%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU401+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 : Fri Sep 25 02:57:21 PM UTC 2026
% Result : Theorem 4.70s 7.28s
% Output : CNFRefutation 10.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 61
% Syntax : Number of formulae : 1526 ( 127 unt; 10 def)
% Number of atoms : 7512 (1571 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 7653 (2880 ~;4201 |; 496 &)
% ( 12 <=>; 63 =>; 0 <=; 1 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 41 ( 39 usr; 11 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 9 con; 0-4 aty)
% Number of variables : 1251 ( 2 sgn1140 !; 111 ?; 625 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X3,X4,X5] :
( ( ! [X6] :
( in(X6,X5)
<=> ( ? [X9] :
( ? [X10] :
( X9 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X10)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X10)))
& X6 = X10
& X3 = topstr_closure(X0,X9)
& element(X10,the_carrier(X1)) )
& netstr_induced_subset(X9,X0,X1) )
& in(X6,the_carrier(X1)) ) )
& ! [X6] :
( in(X6,X4)
<=> ( ? [X7] :
( ? [X8] :
( X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8)))
& X6 = X8
& X3 = topstr_closure(X0,X7)
& element(X8,the_carrier(X1)) )
& netstr_induced_subset(X7,X0,X1) )
& in(X6,the_carrier(X1)) ) ) )
=> X4 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_xboole_0__e6_39_3__yellow19__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X3,X4,X5] :
( ( ! [X6] :
( in(X6,X5)
<=> ( ? [X9] :
( ? [X10] :
( X9 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X10)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X10)))
& X6 = X10
& X3 = topstr_closure(X0,X9)
& element(X10,the_carrier(X1)) )
& netstr_induced_subset(X9,X0,X1) )
& in(X6,the_carrier(X1)) ) )
& ! [X6] :
( in(X6,X4)
<=> ( ? [X7] :
( ? [X8] :
( X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8)))
& X6 = X8
& X3 = topstr_closure(X0,X7)
& element(X8,the_carrier(X1)) )
& netstr_induced_subset(X7,X0,X1) )
& in(X6,the_carrier(X1)) ) ) )
=> X4 = X5 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tops_1) ).
fof(f4,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tops_1) ).
fof(f5,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f6,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f9,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(f10,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tops_1) ).
fof(f11,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tops_1) ).
fof(f12,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tops_1) ).
fof(f16,axiom,
! [X0] :
? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_7) ).
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_waybel_7) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X3,X1,the_carrier(X0))
& quasi_total(X3,X1,the_carrier(X0))
& function(X3)
& relation_of2(X2,X1,X1)
& one_sorted_str(X0) )
=> ! [X4,X5,X6,X7] :
( net_str_of(X0,X1,X2,X3) = net_str_of(X4,X5,X6,X7)
=> ( X3 = X7
& X2 = X6
& X1 = X5
& X0 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_waybel_0) ).
fof(f19,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X3,X1,the_carrier(X0))
& quasi_total(X3,X1,the_carrier(X0))
& function(X3)
& relation_of2(X2,X1,X1)
& one_sorted_str(X0) )
=> ( net_str(net_str_of(X0,X1,X2,X3),X0)
& strict_net_str(net_str_of(X0,X1,X2,X3),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_waybel_0) ).
fof(f21,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f22,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f23,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f24,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f26,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
fof(f27,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
fof(f28,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_pre_topc) ).
fof(f32,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f33,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X3,X1,the_carrier(X0))
& quasi_total(X3,X1,the_carrier(X0))
& function(X3)
& relation_of2(X2,X1,X1)
& ~ empty(X1)
& one_sorted_str(X0) )
=> ( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
& ~ empty_carrier(net_str_of(X0,X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_waybel_0) ).
fof(f34,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f36,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f37,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f38,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f39,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& one_sorted_str(X0) )
=> ( strict_net_str(X1,X0)
=> X1 = net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v6_waybel_0) ).
fof(f40,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X1))
& net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( net_str(netstr_restr_to_element(X0,X1,X2),X0)
& strict_net_str(netstr_restr_to_element(X0,X1,X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_waybel_9) ).
fof(f44,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f47,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f48,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X2] :
( subnet(X2,X0,X1)
=> ( net_str(X2,X0)
& directed_relstr(X2)
& transitive_relstr(X2)
& ~ empty_carrier(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_yellow_6) ).
fof(f49,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f50,axiom,
? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f51,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f53,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] :
( strict_net_str(X1,X0)
& net_str(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_waybel_0) ).
fof(f54,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X1))
& net_str(X1,X0)
& directed_relstr(X1)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( strict_net_str(netstr_restr_to_element(X0,X1,X2),X0)
& ~ empty_carrier(netstr_restr_to_element(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc22_waybel_9) ).
fof(f55,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X1))
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( directed_relstr(netstr_restr_to_element(X0,X1,X2))
& strict_net_str(netstr_restr_to_element(X0,X1,X2),X0)
& transitive_relstr(netstr_restr_to_element(X0,X1,X2))
& ~ empty_carrier(netstr_restr_to_element(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc26_waybel_9) ).
fof(f56,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ? [X2] :
( directed_relstr(X2)
& strict_net_str(X2,X0)
& transitive_relstr(X2)
& ~ empty_carrier(X2)
& subnet(X2,X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_9) ).
fof(f57,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& relation(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_yellow_6) ).
fof(f58,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f59,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
fof(f60,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X1))
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> subnetstr_of_element(X0,X1,X2) = netstr_restr_to_element(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_waybel_9) ).
fof(f61,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
fof(f62,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f63,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X1))
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( subnet(subnetstr_of_element(X0,X1,X2),X0,X1)
& strict_net_str(subnetstr_of_element(X0,X1,X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_waybel_9) ).
fof(f64,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f65,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
fof(f67,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X2] :
( netstr_induced_subset(X2,X0,X1)
=> element(X2,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow19) ).
fof(f69,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& one_sorted_str(X0) )
=> ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
fof(f70,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f71,plain,
~ ! [X0,X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X3,X4,X5] :
( ( ! [X9] :
( in(X9,X5)
<=> ( ? [X10] :
( ? [X11] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) = X10
& X9 = X11
& topstr_closure(X0,X10) = X3
& element(X11,the_carrier(X1)) )
& netstr_induced_subset(X10,X0,X1) )
& in(X9,the_carrier(X1)) ) )
& ! [X6] :
( in(X6,X4)
<=> ( ? [X7] :
( ? [X8] :
( X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8)))
& X6 = X8
& X3 = topstr_closure(X0,X7)
& element(X8,the_carrier(X1)) )
& netstr_induced_subset(X7,X0,X1) )
& in(X6,the_carrier(X1)) ) ) )
=> X4 = X5 ) ),
inference(rectify,[],[f2]) ).
fof(f72,plain,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f3]) ).
fof(f74,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f4]) ).
fof(f76,plain,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f72]) ).
fof(f77,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f74]) ).
fof(f78,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f77]) ).
fof(f80,plain,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f76]) ).
fof(f81,plain,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f80]) ).
fof(f83,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f78]) ).
fof(f85,plain,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f81]) ).
fof(f86,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f83]) ).
fof(f87,plain,
? [X0,X1] :
( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X3,X4,X5] :
( ! [X9] :
( in(X9,X5)
<=> ( ? [X10] :
( ? [X11] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) = X10
& X9 = X11
& topstr_closure(X0,X10) = X3
& element(X11,the_carrier(X1)) )
& netstr_induced_subset(X10,X0,X1) )
& in(X9,the_carrier(X1)) ) )
& ! [X6] :
( in(X6,X4)
<=> ( ? [X7] :
( ? [X8] :
( X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8)))
& X6 = X8
& X3 = topstr_closure(X0,X7)
& element(X8,the_carrier(X1)) )
& netstr_induced_subset(X7,X0,X1) )
& in(X6,the_carrier(X1)) ) )
& X4 != X5 ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f88,plain,
? [X0,X1] :
( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X3,X4,X5] :
( ! [X9] :
( in(X9,X5)
<=> ( ? [X10] :
( ? [X11] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) = X10
& X9 = X11
& topstr_closure(X0,X10) = X3
& element(X11,the_carrier(X1)) )
& netstr_induced_subset(X10,X0,X1) )
& in(X9,the_carrier(X1)) ) )
& ! [X6] :
( in(X6,X4)
<=> ( ? [X7] :
( ? [X8] :
( X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8)))
& X6 = X8
& X3 = topstr_closure(X0,X7)
& element(X8,the_carrier(X1)) )
& netstr_induced_subset(X7,X0,X1) )
& in(X6,the_carrier(X1)) ) )
& X4 != X5 ) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ~ top_str(X0)
| ? [X1] :
( boundary_set(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f85]) ).
fof(f90,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f86]) ).
fof(f91,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f96,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f97,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f98,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f100,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f102,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f101]) ).
fof(f109,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0)
| ! [X4,X5,X6,X7] :
( net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ( X3 = X7
& X2 = X6
& X1 = X5
& X0 = X4 ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0)
| ! [X4,X5,X6,X7] :
( net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ( X3 = X7
& X2 = X6
& X1 = X5
& X0 = X4 ) ) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0)
| ( net_str(net_str_of(X0,X1,X2,X3),X0)
& strict_net_str(net_str_of(X0,X1,X2,X3),X0) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0)
| ( net_str(net_str_of(X0,X1,X2,X3),X0)
& strict_net_str(net_str_of(X0,X1,X2,X3),X0) ) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
! [X0] :
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f115,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f116,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f117,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(flattening,[],[f116]) ).
fof(f119,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f120,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f119]) ).
fof(f121,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f122,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f124,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f123]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| ~ one_sorted_str(X0)
| ( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
& ~ empty_carrier(net_str_of(X0,X1,X2,X3)) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| ~ one_sorted_str(X0)
| ( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
& ~ empty_carrier(net_str_of(X0,X1,X2,X3)) ) ),
inference(flattening,[],[f132]) ).
fof(f135,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f136,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(flattening,[],[f135]) ).
fof(f137,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f138,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| ~ strict_net_str(X1,X0)
| X1 = net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f139,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| ~ strict_net_str(X1,X0)
| X1 = net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( net_str(netstr_restr_to_element(X0,X1,X2),X0)
& strict_net_str(netstr_restr_to_element(X0,X1,X2),X0) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( net_str(netstr_restr_to_element(X0,X1,X2),X0)
& strict_net_str(netstr_restr_to_element(X0,X1,X2),X0) ) ),
inference(flattening,[],[f140]) ).
fof(f142,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f47]) ).
fof(f144,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X2] :
( ~ subnet(X2,X0,X1)
| ( net_str(X2,X0)
& directed_relstr(X2)
& transitive_relstr(X2)
& ~ empty_carrier(X2) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f145,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X2] :
( ~ subnet(X2,X0,X1)
| ( net_str(X2,X0)
& directed_relstr(X2)
& transitive_relstr(X2)
& ~ empty_carrier(X2) ) ) ),
inference(flattening,[],[f144]) ).
fof(f146,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(ennf_transformation,[],[f51]) ).
fof(f147,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(flattening,[],[f146]) ).
fof(f150,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ? [X1] :
( strict_net_str(X1,X0)
& net_str(X1,X0) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( strict_net_str(netstr_restr_to_element(X0,X1,X2),X0)
& ~ empty_carrier(netstr_restr_to_element(X0,X1,X2)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( strict_net_str(netstr_restr_to_element(X0,X1,X2),X0)
& ~ empty_carrier(netstr_restr_to_element(X0,X1,X2)) ) ),
inference(flattening,[],[f151]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( directed_relstr(netstr_restr_to_element(X0,X1,X2))
& strict_net_str(netstr_restr_to_element(X0,X1,X2),X0)
& transitive_relstr(netstr_restr_to_element(X0,X1,X2))
& ~ empty_carrier(netstr_restr_to_element(X0,X1,X2)) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( directed_relstr(netstr_restr_to_element(X0,X1,X2))
& strict_net_str(netstr_restr_to_element(X0,X1,X2),X0)
& transitive_relstr(netstr_restr_to_element(X0,X1,X2))
& ~ empty_carrier(netstr_restr_to_element(X0,X1,X2)) ) ),
inference(flattening,[],[f153]) ).
fof(f155,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ? [X2] :
( directed_relstr(X2)
& strict_net_str(X2,X0)
& transitive_relstr(X2)
& ~ empty_carrier(X2)
& subnet(X2,X0,X1) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f156,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ? [X2] :
( directed_relstr(X2)
& strict_net_str(X2,X0)
& transitive_relstr(X2)
& ~ empty_carrier(X2)
& subnet(X2,X0,X1) ) ),
inference(flattening,[],[f155]) ).
fof(f157,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& relation(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f158,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& relation(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) ) ),
inference(flattening,[],[f157]) ).
fof(f159,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
inference(ennf_transformation,[],[f59]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| subnetstr_of_element(X0,X1,X2) = netstr_restr_to_element(X0,X1,X2) ),
inference(ennf_transformation,[],[f60]) ).
fof(f162,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| subnetstr_of_element(X0,X1,X2) = netstr_restr_to_element(X0,X1,X2) ),
inference(flattening,[],[f161]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
inference(ennf_transformation,[],[f61]) ).
fof(f164,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f62]) ).
fof(f165,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f164]) ).
fof(f166,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( subnet(subnetstr_of_element(X0,X1,X2),X0,X1)
& strict_net_str(subnetstr_of_element(X0,X1,X2),X0) ) ),
inference(ennf_transformation,[],[f63]) ).
fof(f167,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( subnet(subnetstr_of_element(X0,X1,X2),X0,X1)
& strict_net_str(subnetstr_of_element(X0,X1,X2),X0) ) ),
inference(flattening,[],[f166]) ).
fof(f168,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f169,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| rel_str(X1) ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f170,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X2] :
( ~ netstr_induced_subset(X2,X0,X1)
| element(X2,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f67]) ).
fof(f171,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X2] :
( ~ netstr_induced_subset(X2,X0,X1)
| element(X2,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f170]) ).
fof(f172,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f173,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) ) ),
inference(flattening,[],[f172]) ).
fof(f174,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f70]) ).
fof(f175,plain,
? [X0,X1] :
( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X3,X4,X5] :
( ! [X9] :
( ( ~ in(X9,X5)
| ( ? [X10] :
( ? [X11] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) = X10
& X9 = X11
& topstr_closure(X0,X10) = X3
& element(X11,the_carrier(X1)) )
& netstr_induced_subset(X10,X0,X1) )
& in(X9,the_carrier(X1)) ) )
& ( ! [X10] :
( ! [X11] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) != X10
| X9 != X11
| topstr_closure(X0,X10) != X3
| ~ element(X11,the_carrier(X1)) )
| ~ netstr_induced_subset(X10,X0,X1) )
| ~ in(X9,the_carrier(X1))
| in(X9,X5) ) )
& ! [X6] :
( ( ~ in(X6,X4)
| ( ? [X7] :
( ? [X8] :
( X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8)))
& X6 = X8
& X3 = topstr_closure(X0,X7)
& element(X8,the_carrier(X1)) )
& netstr_induced_subset(X7,X0,X1) )
& in(X6,the_carrier(X1)) ) )
& ( ! [X7] :
( ! [X8] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) != X7
| X6 != X8
| topstr_closure(X0,X7) != X3
| ~ element(X8,the_carrier(X1)) )
| ~ netstr_induced_subset(X7,X0,X1) )
| ~ in(X6,the_carrier(X1))
| in(X6,X4) ) )
& X4 != X5 ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f176,plain,
? [X0,X1] :
( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X3,X4,X5] :
( ! [X9] :
( ( ~ in(X9,X5)
| ( ? [X10] :
( ? [X11] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) = X10
& X9 = X11
& topstr_closure(X0,X10) = X3
& element(X11,the_carrier(X1)) )
& netstr_induced_subset(X10,X0,X1) )
& in(X9,the_carrier(X1)) ) )
& ( ! [X10] :
( ! [X11] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) != X10
| X9 != X11
| topstr_closure(X0,X10) != X3
| ~ element(X11,the_carrier(X1)) )
| ~ netstr_induced_subset(X10,X0,X1) )
| ~ in(X9,the_carrier(X1))
| in(X9,X5) ) )
& ! [X6] :
( ( ~ in(X6,X4)
| ( ? [X7] :
( ? [X8] :
( X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8)))
& X6 = X8
& X3 = topstr_closure(X0,X7)
& element(X8,the_carrier(X1)) )
& netstr_induced_subset(X7,X0,X1) )
& in(X6,the_carrier(X1)) ) )
& ( ! [X7] :
( ! [X8] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) != X7
| X6 != X8
| topstr_closure(X0,X7) != X3
| ~ element(X8,the_carrier(X1)) )
| ~ netstr_induced_subset(X7,X0,X1) )
| ~ in(X6,the_carrier(X1))
| in(X6,X4) ) )
& X4 != X5 ) ),
inference(flattening,[],[f175]) ).
fof(f177,plain,
? [X0,X1] :
( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X2,X3,X4] :
( ! [X10] :
( ( ~ in(X10,X4)
| ( ? [X13] :
( ? [X14] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X14)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X14))) = X13
& X10 = X14
& topstr_closure(X0,X13) = X2
& element(X14,the_carrier(X1)) )
& netstr_induced_subset(X13,X0,X1) )
& in(X10,the_carrier(X1)) ) )
& ( ! [X11] :
( ! [X12] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X12)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X12))) != X11
| X10 != X12
| topstr_closure(X0,X11) != X2
| ~ element(X12,the_carrier(X1)) )
| ~ netstr_induced_subset(X11,X0,X1) )
| ~ in(X10,the_carrier(X1))
| in(X10,X4) ) )
& ! [X5] :
( ( ~ in(X5,X3)
| ( ? [X8] :
( ? [X9] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X9)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X9))) = X8
& X5 = X9
& topstr_closure(X0,X8) = X2
& element(X9,the_carrier(X1)) )
& netstr_induced_subset(X8,X0,X1) )
& in(X5,the_carrier(X1)) ) )
& ( ! [X6] :
( ! [X7] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X7)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X7))) != X6
| X5 != X7
| topstr_closure(X0,X6) != X2
| ~ element(X7,the_carrier(X1)) )
| ~ netstr_induced_subset(X6,X0,X1) )
| ~ in(X5,the_carrier(X1))
| in(X5,X3) ) )
& X3 != X4 ) ),
inference(rectify,[],[f176]) ).
fof(f178,plain,
( net_str(sK1,sK0)
& directed_relstr(sK1)
& transitive_relstr(sK1)
& ~ empty_carrier(sK1)
& top_str(sK0)
& topological_space(sK0)
& ~ empty_carrier(sK0)
& ! [X10] :
( ( ~ in(X10,sK4)
| ( sK7(X10) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(X10))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(X10))))
& sK8(X10) = X10
& sK2 = topstr_closure(sK0,sK7(X10))
& element(sK8(X10),the_carrier(sK1))
& netstr_induced_subset(sK7(X10),sK0,sK1)
& in(X10,the_carrier(sK1)) ) )
& ( ! [X11] :
( ! [X12] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X12)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X12))) != X11
| X10 != X12
| sK2 != topstr_closure(sK0,X11)
| ~ element(X12,the_carrier(sK1)) )
| ~ netstr_induced_subset(X11,sK0,sK1) )
| ~ in(X10,the_carrier(sK1))
| in(X10,sK4) ) )
& ! [X5] :
( ( ~ in(X5,sK3)
| ( sK5(X5) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(X5))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(X5))))
& sK6(X5) = X5
& sK2 = topstr_closure(sK0,sK5(X5))
& element(sK6(X5),the_carrier(sK1))
& netstr_induced_subset(sK5(X5),sK0,sK1)
& in(X5,the_carrier(sK1)) ) )
& ( ! [X6] :
( ! [X7] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X7)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X7))) != X6
| X5 != X7
| sK2 != topstr_closure(sK0,X6)
| ~ element(X7,the_carrier(sK1)) )
| ~ netstr_induced_subset(X6,sK0,sK1) )
| ~ in(X5,the_carrier(sK1))
| in(X5,sK3) ) )
& sK3 != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X8,sK5(X5)),skolemize(X9,sK6(X5)),skolemize(X13,sK7(X10)),skolemize(X14,sK8(X10))],[f177]) ).
fof(f179,plain,
! [X0] :
( ~ top_str(X0)
| ( boundary_set(sK9(X0),X0)
& empty(sK9(X0))
& element(sK9(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f89]) ).
fof(f180,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ( nowhere_dense(sK10(X0),X0)
& boundary_set(sK10(X0),X0)
& closed_subset(sK10(X0),X0)
& open_subset(sK10(X0),X0)
& empty(sK10(X0))
& element(sK10(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f91]) ).
fof(f181,plain,
( finite(sK11)
& ~ empty(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f5]) ).
fof(f182,plain,
! [X0] :
( empty(X0)
| ( finite(sK12(X0))
& ~ empty(sK12(X0))
& element(sK12(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X1,sK12(X0))],[f92]) ).
fof(f183,plain,
! [X0] :
( empty(X0)
| ( finite(sK13(X0))
& ~ empty(sK13(X0))
& element(sK13(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X1,sK13(X0))],[f96]) ).
fof(f184,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ( open_subset(sK14(X0),X0)
& element(sK14(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f98]) ).
fof(f185,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ( closed_subset(sK15(X0),X0)
& open_subset(sK15(X0),X0)
& element(sK15(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f100]) ).
fof(f186,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ( closed_subset(sK16(X0),X0)
& open_subset(sK16(X0),X0)
& ~ empty(sK16(X0))
& element(sK16(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X1,sK16(X0))],[f102]) ).
fof(f187,plain,
! [X0] :
( finite(sK17(X0))
& ~ empty(sK17(X0))
& element(sK17(X0),powerset(powerset(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X1,sK17(X0))],[f16]) ).
fof(f188,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ( finite(sK18(X0))
& ~ empty(sK18(X0))
& element(sK18(X0),powerset(powerset(the_carrier(X0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X1,sK18(X0))],[f109]) ).
fof(f189,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK19(X0))
& element(sK19(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X1,sK19(X0))],[f115]) ).
fof(f190,plain,
! [X0] :
( empty(sK20(X0))
& element(sK20(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X1,sK20(X0))],[f24]) ).
fof(f191,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( ~ empty(sK21(X0))
& element(sK21(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X1,sK21(X0))],[f120]) ).
fof(f192,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ( closed_subset(sK22(X0),X0)
& element(sK22(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X1,sK22(X0))],[f122]) ).
fof(f193,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ( closed_subset(sK23(X0),X0)
& ~ empty(sK23(X0))
& element(sK23(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X1,sK23(X0))],[f124]) ).
fof(f194,plain,
( relation(sK24)
& empty(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(X0,sK24)],[f34]) ).
fof(f195,plain,
( relation(sK25)
& ~ empty(sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(X0,sK25)],[f36]) ).
fof(f196,plain,
! [X0,X1,X2] :
( ( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
& ( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f197,plain,
( ~ empty_carrier(sK26)
& one_sorted_str(sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(X0,sK26)],[f50]) ).
fof(f198,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ( strict_net_str(sK27(X0),X0)
& net_str(sK27(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X1,sK27(X0))],[f150]) ).
fof(f199,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( directed_relstr(sK28(X0,X1))
& strict_net_str(sK28(X0,X1),X0)
& transitive_relstr(sK28(X0,X1))
& ~ empty_carrier(sK28(X0,X1))
& subnet(sK28(X0,X1),X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(X2,sK28(X0,X1))],[f156]) ).
fof(f200,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f174]) ).
fof(f201,plain,
! [X0,X1] :
( ( ( in(sK29(X0,X1),X0)
| in(sK29(X0,X1),X1) )
& ( ~ in(sK29(X0,X1),X0)
| ~ in(sK29(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X2,sK29(X0,X1))],[f200]) ).
fof(f202,plain,
net_str(sK1,sK0),
inference(cnf_transformation,[],[f178]) ).
fof(f203,plain,
directed_relstr(sK1),
inference(cnf_transformation,[],[f178]) ).
fof(f204,plain,
transitive_relstr(sK1),
inference(cnf_transformation,[],[f178]) ).
fof(f205,plain,
~ empty_carrier(sK1),
inference(cnf_transformation,[],[f178]) ).
fof(f206,plain,
top_str(sK0),
inference(cnf_transformation,[],[f178]) ).
fof(f207,plain,
topological_space(sK0),
inference(cnf_transformation,[],[f178]) ).
fof(f208,plain,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f178]) ).
fof(f209,plain,
! [X10] :
( ~ in(X10,sK4)
| sK7(X10) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(X10))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(X10)))) ),
inference(cnf_transformation,[],[f178]) ).
fof(f210,plain,
! [X10] :
( ~ in(X10,sK4)
| sK8(X10) = X10 ),
inference(cnf_transformation,[],[f178]) ).
fof(f211,plain,
! [X10] :
( ~ in(X10,sK4)
| sK2 = topstr_closure(sK0,sK7(X10)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f212,plain,
! [X10] :
( ~ in(X10,sK4)
| element(sK8(X10),the_carrier(sK1)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f213,plain,
! [X10] :
( ~ in(X10,sK4)
| netstr_induced_subset(sK7(X10),sK0,sK1) ),
inference(cnf_transformation,[],[f178]) ).
fof(f214,plain,
! [X10] :
( ~ in(X10,sK4)
| in(X10,the_carrier(sK1)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f215,plain,
! [X10,X11,X12] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X12)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X12))) != X11
| X10 != X12
| sK2 != topstr_closure(sK0,X11)
| ~ element(X12,the_carrier(sK1))
| ~ netstr_induced_subset(X11,sK0,sK1)
| ~ in(X10,the_carrier(sK1))
| in(X10,sK4) ),
inference(cnf_transformation,[],[f178]) ).
fof(f216,plain,
! [X5] :
( ~ in(X5,sK3)
| sK5(X5) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(X5))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(X5)))) ),
inference(cnf_transformation,[],[f178]) ).
fof(f217,plain,
! [X5] :
( ~ in(X5,sK3)
| sK6(X5) = X5 ),
inference(cnf_transformation,[],[f178]) ).
fof(f218,plain,
! [X5] :
( ~ in(X5,sK3)
| sK2 = topstr_closure(sK0,sK5(X5)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f219,plain,
! [X5] :
( ~ in(X5,sK3)
| element(sK6(X5),the_carrier(sK1)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f220,plain,
! [X5] :
( ~ in(X5,sK3)
| netstr_induced_subset(sK5(X5),sK0,sK1) ),
inference(cnf_transformation,[],[f178]) ).
fof(f221,plain,
! [X5] :
( ~ in(X5,sK3)
| in(X5,the_carrier(sK1)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f222,plain,
! [X6,X7,X5] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X7)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X7))) != X6
| X5 != X7
| sK2 != topstr_closure(sK0,X6)
| ~ element(X7,the_carrier(sK1))
| ~ netstr_induced_subset(X6,sK0,sK1)
| ~ in(X5,the_carrier(sK1))
| in(X5,sK3) ),
inference(cnf_transformation,[],[f178]) ).
fof(f223,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f178]) ).
fof(f225,plain,
! [X0] :
( ~ top_str(X0)
| empty(sK9(X0)) ),
inference(cnf_transformation,[],[f179]) ).
fof(f226,plain,
! [X0] :
( ~ top_str(X0)
| element(sK9(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f179]) ).
fof(f231,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty(sK10(X0)) ),
inference(cnf_transformation,[],[f180]) ).
fof(f232,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| element(sK10(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f180]) ).
fof(f234,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f181]) ).
fof(f236,plain,
! [X0] :
( empty(X0)
| ~ empty(sK12(X0)) ),
inference(cnf_transformation,[],[f182]) ).
fof(f237,plain,
! [X0] :
( empty(X0)
| element(sK12(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f182]) ).
fof(f241,plain,
! [X0] :
( empty(X0)
| ~ empty(sK13(X0)) ),
inference(cnf_transformation,[],[f183]) ).
fof(f242,plain,
! [X0] :
( empty(X0)
| element(sK13(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f183]) ).
fof(f244,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| element(sK14(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f184]) ).
fof(f247,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| element(sK15(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f185]) ).
fof(f250,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ empty(sK16(X0)) ),
inference(cnf_transformation,[],[f186]) ).
fof(f251,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| element(sK16(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f186]) ).
fof(f261,plain,
! [X0] : ~ empty(sK17(X0)),
inference(cnf_transformation,[],[f187]) ).
fof(f262,plain,
! [X0] : element(sK17(X0),powerset(powerset(X0))),
inference(cnf_transformation,[],[f187]) ).
fof(f264,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ~ empty(sK18(X0)) ),
inference(cnf_transformation,[],[f188]) ).
fof(f265,plain,
! [X0] :
( ~ one_sorted_str(X0)
| element(sK18(X0),powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f188]) ).
fof(f266,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0)
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| X3 = X7 ),
inference(cnf_transformation,[],[f111]) ).
fof(f267,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0)
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| X2 = X6 ),
inference(cnf_transformation,[],[f111]) ).
fof(f268,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0)
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| X1 = X5 ),
inference(cnf_transformation,[],[f111]) ).
fof(f269,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0)
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| X0 = X4 ),
inference(cnf_transformation,[],[f111]) ).
fof(f270,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0)
| net_str(net_str_of(X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f271,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0)
| strict_net_str(net_str_of(X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f272,plain,
! [X0] :
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f114]) ).
fof(f273,plain,
! [X0] :
( empty(X0)
| ~ empty(sK19(X0)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f274,plain,
! [X0] :
( empty(X0)
| element(sK19(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f275,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f276,plain,
! [X0] : empty(sK20(X0)),
inference(cnf_transformation,[],[f190]) ).
fof(f277,plain,
! [X0] : element(sK20(X0),powerset(X0)),
inference(cnf_transformation,[],[f190]) ).
fof(f279,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(sK21(X0)) ),
inference(cnf_transformation,[],[f191]) ).
fof(f280,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| element(sK21(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f191]) ).
fof(f282,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| element(sK22(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f192]) ).
fof(f284,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ empty(sK23(X0)) ),
inference(cnf_transformation,[],[f193]) ).
fof(f285,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| element(sK23(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f193]) ).
fof(f290,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f131]) ).
fof(f292,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| ~ one_sorted_str(X0)
| ~ empty_carrier(net_str_of(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f294,plain,
empty(sK24),
inference(cnf_transformation,[],[f194]) ).
fof(f296,plain,
relation(sK25),
inference(cnf_transformation,[],[f195]) ).
fof(f297,plain,
~ empty(sK25),
inference(cnf_transformation,[],[f195]) ).
fof(f298,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f300,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f301,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| ~ strict_net_str(X1,X0)
| net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f196]) ).
fof(f303,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f196]) ).
fof(f304,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| net_str(netstr_restr_to_element(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f305,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| strict_net_str(netstr_restr_to_element(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f306,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f307,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f143]) ).
fof(f308,plain,
! [X2,X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subnet(X2,X0,X1)
| net_str(X2,X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f309,plain,
! [X2,X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subnet(X2,X0,X1)
| directed_relstr(X2) ),
inference(cnf_transformation,[],[f145]) ).
fof(f310,plain,
! [X2,X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subnet(X2,X0,X1)
| transitive_relstr(X2) ),
inference(cnf_transformation,[],[f145]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subnet(X2,X0,X1)
| ~ empty_carrier(X2) ),
inference(cnf_transformation,[],[f145]) ).
fof(f312,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f49]) ).
fof(f313,plain,
~ empty_carrier(sK26),
inference(cnf_transformation,[],[f197]) ).
fof(f314,plain,
one_sorted_str(sK26),
inference(cnf_transformation,[],[f197]) ).
fof(f315,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f147]) ).
fof(f317,plain,
! [X0] :
( ~ one_sorted_str(X0)
| strict_net_str(sK27(X0),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f318,plain,
! [X0] :
( ~ one_sorted_str(X0)
| net_str(sK27(X0),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f320,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty_carrier(netstr_restr_to_element(X0,X1,X2)) ),
inference(cnf_transformation,[],[f152]) ).
fof(f321,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| directed_relstr(netstr_restr_to_element(X0,X1,X2)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f323,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| transitive_relstr(netstr_restr_to_element(X0,X1,X2)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f325,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| directed_relstr(sK28(X0,X1)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f326,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| strict_net_str(sK28(X0,X1),X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f327,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| transitive_relstr(sK28(X0,X1)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f328,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty_carrier(sK28(X0,X1)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f329,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| subnet(sK28(X0,X1),X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
fof(f332,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| relation(the_mapping(X0,X1)) ),
inference(cnf_transformation,[],[f158]) ).
fof(f333,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_mapping(X0,X1)) ),
inference(cnf_transformation,[],[f158]) ).
fof(f334,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f335,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f336,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| netstr_restr_to_element(X0,X1,X2) = subnetstr_of_element(X0,X1,X2) ),
inference(cnf_transformation,[],[f162]) ).
fof(f337,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f163]) ).
fof(f338,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f165]) ).
fof(f339,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| subnet(subnetstr_of_element(X0,X1,X2),X0,X1) ),
inference(cnf_transformation,[],[f167]) ).
fof(f340,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| strict_net_str(subnetstr_of_element(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f341,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f342,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| rel_str(X1) ),
inference(cnf_transformation,[],[f169]) ).
fof(f343,plain,
! [X2,X0,X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ netstr_induced_subset(X2,X0,X1)
| element(X2,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f171]) ).
fof(f344,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0)) ),
inference(cnf_transformation,[],[f173]) ).
fof(f345,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0)) ),
inference(cnf_transformation,[],[f173]) ).
fof(f346,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| function(the_mapping(X0,X1)) ),
inference(cnf_transformation,[],[f173]) ).
fof(f347,plain,
! [X0,X1] :
( in(sK29(X0,X1),X0)
| in(sK29(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f201]) ).
fof(f348,plain,
! [X0,X1] :
( ~ in(sK29(X0,X1),X0)
| ~ in(sK29(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f201]) ).
fof(f349,plain,
! [X6,X7] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X7)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X7))) != X6
| sK2 != topstr_closure(sK0,X6)
| ~ element(X7,the_carrier(sK1))
| ~ netstr_induced_subset(X6,sK0,sK1)
| ~ in(X7,the_carrier(sK1))
| in(X7,sK3) ),
inference(equality_resolution,[],[f222]) ).
fof(f350,plain,
! [X7] :
( sK2 != topstr_closure(sK0,relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X7)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X7))))
| ~ element(X7,the_carrier(sK1))
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X7)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X7))),sK0,sK1)
| ~ in(X7,the_carrier(sK1))
| in(X7,sK3) ),
inference(equality_resolution,[],[f349]) ).
fof(f351,plain,
! [X11,X12] :
( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X12)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X12))) != X11
| sK2 != topstr_closure(sK0,X11)
| ~ element(X12,the_carrier(sK1))
| ~ netstr_induced_subset(X11,sK0,sK1)
| ~ in(X12,the_carrier(sK1))
| in(X12,sK4) ),
inference(equality_resolution,[],[f215]) ).
fof(f352,plain,
! [X12] :
( sK2 != topstr_closure(sK0,relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X12)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X12))))
| ~ element(X12,the_carrier(sK1))
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X12)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X12))),sK0,sK1)
| ~ in(X12,the_carrier(sK1))
| in(X12,sK4) ),
inference(equality_resolution,[],[f351]) ).
tcf(c_49,negated_conjecture,
sK3 != sK4,
inference(cnf_transformation,[],[f223]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( in(X0,sK3)
| ~ element(X0,the_carrier(sK1))
| ~ in(X0,the_carrier(sK1))
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0)))) != sK2 ) ),
inference(cnf_transformation,[],[f350]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( in(X0,the_carrier(sK1))
| ~ in(X0,sK3) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( netstr_induced_subset(sK5(X0),sK0,sK1)
| ~ in(X0,sK3) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( element(sK6(X0),the_carrier(sK1))
| ~ in(X0,sK3) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( ( topstr_closure(sK0,sK5(X0)) = sK2 )
| ~ in(X0,sK3) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] :
( ( sK6(X0) = X0 )
| ~ in(X0,sK3) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(X0))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(X0)))) = sK5(X0) )
| ~ in(X0,sK3) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_57,negated_conjecture,
! [X0: $i] :
( in(X0,sK4)
| ~ element(X0,the_carrier(sK1))
| ~ in(X0,the_carrier(sK1))
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0)))) != sK2 ) ),
inference(cnf_transformation,[],[f352]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( in(X0,the_carrier(sK1))
| ~ in(X0,sK4) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( netstr_induced_subset(sK7(X0),sK0,sK1)
| ~ in(X0,sK4) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] :
( element(sK8(X0),the_carrier(sK1))
| ~ in(X0,sK4) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_61,negated_conjecture,
! [X0: $i] :
( ( topstr_closure(sK0,sK7(X0)) = sK2 )
| ~ in(X0,sK4) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( ( sK8(X0) = X0 )
| ~ in(X0,sK4) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(X0))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(X0)))) = sK7(X0) )
| ~ in(X0,sK4) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_64,negated_conjecture,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f208]) ).
tcf(c_65,negated_conjecture,
topological_space(sK0),
inference(cnf_transformation,[],[f207]) ).
tcf(c_66,negated_conjecture,
top_str(sK0),
inference(cnf_transformation,[],[f206]) ).
tcf(c_67,negated_conjecture,
~ empty_carrier(sK1),
inference(cnf_transformation,[],[f205]) ).
tcf(c_68,negated_conjecture,
transitive_relstr(sK1),
inference(cnf_transformation,[],[f204]) ).
tcf(c_69,negated_conjecture,
directed_relstr(sK1),
inference(cnf_transformation,[],[f203]) ).
tcf(c_70,negated_conjecture,
net_str(sK1,sK0),
inference(cnf_transformation,[],[f202]) ).
tcf(c_71,plain,
! [X0: $i] :
( element(sK9(X0),powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_72,plain,
! [X0: $i] :
( empty(sK9(X0))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_74,plain,
! [X0: $i] :
( element(sK10(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_75,plain,
! [X0: $i] :
( empty(sK10(X0))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_80,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f234]) ).
tcf(c_82,plain,
! [X0: $i] :
( empty(X0)
| element(sK12(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_83,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK12(X0)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_87,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_88,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK13(X0)) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_90,plain,
! [X0: $i] :
( element(sK14(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_92,plain,
! [X0: $i] :
( element(sK15(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_95,plain,
! [X0: $i] :
( empty_carrier(X0)
| element(sK16(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_96,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(sK16(X0)) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_104,plain,
! [X0: $i] : element(sK17(X0),powerset(powerset(X0))),
inference(cnf_transformation,[],[f262]) ).
tcf(c_105,plain,
! [X0: $i] : ~ empty(sK17(X0)),
inference(cnf_transformation,[],[f261]) ).
tcf(c_107,plain,
! [X0: $i] :
( element(sK18(X0),powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f265]) ).
tcf(c_108,plain,
! [X0: $i] :
( ~ one_sorted_str(X0)
| ~ empty(sK18(X0)) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X0 = X4 )
| ~ function(X3)
| ~ one_sorted_str(X0)
| ~ relation_of2(X2,X1,X1)
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ( net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7) ) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X1 = X5 )
| ~ function(X3)
| ~ one_sorted_str(X0)
| ~ relation_of2(X2,X1,X1)
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ( net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7) ) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X2 = X6 )
| ~ function(X3)
| ~ one_sorted_str(X0)
| ~ relation_of2(X2,X1,X1)
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ( net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7) ) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X3 = X7 )
| ~ function(X3)
| ~ one_sorted_str(X0)
| ~ relation_of2(X2,X1,X1)
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ( net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7) ) ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( strict_net_str(net_str_of(X2,X1,X3,X0),X2)
| ~ function(X0)
| ~ one_sorted_str(X2)
| ~ relation_of2(X3,X1,X1)
| ~ quasi_total(X0,X1,the_carrier(X2))
| ~ relation_of2(X0,X1,the_carrier(X2)) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( net_str(net_str_of(X2,X1,X3,X0),X2)
| ~ function(X0)
| ~ one_sorted_str(X2)
| ~ relation_of2(X3,X1,X1)
| ~ quasi_total(X0,X1,the_carrier(X2))
| ~ relation_of2(X0,X1,the_carrier(X2)) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_116,plain,
! [X0: $i] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_117,plain,
! [X0: $i] :
( empty(X0)
| element(sK19(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_118,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK19(X0)) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_120,plain,
! [X0: $i] : element(sK20(X0),powerset(X0)),
inference(cnf_transformation,[],[f277]) ).
tcf(c_121,plain,
! [X0: $i] : empty(sK20(X0)),
inference(cnf_transformation,[],[f276]) ).
tcf(c_123,plain,
! [X0: $i] :
( empty_carrier(X0)
| element(sK21(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f280]) ).
tcf(c_124,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(sK21(X0)) ),
inference(cnf_transformation,[],[f279]) ).
tcf(c_125,plain,
! [X0: $i] :
( element(sK22(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_127,plain,
! [X0: $i] :
( empty_carrier(X0)
| element(sK23(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f285]) ).
tcf(c_128,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(sK23(X0)) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| ~ function(X3)
| ~ one_sorted_str(X0)
| ~ relation_of2(X2,X1,X1)
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ empty_carrier(net_str_of(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_137,plain,
empty(sK24),
inference(cnf_transformation,[],[f294]) ).
tcf(c_140,plain,
~ empty(sK25),
inference(cnf_transformation,[],[f297]) ).
tcf(c_141,plain,
relation(sK25),
inference(cnf_transformation,[],[f296]) ).
tcf(c_142,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f298]) ).
tcf(c_143,plain,
! [X0: $i] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( ( net_str_of(X1,the_carrier(X0),the_InternalRel(X0),the_mapping(X1,X0)) = X0 )
| ~ one_sorted_str(X1)
| ~ strict_net_str(X0,X1)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f301]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f302]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| strict_net_str(netstr_restr_to_element(X2,X1,X0),X2)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| net_str(netstr_restr_to_element(X2,X1,X0),X2)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f304]) ).
tcf(c_150,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| ~ empty_carrier(X0)
| ~ net_str(X2,X1)
| ~ subnet(X0,X1,X2) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive_relstr(X0)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| ~ net_str(X2,X1)
| ~ subnet(X0,X1,X2) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( directed_relstr(X0)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| ~ net_str(X2,X1)
| ~ subnet(X0,X1,X2) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| net_str(X0,X1)
| ~ one_sorted_str(X1)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| ~ net_str(X2,X1)
| ~ subnet(X0,X1,X2) ),
inference(cnf_transformation,[],[f308]) ).
tcf(c_156,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f312]) ).
tcf(c_157,plain,
one_sorted_str(sK26),
inference(cnf_transformation,[],[f314]) ).
tcf(c_158,plain,
~ empty_carrier(sK26),
inference(cnf_transformation,[],[f313]) ).
tcf(c_159,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f315]) ).
tcf(c_161,plain,
! [X0: $i] :
( net_str(sK27(X0),X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f318]) ).
tcf(c_162,plain,
! [X0: $i] :
( strict_net_str(sK27(X0),X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f317]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X1))
| ~ empty_carrier(netstr_restr_to_element(X0,X1,X2)) ),
inference(cnf_transformation,[],[f320]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| transitive_relstr(netstr_restr_to_element(X2,X1,X0))
| ~ one_sorted_str(X2)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| directed_relstr(netstr_restr_to_element(X2,X1,X0))
| ~ one_sorted_str(X2)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f321]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| subnet(sK28(X1,X0),X1,X0)
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f329]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X0)
| ~ empty_carrier(sK28(X0,X1)) ),
inference(cnf_transformation,[],[f328]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| transitive_relstr(sK28(X1,X0))
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f327]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| strict_net_str(sK28(X1,X0),X1)
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f326]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| directed_relstr(sK28(X1,X0))
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f325]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| ~ empty(the_mapping(X0,X1)) ),
inference(cnf_transformation,[],[f333]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| relation(the_mapping(X1,X0))
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f332]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f334]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_as_subset(X1,X2,X0) = relation_rng(X0) )
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f335]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| ( subnetstr_of_element(X2,X1,X0) = netstr_restr_to_element(X2,X1,X0) )
| ~ one_sorted_str(X2)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f336]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(relation_rng_as_subset(X1,X2,X0),powerset(X2))
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f337]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f338]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| strict_net_str(subnetstr_of_element(X2,X1,X0),X2)
| ~ one_sorted_str(X2)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f340]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| subnet(subnetstr_of_element(X2,X1,X0),X2,X1)
| ~ one_sorted_str(X2)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f339]) ).
tcf(c_185,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f341]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] :
( rel_str(X0)
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f342]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| element(X0,powerset(the_carrier(X1)))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ netstr_induced_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f343]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( function(the_mapping(X1,X0))
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f346]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( quasi_total(the_mapping(X1,X0),the_carrier(X0),the_carrier(X1))
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f345]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( relation_of2_as_subset(the_mapping(X1,X0),the_carrier(X0),the_carrier(X1))
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f344]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK29(X0,X1),X1)
| ~ in(sK29(X0,X1),X0) ),
inference(cnf_transformation,[],[f348]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i] :
( in(sK29(X0,X1),X1)
| in(sK29(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f347]) ).
tcf(c_197,plain,
( one_sorted_str(sK0)
| ~ top_str(sK0) ),
inference(instantiation,[status(thm)],[c_185]) ).
tcf(c_213,plain,
( net_str(sK27(sK0),sK0)
| ~ one_sorted_str(sK0) ),
inference(instantiation,[status(thm)],[c_161]) ).
tcf(c_236,plain,
( empty(sK10(sK0))
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_256,plain,
( empty_carrier(sK0)
| ~ top_str(sK0)
| ~ topological_space(sK0)
| ~ empty(sK23(sK0)) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_257,plain,
( element(sK22(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_260,plain,
( empty_carrier(sK0)
| ~ top_str(sK0)
| ~ topological_space(sK0)
| ~ empty(sK16(sK0)) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_261,plain,
( element(sK15(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_262,plain,
( element(sK14(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_263,plain,
( element(sK10(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_266,plain,
( empty_carrier(sK0)
| element(sK23(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_267,plain,
( empty_carrier(sK0)
| element(sK16(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ topological_space(sK0) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_356,plain,
! [X0: $i] :
( element(sK9(X0),powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_71]) ).
tcf(c_358,plain,
! [X0: $i] :
( empty(sK9(X0))
| ~ top_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_72]) ).
tcf(c_362,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_185]) ).
tcf(c_384,plain,
! [X0: $i] :
( net_str(sK27(X0),X0)
| ~ one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_161]) ).
tcf(c_386,plain,
! [X0: $i] :
( strict_net_str(sK27(X0),X0)
| ~ one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_162]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_134]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_as_subset(X1,X2,X0) = relation_rng(X0) )
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_147,c_179]) ).
tcf(c_430,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(relation_rng_as_subset(X1,X2,X0),powerset(X2))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_147,c_181]) ).
tcf(c_2555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ element(X0,powerset(cartesian_product2(X2,X3)))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_416,c_142]) ).
tcf(c_2556,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ~ empty(relation_rng(X0))
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(unflattening,[status(thm)],[c_2555]) ).
tcf(c_2569,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(relation_rng(X0))
| ( X0 != sK25 ) ),
inference(resolution_lifted,[status(thm)],[c_142,c_141]) ).
tcf(c_2570,plain,
( empty(sK25)
| ~ empty(relation_rng(sK25)) ),
inference(unflattening,[status(thm)],[c_2569]) ).
tcf(c_2571,plain,
~ empty(relation_rng(sK25)),
inference(global_subsumption_just,[status(thm)],[c_2570,c_140,c_2570]) ).
tcf(c_2578,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| empty_carrier(X1)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(relation_rng(X2))
| ~ net_str(X1,X0)
| ( the_mapping(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_142,c_175]) ).
tcf(c_2579,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| empty(the_mapping(X0,X1))
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| ~ empty(relation_rng(the_mapping(X0,X1))) ),
inference(unflattening,[status(thm)],[c_2578]) ).
tcf(c_2581,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ~ empty(relation_rng(the_mapping(X0,X1)))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2579,c_174,c_2579]) ).
tcf(c_2582,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| ~ empty(relation_rng(the_mapping(X0,X1))) ),
inference(renaming,[status(thm)],[c_2581]) ).
tcf(c_2981,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( net_str_of(X2,the_carrier(X1),the_InternalRel(X1),the_mapping(X2,X1)) = X1 )
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X0)
| ~ net_str(X1,X2)
| ( X0 != X2 )
| ( sK27(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_145,c_386]) ).
tcf(c_2982,plain,
! [X0: $i] :
( ( net_str_of(X0,the_carrier(sK27(X0)),the_InternalRel(sK27(X0)),the_mapping(X0,sK27(X0))) = sK27(X0) )
| ~ one_sorted_str(X0)
| ~ net_str(sK27(X0),X0) ),
inference(unflattening,[status(thm)],[c_2981]) ).
tcf(c_2984,plain,
! [X0: $i] :
( ( net_str_of(X0,the_carrier(sK27(X0)),the_InternalRel(sK27(X0)),the_mapping(X0,sK27(X0))) = sK27(X0) )
| ~ one_sorted_str(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2982,c_161,c_2982]) ).
tcf(c_3161,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ top_str(X0)
| ~ empty(sK23(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_128]) ).
tcf(c_3162,plain,
( empty_carrier(sK0)
| ~ top_str(sK0)
| ~ empty(sK23(sK0)) ),
inference(unflattening,[status(thm)],[c_3161]) ).
tcf(c_3163,plain,
~ empty(sK23(sK0)),
inference(global_subsumption_just,[status(thm)],[c_3162,c_66,c_65,c_64,c_256]) ).
tcf(c_3168,plain,
! [X0: $i] :
( empty_carrier(X0)
| element(sK23(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_127]) ).
tcf(c_3169,plain,
( empty_carrier(sK0)
| element(sK23(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(unflattening,[status(thm)],[c_3168]) ).
tcf(c_3170,plain,
element(sK23(sK0),powerset(the_carrier(sK0))),
inference(global_subsumption_just,[status(thm)],[c_3169,c_66,c_65,c_64,c_266]) ).
tcf(c_3175,plain,
! [X0: $i] :
( element(sK22(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_125]) ).
tcf(c_3176,plain,
( element(sK22(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(unflattening,[status(thm)],[c_3175]) ).
tcf(c_3177,plain,
element(sK22(sK0),powerset(the_carrier(sK0))),
inference(global_subsumption_just,[status(thm)],[c_3176,c_66,c_65,c_257]) ).
tcf(c_3182,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ top_str(X0)
| ~ empty(sK16(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_96]) ).
tcf(c_3183,plain,
( empty_carrier(sK0)
| ~ top_str(sK0)
| ~ empty(sK16(sK0)) ),
inference(unflattening,[status(thm)],[c_3182]) ).
tcf(c_3184,plain,
~ empty(sK16(sK0)),
inference(global_subsumption_just,[status(thm)],[c_3183,c_66,c_65,c_64,c_260]) ).
tcf(c_3189,plain,
! [X0: $i] :
( empty_carrier(X0)
| element(sK16(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_95]) ).
tcf(c_3190,plain,
( empty_carrier(sK0)
| element(sK16(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(unflattening,[status(thm)],[c_3189]) ).
tcf(c_3191,plain,
element(sK16(sK0),powerset(the_carrier(sK0))),
inference(global_subsumption_just,[status(thm)],[c_3190,c_66,c_65,c_64,c_267]) ).
tcf(c_3196,plain,
! [X0: $i] :
( element(sK15(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_92]) ).
tcf(c_3197,plain,
( element(sK15(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(unflattening,[status(thm)],[c_3196]) ).
tcf(c_3198,plain,
element(sK15(sK0),powerset(the_carrier(sK0))),
inference(global_subsumption_just,[status(thm)],[c_3197,c_66,c_65,c_261]) ).
tcf(c_3203,plain,
! [X0: $i] :
( element(sK14(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_90]) ).
tcf(c_3204,plain,
( element(sK14(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(unflattening,[status(thm)],[c_3203]) ).
tcf(c_3205,plain,
element(sK14(sK0),powerset(the_carrier(sK0))),
inference(global_subsumption_just,[status(thm)],[c_3204,c_66,c_65,c_262]) ).
tcf(c_3210,plain,
! [X0: $i] :
( empty(sK10(X0))
| ~ top_str(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_75]) ).
tcf(c_3211,plain,
( empty(sK10(sK0))
| ~ top_str(sK0) ),
inference(unflattening,[status(thm)],[c_3210]) ).
tcf(c_3212,plain,
empty(sK10(sK0)),
inference(global_subsumption_just,[status(thm)],[c_3211,c_66,c_65,c_236]) ).
tcf(c_3217,plain,
! [X0: $i] :
( element(sK10(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_74]) ).
tcf(c_3218,plain,
( element(sK10(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(unflattening,[status(thm)],[c_3217]) ).
tcf(c_3219,plain,
element(sK10(sK0),powerset(the_carrier(sK0))),
inference(global_subsumption_just,[status(thm)],[c_3218,c_66,c_65,c_263]) ).
tcf(c_3233,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_362]) ).
tcf(c_3234,plain,
one_sorted_str(sK0),
inference(unflattening,[status(thm)],[c_3233]) ).
tcf(c_3238,plain,
! [X0: $i] :
( empty(sK9(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_358]) ).
tcf(c_3239,plain,
empty(sK9(sK0)),
inference(unflattening,[status(thm)],[c_3238]) ).
tcf(c_3243,plain,
! [X0: $i] :
( element(sK9(X0),powerset(the_carrier(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_356]) ).
tcf(c_3244,plain,
element(sK9(sK0),powerset(the_carrier(sK0))),
inference(unflattening,[status(thm)],[c_3243]) ).
tcf(c_3248,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_182]) ).
tcf(c_3249,plain,
! [X0: $i] :
( element(topstr_closure(sK0,X0),powerset(the_carrier(sK0)))
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(unflattening,[status(thm)],[c_3248]) ).
tcf(c_3760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( empty_carrier(X4)
| empty_carrier(X3)
| empty_carrier(X1)
| empty_carrier(X0)
| net_str(X2,X3)
| ~ one_sorted_str(X3)
| ~ one_sorted_str(X0)
| ~ directed_relstr(X4)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X4)
| ~ transitive_relstr(X1)
| ~ net_str(X4,X3)
| ~ net_str(X1,X0)
| ( X1 != X4 )
| ( X0 != X3 )
| ( sK28(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_155,c_169]) ).
tcf(c_3761,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| net_str(sK28(X1,X0),X1)
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(unflattening,[status(thm)],[c_3760]) ).
tcf(c_3790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( empty_carrier(X5)
| empty_carrier(X4)
| empty_carrier(X1)
| empty_carrier(X0)
| net_str(X3,X4)
| ~ one_sorted_str(X4)
| ~ one_sorted_str(X0)
| ~ directed_relstr(X5)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X5)
| ~ transitive_relstr(X1)
| ~ net_str(X5,X4)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X1))
| ( X1 != X5 )
| ( X0 != X4 )
| ( subnetstr_of_element(X0,X1,X2) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_155,c_184]) ).
tcf(c_3791,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| net_str(subnetstr_of_element(X2,X1,X0),X2)
| ~ one_sorted_str(X2)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(unflattening,[status(thm)],[c_3790]) ).
tcf(c_3817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( directed_relstr(X3)
| empty_carrier(X5)
| empty_carrier(X4)
| empty_carrier(X1)
| empty_carrier(X0)
| ~ one_sorted_str(X4)
| ~ one_sorted_str(X0)
| ~ directed_relstr(X5)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X5)
| ~ transitive_relstr(X1)
| ~ net_str(X5,X4)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X1))
| ( X1 != X5 )
| ( X0 != X4 )
| ( subnetstr_of_element(X0,X1,X2) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_154,c_184]) ).
tcf(c_3818,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| directed_relstr(subnetstr_of_element(X2,X1,X0))
| ~ one_sorted_str(X2)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(unflattening,[status(thm)],[c_3817]) ).
tcf(c_3844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( transitive_relstr(X3)
| empty_carrier(X5)
| empty_carrier(X4)
| empty_carrier(X1)
| empty_carrier(X0)
| ~ one_sorted_str(X4)
| ~ one_sorted_str(X0)
| ~ directed_relstr(X5)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X5)
| ~ transitive_relstr(X1)
| ~ net_str(X5,X4)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X1))
| ( X1 != X5 )
| ( X0 != X4 )
| ( subnetstr_of_element(X0,X1,X2) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_153,c_184]) ).
tcf(c_3845,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| transitive_relstr(subnetstr_of_element(X2,X1,X0))
| ~ one_sorted_str(X2)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(unflattening,[status(thm)],[c_3844]) ).
tcf(c_3871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( empty_carrier(X5)
| empty_carrier(X4)
| empty_carrier(X1)
| empty_carrier(X0)
| ~ one_sorted_str(X4)
| ~ one_sorted_str(X0)
| ~ directed_relstr(X5)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X5)
| ~ transitive_relstr(X1)
| ~ empty_carrier(X3)
| ~ net_str(X5,X4)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X1))
| ( X1 != X5 )
| ( X0 != X4 )
| ( subnetstr_of_element(X0,X1,X2) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_152,c_184]) ).
tcf(c_3872,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X1))
| ~ empty_carrier(subnetstr_of_element(X0,X1,X2)) ),
inference(unflattening,[status(thm)],[c_3871]) ).
tcf(c_4790,plain,
! [X0: $i] :
( net_str(sK27(X0),X0)
| ( X0 != sK26 ) ),
inference(resolution_lifted,[status(thm)],[c_384,c_157]) ).
tcf(c_4791,plain,
net_str(sK27(sK26),sK26),
inference(unflattening,[status(thm)],[c_4790]) ).
tcf(c_6525,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_as_subset(X1,X2,X0) = relation_rng(X0) )
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_428]) ).
tcf(c_6527,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(relation_rng_as_subset(X1,X2,X0),powerset(X2))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_430]) ).
tcf(c_6571,plain,
! [X0: $i] :
( element(topstr_closure(sK0,X0),powerset(the_carrier(sK0)))
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(prop_impl_just,[status(thm)],[c_3249]) ).
tcf(c_11302,definition,
iPr_def_10 = sK9(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_11303,definition,
iPr_def_11 = the_carrier(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_11304,definition,
iPr_def_12 = powerset(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_11305,definition,
iPr_def_13 = sK10(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_11306,definition,
iPr_def_14 = sK14(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_11307,definition,
iPr_def_15 = sK15(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_11308,definition,
iPr_def_16 = sK16(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_11309,definition,
iPr_def_17 = sK22(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_11310,definition,
iPr_def_18 = sK23(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_11311,definition,
iPr_def_19 = the_carrier(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_11312,plain,
element(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_3244,c_11303,c_11304,c_11302]) ).
tcf(c_11313,plain,
empty(iPr_def_10),
inference(demodulation,[status(thm)],[c_3239]) ).
tcf(c_11314,plain,
one_sorted_str(sK0),
inference(demodulation,[status(thm)],[c_3234]) ).
tcf(c_11315,plain,
element(iPr_def_13,iPr_def_12),
inference(demodulation,[status(thm)],[c_3219,c_11305]) ).
tcf(c_11316,plain,
empty(iPr_def_13),
inference(demodulation,[status(thm)],[c_3212]) ).
tcf(c_11317,plain,
element(iPr_def_14,iPr_def_12),
inference(demodulation,[status(thm)],[c_3205,c_11306]) ).
tcf(c_11318,plain,
element(iPr_def_15,iPr_def_12),
inference(demodulation,[status(thm)],[c_3198,c_11307]) ).
tcf(c_11319,plain,
element(iPr_def_16,iPr_def_12),
inference(demodulation,[status(thm)],[c_3191,c_11308]) ).
tcf(c_11320,plain,
~ empty(iPr_def_16),
inference(demodulation,[status(thm)],[c_3184]) ).
tcf(c_11321,plain,
element(iPr_def_17,iPr_def_12),
inference(demodulation,[status(thm)],[c_3177,c_11309]) ).
tcf(c_11322,plain,
element(iPr_def_18,iPr_def_12),
inference(demodulation,[status(thm)],[c_3170,c_11310]) ).
tcf(c_11323,plain,
~ empty(iPr_def_18),
inference(demodulation,[status(thm)],[c_3163]) ).
tcf(c_11324,negated_conjecture,
net_str(sK1,sK0),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_11325,negated_conjecture,
directed_relstr(sK1),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_11326,negated_conjecture,
transitive_relstr(sK1),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_11327,negated_conjecture,
~ empty_carrier(sK1),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_11328,negated_conjecture,
~ empty_carrier(sK0),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_11329,negated_conjecture,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(X0))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(X0)))) = sK7(X0) )
| ~ in(X0,sK4) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_11330,negated_conjecture,
! [X0: $i] :
( ( sK8(X0) = X0 )
| ~ in(X0,sK4) ),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_11331,negated_conjecture,
! [X0: $i] :
( ( topstr_closure(sK0,sK7(X0)) = sK2 )
| ~ in(X0,sK4) ),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_11332,negated_conjecture,
! [X0: $i] :
( element(sK8(X0),iPr_def_19)
| ~ in(X0,sK4) ),
inference(demodulation,[status(thm)],[c_60,c_11311]) ).
tcf(c_11333,negated_conjecture,
! [X0: $i] :
( netstr_induced_subset(sK7(X0),sK0,sK1)
| ~ in(X0,sK4) ),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_11334,negated_conjecture,
! [X0: $i] :
( in(X0,iPr_def_19)
| ~ in(X0,sK4) ),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_11335,negated_conjecture,
! [X0: $i] :
( in(X0,sK4)
| ~ element(X0,iPr_def_19)
| ~ in(X0,iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0)))) != sK2 ) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_11336,negated_conjecture,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(X0))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(X0)))) = sK5(X0) )
| ~ in(X0,sK3) ),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_11337,negated_conjecture,
! [X0: $i] :
( ( sK6(X0) = X0 )
| ~ in(X0,sK3) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_11338,negated_conjecture,
! [X0: $i] :
( ( topstr_closure(sK0,sK5(X0)) = sK2 )
| ~ in(X0,sK3) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_11339,negated_conjecture,
! [X0: $i] :
( element(sK6(X0),iPr_def_19)
| ~ in(X0,sK3) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_11340,negated_conjecture,
! [X0: $i] :
( netstr_induced_subset(sK5(X0),sK0,sK1)
| ~ in(X0,sK3) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_11341,negated_conjecture,
! [X0: $i] :
( in(X0,iPr_def_19)
| ~ in(X0,sK3) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_11342,negated_conjecture,
! [X0: $i] :
( in(X0,sK3)
| ~ element(X0,iPr_def_19)
| ~ in(X0,iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0)))) != sK2 ) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_11343,negated_conjecture,
sK3 != sK4,
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_13898,plain,
element(sK20(iPr_def_11),iPr_def_12),
inference(superposition,[status(thm)],[c_11304,c_120]) ).
tcf(c_13899,plain,
~ empty(iPr_def_12),
inference(superposition,[status(thm)],[c_11304,c_156]) ).
tcf(c_13908,plain,
element(sK17(iPr_def_11),powerset(iPr_def_12)),
inference(superposition,[status(thm)],[c_11304,c_104]) ).
tcf(c_13909,plain,
! [X0: $i] :
( element(topstr_closure(sK0,X0),iPr_def_12)
| ~ element(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_6571,c_11303,c_11304]) ).
tcf(c_13929,plain,
( empty(iPr_def_11)
| element(sK12(iPr_def_11),iPr_def_12) ),
inference(superposition,[status(thm)],[c_11304,c_82]) ).
tcf(c_13936,plain,
( empty(iPr_def_11)
| element(sK13(iPr_def_11),iPr_def_12) ),
inference(superposition,[status(thm)],[c_11304,c_87]) ).
tcf(c_13955,plain,
( empty(iPr_def_11)
| element(sK19(iPr_def_11),iPr_def_12) ),
inference(superposition,[status(thm)],[c_11304,c_117]) ).
tcf(c_14006,plain,
( empty_carrier(sK1)
| ~ one_sorted_str(sK1)
| ~ empty(iPr_def_19) ),
inference(superposition,[status(thm)],[c_11311,c_159]) ).
tcf(c_14007,plain,
( empty_carrier(sK0)
| ~ one_sorted_str(sK0)
| ~ empty(iPr_def_11) ),
inference(superposition,[status(thm)],[c_11303,c_159]) ).
tcf(c_14008,plain,
~ empty(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_14007,c_11328,c_11314]) ).
tcf(c_14009,plain,
( ~ one_sorted_str(sK1)
| ~ empty(iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14006,c_11327]) ).
tcf(c_14012,plain,
element(sK19(iPr_def_11),iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_13955,c_14008]) ).
tcf(c_14013,plain,
element(sK13(iPr_def_11),iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_13936,c_14008]) ).
tcf(c_14014,plain,
element(sK12(iPr_def_11),iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_13929,c_14008]) ).
tcf(c_14021,plain,
( rel_str(sK1)
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_186]) ).
tcf(c_14022,plain,
! [X0: $i] :
( rel_str(sK27(X0))
| ~ one_sorted_str(X0) ),
inference(superposition,[status(thm)],[c_161,c_186]) ).
tcf(c_14023,plain,
rel_str(sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_14021,c_11314]) ).
tcf(c_14026,plain,
( rel_str(sK27(sK0))
| ~ one_sorted_str(sK0) ),
inference(instantiation,[status(thm)],[c_14022]) ).
tcf(c_14031,plain,
( element(sK18(sK1),powerset(powerset(iPr_def_19)))
| ~ one_sorted_str(sK1) ),
inference(superposition,[status(thm)],[c_11311,c_107]) ).
tcf(c_14032,plain,
( element(sK18(sK0),powerset(powerset(iPr_def_11)))
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11303,c_107]) ).
tcf(c_14033,plain,
( element(sK18(sK0),powerset(iPr_def_12))
| ~ one_sorted_str(sK0) ),
inference(light_normalisation,[status(thm)],[c_14032,c_11304]) ).
tcf(c_14034,plain,
element(sK18(sK0),powerset(iPr_def_12)),
inference(forward_subsumption_resolution,[status(thm)],[c_14033,c_11314]) ).
tcf(c_14043,plain,
( relation_of2_as_subset(the_InternalRel(sK1),iPr_def_19,iPr_def_19)
| ~ rel_str(sK1) ),
inference(superposition,[status(thm)],[c_11311,c_116]) ).
tcf(c_14044,plain,
( relation_of2_as_subset(the_InternalRel(sK0),iPr_def_11,iPr_def_11)
| ~ rel_str(sK0) ),
inference(superposition,[status(thm)],[c_11303,c_116]) ).
tcf(c_14045,plain,
! [X0: $i] :
( relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(superposition,[status(thm)],[c_116,c_147]) ).
tcf(c_14052,plain,
one_sorted_str(sK1),
inference(superposition,[status(thm)],[c_14023,c_150]) ).
tcf(c_14053,plain,
~ empty(iPr_def_19),
inference(global_subsumption_just,[status(thm)],[c_14009,c_14009,c_14052]) ).
tcf(c_14059,plain,
! [X0: $i] :
( one_sorted_str(sK27(X0))
| ~ one_sorted_str(X0) ),
inference(superposition,[status(thm)],[c_14022,c_150]) ).
tcf(c_14067,plain,
relation_of2_as_subset(the_InternalRel(sK1),iPr_def_19,iPr_def_19),
inference(global_subsumption_just,[status(thm)],[c_14043,c_14023,c_14043]) ).
tcf(c_14069,plain,
relation_of2(the_InternalRel(sK1),iPr_def_19,iPr_def_19),
inference(superposition,[status(thm)],[c_14067,c_147]) ).
tcf(c_14077,plain,
! [X0: $i] :
( in(sK29(X0,sK3),X0)
| ( X0 = sK3 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(X0,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(X0,sK3))))) = sK5(sK29(X0,sK3)) ) ),
inference(superposition,[status(thm)],[c_192,c_11336]) ).
tcf(c_14078,plain,
! [X0: $i] :
( in(sK29(X0,sK3),X0)
| ( X0 = sK3 )
| ( topstr_closure(sK0,sK5(sK29(X0,sK3))) = sK2 ) ),
inference(superposition,[status(thm)],[c_192,c_11338]) ).
tcf(c_14079,plain,
! [X0: $i] :
( in(sK29(X0,sK3),X0)
| ( X0 = sK3 )
| ( sK6(sK29(X0,sK3)) = sK29(X0,sK3) ) ),
inference(superposition,[status(thm)],[c_192,c_11337]) ).
tcf(c_14080,plain,
! [X0: $i] :
( in(sK29(X0,sK3),iPr_def_19)
| in(sK29(X0,sK3),X0)
| ( X0 = sK3 ) ),
inference(superposition,[status(thm)],[c_192,c_11341]) ).
tcf(c_14081,plain,
! [X0: $i] :
( in(sK29(X0,sK4),X0)
| ( X0 = sK4 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(X0,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(X0,sK4))))) = sK7(sK29(X0,sK4)) ) ),
inference(superposition,[status(thm)],[c_192,c_11329]) ).
tcf(c_14082,plain,
! [X0: $i] :
( in(sK29(X0,sK4),X0)
| ( X0 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(X0,sK4))) = sK2 ) ),
inference(superposition,[status(thm)],[c_192,c_11331]) ).
tcf(c_14083,plain,
! [X0: $i] :
( in(sK29(X0,sK4),X0)
| ( X0 = sK4 )
| ( sK8(sK29(X0,sK4)) = sK29(X0,sK4) ) ),
inference(superposition,[status(thm)],[c_192,c_11330]) ).
tcf(c_14084,plain,
! [X0: $i] :
( in(sK29(X0,sK4),iPr_def_19)
| in(sK29(X0,sK4),X0)
| ( X0 = sK4 ) ),
inference(superposition,[status(thm)],[c_192,c_11334]) ).
tcf(c_14085,plain,
! [X0: $i,X1: $i] :
( in(sK29(X1,X0),X1)
| ( X0 = X1 )
| ~ in(X0,sK29(X1,X0)) ),
inference(superposition,[status(thm)],[c_192,c_178]) ).
tcf(c_14087,plain,
! [X0: $i] :
( in(sK29(sK3,X0),X0)
| ( X0 = sK3 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,X0)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,X0))))) = sK5(sK29(sK3,X0)) ) ),
inference(superposition,[status(thm)],[c_192,c_11336]) ).
tcf(c_14088,plain,
! [X0: $i] :
( in(sK29(sK3,X0),X0)
| ( X0 = sK3 )
| ( topstr_closure(sK0,sK5(sK29(sK3,X0))) = sK2 ) ),
inference(superposition,[status(thm)],[c_192,c_11338]) ).
tcf(c_14089,plain,
! [X0: $i] :
( in(sK29(sK3,X0),X0)
| ( X0 = sK3 )
| ( sK6(sK29(sK3,X0)) = sK29(sK3,X0) ) ),
inference(superposition,[status(thm)],[c_192,c_11337]) ).
tcf(c_14090,plain,
! [X0: $i] :
( in(sK29(sK3,X0),iPr_def_19)
| in(sK29(sK3,X0),X0)
| ( X0 = sK3 ) ),
inference(superposition,[status(thm)],[c_192,c_11341]) ).
tcf(c_14091,plain,
! [X0: $i] :
( in(sK29(sK4,X0),X0)
| ( X0 = sK4 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,X0)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,X0))))) = sK7(sK29(sK4,X0)) ) ),
inference(superposition,[status(thm)],[c_192,c_11329]) ).
tcf(c_14092,plain,
! [X0: $i] :
( in(sK29(sK4,X0),X0)
| ( X0 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK4,X0))) = sK2 ) ),
inference(superposition,[status(thm)],[c_192,c_11331]) ).
tcf(c_14093,plain,
! [X0: $i] :
( in(sK29(sK4,X0),X0)
| ( X0 = sK4 )
| ( sK8(sK29(sK4,X0)) = sK29(sK4,X0) ) ),
inference(superposition,[status(thm)],[c_192,c_11330]) ).
tcf(c_14094,plain,
! [X0: $i] :
( in(sK29(sK4,X0),iPr_def_19)
| in(sK29(sK4,X0),X0)
| ( X0 = sK4 ) ),
inference(superposition,[status(thm)],[c_192,c_11334]) ).
tcf(c_14095,plain,
! [X0: $i,X1: $i] :
( in(sK29(X0,X1),X1)
| ( X0 = X1 )
| ~ in(X0,sK29(X0,X1)) ),
inference(superposition,[status(thm)],[c_192,c_178]) ).
tcf(c_14175,plain,
( empty_carrier(sK1)
| element(sK21(sK1),powerset(iPr_def_19))
| ~ one_sorted_str(sK1) ),
inference(superposition,[status(thm)],[c_11311,c_123]) ).
tcf(c_14176,plain,
( empty_carrier(sK0)
| element(sK21(sK0),powerset(iPr_def_11))
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11303,c_123]) ).
tcf(c_14177,plain,
( empty_carrier(sK0)
| element(sK21(sK0),iPr_def_12)
| ~ one_sorted_str(sK0) ),
inference(light_normalisation,[status(thm)],[c_14176,c_11304]) ).
tcf(c_14178,plain,
element(sK21(sK0),iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_14177,c_11328,c_11314]) ).
tcf(c_14179,plain,
element(sK21(sK1),powerset(iPr_def_19)),
inference(forward_subsumption_resolution,[status(thm)],[c_14175,c_11327,c_14052]) ).
tcf(c_14194,plain,
! [X0: $i,X1: $i] :
( element(relation_rng_as_subset(X1,iPr_def_11,X0),iPr_def_12)
| ~ relation_of2_as_subset(X0,X1,iPr_def_11) ),
inference(superposition,[status(thm)],[c_11304,c_6527]) ).
tcf(c_14202,plain,
( relation_of2(the_InternalRel(sK0),iPr_def_11,iPr_def_11)
| ~ rel_str(sK0) ),
inference(superposition,[status(thm)],[c_14044,c_147]) ).
tcf(c_14216,plain,
! [X0: $i] :
( in(sK29(X0,sK3),X0)
| ( X0 = sK3 )
| ~ in(iPr_def_19,sK29(X0,sK3)) ),
inference(superposition,[status(thm)],[c_14080,c_178]) ).
tcf(c_14225,plain,
( in(sK29(sK4,sK3),iPr_def_19)
| ( sK3 = sK4 ) ),
inference(superposition,[status(thm)],[c_14080,c_11334]) ).
tcf(c_14226,plain,
! [X0: $i] :
( in(sK29(X0,sK3),iPr_def_19)
| ( X0 = sK3 )
| ~ in(X0,sK29(X0,sK3)) ),
inference(superposition,[status(thm)],[c_14080,c_178]) ).
tcf(c_14227,plain,
! [X0: $i] :
( in(sK29(X0,sK3),iPr_def_19)
| ( X0 = sK3 )
| ~ in(sK29(X0,sK3),sK3) ),
inference(superposition,[status(thm)],[c_14080,c_191]) ).
tcf(c_14228,plain,
( in(sK29(iPr_def_19,sK3),iPr_def_19)
| ( sK3 = iPr_def_19 ) ),
inference(equality_factoring,[status(thm)],[c_14080]) ).
tcf(c_14232,plain,
in(sK29(sK4,sK3),iPr_def_19),
inference(forward_subsumption_resolution,[status(thm)],[c_14225,c_11343]) ).
tcf(c_14245,plain,
~ in(iPr_def_19,sK29(sK4,sK3)),
inference(superposition,[status(thm)],[c_14232,c_178]) ).
tcf(c_14252,plain,
! [X0: $i] :
( in(sK29(X0,sK4),X0)
| ( X0 = sK4 )
| ~ in(iPr_def_19,sK29(X0,sK4)) ),
inference(superposition,[status(thm)],[c_14084,c_178]) ).
tcf(c_14257,plain,
( in(sK29(sK3,sK4),iPr_def_19)
| ( sK3 = sK4 ) ),
inference(superposition,[status(thm)],[c_14084,c_11341]) ).
tcf(c_14262,plain,
! [X0: $i] :
( in(sK29(X0,sK4),iPr_def_19)
| ( X0 = sK4 )
| ~ in(X0,sK29(X0,sK4)) ),
inference(superposition,[status(thm)],[c_14084,c_178]) ).
tcf(c_14263,plain,
! [X0: $i] :
( in(sK29(X0,sK4),iPr_def_19)
| ( X0 = sK4 )
| ~ in(sK29(X0,sK4),sK4) ),
inference(superposition,[status(thm)],[c_14084,c_191]) ).
tcf(c_14264,plain,
( in(sK29(iPr_def_19,sK4),iPr_def_19)
| ( sK4 = iPr_def_19 ) ),
inference(equality_factoring,[status(thm)],[c_14084]) ).
tcf(c_14268,plain,
in(sK29(sK3,sK4),iPr_def_19),
inference(forward_subsumption_resolution,[status(thm)],[c_14257,c_11343]) ).
tcf(c_14281,plain,
~ in(iPr_def_19,sK29(sK3,sK4)),
inference(superposition,[status(thm)],[c_14268,c_178]) ).
tcf(c_14288,plain,
! [X0: $i] :
( in(sK29(sK3,X0),X0)
| ( X0 = sK3 )
| ~ in(iPr_def_19,sK29(sK3,X0)) ),
inference(superposition,[status(thm)],[c_14090,c_178]) ).
tcf(c_14297,plain,
! [X0: $i] :
( in(sK29(sK3,X0),iPr_def_19)
| ( X0 = sK3 )
| ~ in(X0,sK29(sK3,X0)) ),
inference(superposition,[status(thm)],[c_14090,c_178]) ).
tcf(c_14299,plain,
( in(sK29(sK3,iPr_def_19),iPr_def_19)
| ( sK3 = iPr_def_19 ) ),
inference(equality_factoring,[status(thm)],[c_14090]) ).
tcf(c_14317,plain,
! [X0: $i] :
( in(sK29(sK4,X0),X0)
| ( X0 = sK4 )
| ~ in(iPr_def_19,sK29(sK4,X0)) ),
inference(superposition,[status(thm)],[c_14094,c_178]) ).
tcf(c_14326,plain,
! [X0: $i] :
( in(sK29(sK4,X0),iPr_def_19)
| ( X0 = sK4 )
| ~ in(X0,sK29(sK4,X0)) ),
inference(superposition,[status(thm)],[c_14094,c_178]) ).
tcf(c_14328,plain,
( in(sK29(sK4,iPr_def_19),iPr_def_19)
| ( sK4 = iPr_def_19 ) ),
inference(equality_factoring,[status(thm)],[c_14094]) ).
tcf(c_14350,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14078,c_11329]) ).
tcf(c_14351,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 ) ),
inference(superposition,[status(thm)],[c_14078,c_11331]) ).
tcf(c_14352,plain,
( ( sK3 = sK4 )
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 ) ),
inference(superposition,[status(thm)],[c_14078,c_11330]) ).
tcf(c_14354,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( topstr_closure(sK0,sK5(sK29(X0,sK3))) = sK2 )
| ~ in(X0,sK29(X0,sK3)) ),
inference(superposition,[status(thm)],[c_14078,c_178]) ).
tcf(c_14355,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( topstr_closure(sK0,sK5(sK29(X0,sK3))) = sK2 )
| ~ in(sK29(X0,sK3),sK3) ),
inference(superposition,[status(thm)],[c_14078,c_191]) ).
tcf(c_14362,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14352,c_11343]) ).
tcf(c_14365,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14351,c_11343]) ).
tcf(c_14368,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14350,c_11343]) ).
tcf(c_14383,plain,
( ( sK3 = sK4 )
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14079,c_11329]) ).
tcf(c_14384,plain,
( ( sK3 = sK4 )
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 ) ),
inference(superposition,[status(thm)],[c_14079,c_11331]) ).
tcf(c_14385,plain,
( ( sK3 = sK4 )
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(superposition,[status(thm)],[c_14079,c_11330]) ).
tcf(c_14387,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( sK6(sK29(X0,sK3)) = sK29(X0,sK3) )
| ~ in(X0,sK29(X0,sK3)) ),
inference(superposition,[status(thm)],[c_14079,c_178]) ).
tcf(c_14388,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( sK6(sK29(X0,sK3)) = sK29(X0,sK3) )
| ~ in(sK29(X0,sK3),sK3) ),
inference(superposition,[status(thm)],[c_14079,c_191]) ).
tcf(c_14395,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14385,c_11343]) ).
tcf(c_14398,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14384,c_11343]) ).
tcf(c_14401,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14383,c_11343]) ).
tcf(c_14410,plain,
( element(sK2,iPr_def_12)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK5(sK29(sK4,sK3)),iPr_def_12) ),
inference(superposition,[status(thm)],[c_14362,c_13909]) ).
tcf(c_14418,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(X0),the_carrier(X0),the_InternalRel(X0)) = relation_rng(the_InternalRel(X0)) )
| ~ rel_str(X0) ),
inference(superposition,[status(thm)],[c_116,c_6525]) ).
tcf(c_14419,plain,
relation_rng_as_subset(iPr_def_19,iPr_def_19,the_InternalRel(sK1)) = relation_rng(the_InternalRel(sK1)),
inference(superposition,[status(thm)],[c_14067,c_6525]) ).
tcf(c_14420,plain,
( ( relation_rng_as_subset(iPr_def_11,iPr_def_11,the_InternalRel(sK0)) = relation_rng(the_InternalRel(sK0)) )
| ~ rel_str(sK0) ),
inference(superposition,[status(thm)],[c_14044,c_6525]) ).
tcf(c_14431,plain,
! [X0: $i] :
( quasi_total(the_mapping(X0,sK1),iPr_def_19,the_carrier(X0))
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_11311,c_189]) ).
tcf(c_14432,plain,
! [X0: $i] :
( quasi_total(the_mapping(X0,sK0),iPr_def_11,the_carrier(X0))
| ~ one_sorted_str(X0)
| ~ net_str(sK0,X0) ),
inference(superposition,[status(thm)],[c_11303,c_189]) ).
tcf(c_14433,plain,
! [X0: $i] :
( quasi_total(the_mapping(sK1,X0),the_carrier(X0),iPr_def_19)
| ~ one_sorted_str(sK1)
| ~ net_str(X0,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_189]) ).
tcf(c_14434,plain,
! [X0: $i] :
( quasi_total(the_mapping(sK0,X0),the_carrier(X0),iPr_def_11)
| ~ one_sorted_str(sK0)
| ~ net_str(X0,sK0) ),
inference(superposition,[status(thm)],[c_11303,c_189]) ).
tcf(c_14435,plain,
! [X0: $i] :
( quasi_total(the_mapping(sK0,X0),the_carrier(X0),iPr_def_11)
| ~ net_str(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14434,c_11314]) ).
tcf(c_14438,plain,
! [X0: $i] :
( quasi_total(the_mapping(sK1,X0),the_carrier(X0),iPr_def_19)
| ~ net_str(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14433,c_14052]) ).
tcf(c_14457,plain,
! [X0: $i] :
( relation_of2_as_subset(the_mapping(X0,sK1),iPr_def_19,the_carrier(X0))
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_11311,c_190]) ).
tcf(c_14458,plain,
! [X0: $i] :
( relation_of2_as_subset(the_mapping(X0,sK0),iPr_def_11,the_carrier(X0))
| ~ one_sorted_str(X0)
| ~ net_str(sK0,X0) ),
inference(superposition,[status(thm)],[c_11303,c_190]) ).
tcf(c_14459,plain,
! [X0: $i] :
( relation_of2_as_subset(the_mapping(sK1,X0),the_carrier(X0),iPr_def_19)
| ~ one_sorted_str(sK1)
| ~ net_str(X0,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_190]) ).
tcf(c_14460,plain,
! [X0: $i] :
( relation_of2_as_subset(the_mapping(sK0,X0),the_carrier(X0),iPr_def_11)
| ~ one_sorted_str(sK0)
| ~ net_str(X0,sK0) ),
inference(superposition,[status(thm)],[c_11303,c_190]) ).
tcf(c_14461,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_as_subset(the_carrier(X0),the_carrier(X1),the_mapping(X1,X0)) = relation_rng(the_mapping(X1,X0)) )
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) ),
inference(superposition,[status(thm)],[c_190,c_6525]) ).
tcf(c_14462,plain,
! [X0: $i,X1: $i] :
( relation_of2(the_mapping(X1,X0),the_carrier(X0),the_carrier(X1))
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) ),
inference(superposition,[status(thm)],[c_190,c_147]) ).
tcf(c_14463,plain,
! [X0: $i] :
( relation_of2_as_subset(the_mapping(sK0,X0),the_carrier(X0),iPr_def_11)
| ~ net_str(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14460,c_11314]) ).
tcf(c_14466,plain,
! [X0: $i] :
( relation_of2_as_subset(the_mapping(sK1,X0),the_carrier(X0),iPr_def_19)
| ~ net_str(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14459,c_14052]) ).
tcf(c_14495,plain,
element(sK18(sK1),powerset(powerset(iPr_def_19))),
inference(global_subsumption_just,[status(thm)],[c_14031,c_14031,c_14052]) ).
tcf(c_14501,plain,
( ( sK3 = iPr_def_19 )
| ~ in(iPr_def_19,sK29(iPr_def_19,sK3)) ),
inference(superposition,[status(thm)],[c_14228,c_178]) ).
tcf(c_14502,plain,
( ( sK3 = iPr_def_19 )
| ~ in(sK29(iPr_def_19,sK3),sK3) ),
inference(superposition,[status(thm)],[c_14228,c_191]) ).
tcf(c_14513,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14082,c_11336]) ).
tcf(c_14514,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 ) ),
inference(superposition,[status(thm)],[c_14082,c_11338]) ).
tcf(c_14515,plain,
( ( sK3 = sK4 )
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 ) ),
inference(superposition,[status(thm)],[c_14082,c_11337]) ).
tcf(c_14521,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(X0,sK4))) = sK2 )
| ~ in(X0,sK29(X0,sK4)) ),
inference(superposition,[status(thm)],[c_14082,c_178]) ).
tcf(c_14522,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(X0,sK4))) = sK2 )
| ~ in(sK29(X0,sK4),sK4) ),
inference(superposition,[status(thm)],[c_14082,c_191]) ).
tcf(c_14529,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14515,c_11343]) ).
tcf(c_14532,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14514,c_11343]) ).
tcf(c_14535,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14513,c_11343]) ).
tcf(c_14546,plain,
( ( sK3 = sK4 )
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14083,c_11336]) ).
tcf(c_14547,plain,
( ( sK3 = sK4 )
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 ) ),
inference(superposition,[status(thm)],[c_14083,c_11338]) ).
tcf(c_14548,plain,
( ( sK3 = sK4 )
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(superposition,[status(thm)],[c_14083,c_11337]) ).
tcf(c_14554,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( sK8(sK29(X0,sK4)) = sK29(X0,sK4) )
| ~ in(X0,sK29(X0,sK4)) ),
inference(superposition,[status(thm)],[c_14083,c_178]) ).
tcf(c_14555,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( sK8(sK29(X0,sK4)) = sK29(X0,sK4) )
| ~ in(sK29(X0,sK4),sK4) ),
inference(superposition,[status(thm)],[c_14083,c_191]) ).
tcf(c_14562,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14548,c_11343]) ).
tcf(c_14565,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14547,c_11343]) ).
tcf(c_14568,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14546,c_11343]) ).
tcf(c_14583,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14088,c_11329]) ).
tcf(c_14587,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( topstr_closure(sK0,sK5(sK29(sK3,X0))) = sK2 )
| ~ in(X0,sK29(sK3,X0)) ),
inference(superposition,[status(thm)],[c_14088,c_178]) ).
tcf(c_14592,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14583,c_11343]) ).
tcf(c_14606,plain,
( ( sK3 = sK4 )
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14089,c_11329]) ).
tcf(c_14610,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( sK6(sK29(sK3,X0)) = sK29(sK3,X0) )
| ~ in(X0,sK29(sK3,X0)) ),
inference(superposition,[status(thm)],[c_14089,c_178]) ).
tcf(c_14615,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14606,c_11343]) ).
tcf(c_14625,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14092,c_11336]) ).
tcf(c_14633,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK4,X0))) = sK2 )
| ~ in(X0,sK29(sK4,X0)) ),
inference(superposition,[status(thm)],[c_14092,c_178]) ).
tcf(c_14638,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14625,c_11343]) ).
tcf(c_14648,plain,
( ( sK3 = sK4 )
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14093,c_11336]) ).
tcf(c_14656,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( sK8(sK29(sK4,X0)) = sK29(sK4,X0) )
| ~ in(X0,sK29(sK4,X0)) ),
inference(superposition,[status(thm)],[c_14093,c_178]) ).
tcf(c_14661,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14648,c_11343]) ).
tcf(c_14669,plain,
( element(sK2,iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK7(sK29(sK4,sK3)),iPr_def_12) ),
inference(superposition,[status(thm)],[c_14365,c_13909]) ).
tcf(c_14677,plain,
( element(sK29(sK4,sK3),iPr_def_19)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ in(sK29(sK4,sK3),sK4) ),
inference(superposition,[status(thm)],[c_14395,c_11332]) ).
tcf(c_14685,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) = sK7(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14395,c_14368]) ).
tcf(c_14687,plain,
( element(sK7(sK29(sK4,sK3)),powerset(iPr_def_11))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_14368,c_6527]) ).
tcf(c_14688,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14368,c_11342]) ).
tcf(c_14689,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14368,c_11335]) ).
tcf(c_14690,plain,
( element(sK7(sK29(sK4,sK3)),iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_14687,c_11304]) ).
tcf(c_14749,plain,
! [X0: $i] :
( empty_carrier(sK0)
| empty_carrier(sK1)
| element(sK5(X0),powerset(the_carrier(sK0)))
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_11340,c_187]) ).
tcf(c_14750,plain,
! [X0: $i] :
( empty_carrier(sK0)
| empty_carrier(sK1)
| element(sK7(X0),powerset(the_carrier(sK0)))
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_11333,c_187]) ).
tcf(c_14751,plain,
! [X0: $i] :
( empty_carrier(sK0)
| empty_carrier(sK1)
| element(sK7(X0),iPr_def_12)
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ in(X0,sK4) ),
inference(light_normalisation,[status(thm)],[c_14750,c_11303,c_11304]) ).
tcf(c_14752,plain,
! [X0: $i] :
( element(sK7(X0),iPr_def_12)
| ~ in(X0,sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14751,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_14755,plain,
! [X0: $i] :
( empty_carrier(sK0)
| empty_carrier(sK1)
| element(sK5(X0),iPr_def_12)
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ in(X0,sK3) ),
inference(light_normalisation,[status(thm)],[c_14749,c_11303,c_11304]) ).
tcf(c_14756,plain,
! [X0: $i] :
( element(sK5(X0),iPr_def_12)
| ~ in(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14755,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_14785,plain,
( ( sK4 = iPr_def_19 )
| ~ in(iPr_def_19,sK29(iPr_def_19,sK4)) ),
inference(superposition,[status(thm)],[c_14264,c_178]) ).
tcf(c_14786,plain,
( ( sK4 = iPr_def_19 )
| ~ in(sK29(iPr_def_19,sK4),sK4) ),
inference(superposition,[status(thm)],[c_14264,c_191]) ).
tcf(c_14795,plain,
( ( sK3 = iPr_def_19 )
| ~ in(iPr_def_19,sK29(sK3,iPr_def_19)) ),
inference(superposition,[status(thm)],[c_14299,c_178]) ).
tcf(c_14802,plain,
( element(sK2,iPr_def_12)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK7(sK29(sK4,sK3)),iPr_def_12) ),
inference(superposition,[status(thm)],[c_14398,c_13909]) ).
tcf(c_14810,plain,
( element(sK2,iPr_def_12)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK7(sK29(sK3,sK4)),iPr_def_12) ),
inference(superposition,[status(thm)],[c_14529,c_13909]) ).
tcf(c_14818,plain,
( element(sK2,iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK7(sK29(sK3,sK4)),iPr_def_12) ),
inference(superposition,[status(thm)],[c_14532,c_13909]) ).
tcf(c_14826,plain,
( element(sK29(sK3,sK4),iPr_def_19)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ in(sK29(sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_14562,c_11332]) ).
tcf(c_14834,plain,
( element(sK2,iPr_def_12)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK5(sK29(sK3,sK4)),iPr_def_12) ),
inference(superposition,[status(thm)],[c_14565,c_13909]) ).
tcf(c_14845,plain,
( element(sK29(sK4,sK3),iPr_def_19)
| ( sK3 = sK4 )
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(superposition,[status(thm)],[c_14079,c_14677]) ).
tcf(c_14848,plain,
( element(sK29(sK4,sK3),iPr_def_19)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14845,c_11343]) ).
tcf(c_14864,plain,
( element(sK29(sK3,sK4),iPr_def_19)
| ( sK3 = sK4 )
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(superposition,[status(thm)],[c_14089,c_14826]) ).
tcf(c_14867,plain,
( element(sK29(sK3,sK4),iPr_def_19)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14864,c_11343]) ).
tcf(c_14876,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) = sK7(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14395,c_14401]) ).
tcf(c_14878,plain,
( element(sK7(sK29(sK4,sK3)),powerset(iPr_def_11))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_14401,c_6527]) ).
tcf(c_14879,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14401,c_11342]) ).
tcf(c_14880,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14401,c_11335]) ).
tcf(c_14883,plain,
( element(sK7(sK29(sK4,sK3)),iPr_def_12)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_14878,c_11304]) ).
tcf(c_14911,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| rel_str(netstr_restr_to_element(X2,X1,X0))
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_149,c_186]) ).
tcf(c_14955,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ( net_str_of(X0,the_carrier(netstr_restr_to_element(X0,X1,X2)),the_InternalRel(netstr_restr_to_element(X0,X1,X2)),the_mapping(X0,netstr_restr_to_element(X0,X1,X2))) = netstr_restr_to_element(X0,X1,X2) )
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X1))
| ~ net_str(netstr_restr_to_element(X0,X1,X2),X0) ),
inference(superposition,[status(thm)],[c_148,c_145]) ).
tcf(c_14956,plain,
! [X0: $i] :
( ( net_str_of(X0,the_carrier(sK27(X0)),the_InternalRel(sK27(X0)),the_mapping(X0,sK27(X0))) = sK27(X0) )
| ~ one_sorted_str(X0)
| ~ net_str(sK27(X0),X0) ),
inference(superposition,[status(thm)],[c_162,c_145]) ).
tcf(c_14957,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ( net_str_of(X0,the_carrier(sK28(X0,X1)),the_InternalRel(sK28(X0,X1)),the_mapping(X0,sK28(X0,X1))) = sK28(X0,X1) )
| ~ one_sorted_str(X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X0)
| ~ net_str(sK28(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_172,c_145]) ).
tcf(c_14980,plain,
( ( sK4 = iPr_def_19 )
| ~ in(iPr_def_19,sK29(sK4,iPr_def_19)) ),
inference(superposition,[status(thm)],[c_14328,c_178]) ).
tcf(c_14992,plain,
( element(relation_rng(the_InternalRel(sK1)),powerset(iPr_def_19))
| ~ relation_of2_as_subset(the_InternalRel(sK1),iPr_def_19,iPr_def_19) ),
inference(superposition,[status(thm)],[c_14419,c_6527]) ).
tcf(c_14993,plain,
element(relation_rng(the_InternalRel(sK1)),powerset(iPr_def_19)),
inference(forward_subsumption_resolution,[status(thm)],[c_14992,c_14067]) ).
tcf(c_15008,plain,
( ( sK3 = sK4 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14077,c_11329]) ).
tcf(c_15012,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(X0,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(X0,sK3))))) = sK5(sK29(X0,sK3)) )
| ~ in(X0,sK29(X0,sK3)) ),
inference(superposition,[status(thm)],[c_14077,c_178]) ).
tcf(c_15013,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(X0,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(X0,sK3))))) = sK5(sK29(X0,sK3)) )
| ~ in(sK29(X0,sK3),sK3) ),
inference(superposition,[status(thm)],[c_14077,c_191]) ).
tcf(c_15020,plain,
( ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15008,c_11343]) ).
tcf(c_15033,plain,
( ( sK3 = sK4 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14081,c_11336]) ).
tcf(c_15041,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(X0,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(X0,sK4))))) = sK7(sK29(X0,sK4)) )
| ~ in(X0,sK29(X0,sK4)) ),
inference(superposition,[status(thm)],[c_14081,c_178]) ).
tcf(c_15042,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(X0,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(X0,sK4))))) = sK7(sK29(X0,sK4)) )
| ~ in(sK29(X0,sK4),sK4) ),
inference(superposition,[status(thm)],[c_14081,c_191]) ).
tcf(c_15049,plain,
( ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15033,c_11343]) ).
tcf(c_15072,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,X0)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,X0))))) = sK5(sK29(sK3,X0)) )
| ~ in(X0,sK29(sK3,X0)) ),
inference(superposition,[status(thm)],[c_14087,c_178]) ).
tcf(c_15092,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,X0)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,X0))))) = sK7(sK29(sK4,X0)) )
| ~ in(X0,sK29(sK4,X0)) ),
inference(superposition,[status(thm)],[c_14091,c_178]) ).
tcf(c_15102,plain,
( element(sK5(sK29(sK3,sK4)),powerset(iPr_def_11))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_14535,c_6527]) ).
tcf(c_15103,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14535,c_11342]) ).
tcf(c_15104,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14535,c_11335]) ).
tcf(c_15105,plain,
( element(sK5(sK29(sK3,sK4)),iPr_def_12)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_15102,c_11304]) ).
tcf(c_15127,plain,
( element(sK5(sK29(sK3,sK4)),powerset(iPr_def_11))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_14568,c_6527]) ).
tcf(c_15128,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14568,c_11342]) ).
tcf(c_15129,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14568,c_11335]) ).
tcf(c_15130,plain,
( element(sK5(sK29(sK3,sK4)),iPr_def_12)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_15127,c_11304]) ).
tcf(c_15152,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = sK7(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14562,c_14592]) ).
tcf(c_15154,plain,
( element(sK7(sK29(sK3,sK4)),powerset(iPr_def_11))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_14592,c_6527]) ).
tcf(c_15155,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14592,c_11342]) ).
tcf(c_15156,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14592,c_11335]) ).
tcf(c_15157,plain,
( element(sK7(sK29(sK3,sK4)),iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_15154,c_11304]) ).
tcf(c_15183,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = sK7(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14562,c_14615]) ).
tcf(c_15185,plain,
( element(sK7(sK29(sK3,sK4)),powerset(iPr_def_11))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_14615,c_6527]) ).
tcf(c_15186,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14615,c_11342]) ).
tcf(c_15187,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14615,c_11335]) ).
tcf(c_15190,plain,
( element(sK7(sK29(sK3,sK4)),iPr_def_12)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_15185,c_11304]) ).
tcf(c_15280,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ( net_str_of(X0,the_carrier(subnetstr_of_element(X0,X1,X2)),the_InternalRel(subnetstr_of_element(X0,X1,X2)),the_mapping(X0,subnetstr_of_element(X0,X1,X2))) = subnetstr_of_element(X0,X1,X2) )
| ~ one_sorted_str(X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| ~ net_str(X1,X0)
| ~ element(X2,the_carrier(X1))
| ~ net_str(subnetstr_of_element(X0,X1,X2),X0) ),
inference(superposition,[status(thm)],[c_183,c_145]) ).
tcf(c_15312,plain,
( element(sK5(sK29(sK4,sK3)),powerset(iPr_def_11))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_14638,c_6527]) ).
tcf(c_15313,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14638,c_11342]) ).
tcf(c_15314,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14638,c_11335]) ).
tcf(c_15315,plain,
( element(sK5(sK29(sK4,sK3)),iPr_def_12)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_15312,c_11304]) ).
tcf(c_15335,plain,
( element(sK5(sK29(sK4,sK3)),powerset(iPr_def_11))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_14661,c_6527]) ).
tcf(c_15336,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14661,c_11342]) ).
tcf(c_15337,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14661,c_11335]) ).
tcf(c_15338,plain,
( element(sK5(sK29(sK4,sK3)),iPr_def_12)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_15335,c_11304]) ).
tcf(c_15363,plain,
( element(sK7(sK29(sK4,sK3)),powerset(iPr_def_11))
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_15020,c_6527]) ).
tcf(c_15364,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_15020,c_11342]) ).
tcf(c_15365,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_15020,c_11335]) ).
tcf(c_15366,plain,
( element(sK7(sK29(sK4,sK3)),iPr_def_12)
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_15363,c_11304]) ).
tcf(c_15393,plain,
( element(sK7(sK29(sK3,sK4)),powerset(iPr_def_11))
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_15049,c_6527]) ).
tcf(c_15394,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_15049,c_11342]) ).
tcf(c_15395,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_15049,c_11335]) ).
tcf(c_15396,plain,
( element(sK7(sK29(sK3,sK4)),iPr_def_12)
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_15393,c_11304]) ).
tcf(c_15415,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_14688,c_14365,c_14688]) ).
tcf(c_15427,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_15020,c_15415]) ).
tcf(c_15428,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14401,c_15415]) ).
tcf(c_15429,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14368,c_15415]) ).
tcf(c_15430,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14395,c_15415]) ).
tcf(c_15458,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_14689,c_14365,c_14689]) ).
tcf(c_15470,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_15020,c_15458]) ).
tcf(c_15471,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14401,c_15458]) ).
tcf(c_15472,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14368,c_15458]) ).
tcf(c_15473,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14395,c_15458]) ).
tcf(c_15498,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ empty(relation_rng(the_mapping(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_2582]) ).
tcf(c_15502,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_14879,c_14398,c_14879]) ).
tcf(c_15514,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_15020,c_15502]) ).
tcf(c_15515,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14401,c_15502]) ).
tcf(c_15517,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14395,c_15502]) ).
tcf(c_15535,plain,
( in(sK29(sK3,sK4),sK4)
| in(sK29(sK3,sK4),sK3)
| ( sK3 = sK4 ) ),
inference(instantiation,[status(thm)],[c_192]) ).
tcf(c_15564,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_14880,c_14398,c_14880]) ).
tcf(c_15576,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_15020,c_15564]) ).
tcf(c_15577,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14401,c_15564]) ).
tcf(c_15579,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14395,c_15564]) ).
tcf(c_15611,plain,
! [X0: $i,X1: $i,X2: $i] :
( strict_net_str(net_str_of(X2,the_carrier(X1),the_InternalRel(X1),X0),X2)
| ~ rel_str(X1)
| ~ function(X0)
| ~ one_sorted_str(X2)
| ~ quasi_total(X0,the_carrier(X1),the_carrier(X2))
| ~ relation_of2(X0,the_carrier(X1),the_carrier(X2)) ),
inference(superposition,[status(thm)],[c_14045,c_114]) ).
tcf(c_15612,plain,
! [X0: $i,X1: $i] :
( strict_net_str(net_str_of(X1,iPr_def_19,the_InternalRel(sK1),X0),X1)
| ~ function(X0)
| ~ one_sorted_str(X1)
| ~ quasi_total(X0,iPr_def_19,the_carrier(X1))
| ~ relation_of2(X0,iPr_def_19,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_14069,c_114]) ).
tcf(c_15613,plain,
! [X0: $i,X1: $i] :
( strict_net_str(net_str_of(X1,iPr_def_11,the_InternalRel(sK0),X0),X1)
| ~ rel_str(sK0)
| ~ function(X0)
| ~ one_sorted_str(X1)
| ~ quasi_total(X0,iPr_def_11,the_carrier(X1))
| ~ relation_of2(X0,iPr_def_11,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_14202,c_114]) ).
tcf(c_15646,plain,
! [X0: $i,X1: $i,X2: $i] :
( net_str(net_str_of(X2,the_carrier(X1),the_InternalRel(X1),X0),X2)
| ~ rel_str(X1)
| ~ function(X0)
| ~ one_sorted_str(X2)
| ~ quasi_total(X0,the_carrier(X1),the_carrier(X2))
| ~ relation_of2(X0,the_carrier(X1),the_carrier(X2)) ),
inference(superposition,[status(thm)],[c_14045,c_115]) ).
tcf(c_15647,plain,
! [X0: $i,X1: $i] :
( net_str(net_str_of(X1,iPr_def_19,the_InternalRel(sK1),X0),X1)
| ~ function(X0)
| ~ one_sorted_str(X1)
| ~ quasi_total(X0,iPr_def_19,the_carrier(X1))
| ~ relation_of2(X0,iPr_def_19,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_14069,c_115]) ).
tcf(c_15648,plain,
! [X0: $i,X1: $i] :
( net_str(net_str_of(X1,iPr_def_11,the_InternalRel(sK0),X0),X1)
| ~ rel_str(sK0)
| ~ function(X0)
| ~ one_sorted_str(X1)
| ~ quasi_total(X0,iPr_def_11,the_carrier(X1))
| ~ relation_of2(X0,iPr_def_11,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_14202,c_115]) ).
tcf(c_15699,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK1)
| empty_carrier(X1)
| ( subnetstr_of_element(X1,sK1,X0) = netstr_restr_to_element(X1,sK1,X0) )
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ one_sorted_str(X1)
| ~ net_str(sK1,X1)
| ~ element(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_11311,c_180]) ).
tcf(c_15700,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK0)
| empty_carrier(X1)
| ( subnetstr_of_element(X1,sK0,X0) = netstr_restr_to_element(X1,sK0,X0) )
| ~ directed_relstr(sK0)
| ~ transitive_relstr(sK0)
| ~ one_sorted_str(X1)
| ~ net_str(sK0,X1)
| ~ element(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_11303,c_180]) ).
tcf(c_15701,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ( subnetstr_of_element(X1,sK0,X0) = netstr_restr_to_element(X1,sK0,X0) )
| ~ directed_relstr(sK0)
| ~ transitive_relstr(sK0)
| ~ one_sorted_str(X1)
| ~ net_str(sK0,X1)
| ~ element(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15700,c_11328]) ).
tcf(c_15709,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ( subnetstr_of_element(X1,sK1,X0) = netstr_restr_to_element(X1,sK1,X0) )
| ~ one_sorted_str(X1)
| ~ net_str(sK1,X1)
| ~ element(X0,iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15699,c_11327,c_11325,c_11326]) ).
tcf(c_15743,plain,
( quasi_total(the_mapping(sK0,sK1),iPr_def_19,iPr_def_11)
| ~ net_str(sK1,sK0) ),
inference(superposition,[status(thm)],[c_11311,c_14435]) ).
tcf(c_15744,plain,
( quasi_total(the_mapping(sK0,sK0),iPr_def_11,iPr_def_11)
| ~ net_str(sK0,sK0) ),
inference(superposition,[status(thm)],[c_11303,c_14435]) ).
tcf(c_15747,plain,
quasi_total(the_mapping(sK0,sK1),iPr_def_19,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_15743,c_11324]) ).
tcf(c_15758,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ( subnetstr_of_element(X1,sK1,sK8(X0)) = netstr_restr_to_element(X1,sK1,sK8(X0)) )
| ~ one_sorted_str(X1)
| ~ net_str(sK1,X1)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_11332,c_15709]) ).
tcf(c_15759,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ( subnetstr_of_element(X1,sK1,sK6(X0)) = netstr_restr_to_element(X1,sK1,sK6(X0)) )
| ~ one_sorted_str(X1)
| ~ net_str(sK1,X1)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_11339,c_15709]) ).
tcf(c_15760,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(X0,sK1,sK29(sK4,sK3)) = netstr_restr_to_element(X0,sK1,sK29(sK4,sK3)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14848,c_15709]) ).
tcf(c_15761,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(X0,sK1,sK29(sK3,sK4)) = netstr_restr_to_element(X0,sK1,sK29(sK3,sK4)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14867,c_15709]) ).
tcf(c_15796,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X0)
| in(sK29(sK4,X1),X1)
| ( X1 = sK4 )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK4,X1))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK4,X1))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_192,c_15758]) ).
tcf(c_15797,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X0)
| in(sK29(X1,sK4),X1)
| ( X1 = sK4 )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(X1,sK4))) = netstr_restr_to_element(X0,sK1,sK8(sK29(X1,sK4))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_192,c_15758]) ).
tcf(c_15798,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK4,sK3))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14077,c_15758]) ).
tcf(c_15799,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK4,sK3))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14079,c_15758]) ).
tcf(c_15800,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK4,sK3))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14078,c_15758]) ).
tcf(c_15806,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK3,sK4))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14087,c_15758]) ).
tcf(c_15807,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK3,sK4))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14089,c_15758]) ).
tcf(c_15808,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK3,sK4))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14088,c_15758]) ).
tcf(c_15826,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK3,sK4))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15808,c_11343]) ).
tcf(c_15832,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK3,sK4))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15807,c_11343]) ).
tcf(c_15838,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK4,sK3))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15800,c_11343]) ).
tcf(c_15844,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK4,sK3))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15799,c_11343]) ).
tcf(c_15850,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK3,sK4))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15806,c_11343]) ).
tcf(c_15856,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( subnetstr_of_element(X0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK8(sK29(sK4,sK3))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15798,c_11343]) ).
tcf(c_15890,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X0)
| in(sK29(sK3,X1),X1)
| ( X1 = sK3 )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK3,X1))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK3,X1))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_192,c_15759]) ).
tcf(c_15891,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X0)
| in(sK29(X1,sK3),X1)
| ( X1 = sK3 )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(X1,sK3))) = netstr_restr_to_element(X0,sK1,sK6(sK29(X1,sK3))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_192,c_15759]) ).
tcf(c_15896,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK3,sK4))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14081,c_15759]) ).
tcf(c_15897,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK3,sK4))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14083,c_15759]) ).
tcf(c_15898,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK3,sK4))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14082,c_15759]) ).
tcf(c_15904,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK4,sK3))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14091,c_15759]) ).
tcf(c_15905,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK4,sK3))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14093,c_15759]) ).
tcf(c_15906,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK3 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK4,sK3))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14092,c_15759]) ).
tcf(c_15920,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK4,sK3))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15906,c_11343]) ).
tcf(c_15926,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK4,sK3))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15905,c_11343]) ).
tcf(c_15932,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK3,sK4))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15898,c_11343]) ).
tcf(c_15938,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK3,sK4))) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15897,c_11343]) ).
tcf(c_15944,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK4,sK3))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15904,c_11343]) ).
tcf(c_15950,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( subnetstr_of_element(X0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(X0,sK1,sK6(sK29(sK3,sK4))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15896,c_11343]) ).
tcf(c_15999,plain,
( empty_carrier(sK0)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15826]) ).
tcf(c_16000,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15999,c_11328,c_11314]) ).
tcf(c_16007,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)) = netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14562,c_16000]) ).
tcf(c_16008,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16000,c_168]) ).
tcf(c_16009,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16000,c_166]) ).
tcf(c_16010,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16000,c_149]) ).
tcf(c_16011,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16000,c_148]) ).
tcf(c_16012,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1))
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))) ),
inference(superposition,[status(thm)],[c_16000,c_163]) ).
tcf(c_16016,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16011,c_11311]) ).
tcf(c_16017,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16016,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_16021,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16010,c_11311]) ).
tcf(c_16022,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16021,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_16026,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))) ),
inference(light_normalisation,[status(thm)],[c_16012,c_11311]) ).
tcf(c_16027,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16026,c_11328,c_11327,c_11314,c_11325,c_11324]) ).
tcf(c_16031,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16009,c_11311]) ).
tcf(c_16032,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16031,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_16036,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16008,c_11311]) ).
tcf(c_16037,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16036,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_16055,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14562,c_16032]) ).
tcf(c_16066,plain,
( element(sK7(sK29(sK4,sK3)),powerset(iPr_def_11))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_14876,c_6527]) ).
tcf(c_16067,plain,
( in(sK29(sK4,sK3),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19)
| ~ in(sK29(sK4,sK3),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14876,c_11342]) ).
tcf(c_16068,plain,
( in(sK29(sK4,sK3),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19)
| ~ in(sK29(sK4,sK3),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_14876,c_11335]) ).
tcf(c_16069,plain,
( element(sK7(sK29(sK4,sK3)),iPr_def_12)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_14876,c_14194]) ).
tcf(c_16074,plain,
( in(sK29(sK4,sK3),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16068,c_14232]) ).
tcf(c_16080,plain,
( in(sK29(sK4,sK3),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16067,c_14232]) ).
tcf(c_16160,plain,
( quasi_total(the_mapping(sK1,sK1),iPr_def_19,iPr_def_19)
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_14438]) ).
tcf(c_16161,plain,
( quasi_total(the_mapping(sK1,sK0),iPr_def_11,iPr_def_19)
| ~ net_str(sK0,sK1) ),
inference(superposition,[status(thm)],[c_11303,c_14438]) ).
tcf(c_16182,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14562,c_16037]) ).
tcf(c_16193,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14562,c_16017]) ).
tcf(c_16194,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0) ),
inference(superposition,[status(thm)],[c_16017,c_145]) ).
tcf(c_16199,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16194,c_11314]) ).
tcf(c_16212,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14562,c_16022]) ).
tcf(c_16213,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16022,c_186]) ).
tcf(c_16214,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16213,c_11314]) ).
tcf(c_16230,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))) ),
inference(superposition,[status(thm)],[c_14562,c_16027]) ).
tcf(c_16247,plain,
( empty_carrier(sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15832]) ).
tcf(c_16248,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16247,c_11328,c_11314]) ).
tcf(c_16257,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)) = netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14562,c_16248]) ).
tcf(c_16258,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16248,c_168]) ).
tcf(c_16259,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16248,c_166]) ).
tcf(c_16260,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16248,c_149]) ).
tcf(c_16261,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16248,c_148]) ).
tcf(c_16262,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1))
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))) ),
inference(superposition,[status(thm)],[c_16248,c_163]) ).
tcf(c_16265,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16261,c_11311]) ).
tcf(c_16266,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16265,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_16270,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16260,c_11311]) ).
tcf(c_16271,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16270,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_16275,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))) ),
inference(light_normalisation,[status(thm)],[c_16262,c_11311]) ).
tcf(c_16276,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16275,c_11328,c_11327,c_11314,c_11325,c_11324]) ).
tcf(c_16280,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16259,c_11311]) ).
tcf(c_16281,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16280,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_16285,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16258,c_11311]) ).
tcf(c_16286,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16285,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_16304,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14562,c_16281]) ).
tcf(c_16314,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14562,c_16286]) ).
tcf(c_16329,plain,
( relation_of2_as_subset(the_mapping(sK0,sK1),iPr_def_19,iPr_def_11)
| ~ net_str(sK1,sK0) ),
inference(superposition,[status(thm)],[c_11311,c_14463]) ).
tcf(c_16330,plain,
( relation_of2_as_subset(the_mapping(sK0,sK0),iPr_def_11,iPr_def_11)
| ~ net_str(sK0,sK0) ),
inference(superposition,[status(thm)],[c_11303,c_14463]) ).
tcf(c_16331,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(X0),iPr_def_11,the_mapping(sK0,X0)) = relation_rng(the_mapping(sK0,X0)) )
| ~ net_str(X0,sK0) ),
inference(superposition,[status(thm)],[c_14463,c_6525]) ).
tcf(c_16332,plain,
! [X0: $i] :
( relation_of2(the_mapping(sK0,X0),the_carrier(X0),iPr_def_11)
| ~ net_str(X0,sK0) ),
inference(superposition,[status(thm)],[c_14463,c_147]) ).
tcf(c_16335,plain,
relation_of2_as_subset(the_mapping(sK0,sK1),iPr_def_19,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_16329,c_11324]) ).
tcf(c_16342,plain,
relation_rng_as_subset(iPr_def_19,iPr_def_11,the_mapping(sK0,sK1)) = relation_rng(the_mapping(sK0,sK1)),
inference(superposition,[status(thm)],[c_16335,c_6525]) ).
tcf(c_16343,plain,
relation_of2(the_mapping(sK0,sK1),iPr_def_19,iPr_def_11),
inference(superposition,[status(thm)],[c_16335,c_147]) ).
tcf(c_16351,plain,
( ( relation_rng_as_subset(iPr_def_11,iPr_def_11,the_mapping(sK0,sK0)) = relation_rng(the_mapping(sK0,sK0)) )
| ~ net_str(sK0,sK0) ),
inference(superposition,[status(thm)],[c_16330,c_6525]) ).
tcf(c_16352,plain,
( relation_of2(the_mapping(sK0,sK0),iPr_def_11,iPr_def_11)
| ~ net_str(sK0,sK0) ),
inference(superposition,[status(thm)],[c_16330,c_147]) ).
tcf(c_16362,plain,
! [X0: $i,X1: $i] :
( net_str(net_str_of(X1,iPr_def_11,the_mapping(sK0,sK0),X0),X1)
| ~ function(X0)
| ~ one_sorted_str(X1)
| ~ net_str(sK0,sK0)
| ~ quasi_total(X0,iPr_def_11,the_carrier(X1))
| ~ relation_of2(X0,iPr_def_11,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_16352,c_115]) ).
tcf(c_16363,plain,
! [X0: $i,X1: $i] :
( strict_net_str(net_str_of(X1,iPr_def_11,the_mapping(sK0,sK0),X0),X1)
| ~ function(X0)
| ~ one_sorted_str(X1)
| ~ net_str(sK0,sK0)
| ~ quasi_total(X0,iPr_def_11,the_carrier(X1))
| ~ relation_of2(X0,iPr_def_11,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_16352,c_114]) ).
tcf(c_16391,plain,
( relation_of2_as_subset(the_mapping(sK1,sK1),iPr_def_19,iPr_def_19)
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_14466]) ).
tcf(c_16392,plain,
( relation_of2_as_subset(the_mapping(sK1,sK0),iPr_def_11,iPr_def_19)
| ~ net_str(sK0,sK1) ),
inference(superposition,[status(thm)],[c_11303,c_14466]) ).
tcf(c_16393,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(X0),iPr_def_19,the_mapping(sK1,X0)) = relation_rng(the_mapping(sK1,X0)) )
| ~ net_str(X0,sK1) ),
inference(superposition,[status(thm)],[c_14466,c_6525]) ).
tcf(c_16394,plain,
! [X0: $i] :
( relation_of2(the_mapping(sK1,X0),the_carrier(X0),iPr_def_19)
| ~ net_str(X0,sK1) ),
inference(superposition,[status(thm)],[c_14466,c_147]) ).
tcf(c_16411,plain,
( ( relation_rng_as_subset(iPr_def_19,iPr_def_19,the_mapping(sK1,sK1)) = relation_rng(the_mapping(sK1,sK1)) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_16391,c_6525]) ).
tcf(c_16412,plain,
( relation_of2(the_mapping(sK1,sK1),iPr_def_19,iPr_def_19)
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_16391,c_147]) ).
tcf(c_16427,plain,
( ( relation_rng_as_subset(iPr_def_11,iPr_def_19,the_mapping(sK1,sK0)) = relation_rng(the_mapping(sK1,sK0)) )
| ~ net_str(sK0,sK1) ),
inference(superposition,[status(thm)],[c_16392,c_6525]) ).
tcf(c_16428,plain,
( relation_of2(the_mapping(sK1,sK0),iPr_def_11,iPr_def_19)
| ~ net_str(sK0,sK1) ),
inference(superposition,[status(thm)],[c_16392,c_147]) ).
tcf(c_16439,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14562,c_16266]) ).
tcf(c_16440,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0) ),
inference(superposition,[status(thm)],[c_16266,c_145]) ).
tcf(c_16444,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16440,c_11314]) ).
tcf(c_16455,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14562,c_16271]) ).
tcf(c_16456,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16271,c_186]) ).
tcf(c_16460,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16456,c_11314]) ).
tcf(c_16470,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))) ),
inference(superposition,[status(thm)],[c_14562,c_16276]) ).
tcf(c_16475,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ in(sK29(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_11330]) ).
tcf(c_16493,plain,
( empty_carrier(sK0)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15838]) ).
tcf(c_16494,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16493,c_11328,c_11314]) ).
tcf(c_16501,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)) = netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14395,c_16494]) ).
tcf(c_16502,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16494,c_168]) ).
tcf(c_16503,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16494,c_166]) ).
tcf(c_16504,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16494,c_149]) ).
tcf(c_16505,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16494,c_148]) ).
tcf(c_16506,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1))
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))) ),
inference(superposition,[status(thm)],[c_16494,c_163]) ).
tcf(c_16510,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16505,c_11311]) ).
tcf(c_16511,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16510,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_16515,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16504,c_11311]) ).
tcf(c_16516,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16515,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_16520,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))) ),
inference(light_normalisation,[status(thm)],[c_16506,c_11311]) ).
tcf(c_16521,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16520,c_11328,c_11327,c_11314,c_11325,c_11324]) ).
tcf(c_16525,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16503,c_11311]) ).
tcf(c_16526,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16525,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_16530,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16502,c_11311]) ).
tcf(c_16531,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16530,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_16541,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14395,c_16526]) ).
tcf(c_16552,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14395,c_16531]) ).
tcf(c_16563,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14395,c_16511]) ).
tcf(c_16564,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0) ),
inference(superposition,[status(thm)],[c_16511,c_145]) ).
tcf(c_16569,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16564,c_11314]) ).
tcf(c_16578,plain,
( element(sK7(sK29(sK3,sK4)),powerset(iPr_def_11))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_15183,c_6527]) ).
tcf(c_16579,plain,
( in(sK29(sK3,sK4),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19)
| ~ in(sK29(sK3,sK4),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_15183,c_11342]) ).
tcf(c_16580,plain,
( in(sK29(sK3,sK4),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19)
| ~ in(sK29(sK3,sK4),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_15183,c_11335]) ).
tcf(c_16581,plain,
( element(sK7(sK29(sK3,sK4)),iPr_def_12)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_15183,c_14194]) ).
tcf(c_16586,plain,
( in(sK29(sK3,sK4),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16580,c_14268]) ).
tcf(c_16592,plain,
( in(sK29(sK3,sK4),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16579,c_14268]) ).
tcf(c_16617,plain,
! [X0: $i,X1: $i] :
( net_str(net_str_of(X1,iPr_def_19,the_mapping(sK1,sK1),X0),X1)
| ~ function(X0)
| ~ one_sorted_str(X1)
| ~ net_str(sK1,sK1)
| ~ quasi_total(X0,iPr_def_19,the_carrier(X1))
| ~ relation_of2(X0,iPr_def_19,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_16412,c_115]) ).
tcf(c_16618,plain,
! [X0: $i,X1: $i] :
( strict_net_str(net_str_of(X1,iPr_def_19,the_mapping(sK1,sK1),X0),X1)
| ~ function(X0)
| ~ one_sorted_str(X1)
| ~ net_str(sK1,sK1)
| ~ quasi_total(X0,iPr_def_19,the_carrier(X1))
| ~ relation_of2(X0,iPr_def_19,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_16412,c_114]) ).
tcf(c_16653,plain,
( element(relation_rng(the_mapping(sK0,sK1)),powerset(iPr_def_11))
| ~ relation_of2_as_subset(the_mapping(sK0,sK1),iPr_def_19,iPr_def_11) ),
inference(superposition,[status(thm)],[c_16342,c_6527]) ).
tcf(c_16654,plain,
( element(relation_rng(the_mapping(sK0,sK1)),iPr_def_12)
| ~ relation_of2_as_subset(the_mapping(sK0,sK1),iPr_def_19,iPr_def_11) ),
inference(superposition,[status(thm)],[c_16342,c_14194]) ).
tcf(c_16655,plain,
element(relation_rng(the_mapping(sK0,sK1)),iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_16654,c_16335]) ).
tcf(c_16664,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| empty(sK12(cartesian_product2(X0,X1)))
| ~ empty(relation_rng(sK12(cartesian_product2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_82,c_2556]) ).
tcf(c_16665,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| empty(sK13(cartesian_product2(X0,X1)))
| ~ empty(relation_rng(sK13(cartesian_product2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_87,c_2556]) ).
tcf(c_16666,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| empty(sK19(cartesian_product2(X0,X1)))
| ~ empty(relation_rng(sK19(cartesian_product2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_117,c_2556]) ).
tcf(c_16667,plain,
! [X0: $i,X1: $i] :
( empty(sK20(cartesian_product2(X0,X1)))
| ~ empty(relation_rng(sK20(cartesian_product2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_120,c_2556]) ).
tcf(c_16668,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ~ empty(relation_rng(X0))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_151,c_2556]) ).
tcf(c_16669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(relation_rng_as_subset(X0,cartesian_product2(X1,X2),X3))
| ~ relation_of2_as_subset(X3,X0,cartesian_product2(X1,X2))
| ~ empty(relation_rng(relation_rng_as_subset(X0,cartesian_product2(X1,X2),X3))) ),
inference(superposition,[status(thm)],[c_6527,c_2556]) ).
tcf(c_16696,plain,
! [X0: $i] :
( empty(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ empty(relation_rng(the_InternalRel(X0))) ),
inference(superposition,[status(thm)],[c_116,c_16668]) ).
tcf(c_16697,plain,
! [X0: $i,X1: $i] :
( empty(the_mapping(X0,X1))
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| ~ empty(relation_rng(the_mapping(X0,X1))) ),
inference(superposition,[status(thm)],[c_190,c_16668]) ).
tcf(c_16698,plain,
( empty(the_InternalRel(sK1))
| ~ empty(relation_rng(the_InternalRel(sK1))) ),
inference(superposition,[status(thm)],[c_14067,c_16668]) ).
tcf(c_16700,plain,
! [X0: $i] :
( empty(the_mapping(sK1,X0))
| ~ net_str(X0,sK1)
| ~ empty(relation_rng(the_mapping(sK1,X0))) ),
inference(superposition,[status(thm)],[c_14466,c_16668]) ).
tcf(c_16701,plain,
! [X0: $i] :
( empty(the_mapping(sK0,X0))
| ~ net_str(X0,sK0)
| ~ empty(relation_rng(the_mapping(sK0,X0))) ),
inference(superposition,[status(thm)],[c_14463,c_16668]) ).
tcf(c_16702,plain,
( empty(the_mapping(sK0,sK1))
| ~ empty(relation_rng(the_mapping(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_16335,c_16668]) ).
tcf(c_16767,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14395,c_16516]) ).
tcf(c_16768,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16516,c_186]) ).
tcf(c_16769,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16768,c_11314]) ).
tcf(c_16783,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))) ),
inference(superposition,[status(thm)],[c_14395,c_16521]) ).
tcf(c_16798,plain,
( empty_carrier(sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15844]) ).
tcf(c_16799,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16798,c_11328,c_11314]) ).
tcf(c_16806,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)) = netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14395,c_16799]) ).
tcf(c_16807,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16799,c_168]) ).
tcf(c_16808,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16799,c_166]) ).
tcf(c_16809,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16799,c_149]) ).
tcf(c_16810,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16799,c_148]) ).
tcf(c_16811,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1))
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))) ),
inference(superposition,[status(thm)],[c_16799,c_163]) ).
tcf(c_16814,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16810,c_11311]) ).
tcf(c_16815,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16814,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_16819,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16809,c_11311]) ).
tcf(c_16820,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16819,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_16824,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))) ),
inference(light_normalisation,[status(thm)],[c_16811,c_11311]) ).
tcf(c_16825,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16824,c_11328,c_11327,c_11314,c_11325,c_11324]) ).
tcf(c_16829,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16808,c_11311]) ).
tcf(c_16830,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16829,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_16834,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_16807,c_11311]) ).
tcf(c_16835,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16834,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_16854,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14395,c_16830]) ).
tcf(c_16864,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14395,c_16835]) ).
tcf(c_16902,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14395,c_16815]) ).
tcf(c_16903,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0) ),
inference(superposition,[status(thm)],[c_16815,c_145]) ).
tcf(c_16907,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16903,c_11314]) ).
tcf(c_16918,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_14395,c_16820]) ).
tcf(c_16919,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16820,c_186]) ).
tcf(c_16923,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16919,c_11314]) ).
tcf(c_16946,plain,
( quasi_total(the_mapping(sK1,sK1),iPr_def_19,iPr_def_19)
| ~ one_sorted_str(sK1)
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_14431]) ).
tcf(c_16955,plain,
( quasi_total(the_mapping(sK1,sK0),iPr_def_11,iPr_def_19)
| ~ one_sorted_str(sK1)
| ~ net_str(sK0,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_14432]) ).
tcf(c_16956,plain,
( quasi_total(the_mapping(sK0,sK0),iPr_def_11,iPr_def_11)
| ~ one_sorted_str(sK0)
| ~ net_str(sK0,sK0) ),
inference(superposition,[status(thm)],[c_11303,c_14432]) ).
tcf(c_16964,plain,
~ empty(relation_rng(the_mapping(sK0,sK1))),
inference(global_subsumption_just,[status(thm)],[c_16702,c_66,c_70,c_67,c_64,c_197,c_15498]) ).
tcf(c_16966,plain,
~ empty(the_mapping(sK0,sK1)),
inference(superposition,[status(thm)],[c_143,c_16964]) ).
tcf(c_16973,plain,
( relation_of2_as_subset(the_mapping(sK1,sK1),iPr_def_19,iPr_def_19)
| ~ one_sorted_str(sK1)
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_14457]) ).
tcf(c_16975,plain,
! [X0: $i] :
( empty(the_mapping(X0,sK1))
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0)
| ~ empty(relation_rng(the_mapping(X0,sK1))) ),
inference(superposition,[status(thm)],[c_14457,c_16668]) ).
tcf(c_16976,plain,
! [X0: $i] :
( ( relation_rng_as_subset(iPr_def_19,the_carrier(X0),the_mapping(X0,sK1)) = relation_rng(the_mapping(X0,sK1)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14457,c_6525]) ).
tcf(c_16977,plain,
! [X0: $i] :
( relation_of2(the_mapping(X0,sK1),iPr_def_19,the_carrier(X0))
| ~ one_sorted_str(X0)
| ~ net_str(sK1,X0) ),
inference(superposition,[status(thm)],[c_14457,c_147]) ).
tcf(c_16997,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))) ),
inference(superposition,[status(thm)],[c_14395,c_16825]) ).
tcf(c_17011,plain,
( empty_carrier(sK0)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15920]) ).
tcf(c_17012,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17011,c_11328,c_11314]) ).
tcf(c_17019,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17012,c_168]) ).
tcf(c_17020,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17012,c_166]) ).
tcf(c_17021,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17012,c_149]) ).
tcf(c_17022,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17012,c_148]) ).
tcf(c_17023,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1))
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))) ),
inference(superposition,[status(thm)],[c_17012,c_163]) ).
tcf(c_17024,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17022,c_11311]) ).
tcf(c_17025,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17024,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17029,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17021,c_11311]) ).
tcf(c_17030,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17029,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17034,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))) ),
inference(light_normalisation,[status(thm)],[c_17023,c_11311]) ).
tcf(c_17035,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17034,c_11328,c_11327,c_11314,c_11325,c_11324]) ).
tcf(c_17039,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17020,c_11311]) ).
tcf(c_17040,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17039,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17044,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17019,c_11311]) ).
tcf(c_17045,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17044,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17067,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0) ),
inference(superposition,[status(thm)],[c_17025,c_145]) ).
tcf(c_17068,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17067,c_11314]) ).
tcf(c_17079,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17030,c_186]) ).
tcf(c_17080,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17079,c_11314]) ).
tcf(c_17094,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK3,sK4),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16257,c_168]) ).
tcf(c_17095,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK3,sK4),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16257,c_166]) ).
tcf(c_17096,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK3,sK4),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16257,c_149]) ).
tcf(c_17097,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK3,sK4),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16257,c_148]) ).
tcf(c_17098,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK3,sK4),the_carrier(sK1))
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))) ),
inference(superposition,[status(thm)],[c_16257,c_163]) ).
tcf(c_17099,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK3,sK4),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17097,c_11311]) ).
tcf(c_17100,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17099,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17104,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK3,sK4),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17096,c_11311]) ).
tcf(c_17105,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17104,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17109,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK3,sK4),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))) ),
inference(light_normalisation,[status(thm)],[c_17098,c_11311]) ).
tcf(c_17110,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17109,c_11328,c_11327,c_11314,c_11325,c_11324]) ).
tcf(c_17114,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK3,sK4),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17095,c_11311]) ).
tcf(c_17115,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17114,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17119,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK3,sK4),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17094,c_11311]) ).
tcf(c_17120,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17119,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17134,plain,
( relation_of2_as_subset(the_mapping(sK1,sK0),iPr_def_11,iPr_def_19)
| ~ one_sorted_str(sK1)
| ~ net_str(sK0,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_14458]) ).
tcf(c_17135,plain,
( relation_of2_as_subset(the_mapping(sK0,sK0),iPr_def_11,iPr_def_11)
| ~ one_sorted_str(sK0)
| ~ net_str(sK0,sK0) ),
inference(superposition,[status(thm)],[c_11303,c_14458]) ).
tcf(c_17136,plain,
! [X0: $i] :
( empty(the_mapping(X0,sK0))
| ~ one_sorted_str(X0)
| ~ net_str(sK0,X0)
| ~ empty(relation_rng(the_mapping(X0,sK0))) ),
inference(superposition,[status(thm)],[c_14458,c_16668]) ).
tcf(c_17137,plain,
! [X0: $i] :
( ( relation_rng_as_subset(iPr_def_11,the_carrier(X0),the_mapping(X0,sK0)) = relation_rng(the_mapping(X0,sK0)) )
| ~ one_sorted_str(X0)
| ~ net_str(sK0,X0) ),
inference(superposition,[status(thm)],[c_14458,c_6525]) ).
tcf(c_17138,plain,
! [X0: $i] :
( relation_of2(the_mapping(X0,sK0),iPr_def_11,the_carrier(X0))
| ~ one_sorted_str(X0)
| ~ net_str(sK0,X0) ),
inference(superposition,[status(thm)],[c_14458,c_147]) ).
tcf(c_17165,plain,
( relation_of2(the_mapping(sK1,sK1),iPr_def_19,iPr_def_19)
| ~ one_sorted_str(sK1)
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_16977]) ).
tcf(c_17177,plain,
( relation_of2(the_mapping(sK1,sK0),iPr_def_11,iPr_def_19)
| ~ one_sorted_str(sK1)
| ~ net_str(sK0,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_17138]) ).
tcf(c_17178,plain,
( relation_of2(the_mapping(sK0,sK0),iPr_def_11,iPr_def_11)
| ~ one_sorted_str(sK0)
| ~ net_str(sK0,sK0) ),
inference(superposition,[status(thm)],[c_11303,c_17138]) ).
tcf(c_17214,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_17115,c_14867,c_17115]) ).
tcf(c_17220,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_17120,c_14867,c_17120]) ).
tcf(c_17248,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_17100,c_14867,c_17100]) ).
tcf(c_17254,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)) )
| ~ one_sorted_str(sK0)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17248,c_145]) ).
tcf(c_17255,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)) )
| ~ net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17254,c_11314]) ).
tcf(c_17259,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK0)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_17105,c_14867,c_17105]) ).
tcf(c_17265,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_17259,c_186]) ).
tcf(c_17266,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17265,c_11314]) ).
tcf(c_17269,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_17110,c_14867,c_17110]) ).
tcf(c_17285,plain,
( empty_carrier(sK0)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15926]) ).
tcf(c_17286,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17285,c_11328,c_11314]) ).
tcf(c_17293,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17286,c_168]) ).
tcf(c_17294,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17286,c_166]) ).
tcf(c_17295,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17286,c_149]) ).
tcf(c_17296,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17286,c_148]) ).
tcf(c_17297,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1))
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))) ),
inference(superposition,[status(thm)],[c_17286,c_163]) ).
tcf(c_17298,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17296,c_11311]) ).
tcf(c_17299,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17298,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17303,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17295,c_11311]) ).
tcf(c_17304,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17303,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17308,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))) ),
inference(light_normalisation,[status(thm)],[c_17297,c_11311]) ).
tcf(c_17309,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17308,c_11328,c_11327,c_11314,c_11325,c_11324]) ).
tcf(c_17313,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17294,c_11311]) ).
tcf(c_17314,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17313,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17318,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17293,c_11311]) ).
tcf(c_17319,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17318,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17451,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0) ),
inference(superposition,[status(thm)],[c_17299,c_145]) ).
tcf(c_17452,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17451,c_11314]) ).
tcf(c_17463,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17304,c_186]) ).
tcf(c_17464,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17463,c_11314]) ).
tcf(c_17484,plain,
( empty_carrier(sK0)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15932]) ).
tcf(c_17485,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17484,c_11328,c_11314]) ).
tcf(c_17492,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17485,c_168]) ).
tcf(c_17493,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17485,c_166]) ).
tcf(c_17494,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17485,c_149]) ).
tcf(c_17495,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17485,c_148]) ).
tcf(c_17496,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1))
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))) ),
inference(superposition,[status(thm)],[c_17485,c_163]) ).
tcf(c_17497,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17495,c_11311]) ).
tcf(c_17498,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17497,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17502,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17494,c_11311]) ).
tcf(c_17503,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17502,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17507,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))) ),
inference(light_normalisation,[status(thm)],[c_17496,c_11311]) ).
tcf(c_17508,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17507,c_11328,c_11327,c_11314,c_11325,c_11324]) ).
tcf(c_17512,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17493,c_11311]) ).
tcf(c_17513,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17512,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17517,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17492,c_11311]) ).
tcf(c_17518,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17517,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17570,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK4,sK3),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16806,c_168]) ).
tcf(c_17571,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK4,sK3),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16806,c_166]) ).
tcf(c_17572,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK4,sK3),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16806,c_149]) ).
tcf(c_17573,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK4,sK3),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16806,c_148]) ).
tcf(c_17574,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK4,sK3),the_carrier(sK1))
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))) ),
inference(superposition,[status(thm)],[c_16806,c_163]) ).
tcf(c_17575,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK4,sK3),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17573,c_11311]) ).
tcf(c_17576,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17575,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17580,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK4,sK3),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17572,c_11311]) ).
tcf(c_17581,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17580,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17585,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK4,sK3),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))) ),
inference(light_normalisation,[status(thm)],[c_17574,c_11311]) ).
tcf(c_17586,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17585,c_11328,c_11327,c_11314,c_11325,c_11324]) ).
tcf(c_17590,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK4,sK3),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17571,c_11311]) ).
tcf(c_17591,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17590,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17595,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK29(sK4,sK3),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17570,c_11311]) ).
tcf(c_17596,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17595,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17626,plain,
relation_rng_as_subset(the_carrier(sK1),the_carrier(sK1),the_InternalRel(sK1)) = relation_rng(the_InternalRel(sK1)),
inference(superposition,[status(thm)],[c_14023,c_14418]) ).
tcf(c_17627,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(sK27(X0)),the_carrier(sK27(X0)),the_InternalRel(sK27(X0))) = relation_rng(the_InternalRel(sK27(X0))) )
| ~ one_sorted_str(X0) ),
inference(superposition,[status(thm)],[c_14022,c_14418]) ).
tcf(c_17646,plain,
! [X0: $i] :
( relation_of2(the_mapping(sK1,X0),the_carrier(X0),iPr_def_19)
| ~ one_sorted_str(sK1)
| ~ net_str(X0,sK1) ),
inference(superposition,[status(thm)],[c_11311,c_14462]) ).
tcf(c_17647,plain,
! [X0: $i] :
( relation_of2(the_mapping(sK0,X0),the_carrier(X0),iPr_def_11)
| ~ one_sorted_str(sK0)
| ~ net_str(X0,sK0) ),
inference(superposition,[status(thm)],[c_11303,c_14462]) ).
tcf(c_17648,plain,
! [X0: $i,X1: $i,X2: $i] :
( net_str(net_str_of(X2,the_carrier(X1),the_mapping(X1,X1),X0),X2)
| ~ function(X0)
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X1)
| ~ net_str(X1,X1)
| ~ quasi_total(X0,the_carrier(X1),the_carrier(X2))
| ~ relation_of2(X0,the_carrier(X1),the_carrier(X2)) ),
inference(superposition,[status(thm)],[c_14462,c_115]) ).
tcf(c_17649,plain,
! [X0: $i,X1: $i,X2: $i] :
( strict_net_str(net_str_of(X2,the_carrier(X1),the_mapping(X1,X1),X0),X2)
| ~ function(X0)
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X1)
| ~ net_str(X1,X1)
| ~ quasi_total(X0,the_carrier(X1),the_carrier(X2))
| ~ relation_of2(X0,the_carrier(X1),the_carrier(X2)) ),
inference(superposition,[status(thm)],[c_14462,c_114]) ).
tcf(c_17706,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| ~ empty(relation_rng(sK12(cartesian_product2(X0,X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16664,c_83]) ).
tcf(c_17713,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| ~ empty(sK12(cartesian_product2(X0,X1))) ),
inference(superposition,[status(thm)],[c_143,c_17706]) ).
tcf(c_17717,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_17591,c_14848,c_17591]) ).
tcf(c_17723,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_17596,c_14848,c_17596]) ).
tcf(c_17729,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_17576,c_14848,c_17576]) ).
tcf(c_17735,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) = subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)) )
| ~ one_sorted_str(sK0)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0) ),
inference(superposition,[status(thm)],[c_17729,c_145]) ).
tcf(c_17736,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) = subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)) )
| ~ net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17735,c_11314]) ).
tcf(c_17742,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK0)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_17581,c_14848,c_17581]) ).
tcf(c_17748,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_17742,c_186]) ).
tcf(c_17749,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17748,c_11314]) ).
tcf(c_17802,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))) ),
inference(global_subsumption_just,[status(thm)],[c_17586,c_14848,c_17586]) ).
tcf(c_17814,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0) ),
inference(superposition,[status(thm)],[c_17498,c_145]) ).
tcf(c_17815,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17814,c_11314]) ).
tcf(c_17826,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17503,c_186]) ).
tcf(c_17827,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17826,c_11314]) ).
tcf(c_17857,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| ~ empty(relation_rng(sK13(cartesian_product2(X0,X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16665,c_88]) ).
tcf(c_17864,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| ~ empty(sK13(cartesian_product2(X0,X1))) ),
inference(superposition,[status(thm)],[c_143,c_17857]) ).
tcf(c_17871,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| ~ empty(relation_rng(sK19(cartesian_product2(X0,X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16666,c_118]) ).
tcf(c_17878,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| ~ empty(sK19(cartesian_product2(X0,X1))) ),
inference(superposition,[status(thm)],[c_143,c_17871]) ).
tcf(c_17901,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = relation_rng(the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) ) ),
inference(superposition,[status(thm)],[c_17266,c_14418]) ).
tcf(c_17902,plain,
( one_sorted_str(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(superposition,[status(thm)],[c_17266,c_150]) ).
tcf(c_17911,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) = relation_rng(the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) ) ),
inference(superposition,[status(thm)],[c_17749,c_14418]) ).
tcf(c_17912,plain,
( one_sorted_str(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(superposition,[status(thm)],[c_17749,c_150]) ).
tcf(c_17935,plain,
( empty_carrier(sK0)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15938]) ).
tcf(c_17936,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17935,c_11328,c_11314]) ).
tcf(c_17943,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17936,c_168]) ).
tcf(c_17944,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17936,c_166]) ).
tcf(c_17945,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17936,c_149]) ).
tcf(c_17946,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17936,c_148]) ).
tcf(c_17947,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1))
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))) ),
inference(superposition,[status(thm)],[c_17936,c_163]) ).
tcf(c_17948,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17946,c_11311]) ).
tcf(c_17949,plain,
( strict_net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17948,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17953,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17945,c_11311]) ).
tcf(c_17954,plain,
( net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17953,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_17958,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))) ),
inference(light_normalisation,[status(thm)],[c_17947,c_11311]) ).
tcf(c_17959,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ empty_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17958,c_11328,c_11327,c_11314,c_11325,c_11324]) ).
tcf(c_17963,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17944,c_11311]) ).
tcf(c_17964,plain,
( transitive_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17963,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_17968,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(sK1)
| ~ transitive_relstr(sK1)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_17943,c_11311]) ).
tcf(c_17969,plain,
( directed_relstr(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17968,c_11328,c_11327,c_11314,c_11325,c_11326,c_11324]) ).
tcf(c_18001,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0) ),
inference(superposition,[status(thm)],[c_17949,c_145]) ).
tcf(c_18002,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( net_str_of(sK0,the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_InternalRel(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ net_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18001,c_11314]) ).
tcf(c_18013,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17954,c_186]) ).
tcf(c_18014,plain,
( rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18013,c_11314]) ).
tcf(c_18044,plain,
( empty_carrier(sK0)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15850]) ).
tcf(c_18045,plain,
( ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18044,c_11328,c_11314]) ).
tcf(c_18052,plain,
( element(relation_rng(the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),powerset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) ),
inference(superposition,[status(thm)],[c_17901,c_6527]) ).
tcf(c_18060,plain,
relation_rng_as_subset(the_carrier(sK1),iPr_def_11,the_mapping(sK0,sK1)) = relation_rng(the_mapping(sK0,sK1)),
inference(superposition,[status(thm)],[c_11324,c_16331]) ).
tcf(c_18061,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK0)
| empty_carrier(X1)
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,X1,X0)),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,X1,X0))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,X1,X0))) )
| ~ one_sorted_str(sK0)
| ~ net_str(X1,sK0)
| ~ element(X0,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_149,c_16331]) ).
tcf(c_18062,plain,
( ( relation_rng_as_subset(the_carrier(sK27(sK0)),iPr_def_11,the_mapping(sK0,sK27(sK0))) = relation_rng(the_mapping(sK0,sK27(sK0))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_161,c_16331]) ).
tcf(c_18063,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16271,c_16331]) ).
tcf(c_18064,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16022,c_16331]) ).
tcf(c_18065,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) ) ),
inference(superposition,[status(thm)],[c_17259,c_16331]) ).
tcf(c_18066,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16820,c_16331]) ).
tcf(c_18067,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16516,c_16331]) ).
tcf(c_18068,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) ) ),
inference(superposition,[status(thm)],[c_17742,c_16331]) ).
tcf(c_18069,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17304,c_16331]) ).
tcf(c_18070,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17030,c_16331]) ).
tcf(c_18071,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17954,c_16331]) ).
tcf(c_18072,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17503,c_16331]) ).
tcf(c_18074,plain,
relation_rng_as_subset(the_carrier(sK27(sK0)),iPr_def_11,the_mapping(sK0,sK27(sK0))) = relation_rng(the_mapping(sK0,sK27(sK0))),
inference(forward_subsumption_resolution,[status(thm)],[c_18062,c_11314]) ).
tcf(c_18079,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,X1,X0)),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,X1,X0))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,X1,X0))) )
| ~ net_str(X1,sK0)
| ~ element(X0,the_carrier(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18061,c_11328,c_11314]) ).
tcf(c_18151,plain,
( element(relation_rng(the_mapping(sK0,sK27(sK0))),powerset(iPr_def_11))
| ~ relation_of2_as_subset(the_mapping(sK0,sK27(sK0)),the_carrier(sK27(sK0)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18074,c_6527]) ).
tcf(c_18152,plain,
( element(relation_rng(the_mapping(sK0,sK27(sK0))),iPr_def_12)
| ~ relation_of2_as_subset(the_mapping(sK0,sK27(sK0)),the_carrier(sK27(sK0)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18074,c_14194]) ).
tcf(c_18160,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK1)
| empty_carrier(X1)
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,X1,X0)),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,X1,X0))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,X1,X0))) )
| ~ one_sorted_str(sK1)
| ~ net_str(X1,sK1)
| ~ element(X0,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_149,c_16393]) ).
tcf(c_18161,plain,
( ( relation_rng_as_subset(the_carrier(sK27(sK1)),iPr_def_19,the_mapping(sK1,sK27(sK1))) = relation_rng(the_mapping(sK1,sK27(sK1))) )
| ~ one_sorted_str(sK1) ),
inference(superposition,[status(thm)],[c_161,c_16393]) ).
tcf(c_18162,plain,
relation_rng_as_subset(the_carrier(sK27(sK1)),iPr_def_19,the_mapping(sK1,sK27(sK1))) = relation_rng(the_mapping(sK1,sK27(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_18161,c_14052]) ).
tcf(c_18163,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,X1,X0)),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,X1,X0))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,X1,X0))) )
| ~ net_str(X1,sK1)
| ~ element(X0,the_carrier(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18160,c_11327,c_14052]) ).
tcf(c_18169,plain,
( element(relation_rng(the_mapping(sK1,sK27(sK1))),powerset(iPr_def_19))
| ~ relation_of2_as_subset(the_mapping(sK1,sK27(sK1)),the_carrier(sK27(sK1)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_18162,c_6527]) ).
tcf(c_18201,plain,
! [X0: $i] :
( empty_carrier(sK1)
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,X0)),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,X0))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,X0))) )
| ~ net_str(sK1,sK0)
| ~ element(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_11311,c_18079]) ).
tcf(c_18202,plain,
! [X0: $i] :
( empty_carrier(sK0)
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK0,X0)),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK0,X0))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK0,X0))) )
| ~ net_str(sK0,sK0)
| ~ element(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_11303,c_18079]) ).
tcf(c_18203,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK0,X0)),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK0,X0))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK0,X0))) )
| ~ net_str(sK0,sK0)
| ~ element(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18202,c_11328]) ).
tcf(c_18207,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,X0)),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,X0))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,X0))) )
| ~ element(X0,iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18201,c_11327,c_11324]) ).
tcf(c_18216,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(X0))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(X0)))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(X0)))) )
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_11332,c_18207]) ).
tcf(c_18217,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(X0))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(X0)))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(X0)))) )
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_11339,c_18207]) ).
tcf(c_18218,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3)))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3)))) ) ),
inference(superposition,[status(thm)],[c_14848,c_18207]) ).
tcf(c_18219,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4)))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4)))) ) ),
inference(superposition,[status(thm)],[c_14867,c_18207]) ).
tcf(c_18251,plain,
! [X0: $i] :
( in(sK29(sK4,X0),X0)
| ( X0 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,X0)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,X0))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,X0))))) ) ),
inference(superposition,[status(thm)],[c_192,c_18216]) ).
tcf(c_18252,plain,
! [X0: $i] :
( in(sK29(X0,sK4),X0)
| ( X0 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(X0,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(X0,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(X0,sK4))))) ) ),
inference(superposition,[status(thm)],[c_192,c_18216]) ).
tcf(c_18253,plain,
( ( sK3 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14077,c_18216]) ).
tcf(c_18254,plain,
( ( sK3 = sK4 )
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_14079,c_18216]) ).
tcf(c_18255,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_14078,c_18216]) ).
tcf(c_18261,plain,
( ( sK3 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14087,c_18216]) ).
tcf(c_18262,plain,
( ( sK3 = sK4 )
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_14089,c_18216]) ).
tcf(c_18263,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_14088,c_18216]) ).
tcf(c_18275,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18263,c_11343]) ).
tcf(c_18278,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18262,c_11343]) ).
tcf(c_18281,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18255,c_11343]) ).
tcf(c_18284,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18254,c_11343]) ).
tcf(c_18287,plain,
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18261,c_11343]) ).
tcf(c_18290,plain,
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18253,c_11343]) ).
tcf(c_18315,plain,
! [X0: $i] :
( in(sK29(sK3,X0),X0)
| ( X0 = sK3 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,X0)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,X0))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,X0))))) ) ),
inference(superposition,[status(thm)],[c_192,c_18217]) ).
tcf(c_18316,plain,
! [X0: $i] :
( in(sK29(X0,sK3),X0)
| ( X0 = sK3 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(X0,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(X0,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(X0,sK3))))) ) ),
inference(superposition,[status(thm)],[c_192,c_18217]) ).
tcf(c_18321,plain,
( ( sK3 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14081,c_18217]) ).
tcf(c_18322,plain,
( ( sK3 = sK4 )
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_14083,c_18217]) ).
tcf(c_18323,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_14082,c_18217]) ).
tcf(c_18329,plain,
( ( sK3 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14091,c_18217]) ).
tcf(c_18330,plain,
( ( sK3 = sK4 )
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_14093,c_18217]) ).
tcf(c_18331,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_14092,c_18217]) ).
tcf(c_18339,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18331,c_11343]) ).
tcf(c_18342,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18330,c_11343]) ).
tcf(c_18345,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18323,c_11343]) ).
tcf(c_18348,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18322,c_11343]) ).
tcf(c_18351,plain,
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18329,c_11343]) ).
tcf(c_18354,plain,
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18321,c_11343]) ).
tcf(c_18398,plain,
! [X0: $i] :
( empty_carrier(sK1)
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,X0)),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,X0))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,X0))) )
| ~ net_str(sK1,sK1)
| ~ element(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_11311,c_18163]) ).
tcf(c_18399,plain,
! [X0: $i] :
( empty_carrier(sK0)
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK0,X0)),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK0,X0))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK0,X0))) )
| ~ net_str(sK0,sK1)
| ~ element(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_11303,c_18163]) ).
tcf(c_18400,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK0,X0)),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK0,X0))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK0,X0))) )
| ~ net_str(sK0,sK1)
| ~ element(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18399,c_11328]) ).
tcf(c_18404,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,X0)),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,X0))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,X0))) )
| ~ net_str(sK1,sK1)
| ~ element(X0,iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18398,c_11327]) ).
tcf(c_18422,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(X0))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(X0)))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(X0)))) )
| ~ net_str(sK1,sK1)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_11332,c_18404]) ).
tcf(c_18423,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(X0))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(X0)))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(X0)))) )
| ~ net_str(sK1,sK1)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_11339,c_18404]) ).
tcf(c_18424,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK29(sK4,sK3))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK29(sK4,sK3)))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK29(sK4,sK3)))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14848,c_18404]) ).
tcf(c_18425,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK29(sK3,sK4))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK29(sK3,sK4)))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK29(sK3,sK4)))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14867,c_18404]) ).
tcf(c_18533,plain,
( element(relation_rng(the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),powerset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_InternalRel(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) ),
inference(superposition,[status(thm)],[c_17911,c_6527]) ).
tcf(c_18541,plain,
( element(relation_rng(the_mapping(sK1,sK27(sK1))),powerset(iPr_def_19))
| ~ net_str(sK27(sK1),sK1) ),
inference(superposition,[status(thm)],[c_14466,c_18169]) ).
tcf(c_18558,plain,
( element(relation_rng(the_mapping(sK0,sK27(sK0))),iPr_def_12)
| ~ net_str(sK27(sK0),sK0) ),
inference(superposition,[status(thm)],[c_14463,c_18152]) ).
tcf(c_18561,plain,
element(relation_rng(the_mapping(sK0,sK27(sK0))),iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_18558,c_66,c_197,c_213,c_18558]) ).
tcf(c_18569,plain,
( element(sK2,iPr_def_12)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ in(sK29(sK4,sK3),sK3) ),
inference(superposition,[status(thm)],[c_14756,c_14410]) ).
tcf(c_18579,plain,
! [X0: $i] :
( in(sK29(sK4,X0),X0)
| ( X0 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,X0)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,X0))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,X0))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_192,c_18422]) ).
tcf(c_18580,plain,
! [X0: $i] :
( in(sK29(X0,sK4),X0)
| ( X0 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(X0,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(X0,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(X0,sK4))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_192,c_18422]) ).
tcf(c_18581,plain,
( ( sK3 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14077,c_18422]) ).
tcf(c_18582,plain,
( ( sK3 = sK4 )
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14079,c_18422]) ).
tcf(c_18583,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14078,c_18422]) ).
tcf(c_18589,plain,
( ( sK3 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14087,c_18422]) ).
tcf(c_18590,plain,
( ( sK3 = sK4 )
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14089,c_18422]) ).
tcf(c_18591,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14088,c_18422]) ).
tcf(c_18605,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18591,c_11343]) ).
tcf(c_18609,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18590,c_11343]) ).
tcf(c_18613,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18583,c_11343]) ).
tcf(c_18617,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18582,c_11343]) ).
tcf(c_18621,plain,
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK3,sK4))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18589,c_11343]) ).
tcf(c_18625,plain,
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK8(sK29(sK4,sK3))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18581,c_11343]) ).
tcf(c_18637,plain,
! [X0: $i] :
( in(sK29(sK3,X0),X0)
| ( X0 = sK3 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,X0)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,X0))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,X0))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_192,c_18423]) ).
tcf(c_18638,plain,
! [X0: $i] :
( in(sK29(X0,sK3),X0)
| ( X0 = sK3 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(X0,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(X0,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(X0,sK3))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_192,c_18423]) ).
tcf(c_18643,plain,
( ( sK3 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14081,c_18423]) ).
tcf(c_18644,plain,
( ( sK3 = sK4 )
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14083,c_18423]) ).
tcf(c_18645,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14082,c_18423]) ).
tcf(c_18651,plain,
( ( sK3 = sK4 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14091,c_18423]) ).
tcf(c_18652,plain,
( ( sK3 = sK4 )
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14093,c_18423]) ).
tcf(c_18653,plain,
( ( sK3 = sK4 )
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) )
| ~ net_str(sK1,sK1) ),
inference(superposition,[status(thm)],[c_14092,c_18423]) ).
tcf(c_18663,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18653,c_11343]) ).
tcf(c_18667,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18652,c_11343]) ).
tcf(c_18671,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18645,c_11343]) ).
tcf(c_18675,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18644,c_11343]) ).
tcf(c_18679,plain,
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK4,sK3))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18651,c_11343]) ).
tcf(c_18683,plain,
( ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4)))),iPr_def_19,the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK1,netstr_restr_to_element(sK1,sK1,sK6(sK29(sK3,sK4))))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ~ net_str(sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18643,c_11343]) ).
tcf(c_18714,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_16000,c_18275]) ).
tcf(c_18715,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4)))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4)))) ) ),
inference(superposition,[status(thm)],[c_14562,c_18275]) ).
tcf(c_18716,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))),powerset(iPr_def_11))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18275,c_6527]) ).
tcf(c_18717,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))),iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18275,c_14194]) ).
tcf(c_18734,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_16248,c_18278]) ).
tcf(c_18737,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))),powerset(iPr_def_11))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18278,c_6527]) ).
tcf(c_18738,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))),iPr_def_12)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18278,c_14194]) ).
tcf(c_18753,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_16494,c_18281]) ).
tcf(c_18754,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3)))) = relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3)))) ) ),
inference(superposition,[status(thm)],[c_14395,c_18281]) ).
tcf(c_18755,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))),powerset(iPr_def_11))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18281,c_6527]) ).
tcf(c_18756,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))),iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18281,c_14194]) ).
tcf(c_18790,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_16799,c_18284]) ).
tcf(c_18793,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))),powerset(iPr_def_11))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18284,c_6527]) ).
tcf(c_18794,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))),iPr_def_12)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18284,c_14194]) ).
tcf(c_18808,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_17012,c_18339]) ).
tcf(c_18809,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))),powerset(iPr_def_11))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18339,c_6527]) ).
tcf(c_18810,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))),iPr_def_12)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18339,c_14194]) ).
tcf(c_18823,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_17286,c_18342]) ).
tcf(c_18825,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))),powerset(iPr_def_11))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18342,c_6527]) ).
tcf(c_18826,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))),iPr_def_12)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18342,c_14194]) ).
tcf(c_18837,plain,
( element(sK5(sK29(sK3,sK4)),powerset(iPr_def_11))
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18045,c_6527]) ).
tcf(c_18838,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_18045,c_11342]) ).
tcf(c_18839,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_18045,c_11335]) ).
tcf(c_18840,plain,
( element(sK5(sK29(sK3,sK4)),iPr_def_12)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18045,c_14194]) ).
tcf(c_18877,plain,
( element(sK2,iPr_def_12)
| ( sK3 = sK4 )
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(superposition,[status(thm)],[c_14093,c_18569]) ).
tcf(c_18880,plain,
( element(sK2,iPr_def_12)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18877,c_11343]) ).
tcf(c_18908,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_17485,c_18345]) ).
tcf(c_18909,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))),powerset(iPr_def_11))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18345,c_6527]) ).
tcf(c_18910,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))),iPr_def_12)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18345,c_14194]) ).
tcf(c_18923,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_17936,c_18348]) ).
tcf(c_18925,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))),powerset(iPr_def_11))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18348,c_6527]) ).
tcf(c_18926,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))),iPr_def_12)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18348,c_14194]) ).
tcf(c_18979,plain,
( element(relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),powerset(iPr_def_11))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18065,c_6527]) ).
tcf(c_18980,plain,
( in(sK29(sK3,sK4),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19)
| ~ in(sK29(sK3,sK4),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))))) != sK2 ) ),
inference(superposition,[status(thm)],[c_18065,c_11342]) ).
tcf(c_18981,plain,
( in(sK29(sK3,sK4),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19)
| ~ in(sK29(sK3,sK4),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))))) != sK2 ) ),
inference(superposition,[status(thm)],[c_18065,c_11335]) ).
tcf(c_18982,plain,
( element(relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),iPr_def_12)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18065,c_14194]) ).
tcf(c_18983,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = sK7(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_18065,c_15183]) ).
tcf(c_18990,plain,
( in(sK29(sK3,sK4),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))))) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18981,c_14268]) ).
tcf(c_18996,plain,
( in(sK29(sK3,sK4),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK29(sK3,sK4),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))))) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18980,c_14268]) ).
tcf(c_19026,plain,
( element(sK2,iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ in(sK29(sK4,sK3),sK4) ),
inference(superposition,[status(thm)],[c_14752,c_14669]) ).
tcf(c_19036,plain,
( element(sK2,iPr_def_12)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ in(sK29(sK4,sK3),sK4) ),
inference(superposition,[status(thm)],[c_14752,c_14802]) ).
tcf(c_19049,plain,
( element(sK2,iPr_def_12)
| ( sK3 = sK4 )
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 ) ),
inference(superposition,[status(thm)],[c_14078,c_19026]) ).
tcf(c_19051,plain,
( element(sK2,iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19049,c_11343]) ).
tcf(c_19068,plain,
( element(sK2,iPr_def_12)
| ( sK3 = sK4 )
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(superposition,[status(thm)],[c_14079,c_19036]) ).
tcf(c_19071,plain,
( element(sK2,iPr_def_12)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19068,c_11343]) ).
tcf(c_19102,plain,
( empty_carrier(sK0)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15856]) ).
tcf(c_19103,plain,
( ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19102,c_11328,c_11314]) ).
tcf(c_19110,plain,
( element(sK5(sK29(sK4,sK3)),powerset(iPr_def_11))
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_19103,c_6527]) ).
tcf(c_19111,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_19103,c_11342]) ).
tcf(c_19112,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_19103,c_11335]) ).
tcf(c_19113,plain,
( element(sK5(sK29(sK4,sK3)),iPr_def_12)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_19103,c_14194]) ).
tcf(c_19144,plain,
( empty_carrier(sK0)
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15944]) ).
tcf(c_19145,plain,
( ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19144,c_11328,c_11314]) ).
tcf(c_19152,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) = sK7(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_14395,c_19145]) ).
tcf(c_19154,plain,
( element(sK7(sK29(sK4,sK3)),powerset(iPr_def_11))
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_19145,c_6527]) ).
tcf(c_19155,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_19145,c_11342]) ).
tcf(c_19156,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) != sK2 ) ),
inference(superposition,[status(thm)],[c_19145,c_11335]) ).
tcf(c_19157,plain,
( element(sK7(sK29(sK4,sK3)),iPr_def_12)
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_19145,c_14194]) ).
tcf(c_19158,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19145,c_15564]) ).
tcf(c_19159,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19145,c_15502]) ).
tcf(c_19160,plain,
( in(sK8(sK29(sK4,sK3)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19145,c_15458]) ).
tcf(c_19161,plain,
( in(sK8(sK29(sK4,sK3)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK8(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19145,c_15415]) ).
tcf(c_19226,plain,
( empty_carrier(sK0)
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_15950]) ).
tcf(c_19227,plain,
( ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19226,c_11328,c_11314]) ).
tcf(c_19234,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = sK7(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_14562,c_19227]) ).
tcf(c_19236,plain,
( element(sK7(sK29(sK3,sK4)),powerset(iPr_def_11))
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_19227,c_6527]) ).
tcf(c_19237,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_19227,c_11342]) ).
tcf(c_19238,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) != sK2 ) ),
inference(superposition,[status(thm)],[c_19227,c_11335]) ).
tcf(c_19239,plain,
( element(sK7(sK29(sK3,sK4)),iPr_def_12)
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_19227,c_14194]) ).
tcf(c_19274,plain,
( element(relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),powerset(iPr_def_11))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18068,c_6527]) ).
tcf(c_19275,plain,
( in(sK29(sK4,sK3),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19)
| ~ in(sK29(sK4,sK3),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))))) != sK2 ) ),
inference(superposition,[status(thm)],[c_18068,c_11342]) ).
tcf(c_19276,plain,
( in(sK29(sK4,sK3),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19)
| ~ in(sK29(sK4,sK3),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))))) != sK2 ) ),
inference(superposition,[status(thm)],[c_18068,c_11335]) ).
tcf(c_19277,plain,
( element(relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),iPr_def_12)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18068,c_14194]) ).
tcf(c_19278,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) = sK7(sK29(sK4,sK3)) ) ),
inference(superposition,[status(thm)],[c_18068,c_14876]) ).
tcf(c_19285,plain,
( in(sK29(sK4,sK3),sK4)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))))) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19276,c_14232]) ).
tcf(c_19291,plain,
( in(sK29(sK4,sK3),sK3)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK29(sK4,sK3),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),sK0,sK1)
| ( topstr_closure(sK0,relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))))) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19275,c_14232]) ).
tcf(c_19318,plain,
( element(sK2,iPr_def_12)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ in(sK29(sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_14752,c_14810]) ).
tcf(c_19328,plain,
( element(sK2,iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ in(sK29(sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_14752,c_14818]) ).
tcf(c_19338,plain,
( element(sK2,iPr_def_12)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ in(sK29(sK3,sK4),sK3) ),
inference(superposition,[status(thm)],[c_14756,c_14834]) ).
tcf(c_19348,plain,
( ( relation_rng_as_subset(iPr_def_19,the_carrier(sK0),the_mapping(sK0,sK1)) = relation_rng(the_mapping(sK0,sK1)) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_16976]) ).
tcf(c_19358,plain,
( element(sK2,iPr_def_12)
| ( sK3 = sK4 )
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(superposition,[status(thm)],[c_14089,c_19318]) ).
tcf(c_19361,plain,
( element(sK2,iPr_def_12)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19358,c_11343]) ).
tcf(c_19379,plain,
( element(sK2,iPr_def_12)
| ( sK3 = sK4 )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 ) ),
inference(superposition,[status(thm)],[c_14088,c_19328]) ).
tcf(c_19381,plain,
( element(sK2,iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19379,c_11343]) ).
tcf(c_19400,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))),powerset(iPr_def_11))
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18287,c_6527]) ).
tcf(c_19401,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))))),iPr_def_12)
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18287,c_14194]) ).
tcf(c_19416,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))),powerset(iPr_def_11))
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18290,c_6527]) ).
tcf(c_19417,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))))),iPr_def_12)
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = sK5(sK29(sK4,sK3)) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18290,c_14194]) ).
tcf(c_19428,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_17286,c_18351]) ).
tcf(c_19429,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_17012,c_18351]) ).
tcf(c_19430,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))),powerset(iPr_def_11))
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18351,c_6527]) ).
tcf(c_19431,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3))))),iPr_def_12)
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = sK7(sK29(sK4,sK3)) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18351,c_14194]) ).
tcf(c_19448,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_17936,c_18354]) ).
tcf(c_19449,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_17485,c_18354]) ).
tcf(c_19450,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))),powerset(iPr_def_11))
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18354,c_6527]) ).
tcf(c_19451,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))))),iPr_def_12)
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18354,c_14194]) ).
tcf(c_19479,plain,
! [X0: $i] :
( relation_of2_as_subset(the_InternalRel(sK27(X0)),the_carrier(sK27(X0)),the_carrier(sK27(X0)))
| ~ rel_str(sK27(X0)) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_19480,plain,
( relation_of2_as_subset(the_InternalRel(sK27(sK0)),the_carrier(sK27(sK0)),the_carrier(sK27(sK0)))
| ~ rel_str(sK27(sK0)) ),
inference(instantiation,[status(thm)],[c_19479]) ).
tcf(c_19505,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3)))),powerset(iPr_def_11))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3))),the_carrier(netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18218,c_6527]) ).
tcf(c_19506,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3)))),iPr_def_12)
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3))),the_carrier(netstr_restr_to_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18218,c_14194]) ).
tcf(c_19538,plain,
( ( relation_rng_as_subset(the_carrier(sK1),the_carrier(sK0),the_mapping(sK0,sK1)) = relation_rng(the_mapping(sK0,sK1)) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_11324,c_14461]) ).
tcf(c_19539,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(X2,X1,X0)),the_carrier(X2),the_mapping(X2,netstr_restr_to_element(X2,X1,X0))) = relation_rng(the_mapping(X2,netstr_restr_to_element(X2,X1,X0))) )
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_149,c_14461]) ).
tcf(c_19540,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(sK27(X0)),the_carrier(X0),the_mapping(X0,sK27(X0))) = relation_rng(the_mapping(X0,sK27(X0))) )
| ~ one_sorted_str(X0) ),
inference(superposition,[status(thm)],[c_161,c_14461]) ).
tcf(c_19541,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16271,c_14461]) ).
tcf(c_19542,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16022,c_14461]) ).
tcf(c_19543,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_17259,c_14461]) ).
tcf(c_19544,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16820,c_14461]) ).
tcf(c_19545,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_16516,c_14461]) ).
tcf(c_19546,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) )
| ~ one_sorted_str(sK0) ),
inference(superposition,[status(thm)],[c_17742,c_14461]) ).
tcf(c_19547,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17304,c_14461]) ).
tcf(c_19548,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17030,c_14461]) ).
tcf(c_19549,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17954,c_14461]) ).
tcf(c_19550,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_17503,c_14461]) ).
tcf(c_19560,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))) )
| ~ one_sorted_str(sK0) ),
inference(light_normalisation,[status(thm)],[c_19546,c_11303]) ).
tcf(c_19562,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) )
| ~ one_sorted_str(sK0) ),
inference(light_normalisation,[status(thm)],[c_19543,c_11303]) ).
tcf(c_19564,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_19550,c_11303]) ).
tcf(c_19566,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_19549,c_11303]) ).
tcf(c_19568,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_19548,c_11303]) ).
tcf(c_19570,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_19547,c_11303]) ).
tcf(c_19572,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_19545,c_11303]) ).
tcf(c_19574,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_19544,c_11303]) ).
tcf(c_19576,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_19542,c_11303]) ).
tcf(c_19578,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) )
| ~ one_sorted_str(sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_19541,c_11303]) ).
tcf(c_19586,plain,
relation_rng_as_subset(the_carrier(sK27(sK26)),the_carrier(sK26),the_mapping(sK26,sK27(sK26))) = relation_rng(the_mapping(sK26,sK27(sK26))),
inference(superposition,[status(thm)],[c_157,c_19540]) ).
tcf(c_19587,plain,
relation_rng_as_subset(the_carrier(sK27(sK0)),the_carrier(sK0),the_mapping(sK0,sK27(sK0))) = relation_rng(the_mapping(sK0,sK27(sK0))),
inference(superposition,[status(thm)],[c_11314,c_19540]) ).
tcf(c_19588,plain,
relation_rng_as_subset(the_carrier(sK27(sK1)),the_carrier(sK1),the_mapping(sK1,sK27(sK1))) = relation_rng(the_mapping(sK1,sK27(sK1))),
inference(superposition,[status(thm)],[c_14052,c_19540]) ).
tcf(c_19589,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(sK27(sK27(X0))),the_carrier(sK27(X0)),the_mapping(sK27(X0),sK27(sK27(X0)))) = relation_rng(the_mapping(sK27(X0),sK27(sK27(X0)))) )
| ~ one_sorted_str(X0) ),
inference(superposition,[status(thm)],[c_14059,c_19540]) ).
tcf(c_19590,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),the_mapping(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))))) = relation_rng(the_mapping(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_17902,c_19540]) ).
tcf(c_19591,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))),the_mapping(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))))) = relation_rng(the_mapping(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_17912,c_19540]) ).
tcf(c_19601,plain,
( element(relation_rng(the_mapping(sK26,sK27(sK26))),powerset(the_carrier(sK26)))
| ~ relation_of2_as_subset(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_19586,c_6527]) ).
tcf(c_19608,plain,
( element(sK2,iPr_def_12)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_19338,c_49,c_15535,c_16475,c_19338]) ).
tcf(c_19624,plain,
relation_rng_as_subset(the_carrier(sK27(sK26)),the_carrier(sK27(sK26)),the_InternalRel(sK27(sK26))) = relation_rng(the_InternalRel(sK27(sK26))),
inference(superposition,[status(thm)],[c_157,c_17627]) ).
tcf(c_19625,plain,
relation_rng_as_subset(the_carrier(sK27(sK0)),the_carrier(sK27(sK0)),the_InternalRel(sK27(sK0))) = relation_rng(the_InternalRel(sK27(sK0))),
inference(superposition,[status(thm)],[c_11314,c_17627]) ).
tcf(c_19626,plain,
relation_rng_as_subset(the_carrier(sK27(sK1)),the_carrier(sK27(sK1)),the_InternalRel(sK27(sK1))) = relation_rng(the_InternalRel(sK27(sK1))),
inference(superposition,[status(thm)],[c_14052,c_17627]) ).
tcf(c_19627,plain,
! [X0: $i] :
( ( relation_rng_as_subset(the_carrier(sK27(sK27(X0))),the_carrier(sK27(sK27(X0))),the_InternalRel(sK27(sK27(X0)))) = relation_rng(the_InternalRel(sK27(sK27(X0)))) )
| ~ one_sorted_str(X0) ),
inference(superposition,[status(thm)],[c_14059,c_17627]) ).
tcf(c_19628,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))))) = relation_rng(the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))))) ) ),
inference(superposition,[status(thm)],[c_17902,c_17627]) ).
tcf(c_19629,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))))) = relation_rng(the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))))) ) ),
inference(superposition,[status(thm)],[c_17912,c_17627]) ).
tcf(c_19689,plain,
( element(relation_rng(the_InternalRel(sK27(sK26))),powerset(the_carrier(sK27(sK26))))
| ~ relation_of2_as_subset(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26))) ),
inference(superposition,[status(thm)],[c_19624,c_6527]) ).
tcf(c_19704,plain,
( element(relation_rng(the_InternalRel(sK27(sK0))),powerset(the_carrier(sK27(sK0))))
| ~ relation_of2_as_subset(the_InternalRel(sK27(sK0)),the_carrier(sK27(sK0)),the_carrier(sK27(sK0))) ),
inference(superposition,[status(thm)],[c_19625,c_6527]) ).
tcf(c_19707,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15103,c_14532,c_15103]) ).
tcf(c_19719,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_18045,c_19707]) ).
tcf(c_19720,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14568,c_19707]) ).
tcf(c_19721,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14535,c_19707]) ).
tcf(c_19739,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15104,c_14532,c_15104]) ).
tcf(c_19751,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_18045,c_19739]) ).
tcf(c_19752,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14568,c_19739]) ).
tcf(c_19753,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14535,c_19739]) ).
tcf(c_19786,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15128,c_14565,c_15128]) ).
tcf(c_19798,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_18045,c_19786]) ).
tcf(c_19799,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14568,c_19786]) ).
tcf(c_19812,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15129,c_14565,c_15129]) ).
tcf(c_19824,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_18045,c_19812]) ).
tcf(c_19825,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14568,c_19812]) ).
tcf(c_19838,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15155,c_14532,c_15155]) ).
tcf(c_19850,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19227,c_19838]) ).
tcf(c_19851,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_15049,c_19838]) ).
tcf(c_19852,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14615,c_19838]) ).
tcf(c_19853,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14592,c_19838]) ).
tcf(c_19854,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14562,c_19838]) ).
tcf(c_19920,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15156,c_14532,c_15156]) ).
tcf(c_19932,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19227,c_19920]) ).
tcf(c_19933,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_15049,c_19920]) ).
tcf(c_19934,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14615,c_19920]) ).
tcf(c_19935,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14592,c_19920]) ).
tcf(c_19936,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14562,c_19920]) ).
tcf(c_19977,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15186,c_14529,c_15186]) ).
tcf(c_19989,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19227,c_19977]) ).
tcf(c_19990,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_15049,c_19977]) ).
tcf(c_19991,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14615,c_19977]) ).
tcf(c_19993,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14562,c_19977]) ).
tcf(c_20035,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15187,c_14529,c_15187]) ).
tcf(c_20047,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19227,c_20035]) ).
tcf(c_20048,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))) = sK5(sK29(sK3,sK4)) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_15049,c_20035]) ).
tcf(c_20049,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK7(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14615,c_20035]) ).
tcf(c_20051,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14562,c_20035]) ).
tcf(c_20081,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4)))),powerset(iPr_def_11))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4))),the_carrier(netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18219,c_6527]) ).
tcf(c_20082,plain,
( element(relation_rng(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4)))),iPr_def_12)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ relation_of2_as_subset(the_mapping(sK0,netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4))),the_carrier(netstr_restr_to_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18219,c_14194]) ).
tcf(c_20091,plain,
( element(relation_rng(the_mapping(sK26,sK27(sK26))),powerset(the_carrier(sK26)))
| ~ one_sorted_str(sK26)
| ~ net_str(sK27(sK26),sK26) ),
inference(superposition,[status(thm)],[c_190,c_19601]) ).
tcf(c_20092,plain,
( element(relation_rng(the_mapping(sK26,sK27(sK26))),powerset(the_carrier(sK26)))
| ~ net_str(sK27(sK26),sK26) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20091,c_157]) ).
tcf(c_20095,plain,
element(relation_rng(the_mapping(sK26,sK27(sK26))),powerset(the_carrier(sK26))),
inference(global_subsumption_just,[status(thm)],[c_20092,c_4791,c_20092]) ).
tcf(c_20101,plain,
( element(relation_rng(the_InternalRel(sK27(sK26))),powerset(the_carrier(sK27(sK26))))
| ~ rel_str(sK27(sK26)) ),
inference(superposition,[status(thm)],[c_116,c_19689]) ).
tcf(c_20109,plain,
( element(relation_rng(the_InternalRel(sK27(sK1))),powerset(the_carrier(sK27(sK1))))
| ~ relation_of2_as_subset(the_InternalRel(sK27(sK1)),the_carrier(sK27(sK1)),the_carrier(sK27(sK1))) ),
inference(superposition,[status(thm)],[c_19626,c_6527]) ).
tcf(c_20112,plain,
element(relation_rng(the_InternalRel(sK27(sK0))),powerset(the_carrier(sK27(sK0)))),
inference(global_subsumption_just,[status(thm)],[c_19704,c_66,c_197,c_14026,c_19480,c_19704]) ).
tcf(c_20145,plain,
( element(relation_rng(the_InternalRel(sK27(sK1))),powerset(the_carrier(sK27(sK1))))
| ~ rel_str(sK27(sK1)) ),
inference(superposition,[status(thm)],[c_116,c_20109]) ).
tcf(c_20170,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15313,c_14365,c_15313]) ).
tcf(c_20182,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19103,c_20170]) ).
tcf(c_20183,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14661,c_20170]) ).
tcf(c_20184,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14638,c_20170]) ).
tcf(c_20202,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15314,c_14365,c_15314]) ).
tcf(c_20214,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19103,c_20202]) ).
tcf(c_20215,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14661,c_20202]) ).
tcf(c_20216,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14638,c_20202]) ).
tcf(c_20234,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15336,c_14362,c_15336]) ).
tcf(c_20246,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19103,c_20234]) ).
tcf(c_20247,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14661,c_20234]) ).
tcf(c_20260,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_15337,c_14362,c_15337]) ).
tcf(c_20272,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19103,c_20260]) ).
tcf(c_20273,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_14661,c_20260]) ).
tcf(c_20313,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_18838,c_16000,c_18838]) ).
tcf(c_20325,plain,
( in(sK6(sK29(sK3,sK4)),sK3)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_18045,c_20313]) ).
tcf(c_20351,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_18839,c_16000,c_18839]) ).
tcf(c_20363,plain,
( in(sK6(sK29(sK3,sK4)),sK4)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK3,sK4))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK6(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK3,sK4)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_18045,c_20351]) ).
tcf(c_20371,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_19111,c_16494,c_19111]) ).
tcf(c_20383,plain,
( in(sK6(sK29(sK4,sK3)),sK3)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19103,c_20371]) ).
tcf(c_20391,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_19112,c_16494,c_19112]) ).
tcf(c_20403,plain,
( in(sK6(sK29(sK4,sK3)),sK4)
| ( subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))) = netstr_restr_to_element(sK0,sK1,sK8(sK29(sK4,sK3))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ in(sK6(sK29(sK4,sK3)),iPr_def_19)
| ~ netstr_induced_subset(sK5(sK29(sK4,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_19103,c_20391]) ).
tcf(c_20419,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))),iPr_def_11,the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) = relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))) ) ),
inference(superposition,[status(thm)],[c_14562,c_18714]) ).
tcf(c_20421,plain,
( element(relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),powerset(iPr_def_11))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18714,c_6527]) ).
tcf(c_20424,plain,
( element(relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),iPr_def_12)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ relation_of2_as_subset(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_18714,c_14194]) ).
tcf(c_20425,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_18714,c_20035]) ).
tcf(c_20426,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_18714,c_19977]) ).
tcf(c_20427,plain,
( in(sK8(sK29(sK3,sK4)),sK4)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_18714,c_19920]) ).
tcf(c_20428,plain,
( in(sK8(sK29(sK3,sK4)),sK3)
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ in(sK8(sK29(sK3,sK4)),iPr_def_19)
| ~ netstr_induced_subset(relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),sK0,sK1) ),
inference(superposition,[status(thm)],[c_18714,c_19838]) ).
tcf(c_20429,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))) = netstr_restr_to_element(sK0,sK1,sK6(sK29(sK3,sK4))) )
| ( relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_18714,c_19227]) ).
tcf(c_20432,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng(the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))) = sK7(sK29(sK3,sK4)) ) ),
inference(superposition,[status(thm)],[c_18714,c_14592]) ).
tcf(c_20512,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16799,c_14911]) ).
tcf(c_20513,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16494,c_14911]) ).
tcf(c_20514,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16248,c_14911]) ).
tcf(c_20515,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16000,c_14911]) ).
tcf(c_20516,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17936,c_14911]) ).
tcf(c_20517,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17485,c_14911]) ).
tcf(c_20518,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17286,c_14911]) ).
tcf(c_20519,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17012,c_14911]) ).
tcf(c_20520,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| ( relation_rng_as_subset(the_carrier(netstr_restr_to_element(X2,X1,X0)),the_carrier(netstr_restr_to_element(X2,X1,X0)),the_InternalRel(netstr_restr_to_element(X2,X1,X0))) = relation_rng(the_InternalRel(netstr_restr_to_element(X2,X1,X0))) )
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_14911,c_14418]) ).
tcf(c_20521,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| one_sorted_str(netstr_restr_to_element(X2,X1,X0))
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_14911,c_150]) ).
tcf(c_20528,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20519,c_11311]) ).
tcf(c_20530,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20518,c_11311]) ).
tcf(c_20532,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20517,c_11311]) ).
tcf(c_20534,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20516,c_11311]) ).
tcf(c_20536,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20515,c_11311]) ).
tcf(c_20538,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20514,c_11311]) ).
tcf(c_20540,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20513,c_11311]) ).
tcf(c_20542,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| rel_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20512,c_11311]) ).
tcf(c_20584,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16799,c_20521]) ).
tcf(c_20585,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16494,c_20521]) ).
tcf(c_20586,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16248,c_20521]) ).
tcf(c_20587,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_16000,c_20521]) ).
tcf(c_20588,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17936,c_20521]) ).
tcf(c_20589,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17485,c_20521]) ).
tcf(c_20590,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17286,c_20521]) ).
tcf(c_20591,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),the_carrier(sK1)) ),
inference(superposition,[status(thm)],[c_17012,c_20521]) ).
tcf(c_20592,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| ( relation_rng_as_subset(the_carrier(sK27(netstr_restr_to_element(X2,X1,X0))),the_carrier(sK27(netstr_restr_to_element(X2,X1,X0))),the_InternalRel(sK27(netstr_restr_to_element(X2,X1,X0)))) = relation_rng(the_InternalRel(sK27(netstr_restr_to_element(X2,X1,X0)))) )
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_20521,c_17627]) ).
tcf(c_20593,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| ( relation_rng_as_subset(the_carrier(sK27(netstr_restr_to_element(X2,X1,X0))),the_carrier(netstr_restr_to_element(X2,X1,X0)),the_mapping(netstr_restr_to_element(X2,X1,X0),sK27(netstr_restr_to_element(X2,X1,X0)))) = relation_rng(the_mapping(netstr_restr_to_element(X2,X1,X0),sK27(netstr_restr_to_element(X2,X1,X0)))) )
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_20521,c_19540]) ).
tcf(c_20594,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20591,c_11311]) ).
tcf(c_20595,plain,
( one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20594,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_20599,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20590,c_11311]) ).
tcf(c_20600,plain,
( one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))
| ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20599,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_20604,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20589,c_11311]) ).
tcf(c_20605,plain,
( one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20604,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_20609,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20588,c_11311]) ).
tcf(c_20610,plain,
( one_sorted_str(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))
| ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20609,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_20614,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20587,c_11311]) ).
tcf(c_20615,plain,
( one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20614,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_20619,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20586,c_11311]) ).
tcf(c_20620,plain,
( one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))
| ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20619,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_20624,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20585,c_11311]) ).
tcf(c_20625,plain,
( one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20624,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_20629,plain,
( empty_carrier(sK0)
| empty_carrier(sK1)
| one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ one_sorted_str(sK0)
| ~ net_str(sK1,sK0)
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(light_normalisation,[status(thm)],[c_20584,c_11311]) ).
tcf(c_20630,plain,
( one_sorted_str(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))
| ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20629,c_11328,c_11327,c_11314,c_11324]) ).
tcf(c_20662,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ( relation_rng_as_subset(the_carrier(sK28(X1,X0)),the_carrier(X1),the_mapping(X1,sK28(X1,X0))) = relation_rng(the_mapping(X1,sK28(X1,X0))) )
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(superposition,[status(thm)],[c_3761,c_14461]) ).
tcf(c_20663,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| rel_str(sK28(X1,X0))
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(superposition,[status(thm)],[c_3761,c_186]) ).
tcf(c_20664,plain,
! [X0: $i] :
( empty_carrier(sK0)
| empty_carrier(X0)
| ( relation_rng_as_subset(the_carrier(sK28(sK0,X0)),iPr_def_11,the_mapping(sK0,sK28(sK0,X0))) = relation_rng(the_mapping(sK0,sK28(sK0,X0))) )
| ~ one_sorted_str(sK0)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,sK0) ),
inference(superposition,[status(thm)],[c_3761,c_16331]) ).
tcf(c_20665,plain,
! [X0: $i] :
( empty_carrier(sK1)
| empty_carrier(X0)
| ( relation_rng_as_subset(the_carrier(sK28(sK1,X0)),iPr_def_19,the_mapping(sK1,sK28(sK1,X0))) = relation_rng(the_mapping(sK1,sK28(sK1,X0))) )
| ~ one_sorted_str(sK1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,sK1) ),
inference(superposition,[status(thm)],[c_3761,c_16393]) ).
tcf(c_20673,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( relation_rng_as_subset(the_carrier(sK28(sK1,X0)),iPr_def_19,the_mapping(sK1,sK28(sK1,X0))) = relation_rng(the_mapping(sK1,sK28(sK1,X0))) )
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20665,c_11327,c_14052]) ).
tcf(c_20679,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( relation_rng_as_subset(the_carrier(sK28(sK0,X0)),iPr_def_11,the_mapping(sK0,sK28(sK0,X0))) = relation_rng(the_mapping(sK0,sK28(sK0,X0))) )
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20664,c_11328,c_11314]) ).
tcf(c_20728,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ( relation_rng_as_subset(the_carrier(sK28(X1,X0)),the_carrier(sK28(X1,X0)),the_InternalRel(sK28(X1,X0))) = relation_rng(the_InternalRel(sK28(X1,X0))) )
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(superposition,[status(thm)],[c_20663,c_14418]) ).
tcf(c_20729,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| one_sorted_str(sK28(X1,X0))
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(superposition,[status(thm)],[c_20663,c_150]) ).
tcf(c_20760,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ( relation_rng_as_subset(the_carrier(sK27(sK28(X1,X0))),the_carrier(sK27(sK28(X1,X0))),the_InternalRel(sK27(sK28(X1,X0)))) = relation_rng(the_InternalRel(sK27(sK28(X1,X0)))) )
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(superposition,[status(thm)],[c_20729,c_17627]) ).
tcf(c_20761,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ( relation_rng_as_subset(the_carrier(sK27(sK28(X1,X0))),the_carrier(sK28(X1,X0)),the_mapping(sK28(X1,X0),sK27(sK28(X1,X0)))) = relation_rng(the_mapping(sK28(X1,X0),sK27(sK28(X1,X0)))) )
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(superposition,[status(thm)],[c_20729,c_19540]) ).
tcf(c_20826,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))))) = relation_rng(the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20595,c_17627]) ).
tcf(c_20827,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))))) = relation_rng(the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20595,c_19540]) ).
tcf(c_20840,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))))) = relation_rng(the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20600,c_17627]) ).
tcf(c_20841,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))),the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))))) = relation_rng(the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20600,c_19540]) ).
tcf(c_20854,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))))) = relation_rng(the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20605,c_17627]) ).
tcf(c_20855,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))))) = relation_rng(the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20605,c_19540]) ).
tcf(c_20868,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))))) = relation_rng(the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20610,c_17627]) ).
tcf(c_20869,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),the_carrier(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))),the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))))) = relation_rng(the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20610,c_19540]) ).
tcf(c_20883,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))))) = relation_rng(the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20615,c_17627]) ).
tcf(c_20884,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))))) = relation_rng(the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20615,c_19540]) ).
tcf(c_20909,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))))) = relation_rng(the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20620,c_17627]) ).
tcf(c_20910,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))),the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))))) = relation_rng(the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20620,c_19540]) ).
tcf(c_20934,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))))) = relation_rng(the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20625,c_17627]) ).
tcf(c_20935,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))))) = relation_rng(the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20625,c_19540]) ).
tcf(c_20975,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))))) = relation_rng(the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20630,c_17627]) ).
tcf(c_20976,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( relation_rng_as_subset(the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),the_carrier(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))),the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))))) = relation_rng(the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20630,c_19540]) ).
tcf(c_20985,plain,
! [X0: $i] :
( ( net_str_of(X0,the_carrier(sK27(X0)),the_InternalRel(sK27(X0)),the_mapping(X0,sK27(X0))) = sK27(X0) )
| ~ one_sorted_str(X0) ),
inference(global_subsumption_just,[status(thm)],[c_14956,c_2984]) ).
tcf(c_20991,plain,
net_str_of(sK26,the_carrier(sK27(sK26)),the_InternalRel(sK27(sK26)),the_mapping(sK26,sK27(sK26))) = sK27(sK26),
inference(superposition,[status(thm)],[c_157,c_20985]) ).
tcf(c_20992,plain,
net_str_of(sK0,the_carrier(sK27(sK0)),the_InternalRel(sK27(sK0)),the_mapping(sK0,sK27(sK0))) = sK27(sK0),
inference(superposition,[status(thm)],[c_11314,c_20985]) ).
tcf(c_20993,plain,
net_str_of(sK1,the_carrier(sK27(sK1)),the_InternalRel(sK27(sK1)),the_mapping(sK1,sK27(sK1))) = sK27(sK1),
inference(superposition,[status(thm)],[c_14052,c_20985]) ).
tcf(c_20994,plain,
! [X0: $i] :
( ( net_str_of(sK27(X0),the_carrier(sK27(sK27(X0))),the_InternalRel(sK27(sK27(X0))),the_mapping(sK27(X0),sK27(sK27(X0)))) = sK27(sK27(X0)) )
| ~ one_sorted_str(X0) ),
inference(superposition,[status(thm)],[c_14059,c_20985]) ).
tcf(c_20995,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( net_str_of(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)))),the_mapping(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4)),sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))))) = sK27(subnetstr_of_element(sK0,sK1,sK29(sK3,sK4))) ) ),
inference(superposition,[status(thm)],[c_17902,c_20985]) ).
tcf(c_20996,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( net_str_of(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)))),the_mapping(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3)),sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))))) = sK27(subnetstr_of_element(sK0,sK1,sK29(sK4,sK3))) ) ),
inference(superposition,[status(thm)],[c_17912,c_20985]) ).
tcf(c_20997,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| ( net_str_of(netstr_restr_to_element(X2,X1,X0),the_carrier(sK27(netstr_restr_to_element(X2,X1,X0))),the_InternalRel(sK27(netstr_restr_to_element(X2,X1,X0))),the_mapping(netstr_restr_to_element(X2,X1,X0),sK27(netstr_restr_to_element(X2,X1,X0)))) = sK27(netstr_restr_to_element(X2,X1,X0)) )
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(superposition,[status(thm)],[c_20521,c_20985]) ).
tcf(c_20998,plain,
( ( sK6(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( net_str_of(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))))) = sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20630,c_20985]) ).
tcf(c_20999,plain,
( ( topstr_closure(sK0,sK5(sK29(sK4,sK3))) = sK2 )
| ( net_str_of(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))))),the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))))) = sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK4,sK3)))) )
| ~ element(sK8(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20625,c_20985]) ).
tcf(c_21000,plain,
( ( sK6(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( net_str_of(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))))) = sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20620,c_20985]) ).
tcf(c_21001,plain,
( ( topstr_closure(sK0,sK5(sK29(sK3,sK4))) = sK2 )
| ( net_str_of(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))))),the_mapping(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))))) = sK27(subnetstr_of_element(sK0,sK1,sK8(sK29(sK3,sK4)))) )
| ~ element(sK8(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20615,c_20985]) ).
tcf(c_21002,plain,
( ( sK8(sK29(sK3,sK4)) = sK29(sK3,sK4) )
| ( net_str_of(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))))) = sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20610,c_20985]) ).
tcf(c_21003,plain,
( ( topstr_closure(sK0,sK7(sK29(sK3,sK4))) = sK2 )
| ( net_str_of(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))))),the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))))) = sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK3,sK4)))) )
| ~ element(sK6(sK29(sK3,sK4)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20605,c_20985]) ).
tcf(c_21004,plain,
( ( sK8(sK29(sK4,sK3)) = sK29(sK4,sK3) )
| ( net_str_of(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))))) = sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20600,c_20985]) ).
tcf(c_21005,plain,
( ( topstr_closure(sK0,sK7(sK29(sK4,sK3))) = sK2 )
| ( net_str_of(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),the_carrier(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),the_InternalRel(sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))))),the_mapping(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3))),sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))))) = sK27(subnetstr_of_element(sK0,sK1,sK6(sK29(sK4,sK3)))) )
| ~ element(sK6(sK29(sK4,sK3)),iPr_def_19) ),
inference(superposition,[status(thm)],[c_20595,c_20985]) ).
tcf(c_21006,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| ( net_str_of(sK28(X1,X0),the_carrier(sK27(sK28(X1,X0))),the_InternalRel(sK27(sK28(X1,X0))),the_mapping(sK28(X1,X0),sK27(sK28(X1,X0)))) = sK27(sK28(X1,X0)) )
| ~ one_sorted_str(X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| ~ net_str(X0,X1) ),
inference(superposition,[status(thm)],[c_20729,c_20985]) ).
tcf(c_21090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( the_mapping(sK26,sK27(sK26)) = X3 )
| ~ one_sorted_str(sK26)
| ~ function(the_mapping(sK26,sK27(sK26)))
| ~ quasi_total(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ~ relation_of2(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26)))
| ~ relation_of2(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(superposition,[status(thm)],[c_20991,c_113]) ).
tcf(c_21091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( the_InternalRel(sK27(sK26)) = X2 )
| ~ one_sorted_str(sK26)
| ~ function(the_mapping(sK26,sK27(sK26)))
| ~ quasi_total(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ~ relation_of2(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26)))
| ~ relation_of2(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(superposition,[status(thm)],[c_20991,c_112]) ).
tcf(c_21092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( the_carrier(sK27(sK26)) = X1 )
| ~ one_sorted_str(sK26)
| ~ function(the_mapping(sK26,sK27(sK26)))
| ~ quasi_total(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ~ relation_of2(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26)))
| ~ relation_of2(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(superposition,[status(thm)],[c_20991,c_111]) ).
tcf(c_21093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sK26 )
| ~ one_sorted_str(sK26)
| ~ function(the_mapping(sK26,sK27(sK26)))
| ~ quasi_total(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ~ relation_of2(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26)))
| ~ relation_of2(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(superposition,[status(thm)],[c_20991,c_110]) ).
tcf(c_21094,plain,
( empty(the_carrier(sK27(sK26)))
| ~ one_sorted_str(sK26)
| ~ empty_carrier(sK27(sK26))
| ~ function(the_mapping(sK26,sK27(sK26)))
| ~ quasi_total(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ~ relation_of2(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26)))
| ~ relation_of2(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_20991,c_135]) ).
tcf(c_21095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( the_mapping(sK26,sK27(sK26)) = X3 )
| ~ function(X3)
| ~ one_sorted_str(X0)
| ~ relation_of2(X2,X1,X1)
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(superposition,[status(thm)],[c_20991,c_113]) ).
tcf(c_21096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( the_InternalRel(sK27(sK26)) = X2 )
| ~ function(X3)
| ~ one_sorted_str(X0)
| ~ relation_of2(X2,X1,X1)
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(superposition,[status(thm)],[c_20991,c_112]) ).
tcf(c_21097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( the_carrier(sK27(sK26)) = X1 )
| ~ function(X3)
| ~ one_sorted_str(X0)
| ~ relation_of2(X2,X1,X1)
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(superposition,[status(thm)],[c_20991,c_111]) ).
tcf(c_21098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sK26 )
| ~ function(X3)
| ~ one_sorted_str(X0)
| ~ relation_of2(X2,X1,X1)
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(superposition,[status(thm)],[c_20991,c_110]) ).
tcf(c_21127,plain,
( empty(the_carrier(sK27(sK26)))
| ~ empty_carrier(sK27(sK26))
| ~ function(the_mapping(sK26,sK27(sK26)))
| ~ quasi_total(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ~ relation_of2(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26)))
| ~ relation_of2(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21094,c_157]) ).
tcf(c_21134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sK26 )
| ~ function(the_mapping(sK26,sK27(sK26)))
| ~ quasi_total(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ~ relation_of2(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26)))
| ~ relation_of2(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21093,c_157]) ).
tcf(c_21141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( the_carrier(sK27(sK26)) = X1 )
| ~ function(the_mapping(sK26,sK27(sK26)))
| ~ quasi_total(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ~ relation_of2(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26)))
| ~ relation_of2(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21092,c_157]) ).
tcf(c_21148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( the_InternalRel(sK27(sK26)) = X2 )
| ~ function(the_mapping(sK26,sK27(sK26)))
| ~ quasi_total(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ~ relation_of2(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26)))
| ~ relation_of2(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21091,c_157]) ).
tcf(c_21155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( the_mapping(sK26,sK27(sK26)) = X3 )
| ~ function(the_mapping(sK26,sK27(sK26)))
| ~ quasi_total(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ~ relation_of2(the_InternalRel(sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK27(sK26)))
| ~ relation_of2(the_mapping(sK26,sK27(sK26)),the_carrier(sK27(sK26)),the_carrier(sK26))
| ( net_str_of(X0,X1,X2,X3) != sK27(sK26) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21090,c_157]) ).
tcf(c_21188,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_21155,c_21148,c_21141,c_21134,c_21127,c_21098,c_21097,c_21096,c_21095,c_21094,c_21093,c_21092,c_21091,c_21090,c_21006,c_21005,c_21004,c_21003,c_21002,c_21001,c_21000,c_20999,c_20998,c_20997,c_20996,c_20995,c_20994,c_20993,c_20992,c_20991,c_20976,c_20975,c_20935,c_20934,c_20910,c_20909,c_20884,c_20883,c_20869,c_20868,c_20855,c_20854,c_20841,c_20840,c_20827,c_20826,c_20761,c_20760,c_20729,c_20728,c_20679,c_20673,c_20665,c_20664,c_20663,c_20662,c_20630,c_20629,c_20625,c_20624,c_20620,c_20619,c_20615,c_20614,c_20610,c_20609,c_20605,c_20604,c_20600,c_20599,c_20595,c_20594,c_20593,c_20592,c_20591,c_20590,c_20589,c_20588,c_20587,c_20586,c_20585,c_20584,c_20542,c_20540,c_20538,c_20536,c_20534,c_20532,c_20530,c_20528,c_20521,c_20520,c_20519,c_20518,c_20517,c_20516,c_20515,c_20514,c_20513,c_20512,c_20428,c_20427,c_20426,c_20425,c_20424,c_20421,c_20419,c_20432,c_20429,c_20403,c_20391,c_20383,c_20371,c_20363,c_20351,c_20325,c_20313,c_20273,c_20272,c_20260,c_20247,c_20246,c_20234,c_20216,c_20215,c_20214,c_20202,c_20184,c_20183,c_20182,c_20170,c_20145,c_20112,c_20109,c_20101,c_20095,c_20092,c_20091,c_20082,c_20081,c_20051,c_20049,c_20048,c_20047,c_20035,c_19993,c_19991,c_19990,c_19989,c_19977,c_19936,c_19935,c_19934,c_19933,c_19932,c_19920,c_19854,c_19853,c_19852,c_19851,c_19850,c_19838,c_19825,c_19824,c_19812,c_19799,c_19798,c_19786,c_19753,c_19752,c_19751,c_19739,c_19721,c_19720,c_19719,c_19707,c_19704,c_19689,c_19629,c_19628,c_19627,c_19626,c_19625,c_19624,c_19608,c_19601,c_19591,c_19590,c_19589,c_19588,c_19587,c_19586,c_19578,c_19576,c_19574,c_19572,c_19570,c_19568,c_19566,c_19564,c_19562,c_19560,c_19550,c_19549,c_19548,c_19547,c_19546,c_19545,c_19544,c_19543,c_19542,c_19541,c_19540,c_19539,c_19538,c_19506,c_19505,c_19451,c_19450,c_19449,c_19448,c_19431,c_19430,c_19429,c_19428,c_19417,c_19416,c_19401,c_19400,c_19381,c_19379,c_19361,c_19358,c_19348,c_19338,c_19328,c_19318,c_19291,c_19285,c_19277,c_19276,c_19275,c_19274,c_19278,c_19239,c_19238,c_19237,c_19236,c_19234,c_19227,c_19226,c_19161,c_19160,c_19159,c_19158,c_19157,c_19156,c_19155,c_19154,c_19152,c_19145,c_19144,c_19113,c_19112,c_19111,c_19110,c_19103,c_19102,c_19071,c_19068,c_19051,c_19049,c_19036,c_19026,c_18996,c_18990,c_18982,c_18981,c_18980,c_18979,c_18983,c_18926,c_18925,c_18923,c_18910,c_18909,c_18908,c_18880,c_18877,c_18840,c_18839,c_18838,c_18837,c_18826,c_18825,c_18823,c_18810,c_18809,c_18808,c_18794,c_18793,c_18790,c_18756,c_18755,c_18754,c_18753,c_18738,c_18737,c_18734,c_18717,c_18716,c_18715,c_18714,c_18683,c_18679,c_18675,c_18671,c_18667,c_18663,c_18653,c_18652,c_18651,c_18645,c_18644,c_18643,c_18638,c_18637,c_18625,c_18621,c_18617,c_18613,c_18609,c_18605,c_18591,c_18590,c_18589,c_18583,c_18582,c_18581,c_18580,c_18579,c_18569,c_18561,c_18558,c_18541,c_18533,c_18425,c_18424,c_18423,c_18422,c_18404,c_18400,c_18399,c_18398,c_18354,c_18351,c_18348,c_18345,c_18342,c_18339,c_18331,c_18330,c_18329,c_18323,c_18322,c_18321,c_18316,c_18315,c_18290,c_18287,c_18284,c_18281,c_18278,c_18275,c_18263,c_18262,c_18261,c_18255,c_18254,c_18253,c_18252,c_18251,c_18219,c_18218,c_18217,c_18216,c_18207,c_18203,c_18202,c_18201,c_18169,c_18163,c_18162,c_18161,c_18160,c_18152,c_18151,c_18079,c_18074,c_18072,c_18071,c_18070,c_18069,c_18068,c_18067,c_18066,c_18065,c_18064,c_18063,c_18062,c_18061,c_18060,c_18052,c_18045,c_18044,c_18014,c_18013,c_18002,c_18001,c_17969,c_17968,c_17964,c_17963,c_17959,c_17958,c_17954,c_17953,c_17949,c_17948,c_17947,c_17946,c_17945,c_17944,c_17943,c_17936,c_17935,c_17912,c_17911,c_17902,c_17901,c_17878,c_17871,c_17864,c_17857,c_17827,c_17826,c_17815,c_17814,c_17802,c_17749,c_17748,c_17742,c_17736,c_17735,c_17729,c_17723,c_17717,c_17713,c_17706,c_17649,c_17648,c_17647,c_17646,c_17627,c_17626,c_17596,c_17595,c_17591,c_17590,c_17586,c_17585,c_17581,c_17580,c_17576,c_17575,c_17574,c_17573,c_17572,c_17571,c_17570,c_17518,c_17517,c_17513,c_17512,c_17508,c_17507,c_17503,c_17502,c_17498,c_17497,c_17496,c_17495,c_17494,c_17493,c_17492,c_17485,c_17484,c_17464,c_17463,c_17452,c_17451,c_17319,c_17318,c_17314,c_17313,c_17309,c_17308,c_17304,c_17303,c_17299,c_17298,c_17297,c_17296,c_17295,c_17294,c_17293,c_17286,c_17285,c_17269,c_17266,c_17265,c_17259,c_17255,c_17254,c_17248,c_17220,c_17214,c_17178,c_17177,c_17165,c_17138,c_17137,c_17136,c_17135,c_17134,c_17120,c_17119,c_17115,c_17114,c_17110,c_17109,c_17105,c_17104,c_17100,c_17099,c_17098,c_17097,c_17096,c_17095,c_17094,c_17080,c_17079,c_17068,c_17067,c_17045,c_17044,c_17040,c_17039,c_17035,c_17034,c_17030,c_17029,c_17025,c_17024,c_17023,c_17022,c_17021,c_17020,c_17019,c_17012,c_17011,c_16997,c_16977,c_16976,c_16975,c_16973,c_16966,c_16964,c_16956,c_16955,c_16946,c_16923,c_16919,c_16918,c_16907,c_16903,c_16902,c_16864,c_16854,c_16835,c_16834,c_16830,c_16829,c_16825,c_16824,c_16820,c_16819,c_16815,c_16814,c_16811,c_16810,c_16809,c_16808,c_16807,c_16806,c_16799,c_16798,c_16783,c_16769,c_16768,c_16767,c_16702,c_16701,c_16700,c_16698,c_16697,c_16696,c_16669,c_16668,c_16667,c_16666,c_16665,c_16664,c_16655,c_16654,c_16653,c_16618,c_16617,c_16592,c_16586,c_16581,c_16580,c_16579,c_16578,c_16569,c_16564,c_16563,c_16552,c_16541,c_16531,c_16530,c_16526,c_16525,c_16521,c_16520,c_16516,c_16515,c_16511,c_16510,c_16506,c_16505,c_16504,c_16503,c_16502,c_16501,c_16494,c_16493,c_16470,c_16460,c_16456,c_16455,c_16444,c_16440,c_16439,c_16428,c_16427,c_16412,c_16411,c_16394,c_16393,c_16392,c_16391,c_16363,c_16362,c_16352,c_16351,c_16343,c_16342,c_16335,c_16332,c_16331,c_16330,c_16329,c_16314,c_16304,c_16286,c_16285,c_16281,c_16280,c_16276,c_16275,c_16271,c_16270,c_16266,c_16265,c_16262,c_16261,c_16260,c_16259,c_16258,c_16257,c_16248,c_16247,c_16230,c_16214,c_16213,c_16212,c_16199,c_16194,c_16193,c_16182,c_16161,c_16160,c_16080,c_16074,c_16069,c_16068,c_16067,c_16066,c_16055,c_16037,c_16036,c_16032,c_16031,c_16027,c_16026,c_16022,c_16021,c_16017,c_16016,c_16012,c_16011,c_16010,c_16009,c_16008,c_16007,c_16000,c_15999,c_15950,c_15944,c_15938,c_15932,c_15926,c_15920,c_15906,c_15905,c_15904,c_15898,c_15897,c_15896,c_15891,c_15890,c_15856,c_15850,c_15844,c_15838,c_15832,c_15826,c_15808,c_15807,c_15806,c_15800,c_15799,c_15798,c_15797,c_15796,c_15761,c_15760,c_15759,c_15758,c_15747,c_15744,c_15743,c_15709,c_15701,c_15700,c_15699,c_15648,c_15647,c_15646,c_15613,c_15612,c_15611,c_15579,c_15577,c_15576,c_15564,c_15517,c_15515,c_15514,c_15502,c_15473,c_15472,c_15471,c_15470,c_15458,c_15430,c_15429,c_15428,c_15427,c_15415,c_15396,c_15395,c_15394,c_15393,c_15366,c_15365,c_15364,c_15363,c_15338,c_15337,c_15336,c_15335,c_15315,c_15314,c_15313,c_15312,c_15190,c_15187,c_15186,c_15185,c_15183,c_15157,c_15156,c_15155,c_15154,c_15152,c_15130,c_15129,c_15128,c_15127,c_15105,c_15104,c_15103,c_15102,c_15092,c_15072,c_15049,c_15042,c_15041,c_15033,c_15020,c_15013,c_15012,c_15008,c_14993,c_14992,c_14980,c_14911,c_14883,c_14880,c_14879,c_14878,c_14876,c_14867,c_14864,c_14848,c_14845,c_14834,c_14826,c_14818,c_14810,c_14802,c_14795,c_14786,c_14785,c_14756,c_14755,c_14752,c_14751,c_14690,c_14689,c_14688,c_14687,c_14685,c_14677,c_14669,c_14661,c_14656,c_14648,c_14638,c_14633,c_14625,c_14615,c_14610,c_14606,c_14592,c_14587,c_14583,c_14568,c_14565,c_14562,c_14555,c_14554,c_14548,c_14547,c_14546,c_14535,c_14532,c_14529,c_14522,c_14521,c_14515,c_14514,c_14513,c_14502,c_14501,c_14495,c_14466,c_14463,c_14460,c_14459,c_14458,c_14457,c_14438,c_14435,c_14434,c_14433,c_14432,c_14431,c_14420,c_14419,c_14410,c_14401,c_14398,c_14395,c_14388,c_14387,c_14385,c_14384,c_14383,c_14368,c_14365,c_14362,c_14355,c_14354,c_14352,c_14351,c_14350,c_14328,c_14326,c_14317,c_14299,c_14297,c_14288,c_14281,c_14268,c_14264,c_14263,c_14262,c_14257,c_14252,c_14245,c_14232,c_14228,c_14227,c_14226,c_14225,c_14216,c_14202,c_14194,c_14179,c_14178,c_14177,c_14176,c_14175,c_14095,c_14094,c_14093,c_14092,c_14091,c_14090,c_14089,c_14088,c_14087,c_14085,c_14084,c_14083,c_14082,c_14081,c_14080,c_14079,c_14078,c_14077,c_14069,c_14067,c_14059,c_14053,c_14052,c_14044,c_14043,c_14034,c_14033,c_14032,c_14031,c_14023,c_14022,c_14021,c_14014,c_14013,c_14012,c_14009,c_14008,c_14007,c_14006,c_13955,c_13936,c_13929,c_13909,c_13908,c_13899,c_13898,c_11342,c_11341,c_11339,c_11336,c_11335,c_11334,c_11332,c_11329,c_11323,c_11322,c_11321,c_11320,c_11319,c_11318,c_11317,c_11316,c_11315,c_11313,c_11312,c_11311,c_11310,c_11309,c_11308,c_11307,c_11306,c_11305,c_11304,c_11303,c_11302,c_3872,c_3845,c_3818,c_3791,c_3761,c_6571,c_11314,c_15280,c_14957,c_20985,c_14956,c_14955,c_14750,c_14749,c_14462,c_14461,c_14045,c_14418,c_2582,c_2571,c_2556,c_6527,c_6525,c_192,c_191,c_190,c_189,c_188,c_187,c_186,c_183,c_180,c_178,c_174,c_173,c_172,c_171,c_170,c_168,c_166,c_163,c_162,c_161,c_159,c_158,c_157,c_156,c_151,c_150,c_149,c_148,c_147,c_146,c_145,c_143,c_140,c_137,c_135,c_124,c_123,c_121,c_120,c_119,c_118,c_117,c_116,c_115,c_114,c_113,c_112,c_111,c_110,c_108,c_107,c_105,c_104,c_88,c_87,c_83,c_82,c_80,c_11324,c_11325,c_11326,c_11327,c_11328,c_11330,c_11331,c_11333,c_11337,c_11338,c_11340,c_11343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU401+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n002.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 14:02:59 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.42
% 0.15/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.42
% 0.15/5.42 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 4.70/7.28 % SZS status Started for theBenchmark.p
% 4.70/7.28 % SZS status Theorem for theBenchmark.p
% 4.70/7.28
% 4.70/7.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.70/7.28
% 4.70/7.28 % ------ iProver source info
% 4.70/7.28
% 4.70/7.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.70/7.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.70/7.28 % git: non_committed_changes: false
% 4.70/7.28
% 4.70/7.28 % ------ Parsing...
% 4.70/7.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.70/7.28
% 4.70/7.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe_e %
% 4.70/7.28
% 4.70/7.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.70/7.28
% 4.70/7.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.70/7.28 % ------ Proving...
% 4.70/7.28 % ------ Problem Properties
% 4.70/7.28
% 4.70/7.28 %
% 4.70/7.28 % clauses 111
% 4.70/7.28 % conjectures 20
% 4.70/7.28 % EPR 30
% 4.70/7.28 % Horn 86
% 4.70/7.28 % unary 39
% 4.70/7.28 % binary 32
% 4.70/7.28 % lits 331
% 4.70/7.28 % lits eq 32
% 4.70/7.28 % fd_pure 0
% 4.70/7.28 % fd_pseudo 0
% 4.70/7.28 % fd_cond 0
% 4.70/7.28 % fd_pseudo_cond 6
% 4.70/7.28 % AC symbols 0
% 4.70/7.28
% 4.70/7.28 % ------ Schedule dynamic 5 is on
% 4.70/7.28
% 4.70/7.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.70/7.28
% 4.70/7.28
% 4.70/7.28 % ------
% 4.70/7.28 % Current options:
% 4.70/7.28 % ------
% 4.70/7.28
% 4.70/7.28
% 4.70/7.28 %
% 4.70/7.28
% 4.70/7.28 % ------ Proving...
% 4.70/7.28 %
% 4.70/7.28
% 4.70/7.28 % SZS status Theorem for theBenchmark.p
% 4.70/7.28
% 4.70/7.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.47/7.33
% 10.47/7.33
%------------------------------------------------------------------------------