_element(filter_of_net_str(U_108,U_107),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(U_108)))))
| ~ net_str(U_107,U_108)
| ~ directed_relstr(U_107)
| ~ transitive_relstr(U_107)
| empty_carrier(U_107)
| ~ one_sorted_str(U_108)
| empty_carrier(U_108) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_68_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_68_1]) ).
fof(f_69_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_69_2,plain,
! [U_110,U_109] :
( ~ empty(cartesian_product2(U_110,U_109))
| empty(U_109)
| empty(U_110) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( ~ empty(cartesian_product2(U_110,U_109))
| empty(U_109)
| empty(U_110) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [A] :
( ( filtered_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) )
| ~ rel_str(A)
| ~ with_infima_relstr(A) ),
inference(fof_nnf,[status(thm)],[fc4_waybel_0]) ).
fof(f_70_2,plain,
! [U_111] :
( ( filtered_subset(cast_as_carrier_subset(U_111),U_111)
& ~ empty(cast_as_carrier_subset(U_111)) )
| ~ rel_str(U_111)
| ~ with_infima_relstr(U_111) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
( ~ empty(cast_as_carrier_subset(U_111))
| ~ rel_str(U_111)
| ~ with_infima_relstr(U_111) ),
inference(clausify,[status(thm)],[f_70_2]) ).
cnf(f_70_4,plain,
( filtered_subset(cast_as_carrier_subset(U_111),U_111)
| ~ rel_str(U_111)
| ~ with_infima_relstr(U_111) ),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [A,B,C] :
( ( strict_net_str(net_of_bool_filter(A,B,C),A)
& transitive_relstr(net_of_bool_filter(A,B,C))
& reflexive_relstr(net_of_bool_filter(A,B,C))
& ~ empty_carrier(net_of_bool_filter(A,B,C)) )
| ~ element(C,powerset(the_carrier(boole_POSet(B))))
| ~ upper_relstr_subset(C,boole_POSet(B))
| ~ filtered_subset(C,boole_POSet(B))
| empty(C)
| ~ element(B,powerset(the_carrier(A)))
| empty(B)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc4_yellow19]) ).
fof(f_71_2,plain,
! [U_114,U_113,U_112] :
( ( strict_net_str(net_of_bool_filter(U_114,U_113,U_112),U_114)
& transitive_relstr(net_of_bool_filter(U_114,U_113,U_112))
& reflexive_relstr(net_of_bool_filter(U_114,U_113,U_112))
& ~ empty_carrier(net_of_bool_filter(U_114,U_113,U_112)) )
| ~ element(U_112,powerset(the_carrier(boole_POSet(U_113))))
| ~ upper_relstr_subset(U_112,boole_POSet(U_113))
| ~ filtered_subset(U_112,boole_POSet(U_113))
| empty(U_112)
| ~ element(U_113,powerset(the_carrier(U_114)))
| empty(U_113)
| ~ one_sorted_str(U_114)
| empty_carrier(U_114) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( ~ empty_carrier(net_of_bool_filter(U_114,U_113,U_112))
| ~ element(U_112,powerset(the_carrier(boole_POSet(U_113))))
| ~ upper_relstr_subset(U_112,boole_POSet(U_113))
| ~ filtered_subset(U_112,boole_POSet(U_113))
| empty(U_112)
| ~ element(U_113,powerset(the_carrier(U_114)))
| empty(U_113)
| ~ one_sorted_str(U_114)
| empty_carrier(U_114) ),
inference(clausify,[status(thm)],[f_71_2]) ).
cnf(f_71_4,plain,
( reflexive_relstr(net_of_bool_filter(U_114,U_113,U_112))
| ~ element(U_112,powerset(the_carrier(boole_POSet(U_113))))
| ~ upper_relstr_subset(U_112,boole_POSet(U_113))
| ~ filtered_subset(U_112,boole_POSet(U_113))
| empty(U_112)
| ~ element(U_113,powerset(the_carrier(U_114)))
| empty(U_113)
| ~ one_sorted_str(U_114)
| empty_carrier(U_114) ),
inference(clausify,[status(thm)],[f_71_2]) ).
cnf(f_71_5,plain,
( transitive_relstr(net_of_bool_filter(U_114,U_113,U_112))
| ~ element(U_112,powerset(the_carrier(boole_POSet(U_113))))
| ~ upper_relstr_subset(U_112,boole_POSet(U_113))
| ~ filtered_subset(U_112,boole_POSet(U_113))
| empty(U_112)
| ~ element(U_113,powerset(the_carrier(U_114)))
| empty(U_113)
| ~ one_sorted_str(U_114)
| empty_carrier(U_114) ),
inference(clausify,[status(thm)],[f_71_2]) ).
cnf(f_71_6,plain,
( strict_net_str(net_of_bool_filter(U_114,U_113,U_112),U_114)
| ~ element(U_112,powerset(the_carrier(boole_POSet(U_113))))
| ~ upper_relstr_subset(U_112,boole_POSet(U_113))
| ~ filtered_subset(U_112,boole_POSet(U_113))
| empty(U_112)
| ~ element(U_113,powerset(the_carrier(U_114)))
| empty(U_113)
| ~ one_sorted_str(U_114)
| empty_carrier(U_114) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
! [A] :
( ( filtered_subset(cast_as_carrier_subset(A),A)
& ~ empty(cast_as_carrier_subset(A)) )
| ~ rel_str(A)
| ~ lower_bounded_relstr(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc5_waybel_0]) ).
fof(f_72_2,plain,
! [U_115] :
( ( filtered_subset(cast_as_carrier_subset(U_115),U_115)
& ~ empty(cast_as_carrier_subset(U_115)) )
| ~ rel_str(U_115)
| ~ lower_bounded_relstr(U_115)
| empty_carrier(U_115) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( ~ empty(cast_as_carrier_subset(U_115))
| ~ rel_str(U_115)
| ~ lower_bounded_relstr(U_115)
| empty_carrier(U_115) ),
inference(clausify,[status(thm)],[f_72_2]) ).
cnf(f_72_4,plain,
( filtered_subset(cast_as_carrier_subset(U_115),U_115)
| ~ rel_str(U_115)
| ~ lower_bounded_relstr(U_115)
| empty_carrier(U_115) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [A,B,C] :
( ( directed_relstr(net_of_bool_filter(A,B,C))
& strict_net_str(net_of_bool_filter(A,B,C),A)
& transitive_relstr(net_of_bool_filter(A,B,C))
& reflexive_relstr(net_of_bool_filter(A,B,C))
& ~ empty_carrier(net_of_bool_filter(A,B,C)) )
| ~ element(C,powerset(the_carrier(boole_POSet(B))))
| ~ proper_element(C,powerset(the_carrier(boole_POSet(B))))
| ~ upper_relstr_subset(C,boole_POSet(B))
| ~ filtered_subset(C,boole_POSet(B))
| empty(C)
| ~ element(B,powerset(the_carrier(A)))
| empty(B)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc5_yellow19]) ).
fof(f_73_2,plain,
! [U_118,U_117,U_116] :
( ( directed_relstr(net_of_bool_filter(U_118,U_117,U_116))
& strict_net_str(net_of_bool_filter(U_118,U_117,U_116),U_118)
& transitive_relstr(net_of_bool_filter(U_118,U_117,U_116))
& reflexive_relstr(net_of_bool_filter(U_118,U_117,U_116))
& ~ empty_carrier(net_of_bool_filter(U_118,U_117,U_116)) )
| ~ element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ proper_element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ upper_relstr_subset(U_116,boole_POSet(U_117))
| ~ filtered_subset(U_116,boole_POSet(U_117))
| empty(U_116)
| ~ element(U_117,powerset(the_carrier(U_118)))
| empty(U_117)
| ~ one_sorted_str(U_118)
| empty_carrier(U_118) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( ~ empty_carrier(net_of_bool_filter(U_118,U_117,U_116))
| ~ element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ proper_element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ upper_relstr_subset(U_116,boole_POSet(U_117))
| ~ filtered_subset(U_116,boole_POSet(U_117))
| empty(U_116)
| ~ element(U_117,powerset(the_carrier(U_118)))
| empty(U_117)
| ~ one_sorted_str(U_118)
| empty_carrier(U_118) ),
inference(clausify,[status(thm)],[f_73_2]) ).
cnf(f_73_4,plain,
( reflexive_relstr(net_of_bool_filter(U_118,U_117,U_116))
| ~ element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ proper_element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ upper_relstr_subset(U_116,boole_POSet(U_117))
| ~ filtered_subset(U_116,boole_POSet(U_117))
| empty(U_116)
| ~ element(U_117,powerset(the_carrier(U_118)))
| empty(U_117)
| ~ one_sorted_str(U_118)
| empty_carrier(U_118) ),
inference(clausify,[status(thm)],[f_73_2]) ).
cnf(f_73_5,plain,
( transitive_relstr(net_of_bool_filter(U_118,U_117,U_116))
| ~ element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ proper_element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ upper_relstr_subset(U_116,boole_POSet(U_117))
| ~ filtered_subset(U_116,boole_POSet(U_117))
| empty(U_116)
| ~ element(U_117,powerset(the_carrier(U_118)))
| empty(U_117)
| ~ one_sorted_str(U_118)
| empty_carrier(U_118) ),
inference(clausify,[status(thm)],[f_73_2]) ).
cnf(f_73_6,plain,
( strict_net_str(net_of_bool_filter(U_118,U_117,U_116),U_118)
| ~ element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ proper_element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ upper_relstr_subset(U_116,boole_POSet(U_117))
| ~ filtered_subset(U_116,boole_POSet(U_117))
| empty(U_116)
| ~ element(U_117,powerset(the_carrier(U_118)))
| empty(U_117)
| ~ one_sorted_str(U_118)
| empty_carrier(U_118) ),
inference(clausify,[status(thm)],[f_73_2]) ).
cnf(f_73_7,plain,
( directed_relstr(net_of_bool_filter(U_118,U_117,U_116))
| ~ element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ proper_element(U_116,powerset(the_carrier(boole_POSet(U_117))))
| ~ upper_relstr_subset(U_116,boole_POSet(U_117))
| ~ filtered_subset(U_116,boole_POSet(U_117))
| empty(U_116)
| ~ element(U_117,powerset(the_carrier(U_118)))
| empty(U_117)
| ~ one_sorted_str(U_118)
| empty_carrier(U_118) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [A,B,C,D] :
( ( strict_net_str(net_str_of(A,B,C,D),A)
& ~ empty_carrier(net_str_of(A,B,C,D)) )
| ~ relation_of2(D,B,the_carrier(A))
| ~ quasi_total(D,B,the_carrier(A))
| ~ function(D)
| ~ relation_of2(C,B,B)
| empty(B)
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[fc6_waybel_0]) ).
fof(f_74_2,plain,
! [U_122,U_121,U_120,U_119] :
( ( strict_net_str(net_str_of(U_122,U_121,U_120,U_119),U_122)
& ~ empty_carrier(net_str_of(U_122,U_121,U_120,U_119)) )
| ~ relation_of2(U_119,U_121,the_carrier(U_122))
| ~ quasi_total(U_119,U_121,the_carrier(U_122))
| ~ function(U_119)
| ~ relation_of2(U_120,U_121,U_121)
| empty(U_121)
| ~ one_sorted_str(U_122) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( ~ empty_carrier(net_str_of(U_122,U_121,U_120,U_119))
| ~ relation_of2(U_119,U_121,the_carrier(U_122))
| ~ quasi_total(U_119,U_121,the_carrier(U_122))
| ~ function(U_119)
| ~ relation_of2(U_120,U_121,U_121)
| empty(U_121)
| ~ one_sorted_str(U_122) ),
inference(clausify,[status(thm)],[f_74_2]) ).
cnf(f_74_4,plain,
( strict_net_str(net_str_of(U_122,U_121,U_120,U_119),U_122)
| ~ relation_of2(U_119,U_121,the_carrier(U_122))
| ~ quasi_total(U_119,U_121,the_carrier(U_122))
| ~ function(U_119)
| ~ relation_of2(U_120,U_121,U_121)
| empty(U_121)
| ~ one_sorted_str(U_122) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [A] :
( antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(fof_nnf,[status(thm)],[fc7_yellow_1]) ).
fof(f_75_2,plain,
! [U_123] :
( antisymmetric_relstr(boole_POSet(U_123))
& transitive_relstr(boole_POSet(U_123))
& reflexive_relstr(boole_POSet(U_123))
& strict_rel_str(boole_POSet(U_123))
& ~ empty_carrier(boole_POSet(U_123)) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
( ! [U_128] : antisymmetric_relstr(boole_POSet(U_128))
& ! [U_127] : transitive_relstr(boole_POSet(U_127))
& ! [U_126] : reflexive_relstr(boole_POSet(U_126))
& ! [U_125] : strict_rel_str(boole_POSet(U_125))
& ! [U_124] : ~ empty_carrier(boole_POSet(U_124)) ),
inference(miniscope,[status(thm)],[f_75_2]) ).
cnf(f_75_4,plain,
~ empty_carrier(boole_POSet(U_124)),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_5,plain,
strict_rel_str(boole_POSet(U_125)),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_6,plain,
reflexive_relstr(boole_POSet(U_126)),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_7,plain,
transitive_relstr(boole_POSet(U_127)),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_8,plain,
antisymmetric_relstr(boole_POSet(U_128)),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(fof_nnf,[status(thm)],[fc8_yellow_1]) ).
fof(f_76_2,plain,
! [U_129] :
( complete_relstr(boole_POSet(U_129))
& with_infima_relstr(boole_POSet(U_129))
& with_suprema_relstr(boole_POSet(U_129))
& bounded_relstr(boole_POSet(U_129))
& upper_bounded_relstr(boole_POSet(U_129))
& lower_bounded_relstr(boole_POSet(U_129))
& antisymmetric_relstr(boole_POSet(U_129))
& transitive_relstr(boole_POSet(U_129))
& reflexive_relstr(boole_POSet(U_129))
& strict_rel_str(boole_POSet(U_129))
& ~ empty_carrier(boole_POSet(U_129)) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_140] : complete_relstr(boole_POSet(U_140))
& ! [U_139] : with_infima_relstr(boole_POSet(U_139))
& ! [U_138] : with_suprema_relstr(boole_POSet(U_138))
& ! [U_137] : bounded_relstr(boole_POSet(U_137))
& ! [U_136] : upper_bounded_relstr(boole_POSet(U_136))
& ! [U_135] : lower_bounded_relstr(boole_POSet(U_135))
& ! [U_134] : antisymmetric_relstr(boole_POSet(U_134))
& ! [U_133] : transitive_relstr(boole_POSet(U_133))
& ! [U_132] : reflexive_relstr(boole_POSet(U_132))
& ! [U_131] : strict_rel_str(boole_POSet(U_131))
& ! [U_130] : ~ empty_carrier(boole_POSet(U_130)) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
cnf(f_76_4,plain,
~ empty_carrier(boole_POSet(U_130)),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_5,plain,
strict_rel_str(boole_POSet(U_131)),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_6,plain,
reflexive_relstr(boole_POSet(U_132)),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_7,plain,
transitive_relstr(boole_POSet(U_133)),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_8,plain,
antisymmetric_relstr(boole_POSet(U_134)),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_9,plain,
lower_bounded_relstr(boole_POSet(U_135)),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_10,plain,
upper_bounded_relstr(boole_POSet(U_136)),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_11,plain,
bounded_relstr(boole_POSet(U_137)),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_12,plain,
with_suprema_relstr(boole_POSet(U_138)),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_13,plain,
with_infima_relstr(boole_POSet(U_139)),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_14,plain,
complete_relstr(boole_POSet(U_140)),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_1,plain,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& directed_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(fof_nnf,[status(thm)],[fc8_yellow_6]) ).
fof(f_77_2,plain,
! [U_141] :
( complete_relstr(boole_POSet(U_141))
& with_infima_relstr(boole_POSet(U_141))
& with_suprema_relstr(boole_POSet(U_141))
& ~ v1_yellow_3(boole_POSet(U_141))
& join_complete_relstr(boole_POSet(U_141))
& up_complete_relstr(boole_POSet(U_141))
& directed_relstr(boole_POSet(U_141))
& bounded_relstr(boole_POSet(U_141))
& upper_bounded_relstr(boole_POSet(U_141))
& lower_bounded_relstr(boole_POSet(U_141))
& antisymmetric_relstr(boole_POSet(U_141))
& transitive_relstr(boole_POSet(U_141))
& reflexive_relstr(boole_POSet(U_141))
& strict_rel_str(boole_POSet(U_141))
& ~ empty_carrier(boole_POSet(U_141)) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
( ! [U_156] : complete_relstr(boole_POSet(U_156))
& ! [U_155] : with_infima_relstr(boole_POSet(U_155))
& ! [U_154] : with_suprema_relstr(boole_POSet(U_154))
& ! [U_153] : ~ v1_yellow_3(boole_POSet(U_153))
& ! [U_152] : join_complete_relstr(boole_POSet(U_152))
& ! [U_151] : up_complete_relstr(boole_POSet(U_151))
& ! [U_150] : directed_relstr(boole_POSet(U_150))
& ! [U_149] : bounded_relstr(boole_POSet(U_149))
& ! [U_148] : upper_bounded_relstr(boole_POSet(U_148))
& ! [U_147] : lower_bounded_relstr(boole_POSet(U_147))
& ! [U_146] : antisymmetric_relstr(boole_POSet(U_146))
& ! [U_145] : transitive_relstr(boole_POSet(U_145))
& ! [U_144] : reflexive_relstr(boole_POSet(U_144))
& ! [U_143] : strict_rel_str(boole_POSet(U_143))
& ! [U_142] : ~ empty_carrier(boole_POSet(U_142)) ),
inference(miniscope,[status(thm)],[f_77_2]) ).
cnf(f_77_4,plain,
~ empty_carrier(boole_POSet(U_142)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_5,plain,
strict_rel_str(boole_POSet(U_143)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_6,plain,
reflexive_relstr(boole_POSet(U_144)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_7,plain,
transitive_relstr(boole_POSet(U_145)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_8,plain,
antisymmetric_relstr(boole_POSet(U_146)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_9,plain,
lower_bounded_relstr(boole_POSet(U_147)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_10,plain,
upper_bounded_relstr(boole_POSet(U_148)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_11,plain,
bounded_relstr(boole_POSet(U_149)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_12,plain,
directed_relstr(boole_POSet(U_150)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_13,plain,
up_complete_relstr(boole_POSet(U_151)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_14,plain,
join_complete_relstr(boole_POSet(U_152)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_15,plain,
~ v1_yellow_3(boole_POSet(U_153)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_16,plain,
with_suprema_relstr(boole_POSet(U_154)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_17,plain,
with_infima_relstr(boole_POSet(U_155)),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_18,plain,
complete_relstr(boole_POSet(U_156)),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_1,plain,
! [A,B,C] :
( ( ( in(A,a_2_1_yellow19(B,C))
| ! [D] :
( ~ is_eventually_in(B,C,D)
| A != D
| ~ element(D,powerset(the_carrier(B))) ) )
& ( ? [D] :
( is_eventually_in(B,C,D)
& A = D
& element(D,powerset(the_carrier(B))) )
| ~ in(A,a_2_1_yellow19(B,C)) ) )
| ~ net_str(C,B)
| empty_carrier(C)
| ~ one_sorted_str(B)
| empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[fraenkel_a_2_1_yellow19]) ).
fof(f_78_2,plain,
! [U_161,U_160,U_159] :
( ( ( in(U_161,a_2_1_yellow19(U_160,U_159))
| ! [U_158] :
( ~ is_eventually_in(U_160,U_159,U_158)
| U_161 != U_158
| ~ element(U_158,powerset(the_carrier(U_160))) ) )
& ( ? [U_157] :
( is_eventually_in(U_160,U_159,U_157)
& U_161 = U_157
& element(U_157,powerset(the_carrier(U_160))) )
| ~ in(U_161,a_2_1_yellow19(U_160,U_159)) ) )
| ~ net_str(U_159,U_160)
| empty_carrier(U_159)
| ~ one_sorted_str(U_160)
| empty_carrier(U_160) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_161,U_160,U_159] :
( ( ( in(U_161,a_2_1_yellow19(U_160,U_159))
| ! [U_158] :
( ~ is_eventually_in(U_160,U_159,U_158)
| U_161 != U_158
| ~ element(U_158,powerset(the_carrier(U_160))) ) )
& ( ( is_eventually_in(U_160,U_159,sK7(U_161,U_160,U_159))
& U_161 = sK7(U_161,U_160,U_159)
& element(sK7(U_161,U_160,U_159),powerset(the_carrier(U_160))) )
| ~ in(U_161,a_2_1_yellow19(U_160,U_159)) ) )
| ~ net_str(U_159,U_160)
| empty_carrier(U_159)
| ~ one_sorted_str(U_160)
| empty_carrier(U_160) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_157,sK7(U_161,U_160,U_159))],[f_78_2]) ).
cnf(f_78_4,plain,
( element(sK7(U_161,U_160,U_159),powerset(the_carrier(U_160)))
| ~ in(U_161,a_2_1_yellow19(U_160,U_159))
| ~ net_str(U_159,U_160)
| empty_carrier(U_159)
| ~ one_sorted_str(U_160)
| empty_carrier(U_160) ),
inference(clausify,[status(thm)],[f_78_3]) ).
cnf(f_78_5,plain,
( U_161 = sK7(U_161,U_160,U_159)
| ~ in(U_161,a_2_1_yellow19(U_160,U_159))
| ~ net_str(U_159,U_160)
| empty_carrier(U_159)
| ~ one_sorted_str(U_160)
| empty_carrier(U_160) ),
inference(clausify,[status(thm)],[f_78_3]) ).
cnf(f_78_6,plain,
( is_eventually_in(U_160,U_159,sK7(U_161,U_160,U_159))
| ~ in(U_161,a_2_1_yellow19(U_160,U_159))
| ~ net_str(U_159,U_160)
| empty_carrier(U_159)
| ~ one_sorted_str(U_160)
| empty_carrier(U_160) ),
inference(clausify,[status(thm)],[f_78_3]) ).
cnf(f_78_7,plain,
( in(U_161,a_2_1_yellow19(U_160,U_159))
| ~ is_eventually_in(U_160,U_159,U_158)
| U_161 != U_158
| ~ element(U_158,powerset(the_carrier(U_160)))
| ~ net_str(U_159,U_160)
| empty_carrier(U_159)
| ~ one_sorted_str(U_160)
| empty_carrier(U_160) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [A,B] :
( ! [C,D] :
( ( B = D
& A = C )
| rel_str_of(A,B) != rel_str_of(C,D) )
| ~ relation_of2(B,A,A) ),
inference(fof_nnf,[status(thm)],[free_g1_orders_2]) ).
fof(f_79_2,plain,
! [U_165,U_164] :
( ! [U_163,U_162] :
( ( U_164 = U_162
& U_165 = U_163 )
| rel_str_of(U_165,U_164) != rel_str_of(U_163,U_162) )
| ~ relation_of2(U_164,U_165,U_165) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( U_165 = U_163
| rel_str_of(U_165,U_164) != rel_str_of(U_163,U_162)
| ~ relation_of2(U_164,U_165,U_165) ),
inference(clausify,[status(thm)],[f_79_2]) ).
cnf(f_79_4,plain,
( U_164 = U_162
| rel_str_of(U_165,U_164) != rel_str_of(U_163,U_162)
| ~ relation_of2(U_164,U_165,U_165) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [A,B,C,D] :
( ! [E,F,G,H] :
( ( D = H
& C = G
& B = F
& A = E )
| net_str_of(A,B,C,D) != net_str_of(E,F,G,H) )
| ~ relation_of2(D,B,the_carrier(A))
| ~ quasi_total(D,B,the_carrier(A))
| ~ function(D)
| ~ relation_of2(C,B,B)
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[free_g1_waybel_0]) ).
fof(f_80_2,plain,
! [U_173,U_172,U_171,U_170] :
( ! [U_169,U_168,U_167,U_166] :
( ( U_170 = U_166
& U_171 = U_167
& U_172 = U_168
& U_173 = U_169 )
| net_str_of(U_173,U_172,U_171,U_170) != net_str_of(U_169,U_168,U_167,U_166) )
| ~ relation_of2(U_170,U_172,the_carrier(U_173))
| ~ quasi_total(U_170,U_172,the_carrier(U_173))
| ~ function(U_170)
| ~ relation_of2(U_171,U_172,U_172)
| ~ one_sorted_str(U_173) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( U_173 = U_169
| net_str_of(U_173,U_172,U_171,U_170) != net_str_of(U_169,U_168,U_167,U_166)
| ~ relation_of2(U_170,U_172,the_carrier(U_173))
| ~ quasi_total(U_170,U_172,the_carrier(U_173))
| ~ function(U_170)
| ~ relation_of2(U_171,U_172,U_172)
| ~ one_sorted_str(U_173) ),
inference(clausify,[status(thm)],[f_80_2]) ).
cnf(f_80_4,plain,
( U_172 = U_168
| net_str_of(U_173,U_172,U_171,U_170) != net_str_of(U_169,U_168,U_167,U_166)
| ~ relation_of2(U_170,U_172,the_carrier(U_173))
| ~ quasi_total(U_170,U_172,the_carrier(U_173))
| ~ function(U_170)
| ~ relation_of2(U_171,U_172,U_172)
| ~ one_sorted_str(U_173) ),
inference(clausify,[status(thm)],[f_80_2]) ).
cnf(f_80_5,plain,
( U_171 = U_167
| net_str_of(U_173,U_172,U_171,U_170) != net_str_of(U_169,U_168,U_167,U_166)
| ~ relation_of2(U_170,U_172,the_carrier(U_173))
| ~ quasi_total(U_170,U_172,the_carrier(U_173))
| ~ function(U_170)
| ~ relation_of2(U_171,U_172,U_172)
| ~ one_sorted_str(U_173) ),
inference(clausify,[status(thm)],[f_80_2]) ).
cnf(f_80_6,plain,
( U_170 = U_166
| net_str_of(U_173,U_172,U_171,U_170) != net_str_of(U_169,U_168,U_167,U_166)
| ~ relation_of2(U_170,U_172,the_carrier(U_173))
| ~ quasi_total(U_170,U_172,the_carrier(U_173))
| ~ function(U_170)
| ~ relation_of2(U_171,U_172,U_172)
| ~ one_sorted_str(U_173) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
! [A] :
( ? [B] :
( upper_relstr_subset(B,A)
& filtered_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc10_waybel_0]) ).
fof(f_81_2,plain,
! [U_175] :
( ? [U_174] :
( upper_relstr_subset(U_174,U_175)
& filtered_subset(U_174,U_175)
& ~ empty(U_174)
& element(U_174,powerset(the_carrier(U_175))) )
| ~ rel_str(U_175)
| ~ transitive_relstr(U_175)
| ~ reflexive_relstr(U_175)
| empty_carrier(U_175) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_175] :
( ( upper_relstr_subset(sK8(U_175),U_175)
& filtered_subset(sK8(U_175),U_175)
& ~ empty(sK8(U_175))
& element(sK8(U_175),powerset(the_carrier(U_175))) )
| ~ rel_str(U_175)
| ~ transitive_relstr(U_175)
| ~ reflexive_relstr(U_175)
| empty_carrier(U_175) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_174,sK8(U_175))],[f_81_2]) ).
cnf(f_81_4,plain,
( element(sK8(U_175),powerset(the_carrier(U_175)))
| ~ rel_str(U_175)
| ~ transitive_relstr(U_175)
| ~ reflexive_relstr(U_175)
| empty_carrier(U_175) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_5,plain,
( ~ empty(sK8(U_175))
| ~ rel_str(U_175)
| ~ transitive_relstr(U_175)
| ~ reflexive_relstr(U_175)
| empty_carrier(U_175) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_6,plain,
( filtered_subset(sK8(U_175),U_175)
| ~ rel_str(U_175)
| ~ transitive_relstr(U_175)
| ~ reflexive_relstr(U_175)
| empty_carrier(U_175) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_7,plain,
( upper_relstr_subset(sK8(U_175),U_175)
| ~ rel_str(U_175)
| ~ transitive_relstr(U_175)
| ~ reflexive_relstr(U_175)
| empty_carrier(U_175) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_1,plain,
! [A] :
( ? [B] :
( upper_relstr_subset(B,A)
& lower_relstr_subset(B,A)
& filtered_subset(B,A)
& directed_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ with_infima_relstr(A)
| ~ with_suprema_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A) ),
inference(fof_nnf,[status(thm)],[rc11_waybel_0]) ).
fof(f_82_2,plain,
! [U_177] :
( ? [U_176] :
( upper_relstr_subset(U_176,U_177)
& lower_relstr_subset(U_176,U_177)
& filtered_subset(U_176,U_177)
& directed_subset(U_176,U_177)
& ~ empty(U_176)
& element(U_176,powerset(the_carrier(U_177))) )
| ~ rel_str(U_177)
| ~ with_infima_relstr(U_177)
| ~ with_suprema_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_177] :
( ( upper_relstr_subset(sK9(U_177),U_177)
& lower_relstr_subset(sK9(U_177),U_177)
& filtered_subset(sK9(U_177),U_177)
& directed_subset(sK9(U_177),U_177)
& ~ empty(sK9(U_177))
& element(sK9(U_177),powerset(the_carrier(U_177))) )
| ~ rel_str(U_177)
| ~ with_infima_relstr(U_177)
| ~ with_suprema_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_176,sK9(U_177))],[f_82_2]) ).
cnf(f_82_4,plain,
( element(sK9(U_177),powerset(the_carrier(U_177)))
| ~ rel_str(U_177)
| ~ with_infima_relstr(U_177)
| ~ with_suprema_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_5,plain,
( ~ empty(sK9(U_177))
| ~ rel_str(U_177)
| ~ with_infima_relstr(U_177)
| ~ with_suprema_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_6,plain,
( directed_subset(sK9(U_177),U_177)
| ~ rel_str(U_177)
| ~ with_infima_relstr(U_177)
| ~ with_suprema_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_7,plain,
( filtered_subset(sK9(U_177),U_177)
| ~ rel_str(U_177)
| ~ with_infima_relstr(U_177)
| ~ with_suprema_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_8,plain,
( lower_relstr_subset(sK9(U_177),U_177)
| ~ rel_str(U_177)
| ~ with_infima_relstr(U_177)
| ~ with_suprema_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_9,plain,
( upper_relstr_subset(sK9(U_177),U_177)
| ~ rel_str(U_177)
| ~ with_infima_relstr(U_177)
| ~ with_suprema_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_1,plain,
? [A] :
( connected_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc12_waybel_0]) ).
fof(f_83_2,plain,
? [U_178] :
( connected_relstr(U_178)
& antisymmetric_relstr(U_178)
& transitive_relstr(U_178)
& reflexive_relstr(U_178)
& ~ empty_carrier(U_178)
& rel_str(U_178) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
( connected_relstr(sK10)
& antisymmetric_relstr(sK10)
& transitive_relstr(sK10)
& reflexive_relstr(sK10)
& ~ empty_carrier(sK10)
& rel_str(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_178,sK10)],[f_83_2]) ).
cnf(f_83_4,plain,
rel_str(sK10),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_5,plain,
~ empty_carrier(sK10),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_6,plain,
reflexive_relstr(sK10),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_7,plain,
transitive_relstr(sK10),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_8,plain,
antisymmetric_relstr(sK10),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_9,plain,
connected_relstr(sK10),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
? [A] :
( join_complete_relstr(A)
& up_complete_relstr(A)
& bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc13_waybel_0]) ).
fof(f_84_2,plain,
? [U_179] :
( join_complete_relstr(U_179)
& up_complete_relstr(U_179)
& bounded_relstr(U_179)
& upper_bounded_relstr(U_179)
& lower_bounded_relstr(U_179)
& complete_relstr(U_179)
& with_infima_relstr(U_179)
& with_suprema_relstr(U_179)
& antisymmetric_relstr(U_179)
& transitive_relstr(U_179)
& reflexive_relstr(U_179)
& strict_rel_str(U_179)
& ~ empty_carrier(U_179)
& rel_str(U_179) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( join_complete_relstr(sK11)
& up_complete_relstr(sK11)
& bounded_relstr(sK11)
& upper_bounded_relstr(sK11)
& lower_bounded_relstr(sK11)
& complete_relstr(sK11)
& with_infima_relstr(sK11)
& with_suprema_relstr(sK11)
& antisymmetric_relstr(sK11)
& transitive_relstr(sK11)
& reflexive_relstr(sK11)
& strict_rel_str(sK11)
& ~ empty_carrier(sK11)
& rel_str(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_179,sK11)],[f_84_2]) ).
cnf(f_84_4,plain,
rel_str(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_5,plain,
~ empty_carrier(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_6,plain,
strict_rel_str(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_7,plain,
reflexive_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_8,plain,
transitive_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_9,plain,
antisymmetric_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_10,plain,
with_suprema_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_11,plain,
with_infima_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_12,plain,
complete_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_13,plain,
lower_bounded_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_14,plain,
upper_bounded_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_15,plain,
bounded_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_16,plain,
up_complete_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_17,plain,
join_complete_relstr(sK11),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_85_2,plain,
? [U_180] :
( finite(U_180)
& ~ empty(U_180) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
( finite(sK12)
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_180,sK12)],[f_85_2]) ).
cnf(f_85_4,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_85_3]) ).
cnf(f_85_5,plain,
finite(sK12),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
? [A] :
( complete_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc1_lattice3]) ).
fof(f_86_2,plain,
? [U_181] :
( complete_relstr(U_181)
& antisymmetric_relstr(U_181)
& transitive_relstr(U_181)
& reflexive_relstr(U_181)
& strict_rel_str(U_181)
& ~ empty_carrier(U_181)
& rel_str(U_181) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
( complete_relstr(sK13)
& antisymmetric_relstr(sK13)
& transitive_relstr(sK13)
& reflexive_relstr(sK13)
& strict_rel_str(sK13)
& ~ empty_carrier(sK13)
& rel_str(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_181,sK13)],[f_86_2]) ).
cnf(f_86_4,plain,
rel_str(sK13),
inference(clausify,[status(thm)],[f_86_3]) ).
cnf(f_86_5,plain,
~ empty_carrier(sK13),
inference(clausify,[status(thm)],[f_86_3]) ).
cnf(f_86_6,plain,
strict_rel_str(sK13),
inference(clausify,[status(thm)],[f_86_3]) ).
cnf(f_86_7,plain,
reflexive_relstr(sK13),
inference(clausify,[status(thm)],[f_86_3]) ).
cnf(f_86_8,plain,
transitive_relstr(sK13),
inference(clausify,[status(thm)],[f_86_3]) ).
cnf(f_86_9,plain,
antisymmetric_relstr(sK13),
inference(clausify,[status(thm)],[f_86_3]) ).
cnf(f_86_10,plain,
complete_relstr(sK13),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_87_2,plain,
? [U_182] :
( relation(U_182)
& empty(U_182) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
( relation(sK14)
& empty(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_182,sK14)],[f_87_2]) ).
cnf(f_87_4,plain,
empty(sK14),
inference(clausify,[status(thm)],[f_87_3]) ).
cnf(f_87_5,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_88_2,plain,
! [U_184] :
( ? [U_183] :
( ~ empty(U_183)
& element(U_183,powerset(U_184)) )
| empty(U_184) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_184] :
( ( ~ empty(sK15(U_184))
& element(sK15(U_184),powerset(U_184)) )
| empty(U_184) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_183,sK15(U_184))],[f_88_2]) ).
cnf(f_88_4,plain,
( element(sK15(U_184),powerset(U_184))
| empty(U_184) ),
inference(clausify,[status(thm)],[f_88_3]) ).
cnf(f_88_5,plain,
( ~ empty(sK15(U_184))
| empty(U_184) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_1,plain,
! [A] :
( ? [B] :
( filtered_subset(B,A)
& directed_subset(B,A)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc1_waybel_0]) ).
fof(f_89_2,plain,
! [U_186] :
( ? [U_185] :
( filtered_subset(U_185,U_186)
& directed_subset(U_185,U_186)
& element(U_185,powerset(the_carrier(U_186))) )
| ~ rel_str(U_186) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
! [U_186] :
( ( filtered_subset(sK16(U_186),U_186)
& directed_subset(sK16(U_186),U_186)
& element(sK16(U_186),powerset(the_carrier(U_186))) )
| ~ rel_str(U_186) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_185,sK16(U_186))],[f_89_2]) ).
cnf(f_89_4,plain,
( element(sK16(U_186),powerset(the_carrier(U_186)))
| ~ rel_str(U_186) ),
inference(clausify,[status(thm)],[f_89_3]) ).
cnf(f_89_5,plain,
( directed_subset(sK16(U_186),U_186)
| ~ rel_str(U_186) ),
inference(clausify,[status(thm)],[f_89_3]) ).
cnf(f_89_6,plain,
( filtered_subset(sK16(U_186),U_186)
| ~ rel_str(U_186) ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_1,plain,
? [A] :
( with_infima_relstr(A)
& with_suprema_relstr(A)
& boolean_relstr(A)
& complemented_relstr(A)
& heyting_relstr(A)
& distributive_relstr(A)
& ~ v1_yellow_3(A)
& bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ trivial_carrier(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc1_waybel_7]) ).
fof(f_90_2,plain,
? [U_187] :
( with_infima_relstr(U_187)
& with_suprema_relstr(U_187)
& boolean_relstr(U_187)
& complemented_relstr(U_187)
& heyting_relstr(U_187)
& distributive_relstr(U_187)
& ~ v1_yellow_3(U_187)
& bounded_relstr(U_187)
& upper_bounded_relstr(U_187)
& lower_bounded_relstr(U_187)
& antisymmetric_relstr(U_187)
& transitive_relstr(U_187)
& reflexive_relstr(U_187)
& strict_rel_str(U_187)
& ~ trivial_carrier(U_187)
& ~ empty_carrier(U_187)
& rel_str(U_187) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
( with_infima_relstr(sK17)
& with_suprema_relstr(sK17)
& boolean_relstr(sK17)
& complemented_relstr(sK17)
& heyting_relstr(sK17)
& distributive_relstr(sK17)
& ~ v1_yellow_3(sK17)
& bounded_relstr(sK17)
& upper_bounded_relstr(sK17)
& lower_bounded_relstr(sK17)
& antisymmetric_relstr(sK17)
& transitive_relstr(sK17)
& reflexive_relstr(sK17)
& strict_rel_str(sK17)
& ~ trivial_carrier(sK17)
& ~ empty_carrier(sK17)
& rel_str(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_187,sK17)],[f_90_2]) ).
cnf(f_90_4,plain,
rel_str(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_5,plain,
~ empty_carrier(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_6,plain,
~ trivial_carrier(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_7,plain,
strict_rel_str(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_8,plain,
reflexive_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_9,plain,
transitive_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_10,plain,
antisymmetric_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_11,plain,
lower_bounded_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_12,plain,
upper_bounded_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_13,plain,
bounded_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_14,plain,
~ v1_yellow_3(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_15,plain,
distributive_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_16,plain,
heyting_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_17,plain,
complemented_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_18,plain,
boolean_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_19,plain,
with_suprema_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_20,plain,
with_infima_relstr(sK17),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_1,plain,
? [A] :
( trivial_carrier(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc1_yellow_0]) ).
fof(f_91_2,plain,
? [U_188] :
( trivial_carrier(U_188)
& complete_relstr(U_188)
& with_infima_relstr(U_188)
& with_suprema_relstr(U_188)
& antisymmetric_relstr(U_188)
& transitive_relstr(U_188)
& reflexive_relstr(U_188)
& strict_rel_str(U_188)
& ~ empty_carrier(U_188)
& rel_str(U_188) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
( trivial_carrier(sK18)
& complete_relstr(sK18)
& with_infima_relstr(sK18)
& with_suprema_relstr(sK18)
& antisymmetric_relstr(sK18)
& transitive_relstr(sK18)
& reflexive_relstr(sK18)
& strict_rel_str(sK18)
& ~ empty_carrier(sK18)
& rel_str(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_188,sK18)],[f_91_2]) ).
cnf(f_91_4,plain,
rel_str(sK18),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_5,plain,
~ empty_carrier(sK18),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_6,plain,
strict_rel_str(sK18),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_7,plain,
reflexive_relstr(sK18),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_8,plain,
transitive_relstr(sK18),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_9,plain,
antisymmetric_relstr(sK18),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_10,plain,
with_suprema_relstr(sK18),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_11,plain,
with_infima_relstr(sK18),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_12,plain,
complete_relstr(sK18),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_13,plain,
trivial_carrier(sK18),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
? [A] :
( complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc2_lattice3]) ).
fof(f_92_2,plain,
? [U_189] :
( complete_relstr(U_189)
& with_infima_relstr(U_189)
& with_suprema_relstr(U_189)
& antisymmetric_relstr(U_189)
& transitive_relstr(U_189)
& reflexive_relstr(U_189)
& strict_rel_str(U_189)
& ~ empty_carrier(U_189)
& rel_str(U_189) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
( complete_relstr(sK19)
& with_infima_relstr(sK19)
& with_suprema_relstr(sK19)
& antisymmetric_relstr(sK19)
& transitive_relstr(sK19)
& reflexive_relstr(sK19)
& strict_rel_str(sK19)
& ~ empty_carrier(sK19)
& rel_str(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_189,sK19)],[f_92_2]) ).
cnf(f_92_4,plain,
rel_str(sK19),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_5,plain,
~ empty_carrier(sK19),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_6,plain,
strict_rel_str(sK19),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_7,plain,
reflexive_relstr(sK19),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_8,plain,
transitive_relstr(sK19),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_9,plain,
antisymmetric_relstr(sK19),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_10,plain,
with_suprema_relstr(sK19),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_11,plain,
with_infima_relstr(sK19),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_12,plain,
complete_relstr(sK19),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_93_2,plain,
? [U_190] :
( relation(U_190)
& ~ empty(U_190) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
( relation(sK20)
& ~ empty(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_190,sK20)],[f_93_2]) ).
cnf(f_93_4,plain,
~ empty(sK20),
inference(clausify,[status(thm)],[f_93_3]) ).
cnf(f_93_5,plain,
relation(sK20),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_94_2,plain,
! [U_192] :
? [U_191] :
( empty(U_191)
& element(U_191,powerset(U_192)) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_192] :
( empty(sK21(U_192))
& element(sK21(U_192),powerset(U_192)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_191,sK21(U_192))],[f_94_2]) ).
cnf(f_94_4,plain,
element(sK21(U_192),powerset(U_192)),
inference(clausify,[status(thm)],[f_94_3]) ).
cnf(f_94_5,plain,
empty(sK21(U_192)),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
! [A] :
( ? [B] :
( filtered_subset(B,A)
& directed_subset(B,A)
& finite(B)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ reflexive_relstr(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc2_waybel_0]) ).
fof(f_95_2,plain,
! [U_194] :
( ? [U_193] :
( filtered_subset(U_193,U_194)
& directed_subset(U_193,U_194)
& finite(U_193)
& ~ empty(U_193)
& element(U_193,powerset(the_carrier(U_194))) )
| ~ rel_str(U_194)
| ~ reflexive_relstr(U_194)
| empty_carrier(U_194) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_194] :
( ( filtered_subset(sK22(U_194),U_194)
& directed_subset(sK22(U_194),U_194)
& finite(sK22(U_194))
& ~ empty(sK22(U_194))
& element(sK22(U_194),powerset(the_carrier(U_194))) )
| ~ rel_str(U_194)
| ~ reflexive_relstr(U_194)
| empty_carrier(U_194) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_193,sK22(U_194))],[f_95_2]) ).
cnf(f_95_4,plain,
( element(sK22(U_194),powerset(the_carrier(U_194)))
| ~ rel_str(U_194)
| ~ reflexive_relstr(U_194)
| empty_carrier(U_194) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_5,plain,
( ~ empty(sK22(U_194))
| ~ rel_str(U_194)
| ~ reflexive_relstr(U_194)
| empty_carrier(U_194) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_6,plain,
( finite(sK22(U_194))
| ~ rel_str(U_194)
| ~ reflexive_relstr(U_194)
| empty_carrier(U_194) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_7,plain,
( directed_subset(sK22(U_194),U_194)
| ~ rel_str(U_194)
| ~ reflexive_relstr(U_194)
| empty_carrier(U_194) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_8,plain,
( filtered_subset(sK22(U_194),U_194)
| ~ rel_str(U_194)
| ~ reflexive_relstr(U_194)
| empty_carrier(U_194) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_1,plain,
! [A] :
? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[rc2_waybel_7]) ).
fof(f_96_2,plain,
! [U_196] :
? [U_195] :
( finite(U_195)
& ~ empty(U_195)
& element(U_195,powerset(powerset(U_196))) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_196] :
( finite(sK23(U_196))
& ~ empty(sK23(U_196))
& element(sK23(U_196),powerset(powerset(U_196))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_195,sK23(U_196))],[f_96_2]) ).
cnf(f_96_4,plain,
element(sK23(U_196),powerset(powerset(U_196))),
inference(clausify,[status(thm)],[f_96_3]) ).
cnf(f_96_5,plain,
~ empty(sK23(U_196)),
inference(clausify,[status(thm)],[f_96_3]) ).
cnf(f_96_6,plain,
finite(sK23(U_196)),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_1,plain,
? [A] :
( bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc2_yellow_0]) ).
fof(f_97_2,plain,
? [U_197] :
( bounded_relstr(U_197)
& upper_bounded_relstr(U_197)
& lower_bounded_relstr(U_197)
& complete_relstr(U_197)
& with_infima_relstr(U_197)
& with_suprema_relstr(U_197)
& antisymmetric_relstr(U_197)
& transitive_relstr(U_197)
& reflexive_relstr(U_197)
& ~ empty_carrier(U_197)
& rel_str(U_197) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
( bounded_relstr(sK24)
& upper_bounded_relstr(sK24)
& lower_bounded_relstr(sK24)
& complete_relstr(sK24)
& with_infima_relstr(sK24)
& with_suprema_relstr(sK24)
& antisymmetric_relstr(sK24)
& transitive_relstr(sK24)
& reflexive_relstr(sK24)
& ~ empty_carrier(sK24)
& rel_str(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_197,sK24)],[f_97_2]) ).
cnf(f_97_4,plain,
rel_str(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_5,plain,
~ empty_carrier(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_6,plain,
reflexive_relstr(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_7,plain,
transitive_relstr(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_8,plain,
antisymmetric_relstr(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_9,plain,
with_suprema_relstr(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_10,plain,
with_infima_relstr(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_11,plain,
complete_relstr(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_12,plain,
lower_bounded_relstr(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_13,plain,
upper_bounded_relstr(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_14,plain,
bounded_relstr(sK24),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_98_2,plain,
! [U_199] :
( ? [U_198] :
( finite(U_198)
& ~ empty(U_198)
& element(U_198,powerset(U_199)) )
| empty(U_199) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_199] :
( ( finite(sK25(U_199))
& ~ empty(sK25(U_199))
& element(sK25(U_199),powerset(U_199)) )
| empty(U_199) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_198,sK25(U_199))],[f_98_2]) ).
cnf(f_98_4,plain,
( element(sK25(U_199),powerset(U_199))
| empty(U_199) ),
inference(clausify,[status(thm)],[f_98_3]) ).
cnf(f_98_5,plain,
( ~ empty(sK25(U_199))
| empty(U_199) ),
inference(clausify,[status(thm)],[f_98_3]) ).
cnf(f_98_6,plain,
( finite(sK25(U_199))
| empty(U_199) ),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_99_2,plain,
? [U_200] :
( relation_empty_yielding(U_200)
& relation(U_200) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
( relation_empty_yielding(sK26)
& relation(sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_200,sK26)],[f_99_2]) ).
cnf(f_99_4,plain,
relation(sK26),
inference(clausify,[status(thm)],[f_99_3]) ).
cnf(f_99_5,plain,
relation_empty_yielding(sK26),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_100_2,plain,
? [U_201] :
( ~ empty_carrier(U_201)
& one_sorted_str(U_201) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
( ~ empty_carrier(sK27)
& one_sorted_str(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_201,sK27)],[f_100_2]) ).
cnf(f_100_4,plain,
one_sorted_str(sK27),
inference(clausify,[status(thm)],[f_100_3]) ).
cnf(f_100_5,plain,
~ empty_carrier(sK27),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(powerset(the_carrier(A)))) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_waybel_7]) ).
fof(f_101_2,plain,
! [U_203] :
( ? [U_202] :
( finite(U_202)
& ~ empty(U_202)
& element(U_202,powerset(powerset(the_carrier(U_203)))) )
| ~ one_sorted_str(U_203) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_203] :
( ( finite(sK28(U_203))
& ~ empty(sK28(U_203))
& element(sK28(U_203),powerset(powerset(the_carrier(U_203)))) )
| ~ one_sorted_str(U_203) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_202,sK28(U_203))],[f_101_2]) ).
cnf(f_101_4,plain,
( element(sK28(U_203),powerset(powerset(the_carrier(U_203))))
| ~ one_sorted_str(U_203) ),
inference(clausify,[status(thm)],[f_101_3]) ).
cnf(f_101_5,plain,
( ~ empty(sK28(U_203))
| ~ one_sorted_str(U_203) ),
inference(clausify,[status(thm)],[f_101_3]) ).
cnf(f_101_6,plain,
( finite(sK28(U_203))
| ~ one_sorted_str(U_203) ),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_102_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc4_finset_1]) ).
fof(f_102_2,plain,
! [U_205] :
( ? [U_204] :
( finite(U_204)
& ~ empty(U_204)
& element(U_204,powerset(U_205)) )
| empty(U_205) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_205] :
( ( finite(sK29(U_205))
& ~ empty(sK29(U_205))
& element(sK29(U_205),powerset(U_205)) )
| empty(U_205) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_204,sK29(U_205))],[f_102_2]) ).
cnf(f_102_4,plain,
( element(sK29(U_205),powerset(U_205))
| empty(U_205) ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_5,plain,
( ~ empty(sK29(U_205))
| empty(U_205) ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_6,plain,
( finite(sK29(U_205))
| empty(U_205) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
! [A] :
( ? [B] :
( strict_net_str(B,A)
& net_str(B,A) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc4_waybel_0]) ).
fof(f_103_2,plain,
! [U_207] :
( ? [U_206] :
( strict_net_str(U_206,U_207)
& net_str(U_206,U_207) )
| ~ one_sorted_str(U_207) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_207] :
( ( strict_net_str(sK30(U_207),U_207)
& net_str(sK30(U_207),U_207) )
| ~ one_sorted_str(U_207) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_206,sK30(U_207))],[f_103_2]) ).
cnf(f_103_4,plain,
( net_str(sK30(U_207),U_207)
| ~ one_sorted_str(U_207) ),
inference(clausify,[status(thm)],[f_103_3]) ).
cnf(f_103_5,plain,
( strict_net_str(sK30(U_207),U_207)
| ~ one_sorted_str(U_207) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_1,plain,
! [A] :
( ? [B] :
( upper_relstr_subset(B,A)
& filtered_subset(B,A)
& proper_element(B,powerset(the_carrier(A)))
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ upper_bounded_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| trivial_carrier(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc4_waybel_7]) ).
fof(f_104_2,plain,
! [U_209] :
( ? [U_208] :
( upper_relstr_subset(U_208,U_209)
& filtered_subset(U_208,U_209)
& proper_element(U_208,powerset(the_carrier(U_209)))
& ~ empty(U_208)
& element(U_208,powerset(the_carrier(U_209))) )
| ~ rel_str(U_209)
| ~ upper_bounded_relstr(U_209)
| ~ antisymmetric_relstr(U_209)
| ~ transitive_relstr(U_209)
| ~ reflexive_relstr(U_209)
| trivial_carrier(U_209)
| empty_carrier(U_209) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_209] :
( ( upper_relstr_subset(sK31(U_209),U_209)
& filtered_subset(sK31(U_209),U_209)
& proper_element(sK31(U_209),powerset(the_carrier(U_209)))
& ~ empty(sK31(U_209))
& element(sK31(U_209),powerset(the_carrier(U_209))) )
| ~ rel_str(U_209)
| ~ upper_bounded_relstr(U_209)
| ~ antisymmetric_relstr(U_209)
| ~ transitive_relstr(U_209)
| ~ reflexive_relstr(U_209)
| trivial_carrier(U_209)
| empty_carrier(U_209) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_208,sK31(U_209))],[f_104_2]) ).
cnf(f_104_4,plain,
( element(sK31(U_209),powerset(the_carrier(U_209)))
| ~ rel_str(U_209)
| ~ upper_bounded_relstr(U_209)
| ~ antisymmetric_relstr(U_209)
| ~ transitive_relstr(U_209)
| ~ reflexive_relstr(U_209)
| trivial_carrier(U_209)
| empty_carrier(U_209) ),
inference(clausify,[status(thm)],[f_104_3]) ).
cnf(f_104_5,plain,
( ~ empty(sK31(U_209))
| ~ rel_str(U_209)
| ~ upper_bounded_relstr(U_209)
| ~ antisymmetric_relstr(U_209)
| ~ transitive_relstr(U_209)
| ~ reflexive_relstr(U_209)
| trivial_carrier(U_209)
| empty_carrier(U_209) ),
inference(clausify,[status(thm)],[f_104_3]) ).
cnf(f_104_6,plain,
( proper_element(sK31(U_209),powerset(the_carrier(U_209)))
| ~ rel_str(U_209)
| ~ upper_bounded_relstr(U_209)
| ~ antisymmetric_relstr(U_209)
| ~ transitive_relstr(U_209)
| ~ reflexive_relstr(U_209)
| trivial_carrier(U_209)
| empty_carrier(U_209) ),
inference(clausify,[status(thm)],[f_104_3]) ).
cnf(f_104_7,plain,
( filtered_subset(sK31(U_209),U_209)
| ~ rel_str(U_209)
| ~ upper_bounded_relstr(U_209)
| ~ antisymmetric_relstr(U_209)
| ~ transitive_relstr(U_209)
| ~ reflexive_relstr(U_209)
| trivial_carrier(U_209)
| empty_carrier(U_209) ),
inference(clausify,[status(thm)],[f_104_3]) ).
cnf(f_104_8,plain,
( upper_relstr_subset(sK31(U_209),U_209)
| ~ rel_str(U_209)
| ~ upper_bounded_relstr(U_209)
| ~ antisymmetric_relstr(U_209)
| ~ transitive_relstr(U_209)
| ~ reflexive_relstr(U_209)
| trivial_carrier(U_209)
| empty_carrier(U_209) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
? [A] :
( directed_relstr(A)
& transitive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc4_yellow_6]) ).
fof(f_105_2,plain,
? [U_210] :
( directed_relstr(U_210)
& transitive_relstr(U_210)
& strict_rel_str(U_210)
& ~ empty_carrier(U_210)
& rel_str(U_210) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
( directed_relstr(sK32)
& transitive_relstr(sK32)
& strict_rel_str(sK32)
& ~ empty_carrier(sK32)
& rel_str(sK32) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_210,sK32)],[f_105_2]) ).
cnf(f_105_4,plain,
rel_str(sK32),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_5,plain,
~ empty_carrier(sK32),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_6,plain,
strict_rel_str(sK32),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_7,plain,
transitive_relstr(sK32),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_8,plain,
directed_relstr(sK32),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc5_struct_0]) ).
fof(f_106_2,plain,
! [U_212] :
( ? [U_211] :
( ~ empty(U_211)
& element(U_211,powerset(the_carrier(U_212))) )
| ~ one_sorted_str(U_212)
| empty_carrier(U_212) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_212] :
( ( ~ empty(sK33(U_212))
& element(sK33(U_212),powerset(the_carrier(U_212))) )
| ~ one_sorted_str(U_212)
| empty_carrier(U_212) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_211,sK33(U_212))],[f_106_2]) ).
cnf(f_106_4,plain,
( element(sK33(U_212),powerset(the_carrier(U_212)))
| ~ one_sorted_str(U_212)
| empty_carrier(U_212) ),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_5,plain,
( ~ empty(sK33(U_212))
| ~ one_sorted_str(U_212)
| empty_carrier(U_212) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [A] :
( ? [B] :
( directed_relstr(B)
& strict_net_str(B,A)
& antisymmetric_relstr(B)
& transitive_relstr(B)
& reflexive_relstr(B)
& ~ empty_carrier(B)
& net_str(B,A) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc5_waybel_0]) ).
fof(f_107_2,plain,
! [U_214] :
( ? [U_213] :
( directed_relstr(U_213)
& strict_net_str(U_213,U_214)
& antisymmetric_relstr(U_213)
& transitive_relstr(U_213)
& reflexive_relstr(U_213)
& ~ empty_carrier(U_213)
& net_str(U_213,U_214) )
| ~ one_sorted_str(U_214) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_214] :
( ( directed_relstr(sK34(U_214))
& strict_net_str(sK34(U_214),U_214)
& antisymmetric_relstr(sK34(U_214))
& transitive_relstr(sK34(U_214))
& reflexive_relstr(sK34(U_214))
& ~ empty_carrier(sK34(U_214))
& net_str(sK34(U_214),U_214) )
| ~ one_sorted_str(U_214) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_213,sK34(U_214))],[f_107_2]) ).
cnf(f_107_4,plain,
( net_str(sK34(U_214),U_214)
| ~ one_sorted_str(U_214) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_5,plain,
( ~ empty_carrier(sK34(U_214))
| ~ one_sorted_str(U_214) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_6,plain,
( reflexive_relstr(sK34(U_214))
| ~ one_sorted_str(U_214) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_7,plain,
( transitive_relstr(sK34(U_214))
| ~ one_sorted_str(U_214) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_8,plain,
( antisymmetric_relstr(sK34(U_214))
| ~ one_sorted_str(U_214) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_9,plain,
( strict_net_str(sK34(U_214),U_214)
| ~ one_sorted_str(U_214) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_10,plain,
( directed_relstr(sK34(U_214))
| ~ one_sorted_str(U_214) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [A] :
( ? [B] :
( upper_relstr_subset(B,A)
& lower_relstr_subset(B,A)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc7_waybel_0]) ).
fof(f_108_2,plain,
! [U_216] :
( ? [U_215] :
( upper_relstr_subset(U_215,U_216)
& lower_relstr_subset(U_215,U_216)
& element(U_215,powerset(the_carrier(U_216))) )
| ~ rel_str(U_216) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_216] :
( ( upper_relstr_subset(sK35(U_216),U_216)
& lower_relstr_subset(sK35(U_216),U_216)
& element(sK35(U_216),powerset(the_carrier(U_216))) )
| ~ rel_str(U_216) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_215,sK35(U_216))],[f_108_2]) ).
cnf(f_108_4,plain,
( element(sK35(U_216),powerset(the_carrier(U_216)))
| ~ rel_str(U_216) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_5,plain,
( lower_relstr_subset(sK35(U_216),U_216)
| ~ rel_str(U_216) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_6,plain,
( upper_relstr_subset(sK35(U_216),U_216)
| ~ rel_str(U_216) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
! [A] :
( ? [B] :
( upper_relstr_subset(B,A)
& lower_relstr_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc8_waybel_0]) ).
fof(f_109_2,plain,
! [U_218] :
( ? [U_217] :
( upper_relstr_subset(U_217,U_218)
& lower_relstr_subset(U_217,U_218)
& ~ empty(U_217)
& element(U_217,powerset(the_carrier(U_218))) )
| ~ rel_str(U_218)
| empty_carrier(U_218) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_218] :
( ( upper_relstr_subset(sK36(U_218),U_218)
& lower_relstr_subset(sK36(U_218),U_218)
& ~ empty(sK36(U_218))
& element(sK36(U_218),powerset(the_carrier(U_218))) )
| ~ rel_str(U_218)
| empty_carrier(U_218) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_217,sK36(U_218))],[f_109_2]) ).
cnf(f_109_4,plain,
( element(sK36(U_218),powerset(the_carrier(U_218)))
| ~ rel_str(U_218)
| empty_carrier(U_218) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_5,plain,
( ~ empty(sK36(U_218))
| ~ rel_str(U_218)
| empty_carrier(U_218) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_6,plain,
( lower_relstr_subset(sK36(U_218),U_218)
| ~ rel_str(U_218)
| empty_carrier(U_218) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_7,plain,
( upper_relstr_subset(sK36(U_218),U_218)
| ~ rel_str(U_218)
| empty_carrier(U_218) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
! [A] :
( ? [B] :
( lower_relstr_subset(B,A)
& directed_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc9_waybel_0]) ).
fof(f_110_2,plain,
! [U_220] :
( ? [U_219] :
( lower_relstr_subset(U_219,U_220)
& directed_subset(U_219,U_220)
& ~ empty(U_219)
& element(U_219,powerset(the_carrier(U_220))) )
| ~ rel_str(U_220)
| ~ transitive_relstr(U_220)
| ~ reflexive_relstr(U_220)
| empty_carrier(U_220) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_220] :
( ( lower_relstr_subset(sK37(U_220),U_220)
& directed_subset(sK37(U_220),U_220)
& ~ empty(sK37(U_220))
& element(sK37(U_220),powerset(the_carrier(U_220))) )
| ~ rel_str(U_220)
| ~ transitive_relstr(U_220)
| ~ reflexive_relstr(U_220)
| empty_carrier(U_220) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_219,sK37(U_220))],[f_110_2]) ).
cnf(f_110_4,plain,
( element(sK37(U_220),powerset(the_carrier(U_220)))
| ~ rel_str(U_220)
| ~ transitive_relstr(U_220)
| ~ reflexive_relstr(U_220)
| empty_carrier(U_220) ),
inference(clausify,[status(thm)],[f_110_3]) ).
cnf(f_110_5,plain,
( ~ empty(sK37(U_220))
| ~ rel_str(U_220)
| ~ transitive_relstr(U_220)
| ~ reflexive_relstr(U_220)
| empty_carrier(U_220) ),
inference(clausify,[status(thm)],[f_110_3]) ).
cnf(f_110_6,plain,
( directed_subset(sK37(U_220),U_220)
| ~ rel_str(U_220)
| ~ transitive_relstr(U_220)
| ~ reflexive_relstr(U_220)
| empty_carrier(U_220) ),
inference(clausify,[status(thm)],[f_110_3]) ).
cnf(f_110_7,plain,
( lower_relstr_subset(sK37(U_220),U_220)
| ~ rel_str(U_220)
| ~ transitive_relstr(U_220)
| ~ reflexive_relstr(U_220)
| empty_carrier(U_220) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [A,B,C] :
( ( relation_of2_as_subset(C,A,B)
| ~ relation_of2(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_111_2,plain,
! [U_223,U_222,U_221] :
( ( relation_of2_as_subset(U_221,U_223,U_222)
| ~ relation_of2(U_221,U_223,U_222) )
& ( relation_of2(U_221,U_223,U_222)
| ~ relation_of2_as_subset(U_221,U_223,U_222) ) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
( ! [U_229,U_227,U_225] :
( relation_of2_as_subset(U_225,U_229,U_227)
| ~ relation_of2(U_225,U_229,U_227) )
& ! [U_228,U_226,U_224] :
( relation_of2(U_224,U_228,U_226)
| ~ relation_of2_as_subset(U_224,U_228,U_226) ) ),
inference(miniscope,[status(thm)],[f_111_2]) ).
cnf(f_111_4,plain,
( relation_of2(U_224,U_228,U_226)
| ~ relation_of2_as_subset(U_224,U_228,U_226) ),
inference(clausify,[status(thm)],[f_111_3]) ).
cnf(f_111_5,plain,
( relation_of2_as_subset(U_225,U_229,U_227)
| ~ relation_of2(U_225,U_229,U_227) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_112_2,plain,
! [U_231,U_230] : subset(U_231,U_231),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_231] : subset(U_231,U_231),
inference(miniscope,[status(thm)],[f_112_2]) ).
cnf(f_112_4,plain,
subset(U_231,U_231),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [A] :
( ! [B] :
( set_difference(B,singleton(empty_set)) = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B))
| ~ element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
| ~ upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
| ~ filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
| empty(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t14_yellow19]) ).
fof(f_113_2,plain,
! [U_233] :
( ! [U_232] :
( set_difference(U_232,singleton(empty_set)) = filter_of_net_str(U_233,net_of_bool_filter(U_233,cast_as_carrier_subset(U_233),U_232))
| ~ element(U_232,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(U_233)))))
| ~ upper_relstr_subset(U_232,boole_POSet(cast_as_carrier_subset(U_233)))
| ~ filtered_subset(U_232,boole_POSet(cast_as_carrier_subset(U_233)))
| empty(U_232) )
| ~ one_sorted_str(U_233)
| empty_carrier(U_233) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( set_difference(U_232,singleton(empty_set)) = filter_of_net_str(U_233,net_of_bool_filter(U_233,cast_as_carrier_subset(U_233),U_232))
| ~ element(U_232,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(U_233)))))
| ~ upper_relstr_subset(U_232,boole_POSet(cast_as_carrier_subset(U_233)))
| ~ filtered_subset(U_232,boole_POSet(cast_as_carrier_subset(U_233)))
| empty(U_232)
| ~ one_sorted_str(U_233)
| empty_carrier(U_233) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_1,negated_conjecture,
~ ! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(B) )
=> B = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) ) ),
inference(negate,[status(cth)],[t15_yellow19]) ).
fof(f_114_2,negated_conjecture,
? [A] :
( ? [B] :
( B != filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B))
& element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(B) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[f_114_1]) ).
fof(f_114_3,negated_conjecture,
? [U_235] :
( ? [U_234] :
( U_234 != filter_of_net_str(U_235,net_of_bool_filter(U_235,cast_as_carrier_subset(U_235),U_234))
& element(U_234,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(U_235)))))
& proper_element(U_234,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(U_235)))))
& upper_relstr_subset(U_234,boole_POSet(cast_as_carrier_subset(U_235)))
& filtered_subset(U_234,boole_POSet(cast_as_carrier_subset(U_235)))
& ~ empty(U_234) )
& one_sorted_str(U_235)
& ~ empty_carrier(U_235) ),
inference(variable_rename,[status(thm)],[f_114_2]) ).
fof(f_114_4,negated_conjecture,
( ? [U_234] :
( U_234 != filter_of_net_str(sK38,net_of_bool_filter(sK38,cast_as_carrier_subset(sK38),U_234))
& element(U_234,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK38)))))
& proper_element(U_234,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK38)))))
& upper_relstr_subset(U_234,boole_POSet(cast_as_carrier_subset(sK38)))
& filtered_subset(U_234,boole_POSet(cast_as_carrier_subset(sK38)))
& ~ empty(U_234) )
& one_sorted_str(sK38)
& ~ empty_carrier(sK38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_235,sK38)],[f_114_3]) ).
fof(f_114_5,negated_conjecture,
( sK39 != filter_of_net_str(sK38,net_of_bool_filter(sK38,cast_as_carrier_subset(sK38),sK39))
& element(sK39,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK38)))))
& proper_element(sK39,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK38)))))
& upper_relstr_subset(sK39,boole_POSet(cast_as_carrier_subset(sK38)))
& filtered_subset(sK39,boole_POSet(cast_as_carrier_subset(sK38)))
& ~ empty(sK39)
& one_sorted_str(sK38)
& ~ empty_carrier(sK38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_234,sK39)],[f_114_4]) ).
cnf(f_114_6,negated_conjecture,
~ empty_carrier(sK38),
inference(clausify,[status(thm)],[f_114_5]) ).
cnf(f_114_7,negated_conjecture,
one_sorted_str(sK38),
inference(clausify,[status(thm)],[f_114_5]) ).
cnf(f_114_8,negated_conjecture,
~ empty(sK39),
inference(clausify,[status(thm)],[f_114_5]) ).
cnf(f_114_9,negated_conjecture,
filtered_subset(sK39,boole_POSet(cast_as_carrier_subset(sK38))),
inference(clausify,[status(thm)],[f_114_5]) ).
cnf(f_114_10,negated_conjecture,
upper_relstr_subset(sK39,boole_POSet(cast_as_carrier_subset(sK38))),
inference(clausify,[status(thm)],[f_114_5]) ).
cnf(f_114_11,negated_conjecture,
proper_element(sK39,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK38))))),
inference(clausify,[status(thm)],[f_114_5]) ).
cnf(f_114_12,negated_conjecture,
element(sK39,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK38))))),
inference(clausify,[status(thm)],[f_114_5]) ).
cnf(f_114_13,negated_conjecture,
sK39 != filter_of_net_str(sK38,net_of_bool_filter(sK38,cast_as_carrier_subset(sK38),sK39)),
inference(clausify,[status(thm)],[f_114_5]) ).
fof(f_115_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_115_2,plain,
! [U_237,U_236] :
( element(U_237,U_236)
| ~ in(U_237,U_236) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( element(U_237,U_236)
| ~ in(U_237,U_236) ),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_116_2,plain,
! [U_239,U_238] :
( in(U_239,U_238)
| empty(U_238)
| ~ element(U_239,U_238) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( in(U_239,U_238)
| empty(U_238)
| ~ element(U_239,U_238) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_117_2,plain,
! [U_242,U_241] :
( U_242 = U_241
| ? [U_240] :
( ( ~ in(U_240,U_242)
& in(U_240,U_241) )
| ( ~ in(U_240,U_241)
& in(U_240,U_242) ) ) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_242,U_241] :
( U_242 = U_241
| ? [U_244] :
( ~ in(U_244,U_242)
& in(U_244,U_241) )
| ? [U_243] :
( ~ in(U_243,U_241)
& in(U_243,U_242) ) ),
inference(miniscope,[status(thm)],[f_117_2]) ).
fof(f_117_4,plain,
! [U_242,U_241] :
( U_242 = U_241
| ? [U_244] :
( ~ in(U_244,U_242)
& in(U_244,U_241) )
| ( ~ in(sK40(U_242,U_241),U_241)
& in(sK40(U_242,U_241),U_242) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_243,sK40(U_242,U_241))],[f_117_3]) ).
fof(f_117_5,plain,
! [U_242,U_241] :
( U_242 = U_241
| ( ~ in(sK41(U_242,U_241),U_242)
& in(sK41(U_242,U_241),U_241) )
| ( ~ in(sK40(U_242,U_241),U_241)
& in(sK40(U_242,U_241),U_242) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_244,sK41(U_242,U_241))],[f_117_4]) ).
cnf(f_117_6,plain,
( in(sK41(U_242,U_241),U_241)
| in(sK40(U_242,U_241),U_242)
| U_242 = U_241 ),
inference(clausify,[status(thm)],[f_117_5]) ).
cnf(f_117_7,plain,
( ~ in(sK41(U_242,U_241),U_242)
| in(sK40(U_242,U_241),U_242)
| U_242 = U_241 ),
inference(clausify,[status(thm)],[f_117_5]) ).
cnf(f_117_8,plain,
( in(sK41(U_242,U_241),U_241)
| ~ in(sK40(U_242,U_241),U_241)
| U_242 = U_241 ),
inference(clausify,[status(thm)],[f_117_5]) ).
cnf(f_117_9,plain,
( ~ in(sK41(U_242,U_241),U_242)
| ~ in(sK40(U_242,U_241),U_241)
| U_242 = U_241 ),
inference(clausify,[status(thm)],[f_117_5]) ).
fof(f_118_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ~ empty(C)
| ~ in(C,B) )
| ~ element(B,powerset(the_carrier(boole_POSet(A))))
| ~ proper_element(B,powerset(the_carrier(boole_POSet(A))))
| ~ upper_relstr_subset(B,boole_POSet(A))
| ~ filtered_subset(B,boole_POSet(A))
| empty(B) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[t2_yellow19]) ).
fof(f_118_2,plain,
! [U_247] :
( ! [U_246] :
( ! [U_245] :
( ~ empty(U_245)
| ~ in(U_245,U_246) )
| ~ element(U_246,powerset(the_carrier(boole_POSet(U_247))))
| ~ proper_element(U_246,powerset(the_carrier(boole_POSet(U_247))))
| ~ upper_relstr_subset(U_246,boole_POSet(U_247))
| ~ filtered_subset(U_246,boole_POSet(U_247))
| empty(U_246) )
| empty(U_247) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( ~ empty(U_245)
| ~ in(U_245,U_246)
| ~ element(U_246,powerset(the_carrier(boole_POSet(U_247))))
| ~ proper_element(U_246,powerset(the_carrier(boole_POSet(U_247))))
| ~ upper_relstr_subset(U_246,boole_POSet(U_247))
| ~ filtered_subset(U_246,boole_POSet(U_247))
| empty(U_246)
| empty(U_247) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_119_2,plain,
! [U_248] : set_difference(U_248,empty_set) = U_248,
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
set_difference(U_248,empty_set) = U_248,
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_120_2,plain,
! [U_250,U_249] :
( ( element(U_250,powerset(U_249))
| ~ subset(U_250,U_249) )
& ( subset(U_250,U_249)
| ~ element(U_250,powerset(U_249)) ) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
( ! [U_254,U_252] :
( element(U_254,powerset(U_252))
| ~ subset(U_254,U_252) )
& ! [U_253,U_251] :
( subset(U_253,U_251)
| ~ element(U_253,powerset(U_251)) ) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( subset(U_253,U_251)
| ~ element(U_253,powerset(U_251)) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_5,plain,
( element(U_254,powerset(U_252))
| ~ subset(U_254,U_252) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_121_2,plain,
! [U_255] : set_difference(empty_set,U_255) = empty_set,
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
set_difference(empty_set,U_255) = empty_set,
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_122_2,plain,
! [U_258,U_257,U_256] :
( element(U_258,U_256)
| ~ element(U_257,powerset(U_256))
| ~ in(U_258,U_257) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( element(U_258,U_256)
| ~ element(U_257,powerset(U_256))
| ~ in(U_258,U_257) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_123_2,plain,
! [U_261,U_260,U_259] :
( ~ empty(U_259)
| ~ element(U_260,powerset(U_259))
| ~ in(U_261,U_260) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_261,U_260] :
( ! [U_259] :
( ~ empty(U_259)
| ~ element(U_260,powerset(U_259)) )
| ~ in(U_261,U_260) ),
inference(miniscope,[status(thm)],[f_123_2]) ).
cnf(f_123_4,plain,
( ~ empty(U_259)
| ~ element(U_260,powerset(U_259))
| ~ in(U_261,U_260) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [A,B] :
( ( set_difference(A,singleton(B)) = A
| in(B,A) )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(fof_nnf,[status(thm)],[t65_zfmisc_1]) ).
fof(f_124_2,plain,
! [U_263,U_262] :
( ( set_difference(U_263,singleton(U_262)) = U_263
| in(U_262,U_263) )
& ( ~ in(U_262,U_263)
| set_difference(U_263,singleton(U_262)) != U_263 ) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
( ! [U_267,U_265] :
( set_difference(U_267,singleton(U_265)) = U_267
| in(U_265,U_267) )
& ! [U_266,U_264] :
( ~ in(U_264,U_266)
| set_difference(U_266,singleton(U_264)) != U_266 ) ),
inference(miniscope,[status(thm)],[f_124_2]) ).
cnf(f_124_4,plain,
( ~ in(U_264,U_266)
| set_difference(U_266,singleton(U_264)) != U_266 ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_5,plain,
( set_difference(U_267,singleton(U_265)) = U_267
| in(U_265,U_267) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_125_2,plain,
! [U_268] :
( U_268 = empty_set
| ~ empty(U_268) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( U_268 = empty_set
| ~ empty(U_268) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_126_2,plain,
! [U_270,U_269] :
( ~ empty(U_269)
| ~ in(U_270,U_269) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( ~ empty(U_269)
| ~ in(U_270,U_269) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_127_2,plain,
! [U_272,U_271] :
( ~ empty(U_271)
| U_272 = U_271
| ~ empty(U_272) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_272] :
( ! [U_271] :
( ~ empty(U_271)
| U_272 = U_271 )
| ~ empty(U_272) ),
inference(miniscope,[status(thm)],[f_127_2]) ).
cnf(f_127_4,plain,
( ~ empty(U_271)
| U_272 = U_271
| ~ empty(U_272) ),
inference(clausify,[status(thm)],[f_127_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_5_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_4]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_6_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_4]) ).
cnf(f_6_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_5]) ).
cnf(f_6_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_6]) ).
cnf(f_6_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_7]) ).
cnf(f_6_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_10]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_7_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_4]) ).
cnf(f_7_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_5]) ).
cnf(f_8_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_3]) ).
cnf(f_8_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_4]) ).
cnf(f_8_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_5]) ).
cnf(f_8_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_7]) ).
cnf(f_13_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_3]) ).
cnf(f_16_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_3]) ).
cnf(f_16_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_4]) ).
cnf(f_17_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_3]) ).
cnf(f_19_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_3]) ).
cnf(f_19_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_4]) ).
cnf(f_21_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_4]) ).
cnf(f_21_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_5]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_2]) ).
cnf(f_26_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_26_2]) ).
cnf(f_27_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_27_2]) ).
cnf(f_30_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_2]) ).
cnf(f_33_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_33_2]) ).
cnf(f_35_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_35_2]) ).
cnf(f_37_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_37_2]) ).
cnf(f_38_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_2]) ).
cnf(f_41_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_41_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( the_InternalRel(Eq_x_0) = the_InternalRel(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( rel_str_of(Eq_x_0,Eq_x_1) = rel_str_of(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( the_mapping(Eq_x_0,Eq_x_1) = the_mapping(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( net_str_of(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = net_str_of(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( filter_of_net_str(Eq_x_0,Eq_x_1) = filter_of_net_str(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( a_2_1_yellow19(Eq_x_0,Eq_x_1) = a_2_1_yellow19(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( cast_as_carrier_subset(Eq_x_0) = cast_as_carrier_subset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( boole_POSet(Eq_x_0) = boole_POSet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( net_of_bool_filter(Eq_x_0,Eq_x_1,Eq_x_2) = net_of_bool_filter(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( sK21(Eq_x_0) = sK21(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK22(Eq_x_0) = sK22(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK25(Eq_x_0) = sK25(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( sK28(Eq_x_0) = sK28(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK29(Eq_x_0) = sK29(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( sK30(Eq_x_0) = sK30(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK33(Eq_x_0) = sK33(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK34(Eq_x_0) = sK34(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK35(Eq_x_0) = sK35(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK36(Eq_x_0) = sK36(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK37(Eq_x_0) = sK37(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( rel_str(Eq_y_0)
| ~ rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( strict_rel_str(Eq_y_0)
| ~ strict_rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( net_str(Eq_y_0,Eq_y_1)
| ~ net_str(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( strict_net_str(Eq_y_0,Eq_y_1)
| ~ strict_net_str(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( empty_carrier(Eq_y_0)
| ~ empty_carrier(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( reflexive_relstr(Eq_y_0)
| ~ reflexive_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( complete_relstr(Eq_y_0)
| ~ complete_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( up_complete_relstr(Eq_y_0)
| ~ up_complete_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( join_complete_relstr(Eq_y_0)
| ~ join_complete_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( lower_bounded_relstr(Eq_y_0)
| ~ lower_bounded_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( transitive_relstr(Eq_y_0)
| ~ transitive_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( antisymmetric_relstr(Eq_y_0)
| ~ antisymmetric_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( with_suprema_relstr(Eq_y_0)
| ~ with_suprema_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( with_infima_relstr(Eq_y_0)
| ~ with_infima_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( upper_bounded_relstr(Eq_y_0)
| ~ upper_bounded_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_59,axiom,
( bounded_relstr(Eq_y_0)
| ~ bounded_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_60,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_64,axiom,
( trivial_carrier(Eq_y_0)
| ~ trivial_carrier(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_65,axiom,
( connected_relstr(Eq_y_0)
| ~ connected_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_66,axiom,
( relation_of2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_67,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_68,axiom,
( quasi_total(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ quasi_total(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_69,axiom,
( filtered_subset(Eq_y_0,Eq_y_1)
| ~ filtered_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_70,axiom,
( upper_relstr_subset(Eq_y_0,Eq_y_1)
| ~ upper_relstr_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_71,axiom,
( relation_of2_as_subset(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2_as_subset(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_72,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_73,axiom,
( lower_relstr_subset(Eq_y_0,Eq_y_1)
| ~ lower_relstr_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_74,axiom,
( v1_yellow_3(Eq_y_0)
| ~ v1_yellow_3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_75,axiom,
( distributive_relstr(Eq_y_0)
| ~ distributive_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_76,axiom,
( heyting_relstr(Eq_y_0)
| ~ heyting_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_77,axiom,
( complemented_relstr(Eq_y_0)
| ~ complemented_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_78,axiom,
( boolean_relstr(Eq_y_0)
| ~ boolean_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_79,axiom,
( directed_subset(Eq_y_0,Eq_y_1)
| ~ directed_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_80,axiom,
( directed_relstr(Eq_y_0)
| ~ directed_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_81,axiom,
( proper_element(Eq_y_0,Eq_y_1)
| ~ proper_element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_82,axiom,
( is_eventually_in(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ is_eventually_in(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_83,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU394+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42 % Computer : n019.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Sun Sep 20 00:11:09 UTC 2026
% 0.10/0.42 % CPUTime :
% 252.59/252.90 % SZS status Theorem for theBenchmark
% 252.59/252.90 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------