%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET653+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Wed Oct 7 10:40:45 AM UTC 2026
% Result : Theorem 1.55s 0.53s
% Output : CNFRefutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 23
% Syntax : Number of formulae : 412 ( 115 unt; 0 typ; 0 def)
% Number of atoms : 4010 (1080 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 7516 (1396 ~;1324 |; 27 &;4572 @)
% ( 18 <=>; 179 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 8 con; 0-2 aty)
% Number of variables : 1022 ( 0 ^;1007 !; 15 ?;1022 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binary_relation_type,type,
binary_relation_type: $i ).
thf(tp_cross_product,type,
cross_product: $i > $i > $i ).
thf(tp_domain_of,type,
domain_of: $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_ilf_type,type,
ilf_type: $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_member_type,type,
member_type: $i > $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_range_of,type,
range_of: $i > $i ).
thf(tp_relation_like,type,
relation_like: $i > $o ).
thf(tp_relation_type,type,
relation_type: $i > $i > $i ).
thf(tp_sK10_SY94,type,
sK10_SY94: $i > $i > $i ).
thf(tp_sK11_SY101,type,
sK11_SY101: $i > $i > $i ).
thf(tp_sK12_SY107,type,
sK12_SY107: $i > $i > $i ).
thf(tp_sK13_SY112,type,
sK13_SY112: $i > $i > $i ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY91,type,
sK3_SY91: $i ).
thf(tp_sK4_SY88,type,
sK4_SY88: $i > $i ).
thf(tp_sK5_SY97,type,
sK5_SY97: $i ).
thf(tp_sK6_SY104,type,
sK6_SY104: $i > $i > $i ).
thf(tp_sK7_SY73,type,
sK7_SY73: $i > $i ).
thf(tp_sK8_SY83,type,
sK8_SY83: $i > $i ).
thf(tp_sK9_SY71,type,
sK9_SY71: $i > $i ).
thf(tp_set_type,type,
set_type: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_type,type,
subset_type: $i > $i ).
thf(1,axiom,
! [B: $i] : ( ilf_type @ B @ set_type ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
thf(2,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( ordered_pair @ B @ C ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
thf(3,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) )
=> ( relation_like @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
thf(4,axiom,
! [B: $i] :
( ( ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( relation_like @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
thf(5,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( relation_like @ B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ B )
=> ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ? [E: $i] :
( ( ilf_type @ E @ set_type )
& ( C
= ( ordered_pair @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
thf(6,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( empty @ B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ~ ( member @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).
thf(7,axiom,
! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ? [C: $i] : ( ilf_type @ C @ ( member_type @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).
thf(8,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ~ ( empty @ C )
& ( ilf_type @ C @ set_type ) )
=> ( ( ilf_type @ B @ ( member_type @ C ) )
<=> ( member @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
thf(9,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ~ ( empty @ ( power_set @ B ) )
& ( ilf_type @ ( power_set @ B ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
thf(10,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ B @ ( power_set @ C ) )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
thf(11,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
thf(12,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
thf(13,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ilf_type @ C @ ( subset_type @ B ) )
<=> ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
thf(14,axiom,
! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( range_of @ B ) @ set_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
thf(15,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( cross_product @ B @ C ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
thf(16,axiom,
! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ B ) @ set_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
thf(17,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ B @ C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
thf(18,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ? [D: $i] : ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
thf(19,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ! [D: $i] :
( ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) )
=> ( ilf_type @ D @ ( relation_type @ B @ C ) ) )
& ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ B @ C ) )
=> ( ilf_type @ E @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
thf(20,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ B @ D ) )
=> ( ( subset @ ( domain_of @ E ) @ C )
=> ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
thf(21,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( subset @ ( domain_of @ D ) @ B )
& ( subset @ ( range_of @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(22,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( ( subset @ B @ C )
& ( subset @ C @ D ) )
=> ( subset @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(23,conjecture,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ B @ D ) )
=> ( ( subset @ B @ C )
=> ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_15) ).
thf(24,negated_conjecture,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ B @ D ) )
=> ( ( subset @ B @ C )
=> ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[23]) ).
thf(25,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ B @ D ) )
=> ( ( subset @ B @ C )
=> ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[24]) ).
thf(26,plain,
( ( ! [B: $i] : ( ilf_type @ B @ set_type ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(27,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( ordered_pair @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(28,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) )
=> ( relation_like @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [B: $i] :
( ( ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( relation_like @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(30,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( relation_like @ B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ B )
=> ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ? [E: $i] :
( ( ilf_type @ E @ set_type )
& ( C
= ( ordered_pair @ D @ E ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(31,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( empty @ B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ~ ( member @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(32,plain,
( ( ! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ? [C: $i] : ( ilf_type @ C @ ( member_type @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(33,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ~ ( empty @ C )
& ( ilf_type @ C @ set_type ) )
=> ( ( ilf_type @ B @ ( member_type @ C ) )
<=> ( member @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(34,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ~ ( empty @ ( power_set @ B ) )
& ( ilf_type @ ( power_set @ B ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(35,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ B @ ( power_set @ C ) )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(36,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(37,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(38,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ilf_type @ C @ ( subset_type @ B ) )
<=> ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(39,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( range_of @ B ) @ set_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(40,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( cross_product @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(41,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ B ) @ set_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(42,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ B @ C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(43,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ? [D: $i] : ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(44,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ! [D: $i] :
( ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) )
=> ( ilf_type @ D @ ( relation_type @ B @ C ) ) )
& ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ B @ C ) )
=> ( ilf_type @ E @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(45,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ B @ D ) )
=> ( ( subset @ ( domain_of @ E ) @ C )
=> ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(46,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( subset @ ( domain_of @ D ) @ B )
& ( subset @ ( range_of @ D ) @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(47,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( ( subset @ B @ C )
& ( subset @ C @ D ) )
=> ( subset @ B @ D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(48,plain,
( ( ( ilf_type @ sK1_B @ set_type )
=> ! [SY54: $i] :
( ( ilf_type @ SY54 @ set_type )
=> ! [SY55: $i] :
( ( ilf_type @ SY55 @ set_type )
=> ! [SY56: $i] :
( ( ilf_type @ SY56 @ ( relation_type @ sK1_B @ SY55 ) )
=> ( ( subset @ sK1_B @ SY54 )
=> ( ilf_type @ SY56 @ ( relation_type @ SY54 @ SY55 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(49,plain,
( ( ilf_type @ sK1_B @ set_type )
= $true ),
inference(standard_cnf,[status(thm)],[48]) ).
thf(50,plain,
( ( ! [SY54: $i] :
( ( ilf_type @ SY54 @ set_type )
=> ! [SY55: $i] :
( ( ilf_type @ SY55 @ set_type )
=> ! [SY56: $i] :
( ( ilf_type @ SY56 @ ( relation_type @ sK1_B @ SY55 ) )
=> ( ( subset @ sK1_B @ SY54 )
=> ( ilf_type @ SY56 @ ( relation_type @ SY54 @ SY55 ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[48]) ).
thf(51,plain,
( ( ~ ! [SY54: $i] :
( ( ilf_type @ SY54 @ set_type )
=> ! [SY55: $i] :
( ( ilf_type @ SY55 @ set_type )
=> ! [SY56: $i] :
( ( ilf_type @ SY56 @ ( relation_type @ sK1_B @ SY55 ) )
=> ( ( subset @ sK1_B @ SY54 )
=> ( ilf_type @ SY56 @ ( relation_type @ SY54 @ SY55 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[50]) ).
thf(52,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( ( subset @ B @ C )
& ( subset @ C @ D ) )
=> ( subset @ B @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(53,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( subset @ ( domain_of @ D ) @ B )
& ( subset @ ( range_of @ D ) @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(54,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ B @ D ) )
=> ( ( subset @ ( domain_of @ E ) @ C )
=> ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(55,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ! [D: $i] :
( ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) )
=> ( ilf_type @ D @ ( relation_type @ B @ C ) ) )
& ! [E: $i] :
( ( ilf_type @ E @ ( relation_type @ B @ C ) )
=> ( ilf_type @ E @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(56,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ? [D: $i] : ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(57,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ B @ C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(58,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ B ) @ set_type ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(59,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( cross_product @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(60,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( range_of @ B ) @ set_type ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(61,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ilf_type @ C @ ( subset_type @ B ) )
<=> ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(62,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(63,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(64,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ B @ ( power_set @ C ) )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(65,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ~ ( empty @ ( power_set @ B ) )
& ( ilf_type @ ( power_set @ B ) @ set_type ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(66,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ~ ( empty @ C )
& ( ilf_type @ C @ set_type ) )
=> ( ( ilf_type @ B @ ( member_type @ C ) )
<=> ( member @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(67,plain,
( ( ! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ? [C: $i] : ( ilf_type @ C @ ( member_type @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(68,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( empty @ B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ~ ( member @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(69,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( relation_like @ B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ B )
=> ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ? [E: $i] :
( ( ilf_type @ E @ set_type )
& ( C
= ( ordered_pair @ D @ E ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(70,plain,
( ( ! [B: $i] :
( ( ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( relation_like @ B ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(71,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) )
=> ( relation_like @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(72,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( ordered_pair @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(73,plain,
( ( ! [B: $i] : ( ilf_type @ B @ set_type ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(74,plain,
( ( ilf_type @ sK1_B @ set_type )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(75,plain,
( ( ~ ! [SY54: $i] :
( ( ilf_type @ SY54 @ set_type )
=> ! [SY55: $i] :
( ( ilf_type @ SY55 @ set_type )
=> ! [SY56: $i] :
( ( ilf_type @ SY56 @ ( relation_type @ sK1_B @ SY55 ) )
=> ( ( subset @ sK1_B @ SY54 )
=> ( ilf_type @ SY56 @ ( relation_type @ SY54 @ SY55 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(76,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ~ ( ~ ~ ( empty @ SX1 )
| ~ ( ilf_type @ SX1 @ set_type ) )
| ~ ( ~ ( ~ ( ilf_type @ SX0 @ ( member_type @ SX1 ) )
| ( member @ SX0 @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ SX1 )
| ( ilf_type @ SX0 @ ( member_type @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(77,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( ilf_type @ ( ordered_pair @ SX0 @ SX1 ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(79,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ~ ( empty @ ( power_set @ SX0 ) )
| ~ ( ilf_type @ ( power_set @ SX0 ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ ( domain_of @ SX2 ) @ SX0 )
| ~ ( subset @ ( range_of @ SX2 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(81,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( subset_type @ ( cross_product @ SX0 @ SX1 ) ) )
| ( relation_like @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(82,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ sK1_B @ SX1 ) )
| ~ ( subset @ sK1_B @ SX0 )
| ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(83,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ( ilf_type @ ( domain_of @ SX0 ) @ set_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(84,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SX1 @ ( subset_type @ SX0 ) )
| ( ilf_type @ SX1 @ ( member_type @ ( power_set @ SX0 ) ) ) )
| ~ ( ~ ( ilf_type @ SX1 @ ( member_type @ ( power_set @ SX0 ) ) )
| ( ilf_type @ SX1 @ ( subset_type @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(85,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( ilf_type @ ( cross_product @ SX0 @ SX1 ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(86,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ( ilf_type @ ( range_of @ SX0 ) @ set_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(87,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( subset_type @ ( cross_product @ SX0 @ SX1 ) ) )
| ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) )
| ( ilf_type @ SX2 @ ( subset_type @ ( cross_product @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(88,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( ilf_type @ SX0 @ set_type ) )
| ~ ! [SX1: $i] :
~ ( ilf_type @ SX1 @ ( member_type @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(89,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ( subset @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(90,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 ) )
| ( empty @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(91,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(92,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( empty @ SX0 )
| ~ ( ilf_type @ SX0 @ set_type ) )
| ( relation_like @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(93,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ! [SX3: $i] :
( ~ ( ilf_type @ SX3 @ ( relation_type @ SX0 @ SX2 ) )
| ~ ( subset @ ( domain_of @ SX3 ) @ SX1 )
| ( ilf_type @ SX3 @ ( relation_type @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(94,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ~ ( relation_like @ SX0 )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(95,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ! [SX2: $i] :
~ ( ilf_type @ SX2 @ ( relation_type @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(96,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ! [SX1: $i] :
~ ( ilf_type @ SX1 @ ( subset_type @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(97,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(98,plain,
! [SV1: $i] :
( ( ilf_type @ SV1 @ set_type )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(99,plain,
! [SV2: $i] :
( ( ~ ( ilf_type @ SV2 @ set_type )
| ! [SY57: $i] :
( ~ ~ ( ~ ~ ( empty @ SY57 )
| ~ ( ilf_type @ SY57 @ set_type ) )
| ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SY57 ) )
| ( member @ SV2 @ SY57 ) )
| ~ ( ~ ( member @ SV2 @ SY57 )
| ( ilf_type @ SV2 @ ( member_type @ SY57 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(100,plain,
! [SV3: $i] :
( ( ~ ( ilf_type @ SV3 @ set_type )
| ! [SY58: $i] :
( ~ ( ilf_type @ SY58 @ set_type )
| ~ ( ~ ( ~ ( member @ SV3 @ ( power_set @ SY58 ) )
| ! [SY59: $i] :
( ~ ( ilf_type @ SY59 @ set_type )
| ~ ( member @ SY59 @ SV3 )
| ( member @ SY59 @ SY58 ) ) )
| ~ ( ~ ! [SY60: $i] :
( ~ ( ilf_type @ SY60 @ set_type )
| ~ ( member @ SY60 @ SV3 )
| ( member @ SY60 @ SY58 ) )
| ( member @ SV3 @ ( power_set @ SY58 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(101,plain,
! [SV4: $i] :
( ( ~ ( ilf_type @ SV4 @ set_type )
| ! [SY61: $i] :
( ~ ( ilf_type @ SY61 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV4 @ SY61 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(102,plain,
! [SV5: $i] :
( ( ~ ( ilf_type @ SV5 @ set_type )
| ~ ( ~ ~ ( empty @ ( power_set @ SV5 ) )
| ~ ( ilf_type @ ( power_set @ SV5 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(103,plain,
! [SV6: $i] :
( ( ~ ( ilf_type @ SV6 @ set_type )
| ! [SY62: $i] :
( ~ ( ilf_type @ SY62 @ set_type )
| ! [SY63: $i] :
( ~ ( ilf_type @ SY63 @ ( relation_type @ SV6 @ SY62 ) )
| ~ ( ~ ( subset @ ( domain_of @ SY63 ) @ SV6 )
| ~ ( subset @ ( range_of @ SY63 ) @ SY62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(104,plain,
! [SV7: $i] :
( ( ~ ( ilf_type @ SV7 @ set_type )
| ! [SY64: $i] :
( ~ ( ilf_type @ SY64 @ set_type )
| ! [SY65: $i] :
( ~ ( ilf_type @ SY65 @ ( subset_type @ ( cross_product @ SV7 @ SY64 ) ) )
| ( relation_like @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(105,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ sK1_B @ SX1 ) )
| ~ ( subset @ sK1_B @ SX0 )
| ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(106,plain,
! [SV8: $i] :
( ( ~ ( ilf_type @ SV8 @ binary_relation_type )
| ( ilf_type @ ( domain_of @ SV8 ) @ set_type ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(107,plain,
! [SV9: $i] :
( ( ~ ( ilf_type @ SV9 @ set_type )
| ! [SY66: $i] :
( ~ ( ilf_type @ SY66 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY66 @ ( subset_type @ SV9 ) )
| ( ilf_type @ SY66 @ ( member_type @ ( power_set @ SV9 ) ) ) )
| ~ ( ~ ( ilf_type @ SY66 @ ( member_type @ ( power_set @ SV9 ) ) )
| ( ilf_type @ SY66 @ ( subset_type @ SV9 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(108,plain,
! [SV10: $i] :
( ( ~ ( ilf_type @ SV10 @ set_type )
| ! [SY67: $i] :
( ~ ( ilf_type @ SY67 @ set_type )
| ( ilf_type @ ( cross_product @ SV10 @ SY67 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(109,plain,
! [SV11: $i] :
( ( ~ ( ilf_type @ SV11 @ binary_relation_type )
| ( ilf_type @ ( range_of @ SV11 ) @ set_type ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(110,plain,
! [SV12: $i] :
( ( ~ ( ilf_type @ SV12 @ set_type )
| ! [SY68: $i] :
( ~ ( ilf_type @ SY68 @ set_type )
| ~ ( ~ ! [SY69: $i] :
( ~ ( ilf_type @ SY69 @ ( subset_type @ ( cross_product @ SV12 @ SY68 ) ) )
| ( ilf_type @ SY69 @ ( relation_type @ SV12 @ SY68 ) ) )
| ~ ! [SY70: $i] :
( ~ ( ilf_type @ SY70 @ ( relation_type @ SV12 @ SY68 ) )
| ( ilf_type @ SY70 @ ( subset_type @ ( cross_product @ SV12 @ SY68 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(111,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV13 )
| ~ ( ilf_type @ SV13 @ set_type ) )
| ~ ! [SY71: $i] :
~ ( ilf_type @ SY71 @ ( member_type @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(112,plain,
! [SV14: $i] :
( ( ~ ( ilf_type @ SV14 @ set_type )
| ( subset @ SV14 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(113,plain,
! [SV15: $i] :
( ( ~ ( ilf_type @ SV15 @ set_type )
| ~ ( ~ ( ~ ( empty @ SV15 )
| ! [SY72: $i] :
( ~ ( ilf_type @ SY72 @ set_type )
| ~ ( member @ SY72 @ SV15 ) ) )
| ~ ( ~ ! [SY73: $i] :
( ~ ( ilf_type @ SY73 @ set_type )
| ~ ( member @ SY73 @ SV15 ) )
| ( empty @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(114,plain,
! [SV16: $i] :
( ( ~ ( ilf_type @ SV16 @ set_type )
| ! [SY74: $i] :
( ~ ( ilf_type @ SY74 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV16 @ SY74 )
| ! [SY75: $i] :
( ~ ( ilf_type @ SY75 @ set_type )
| ~ ( member @ SY75 @ SV16 )
| ( member @ SY75 @ SY74 ) ) )
| ~ ( ~ ! [SY76: $i] :
( ~ ( ilf_type @ SY76 @ set_type )
| ~ ( member @ SY76 @ SV16 )
| ( member @ SY76 @ SY74 ) )
| ( subset @ SV16 @ SY74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(115,plain,
! [SV17: $i] :
( ( ~ ~ ( ~ ( empty @ SV17 )
| ~ ( ilf_type @ SV17 @ set_type ) )
| ( relation_like @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(116,plain,
! [SV18: $i] :
( ( ~ ( ilf_type @ SV18 @ set_type )
| ! [SY77: $i] :
( ~ ( ilf_type @ SY77 @ set_type )
| ! [SY78: $i] :
( ~ ( ilf_type @ SY78 @ set_type )
| ! [SY79: $i] :
( ~ ( ilf_type @ SY79 @ ( relation_type @ SV18 @ SY78 ) )
| ~ ( subset @ ( domain_of @ SY79 ) @ SY77 )
| ( ilf_type @ SY79 @ ( relation_type @ SY77 @ SY78 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(117,plain,
! [SV19: $i] :
( ( ~ ( ilf_type @ SV19 @ set_type )
| ~ ( ~ ( ~ ( relation_like @ SV19 )
| ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ set_type )
| ~ ( member @ SY80 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
| ~ ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( member @ SY83 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY83
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(118,plain,
! [SV20: $i] :
( ( ~ ( ilf_type @ SV20 @ set_type )
| ! [SY86: $i] :
( ~ ( ilf_type @ SY86 @ set_type )
| ~ ! [SY87: $i] :
~ ( ilf_type @ SY87 @ ( relation_type @ SY86 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(119,plain,
! [SV21: $i] :
( ( ~ ( ilf_type @ SV21 @ set_type )
| ~ ! [SY88: $i] :
~ ( ilf_type @ SY88 @ ( subset_type @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(120,plain,
! [SV22: $i] :
( ( ~ ( ilf_type @ SV22 @ set_type )
| ! [SY89: $i] :
( ~ ( ilf_type @ SY89 @ set_type )
| ! [SY90: $i] :
( ~ ( ilf_type @ SY90 @ set_type )
| ~ ~ ( ~ ( subset @ SV22 @ SY89 )
| ~ ( subset @ SY89 @ SY90 ) )
| ( subset @ SV22 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(121,plain,
! [SV2: $i] :
( ( ( ~ ( ilf_type @ SV2 @ set_type ) )
= $true )
| ( ( ! [SY57: $i] :
( ~ ~ ( ~ ~ ( empty @ SY57 )
| ~ ( ilf_type @ SY57 @ set_type ) )
| ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SY57 ) )
| ( member @ SV2 @ SY57 ) )
| ~ ( ~ ( member @ SV2 @ SY57 )
| ( ilf_type @ SV2 @ ( member_type @ SY57 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(122,plain,
! [SV3: $i] :
( ( ( ~ ( ilf_type @ SV3 @ set_type ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( ilf_type @ SY58 @ set_type )
| ~ ( ~ ( ~ ( member @ SV3 @ ( power_set @ SY58 ) )
| ! [SY59: $i] :
( ~ ( ilf_type @ SY59 @ set_type )
| ~ ( member @ SY59 @ SV3 )
| ( member @ SY59 @ SY58 ) ) )
| ~ ( ~ ! [SY60: $i] :
( ~ ( ilf_type @ SY60 @ set_type )
| ~ ( member @ SY60 @ SV3 )
| ( member @ SY60 @ SY58 ) )
| ( member @ SV3 @ ( power_set @ SY58 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(123,plain,
! [SV4: $i] :
( ( ( ~ ( ilf_type @ SV4 @ set_type ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( ilf_type @ SY61 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV4 @ SY61 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(124,plain,
! [SV5: $i] :
( ( ( ~ ( ilf_type @ SV5 @ set_type ) )
= $true )
| ( ( ~ ( ~ ~ ( empty @ ( power_set @ SV5 ) )
| ~ ( ilf_type @ ( power_set @ SV5 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(125,plain,
! [SV6: $i] :
( ( ( ~ ( ilf_type @ SV6 @ set_type ) )
= $true )
| ( ( ! [SY62: $i] :
( ~ ( ilf_type @ SY62 @ set_type )
| ! [SY63: $i] :
( ~ ( ilf_type @ SY63 @ ( relation_type @ SV6 @ SY62 ) )
| ~ ( ~ ( subset @ ( domain_of @ SY63 ) @ SV6 )
| ~ ( subset @ ( range_of @ SY63 ) @ SY62 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(126,plain,
! [SV7: $i] :
( ( ( ~ ( ilf_type @ SV7 @ set_type ) )
= $true )
| ( ( ! [SY64: $i] :
( ~ ( ilf_type @ SY64 @ set_type )
| ! [SY65: $i] :
( ~ ( ilf_type @ SY65 @ ( subset_type @ ( cross_product @ SV7 @ SY64 ) ) )
| ( relation_like @ SY65 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(127,plain,
( ( ~ ( ilf_type @ sK2_SX0 @ set_type )
| ! [SY91: $i] :
( ~ ( ilf_type @ SY91 @ set_type )
| ! [SY92: $i] :
( ~ ( ilf_type @ SY92 @ ( relation_type @ sK1_B @ SY91 ) )
| ~ ( subset @ sK1_B @ sK2_SX0 )
| ( ilf_type @ SY92 @ ( relation_type @ sK2_SX0 @ SY91 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[105]) ).
thf(128,plain,
! [SV8: $i] :
( ( ( ~ ( ilf_type @ SV8 @ binary_relation_type ) )
= $true )
| ( ( ilf_type @ ( domain_of @ SV8 ) @ set_type )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(129,plain,
! [SV9: $i] :
( ( ( ~ ( ilf_type @ SV9 @ set_type ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( ilf_type @ SY66 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY66 @ ( subset_type @ SV9 ) )
| ( ilf_type @ SY66 @ ( member_type @ ( power_set @ SV9 ) ) ) )
| ~ ( ~ ( ilf_type @ SY66 @ ( member_type @ ( power_set @ SV9 ) ) )
| ( ilf_type @ SY66 @ ( subset_type @ SV9 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(130,plain,
! [SV10: $i] :
( ( ( ~ ( ilf_type @ SV10 @ set_type ) )
= $true )
| ( ( ! [SY67: $i] :
( ~ ( ilf_type @ SY67 @ set_type )
| ( ilf_type @ ( cross_product @ SV10 @ SY67 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(131,plain,
! [SV11: $i] :
( ( ( ~ ( ilf_type @ SV11 @ binary_relation_type ) )
= $true )
| ( ( ilf_type @ ( range_of @ SV11 ) @ set_type )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(132,plain,
! [SV12: $i] :
( ( ( ~ ( ilf_type @ SV12 @ set_type ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( ilf_type @ SY68 @ set_type )
| ~ ( ~ ! [SY69: $i] :
( ~ ( ilf_type @ SY69 @ ( subset_type @ ( cross_product @ SV12 @ SY68 ) ) )
| ( ilf_type @ SY69 @ ( relation_type @ SV12 @ SY68 ) ) )
| ~ ! [SY70: $i] :
( ~ ( ilf_type @ SY70 @ ( relation_type @ SV12 @ SY68 ) )
| ( ilf_type @ SY70 @ ( subset_type @ ( cross_product @ SV12 @ SY68 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(133,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV13 )
| ~ ( ilf_type @ SV13 @ set_type ) ) )
= $true )
| ( ( ~ ! [SY71: $i] :
~ ( ilf_type @ SY71 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(134,plain,
! [SV14: $i] :
( ( ( ~ ( ilf_type @ SV14 @ set_type ) )
= $true )
| ( ( subset @ SV14 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(135,plain,
! [SV15: $i] :
( ( ( ~ ( ilf_type @ SV15 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( empty @ SV15 )
| ! [SY72: $i] :
( ~ ( ilf_type @ SY72 @ set_type )
| ~ ( member @ SY72 @ SV15 ) ) )
| ~ ( ~ ! [SY73: $i] :
( ~ ( ilf_type @ SY73 @ set_type )
| ~ ( member @ SY73 @ SV15 ) )
| ( empty @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(136,plain,
! [SV16: $i] :
( ( ( ~ ( ilf_type @ SV16 @ set_type ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( ilf_type @ SY74 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV16 @ SY74 )
| ! [SY75: $i] :
( ~ ( ilf_type @ SY75 @ set_type )
| ~ ( member @ SY75 @ SV16 )
| ( member @ SY75 @ SY74 ) ) )
| ~ ( ~ ! [SY76: $i] :
( ~ ( ilf_type @ SY76 @ set_type )
| ~ ( member @ SY76 @ SV16 )
| ( member @ SY76 @ SY74 ) )
| ( subset @ SV16 @ SY74 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(137,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ( empty @ SV17 )
| ~ ( ilf_type @ SV17 @ set_type ) ) )
= $true )
| ( ( relation_like @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(138,plain,
! [SV18: $i] :
( ( ( ~ ( ilf_type @ SV18 @ set_type ) )
= $true )
| ( ( ! [SY77: $i] :
( ~ ( ilf_type @ SY77 @ set_type )
| ! [SY78: $i] :
( ~ ( ilf_type @ SY78 @ set_type )
| ! [SY79: $i] :
( ~ ( ilf_type @ SY79 @ ( relation_type @ SV18 @ SY78 ) )
| ~ ( subset @ ( domain_of @ SY79 ) @ SY77 )
| ( ilf_type @ SY79 @ ( relation_type @ SY77 @ SY78 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(139,plain,
! [SV19: $i] :
( ( ( ~ ( ilf_type @ SV19 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( relation_like @ SV19 )
| ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ set_type )
| ~ ( member @ SY80 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
| ~ ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( member @ SY83 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY83
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(140,plain,
! [SV20: $i] :
( ( ( ~ ( ilf_type @ SV20 @ set_type ) )
= $true )
| ( ( ! [SY86: $i] :
( ~ ( ilf_type @ SY86 @ set_type )
| ~ ! [SY87: $i] :
~ ( ilf_type @ SY87 @ ( relation_type @ SY86 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(141,plain,
! [SV21: $i] :
( ( ( ~ ( ilf_type @ SV21 @ set_type ) )
= $true )
| ( ( ~ ! [SY88: $i] :
~ ( ilf_type @ SY88 @ ( subset_type @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(142,plain,
! [SV22: $i] :
( ( ( ~ ( ilf_type @ SV22 @ set_type ) )
= $true )
| ( ( ! [SY89: $i] :
( ~ ( ilf_type @ SY89 @ set_type )
| ! [SY90: $i] :
( ~ ( ilf_type @ SY90 @ set_type )
| ~ ~ ( ~ ( subset @ SV22 @ SY89 )
| ~ ( subset @ SY89 @ SY90 ) )
| ( subset @ SV22 @ SY90 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(143,plain,
! [SV2: $i] :
( ( ( ilf_type @ SV2 @ set_type )
= $false )
| ( ( ! [SY57: $i] :
( ~ ~ ( ~ ~ ( empty @ SY57 )
| ~ ( ilf_type @ SY57 @ set_type ) )
| ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SY57 ) )
| ( member @ SV2 @ SY57 ) )
| ~ ( ~ ( member @ SV2 @ SY57 )
| ( ilf_type @ SV2 @ ( member_type @ SY57 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(144,plain,
! [SV3: $i] :
( ( ( ilf_type @ SV3 @ set_type )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( ilf_type @ SY58 @ set_type )
| ~ ( ~ ( ~ ( member @ SV3 @ ( power_set @ SY58 ) )
| ! [SY59: $i] :
( ~ ( ilf_type @ SY59 @ set_type )
| ~ ( member @ SY59 @ SV3 )
| ( member @ SY59 @ SY58 ) ) )
| ~ ( ~ ! [SY60: $i] :
( ~ ( ilf_type @ SY60 @ set_type )
| ~ ( member @ SY60 @ SV3 )
| ( member @ SY60 @ SY58 ) )
| ( member @ SV3 @ ( power_set @ SY58 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(145,plain,
! [SV4: $i] :
( ( ( ilf_type @ SV4 @ set_type )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( ilf_type @ SY61 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV4 @ SY61 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(146,plain,
! [SV5: $i] :
( ( ( ilf_type @ SV5 @ set_type )
= $false )
| ( ( ~ ( ~ ~ ( empty @ ( power_set @ SV5 ) )
| ~ ( ilf_type @ ( power_set @ SV5 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(147,plain,
! [SV6: $i] :
( ( ( ilf_type @ SV6 @ set_type )
= $false )
| ( ( ! [SY62: $i] :
( ~ ( ilf_type @ SY62 @ set_type )
| ! [SY63: $i] :
( ~ ( ilf_type @ SY63 @ ( relation_type @ SV6 @ SY62 ) )
| ~ ( ~ ( subset @ ( domain_of @ SY63 ) @ SV6 )
| ~ ( subset @ ( range_of @ SY63 ) @ SY62 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(148,plain,
! [SV7: $i] :
( ( ( ilf_type @ SV7 @ set_type )
= $false )
| ( ( ! [SY64: $i] :
( ~ ( ilf_type @ SY64 @ set_type )
| ! [SY65: $i] :
( ~ ( ilf_type @ SY65 @ ( subset_type @ ( cross_product @ SV7 @ SY64 ) ) )
| ( relation_like @ SY65 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(149,plain,
( ( ~ ( ilf_type @ sK2_SX0 @ set_type ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(150,plain,
( ( ! [SY91: $i] :
( ~ ( ilf_type @ SY91 @ set_type )
| ! [SY92: $i] :
( ~ ( ilf_type @ SY92 @ ( relation_type @ sK1_B @ SY91 ) )
| ~ ( subset @ sK1_B @ sK2_SX0 )
| ( ilf_type @ SY92 @ ( relation_type @ sK2_SX0 @ SY91 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(151,plain,
! [SV8: $i] :
( ( ( ilf_type @ SV8 @ binary_relation_type )
= $false )
| ( ( ilf_type @ ( domain_of @ SV8 ) @ set_type )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(152,plain,
! [SV9: $i] :
( ( ( ilf_type @ SV9 @ set_type )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( ilf_type @ SY66 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY66 @ ( subset_type @ SV9 ) )
| ( ilf_type @ SY66 @ ( member_type @ ( power_set @ SV9 ) ) ) )
| ~ ( ~ ( ilf_type @ SY66 @ ( member_type @ ( power_set @ SV9 ) ) )
| ( ilf_type @ SY66 @ ( subset_type @ SV9 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(153,plain,
! [SV10: $i] :
( ( ( ilf_type @ SV10 @ set_type )
= $false )
| ( ( ! [SY67: $i] :
( ~ ( ilf_type @ SY67 @ set_type )
| ( ilf_type @ ( cross_product @ SV10 @ SY67 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(154,plain,
! [SV11: $i] :
( ( ( ilf_type @ SV11 @ binary_relation_type )
= $false )
| ( ( ilf_type @ ( range_of @ SV11 ) @ set_type )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(155,plain,
! [SV12: $i] :
( ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( ilf_type @ SY68 @ set_type )
| ~ ( ~ ! [SY69: $i] :
( ~ ( ilf_type @ SY69 @ ( subset_type @ ( cross_product @ SV12 @ SY68 ) ) )
| ( ilf_type @ SY69 @ ( relation_type @ SV12 @ SY68 ) ) )
| ~ ! [SY70: $i] :
( ~ ( ilf_type @ SY70 @ ( relation_type @ SV12 @ SY68 ) )
| ( ilf_type @ SY70 @ ( subset_type @ ( cross_product @ SV12 @ SY68 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(156,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV13 )
| ~ ( ilf_type @ SV13 @ set_type ) ) )
= $false )
| ( ( ~ ! [SY71: $i] :
~ ( ilf_type @ SY71 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(157,plain,
! [SV14: $i] :
( ( ( ilf_type @ SV14 @ set_type )
= $false )
| ( ( subset @ SV14 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(158,plain,
! [SV15: $i] :
( ( ( ilf_type @ SV15 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( empty @ SV15 )
| ! [SY72: $i] :
( ~ ( ilf_type @ SY72 @ set_type )
| ~ ( member @ SY72 @ SV15 ) ) )
| ~ ( ~ ! [SY73: $i] :
( ~ ( ilf_type @ SY73 @ set_type )
| ~ ( member @ SY73 @ SV15 ) )
| ( empty @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(159,plain,
! [SV16: $i] :
( ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ! [SY74: $i] :
( ~ ( ilf_type @ SY74 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV16 @ SY74 )
| ! [SY75: $i] :
( ~ ( ilf_type @ SY75 @ set_type )
| ~ ( member @ SY75 @ SV16 )
| ( member @ SY75 @ SY74 ) ) )
| ~ ( ~ ! [SY76: $i] :
( ~ ( ilf_type @ SY76 @ set_type )
| ~ ( member @ SY76 @ SV16 )
| ( member @ SY76 @ SY74 ) )
| ( subset @ SV16 @ SY74 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(160,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( empty @ SV17 )
| ~ ( ilf_type @ SV17 @ set_type ) ) )
= $false )
| ( ( relation_like @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(161,plain,
! [SV18: $i] :
( ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ! [SY77: $i] :
( ~ ( ilf_type @ SY77 @ set_type )
| ! [SY78: $i] :
( ~ ( ilf_type @ SY78 @ set_type )
| ! [SY79: $i] :
( ~ ( ilf_type @ SY79 @ ( relation_type @ SV18 @ SY78 ) )
| ~ ( subset @ ( domain_of @ SY79 ) @ SY77 )
| ( ilf_type @ SY79 @ ( relation_type @ SY77 @ SY78 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(162,plain,
! [SV19: $i] :
( ( ( ilf_type @ SV19 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( relation_like @ SV19 )
| ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ set_type )
| ~ ( member @ SY80 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
| ~ ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( member @ SY83 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY83
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(163,plain,
! [SV20: $i] :
( ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ! [SY86: $i] :
( ~ ( ilf_type @ SY86 @ set_type )
| ~ ! [SY87: $i] :
~ ( ilf_type @ SY87 @ ( relation_type @ SY86 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(164,plain,
! [SV21: $i] :
( ( ( ilf_type @ SV21 @ set_type )
= $false )
| ( ( ~ ! [SY88: $i] :
~ ( ilf_type @ SY88 @ ( subset_type @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(165,plain,
! [SV22: $i] :
( ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ! [SY89: $i] :
( ~ ( ilf_type @ SY89 @ set_type )
| ! [SY90: $i] :
( ~ ( ilf_type @ SY90 @ set_type )
| ~ ~ ( ~ ( subset @ SV22 @ SY89 )
| ~ ( subset @ SY89 @ SY90 ) )
| ( subset @ SV22 @ SY90 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(166,plain,
! [SV2: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV23 )
| ~ ( ilf_type @ SV23 @ set_type ) )
| ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) )
| ~ ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(167,plain,
! [SV3: $i,SV24: $i] :
( ( ( ~ ( ilf_type @ SV24 @ set_type )
| ~ ( ~ ( ~ ( member @ SV3 @ ( power_set @ SV24 ) )
| ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ SY93 @ SV3 )
| ( member @ SY93 @ SV24 ) ) )
| ~ ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ~ ( member @ SY94 @ SV3 )
| ( member @ SY94 @ SV24 ) )
| ( member @ SV3 @ ( power_set @ SV24 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(168,plain,
! [SV4: $i,SV25: $i] :
( ( ( ~ ( ilf_type @ SV25 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV4 @ SV25 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(169,plain,
! [SV5: $i] :
( ( ( ~ ~ ( empty @ ( power_set @ SV5 ) )
| ~ ( ilf_type @ ( power_set @ SV5 ) @ set_type ) )
= $false )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(170,plain,
! [SV6: $i,SV26: $i] :
( ( ( ~ ( ilf_type @ SV26 @ set_type )
| ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ ( relation_type @ SV6 @ SV26 ) )
| ~ ( ~ ( subset @ ( domain_of @ SY95 ) @ SV6 )
| ~ ( subset @ ( range_of @ SY95 ) @ SV26 ) ) ) )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(171,plain,
! [SV7: $i,SV27: $i] :
( ( ( ~ ( ilf_type @ SV27 @ set_type )
| ! [SY96: $i] :
( ~ ( ilf_type @ SY96 @ ( subset_type @ ( cross_product @ SV7 @ SV27 ) ) )
| ( relation_like @ SY96 ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(172,plain,
( ( ilf_type @ sK2_SX0 @ set_type )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(173,plain,
( ( ~ ( ilf_type @ sK3_SY91 @ set_type )
| ! [SY97: $i] :
( ~ ( ilf_type @ SY97 @ ( relation_type @ sK1_B @ sK3_SY91 ) )
| ~ ( subset @ sK1_B @ sK2_SX0 )
| ( ilf_type @ SY97 @ ( relation_type @ sK2_SX0 @ sK3_SY91 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[150]) ).
thf(174,plain,
! [SV9: $i,SV28: $i] :
( ( ( ~ ( ilf_type @ SV28 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SV28 @ ( subset_type @ SV9 ) )
| ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) ) )
| ~ ( ~ ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) )
| ( ilf_type @ SV28 @ ( subset_type @ SV9 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(175,plain,
! [SV10: $i,SV29: $i] :
( ( ( ~ ( ilf_type @ SV29 @ set_type )
| ( ilf_type @ ( cross_product @ SV10 @ SV29 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV10 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(176,plain,
! [SV12: $i,SV30: $i] :
( ( ( ~ ( ilf_type @ SV30 @ set_type )
| ~ ( ~ ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) )
| ( ilf_type @ SY98 @ ( relation_type @ SV12 @ SV30 ) ) )
| ~ ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ ( relation_type @ SV12 @ SV30 ) )
| ( ilf_type @ SY99 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(177,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ SV13 )
| ~ ( ilf_type @ SV13 @ set_type ) )
= $true )
| ( ( ~ ! [SY71: $i] :
~ ( ilf_type @ SY71 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(178,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( empty @ SV15 )
| ! [SY72: $i] :
( ~ ( ilf_type @ SY72 @ set_type )
| ~ ( member @ SY72 @ SV15 ) ) )
| ~ ( ~ ! [SY73: $i] :
( ~ ( ilf_type @ SY73 @ set_type )
| ~ ( member @ SY73 @ SV15 ) )
| ( empty @ SV15 ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(179,plain,
! [SV16: $i,SV31: $i] :
( ( ( ~ ( ilf_type @ SV31 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV16 @ SV31 )
| ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( member @ SY100 @ SV16 )
| ( member @ SY100 @ SV31 ) ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ~ ( member @ SY101 @ SV16 )
| ( member @ SY101 @ SV31 ) )
| ( subset @ SV16 @ SV31 ) ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(180,plain,
! [SV17: $i] :
( ( ( ~ ( empty @ SV17 )
| ~ ( ilf_type @ SV17 @ set_type ) )
= $true )
| ( ( relation_like @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(181,plain,
! [SV18: $i,SV32: $i] :
( ( ( ~ ( ilf_type @ SV32 @ set_type )
| ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ set_type )
| ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ ( relation_type @ SV18 @ SY102 ) )
| ~ ( subset @ ( domain_of @ SY103 ) @ SV32 )
| ( ilf_type @ SY103 @ ( relation_type @ SV32 @ SY102 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(182,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( relation_like @ SV19 )
| ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ set_type )
| ~ ( member @ SY80 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
| ~ ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( member @ SY83 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY83
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV19 ) ) )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(183,plain,
! [SV20: $i,SV33: $i] :
( ( ( ~ ( ilf_type @ SV33 @ set_type )
| ~ ! [SY104: $i] :
~ ( ilf_type @ SY104 @ ( relation_type @ SV33 @ SV20 ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(184,plain,
! [SV21: $i] :
( ( ( ! [SY88: $i] :
~ ( ilf_type @ SY88 @ ( subset_type @ SV21 ) ) )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(185,plain,
! [SV22: $i,SV34: $i] :
( ( ( ~ ( ilf_type @ SV34 @ set_type )
| ! [SY105: $i] :
( ~ ( ilf_type @ SY105 @ set_type )
| ~ ~ ( ~ ( subset @ SV22 @ SV34 )
| ~ ( subset @ SV34 @ SY105 ) )
| ( subset @ SV22 @ SY105 ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(186,plain,
! [SV2: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV23 )
| ~ ( ilf_type @ SV23 @ set_type ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) )
| ~ ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(187,plain,
! [SV3: $i,SV24: $i] :
( ( ( ~ ( ilf_type @ SV24 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV3 @ ( power_set @ SV24 ) )
| ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ SY93 @ SV3 )
| ( member @ SY93 @ SV24 ) ) )
| ~ ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ~ ( member @ SY94 @ SV3 )
| ( member @ SY94 @ SV24 ) )
| ( member @ SV3 @ ( power_set @ SV24 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(188,plain,
! [SV4: $i,SV25: $i] :
( ( ( ~ ( ilf_type @ SV25 @ set_type ) )
= $true )
| ( ( ilf_type @ ( ordered_pair @ SV4 @ SV25 ) @ set_type )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(189,plain,
! [SV5: $i] :
( ( ( ~ ~ ( empty @ ( power_set @ SV5 ) ) )
= $false )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(190,plain,
! [SV5: $i] :
( ( ( ~ ( ilf_type @ ( power_set @ SV5 ) @ set_type ) )
= $false )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(191,plain,
! [SV6: $i,SV26: $i] :
( ( ( ~ ( ilf_type @ SV26 @ set_type ) )
= $true )
| ( ( ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ ( relation_type @ SV6 @ SV26 ) )
| ~ ( ~ ( subset @ ( domain_of @ SY95 ) @ SV6 )
| ~ ( subset @ ( range_of @ SY95 ) @ SV26 ) ) ) )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(192,plain,
! [SV7: $i,SV27: $i] :
( ( ( ~ ( ilf_type @ SV27 @ set_type ) )
= $true )
| ( ( ! [SY96: $i] :
( ~ ( ilf_type @ SY96 @ ( subset_type @ ( cross_product @ SV7 @ SV27 ) ) )
| ( relation_like @ SY96 ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(193,plain,
( ( ~ ( ilf_type @ sK3_SY91 @ set_type ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(194,plain,
( ( ! [SY97: $i] :
( ~ ( ilf_type @ SY97 @ ( relation_type @ sK1_B @ sK3_SY91 ) )
| ~ ( subset @ sK1_B @ sK2_SX0 )
| ( ilf_type @ SY97 @ ( relation_type @ sK2_SX0 @ sK3_SY91 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(195,plain,
! [SV9: $i,SV28: $i] :
( ( ( ~ ( ilf_type @ SV28 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV28 @ ( subset_type @ SV9 ) )
| ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) ) )
| ~ ( ~ ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) )
| ( ilf_type @ SV28 @ ( subset_type @ SV9 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(196,plain,
! [SV10: $i,SV29: $i] :
( ( ( ~ ( ilf_type @ SV29 @ set_type ) )
= $true )
| ( ( ilf_type @ ( cross_product @ SV10 @ SV29 ) @ set_type )
= $true )
| ( ( ilf_type @ SV10 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(197,plain,
! [SV12: $i,SV30: $i] :
( ( ( ~ ( ilf_type @ SV30 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) )
| ( ilf_type @ SY98 @ ( relation_type @ SV12 @ SV30 ) ) )
| ~ ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ ( relation_type @ SV12 @ SV30 ) )
| ( ilf_type @ SY99 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(198,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ( ilf_type @ SV13 @ set_type ) )
= $true )
| ( ( ~ ! [SY71: $i] :
~ ( ilf_type @ SY71 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(199,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( empty @ SV15 )
| ! [SY72: $i] :
( ~ ( ilf_type @ SY72 @ set_type )
| ~ ( member @ SY72 @ SV15 ) ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(200,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ! [SY73: $i] :
( ~ ( ilf_type @ SY73 @ set_type )
| ~ ( member @ SY73 @ SV15 ) )
| ( empty @ SV15 ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(201,plain,
! [SV16: $i,SV31: $i] :
( ( ( ~ ( ilf_type @ SV31 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV16 @ SV31 )
| ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( member @ SY100 @ SV16 )
| ( member @ SY100 @ SV31 ) ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ~ ( member @ SY101 @ SV16 )
| ( member @ SY101 @ SV31 ) )
| ( subset @ SV16 @ SV31 ) ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(202,plain,
! [SV17: $i] :
( ( ( ~ ( empty @ SV17 ) )
= $true )
| ( ( ~ ( ilf_type @ SV17 @ set_type ) )
= $true )
| ( ( relation_like @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(203,plain,
! [SV18: $i,SV32: $i] :
( ( ( ~ ( ilf_type @ SV32 @ set_type ) )
= $true )
| ( ( ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ set_type )
| ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ ( relation_type @ SV18 @ SY102 ) )
| ~ ( subset @ ( domain_of @ SY103 ) @ SV32 )
| ( ilf_type @ SY103 @ ( relation_type @ SV32 @ SY102 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(204,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( relation_like @ SV19 )
| ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ set_type )
| ~ ( member @ SY80 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) ) )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(205,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( member @ SY83 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY83
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV19 ) ) )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(206,plain,
! [SV20: $i,SV33: $i] :
( ( ( ~ ( ilf_type @ SV33 @ set_type ) )
= $true )
| ( ( ~ ! [SY104: $i] :
~ ( ilf_type @ SY104 @ ( relation_type @ SV33 @ SV20 ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(207,plain,
! [SV21: $i] :
( ( ( ~ ( ilf_type @ ( sK4_SY88 @ SV21 ) @ ( subset_type @ SV21 ) ) )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[184]) ).
thf(208,plain,
! [SV22: $i,SV34: $i] :
( ( ( ~ ( ilf_type @ SV34 @ set_type ) )
= $true )
| ( ( ! [SY105: $i] :
( ~ ( ilf_type @ SY105 @ set_type )
| ~ ~ ( ~ ( subset @ SV22 @ SV34 )
| ~ ( subset @ SV34 @ SY105 ) )
| ( subset @ SV22 @ SY105 ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(209,plain,
! [SV2: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV23 )
| ~ ( ilf_type @ SV23 @ set_type ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) )
| ~ ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(210,plain,
! [SV3: $i,SV24: $i] :
( ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV3 @ ( power_set @ SV24 ) )
| ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ SY93 @ SV3 )
| ( member @ SY93 @ SV24 ) ) )
| ~ ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ~ ( member @ SY94 @ SV3 )
| ( member @ SY94 @ SV24 ) )
| ( member @ SV3 @ ( power_set @ SV24 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(211,plain,
! [SV4: $i,SV25: $i] :
( ( ( ilf_type @ SV25 @ set_type )
= $false )
| ( ( ilf_type @ ( ordered_pair @ SV4 @ SV25 ) @ set_type )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(212,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ ( power_set @ SV5 ) ) )
= $true )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(213,plain,
! [SV5: $i] :
( ( ( ilf_type @ ( power_set @ SV5 ) @ set_type )
= $true )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(214,plain,
! [SV6: $i,SV26: $i] :
( ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ ( relation_type @ SV6 @ SV26 ) )
| ~ ( ~ ( subset @ ( domain_of @ SY95 ) @ SV6 )
| ~ ( subset @ ( range_of @ SY95 ) @ SV26 ) ) ) )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(215,plain,
! [SV7: $i,SV27: $i] :
( ( ( ilf_type @ SV27 @ set_type )
= $false )
| ( ( ! [SY96: $i] :
( ~ ( ilf_type @ SY96 @ ( subset_type @ ( cross_product @ SV7 @ SV27 ) ) )
| ( relation_like @ SY96 ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(216,plain,
( ( ilf_type @ sK3_SY91 @ set_type )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(217,plain,
( ( ~ ( ilf_type @ sK5_SY97 @ ( relation_type @ sK1_B @ sK3_SY91 ) )
| ~ ( subset @ sK1_B @ sK2_SX0 )
| ( ilf_type @ sK5_SY97 @ ( relation_type @ sK2_SX0 @ sK3_SY91 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[194]) ).
thf(218,plain,
! [SV9: $i,SV28: $i] :
( ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV28 @ ( subset_type @ SV9 ) )
| ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) ) )
| ~ ( ~ ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) )
| ( ilf_type @ SV28 @ ( subset_type @ SV9 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(219,plain,
! [SV10: $i,SV29: $i] :
( ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ ( cross_product @ SV10 @ SV29 ) @ set_type )
= $true )
| ( ( ilf_type @ SV10 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(220,plain,
! [SV12: $i,SV30: $i] :
( ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) )
| ( ilf_type @ SY98 @ ( relation_type @ SV12 @ SV30 ) ) )
| ~ ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ ( relation_type @ SV12 @ SV30 ) )
| ( ilf_type @ SY99 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(221,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $false )
| ( ( ~ ( ilf_type @ SV13 @ set_type ) )
= $true )
| ( ( ~ ! [SY71: $i] :
~ ( ilf_type @ SY71 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(222,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ SV15 )
| ! [SY72: $i] :
( ~ ( ilf_type @ SY72 @ set_type )
| ~ ( member @ SY72 @ SV15 ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(223,plain,
! [SV15: $i] :
( ( ( ~ ! [SY73: $i] :
( ~ ( ilf_type @ SY73 @ set_type )
| ~ ( member @ SY73 @ SV15 ) )
| ( empty @ SV15 ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(224,plain,
! [SV16: $i,SV31: $i] :
( ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV16 @ SV31 )
| ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( member @ SY100 @ SV16 )
| ( member @ SY100 @ SV31 ) ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ~ ( member @ SY101 @ SV16 )
| ( member @ SY101 @ SV31 ) )
| ( subset @ SV16 @ SV31 ) ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(225,plain,
! [SV17: $i] :
( ( ( empty @ SV17 )
= $false )
| ( ( ~ ( ilf_type @ SV17 @ set_type ) )
= $true )
| ( ( relation_like @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(226,plain,
! [SV18: $i,SV32: $i] :
( ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ set_type )
| ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ ( relation_type @ SV18 @ SY102 ) )
| ~ ( subset @ ( domain_of @ SY103 ) @ SV32 )
| ( ilf_type @ SY103 @ ( relation_type @ SV32 @ SY102 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(227,plain,
! [SV19: $i] :
( ( ( ~ ( relation_like @ SV19 )
| ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ set_type )
| ~ ( member @ SY80 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(228,plain,
! [SV19: $i] :
( ( ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( member @ SY83 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY83
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV19 ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(229,plain,
! [SV20: $i,SV33: $i] :
( ( ( ilf_type @ SV33 @ set_type )
= $false )
| ( ( ~ ! [SY104: $i] :
~ ( ilf_type @ SY104 @ ( relation_type @ SV33 @ SV20 ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(230,plain,
! [SV21: $i] :
( ( ( ilf_type @ ( sK4_SY88 @ SV21 ) @ ( subset_type @ SV21 ) )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(231,plain,
! [SV22: $i,SV34: $i] :
( ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ! [SY105: $i] :
( ~ ( ilf_type @ SY105 @ set_type )
| ~ ~ ( ~ ( subset @ SV22 @ SV34 )
| ~ ( subset @ SV34 @ SY105 ) )
| ( subset @ SV22 @ SY105 ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(232,plain,
! [SV2: $i,SV23: $i] :
( ( ( ~ ~ ( empty @ SV23 )
| ~ ( ilf_type @ SV23 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) )
| ~ ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(233,plain,
! [SV24: $i,SV3: $i] :
( ( ( ~ ( ~ ( member @ SV3 @ ( power_set @ SV24 ) )
| ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ SY93 @ SV3 )
| ( member @ SY93 @ SV24 ) ) )
| ~ ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ~ ( member @ SY94 @ SV3 )
| ( member @ SY94 @ SV24 ) )
| ( member @ SV3 @ ( power_set @ SV24 ) ) ) )
= $false )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(234,plain,
! [SV5: $i] :
( ( ( empty @ ( power_set @ SV5 ) )
= $false )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(235,plain,
! [SV26: $i,SV6: $i,SV35: $i] :
( ( ( ~ ( ilf_type @ SV35 @ ( relation_type @ SV6 @ SV26 ) )
| ~ ( ~ ( subset @ ( domain_of @ SV35 ) @ SV6 )
| ~ ( subset @ ( range_of @ SV35 ) @ SV26 ) ) )
= $true )
| ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(236,plain,
! [SV27: $i,SV7: $i,SV36: $i] :
( ( ( ~ ( ilf_type @ SV36 @ ( subset_type @ ( cross_product @ SV7 @ SV27 ) ) )
| ( relation_like @ SV36 ) )
= $true )
| ( ( ilf_type @ SV27 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(237,plain,
( ( ~ ( ilf_type @ sK5_SY97 @ ( relation_type @ sK1_B @ sK3_SY91 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(238,plain,
( ( ~ ( subset @ sK1_B @ sK2_SX0 )
| ( ilf_type @ sK5_SY97 @ ( relation_type @ sK2_SX0 @ sK3_SY91 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(239,plain,
! [SV9: $i,SV28: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV28 @ ( subset_type @ SV9 ) )
| ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) ) )
| ~ ( ~ ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) )
| ( ilf_type @ SV28 @ ( subset_type @ SV9 ) ) ) )
= $false )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(240,plain,
! [SV30: $i,SV12: $i] :
( ( ( ~ ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) )
| ( ilf_type @ SY98 @ ( relation_type @ SV12 @ SV30 ) ) )
| ~ ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ ( relation_type @ SV12 @ SV30 ) )
| ( ilf_type @ SY99 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(241,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
= $true )
| ( ( ~ ( ilf_type @ SV13 @ set_type ) )
= $true )
| ( ( ~ ! [SY71: $i] :
~ ( ilf_type @ SY71 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(242,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ SV15 ) )
= $true )
| ( ( ! [SY72: $i] :
( ~ ( ilf_type @ SY72 @ set_type )
| ~ ( member @ SY72 @ SV15 ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(243,plain,
! [SV15: $i] :
( ( ( ~ ! [SY73: $i] :
( ~ ( ilf_type @ SY73 @ set_type )
| ~ ( member @ SY73 @ SV15 ) ) )
= $true )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(244,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( ~ ( subset @ SV16 @ SV31 )
| ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( member @ SY100 @ SV16 )
| ( member @ SY100 @ SV31 ) ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ~ ( member @ SY101 @ SV16 )
| ( member @ SY101 @ SV31 ) )
| ( subset @ SV16 @ SV31 ) ) )
= $false )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(245,plain,
! [SV17: $i] :
( ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( empty @ SV17 )
= $false )
| ( ( relation_like @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(246,plain,
! [SV32: $i,SV18: $i,SV37: $i] :
( ( ( ~ ( ilf_type @ SV37 @ set_type )
| ! [SY106: $i] :
( ~ ( ilf_type @ SY106 @ ( relation_type @ SV18 @ SV37 ) )
| ~ ( subset @ ( domain_of @ SY106 ) @ SV32 )
| ( ilf_type @ SY106 @ ( relation_type @ SV32 @ SV37 ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(247,plain,
! [SV19: $i] :
( ( ( ~ ( relation_like @ SV19 ) )
= $true )
| ( ( ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ set_type )
| ~ ( member @ SY80 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(248,plain,
! [SV19: $i] :
( ( ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( member @ SY83 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY83
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(249,plain,
! [SV20: $i,SV33: $i] :
( ( ( ! [SY104: $i] :
~ ( ilf_type @ SY104 @ ( relation_type @ SV33 @ SV20 ) ) )
= $false )
| ( ( ilf_type @ SV33 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(250,plain,
! [SV34: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( ilf_type @ SV38 @ set_type )
| ~ ~ ( ~ ( subset @ SV22 @ SV34 )
| ~ ( subset @ SV34 @ SV38 ) )
| ( subset @ SV22 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(251,plain,
! [SV2: $i,SV23: $i] :
( ( ( ~ ~ ( empty @ SV23 ) )
= $true )
| ( ( ~ ( ilf_type @ SV23 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) )
| ~ ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(252,plain,
! [SV24: $i,SV3: $i] :
( ( ( ~ ( ~ ( member @ SV3 @ ( power_set @ SV24 ) )
| ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ SY93 @ SV3 )
| ( member @ SY93 @ SV24 ) ) ) )
= $false )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(253,plain,
! [SV24: $i,SV3: $i] :
( ( ( ~ ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ~ ( member @ SY94 @ SV3 )
| ( member @ SY94 @ SV24 ) )
| ( member @ SV3 @ ( power_set @ SV24 ) ) ) )
= $false )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(254,plain,
! [SV26: $i,SV6: $i,SV35: $i] :
( ( ( ~ ( ilf_type @ SV35 @ ( relation_type @ SV6 @ SV26 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( domain_of @ SV35 ) @ SV6 )
| ~ ( subset @ ( range_of @ SV35 ) @ SV26 ) ) )
= $true )
| ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(255,plain,
! [SV27: $i,SV7: $i,SV36: $i] :
( ( ( ~ ( ilf_type @ SV36 @ ( subset_type @ ( cross_product @ SV7 @ SV27 ) ) ) )
= $true )
| ( ( relation_like @ SV36 )
= $true )
| ( ( ilf_type @ SV27 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(256,plain,
( ( ilf_type @ sK5_SY97 @ ( relation_type @ sK1_B @ sK3_SY91 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(257,plain,
( ( ~ ( subset @ sK1_B @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(258,plain,
( ( ilf_type @ sK5_SY97 @ ( relation_type @ sK2_SX0 @ sK3_SY91 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(259,plain,
! [SV9: $i,SV28: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV28 @ ( subset_type @ SV9 ) )
| ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(260,plain,
! [SV9: $i,SV28: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) )
| ( ilf_type @ SV28 @ ( subset_type @ SV9 ) ) ) )
= $false )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(261,plain,
! [SV30: $i,SV12: $i] :
( ( ( ~ ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) )
| ( ilf_type @ SY98 @ ( relation_type @ SV12 @ SV30 ) ) ) )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(262,plain,
! [SV30: $i,SV12: $i] :
( ( ( ~ ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ ( relation_type @ SV12 @ SV30 ) )
| ( ilf_type @ SY99 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(263,plain,
! [SV13: $i] :
( ( ( ilf_type @ SV13 @ set_type )
= $false )
| ( ( empty @ SV13 )
= $true )
| ( ( ~ ! [SY71: $i] :
~ ( ilf_type @ SY71 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(264,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
= $false )
| ( ( ! [SY72: $i] :
( ~ ( ilf_type @ SY72 @ set_type )
| ~ ( member @ SY72 @ SV15 ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(265,plain,
! [SV15: $i] :
( ( ( ! [SY73: $i] :
( ~ ( ilf_type @ SY73 @ set_type )
| ~ ( member @ SY73 @ SV15 ) ) )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(266,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( ~ ( subset @ SV16 @ SV31 )
| ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( member @ SY100 @ SV16 )
| ( member @ SY100 @ SV31 ) ) ) )
= $false )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(267,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ~ ( member @ SY101 @ SV16 )
| ( member @ SY101 @ SV31 ) )
| ( subset @ SV16 @ SV31 ) ) )
= $false )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(268,plain,
! [SV32: $i,SV18: $i,SV37: $i] :
( ( ( ~ ( ilf_type @ SV37 @ set_type ) )
= $true )
| ( ( ! [SY106: $i] :
( ~ ( ilf_type @ SY106 @ ( relation_type @ SV18 @ SV37 ) )
| ~ ( subset @ ( domain_of @ SY106 ) @ SV32 )
| ( ilf_type @ SY106 @ ( relation_type @ SV32 @ SV37 ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(269,plain,
! [SV19: $i] :
( ( ( relation_like @ SV19 )
= $false )
| ( ( ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ set_type )
| ~ ( member @ SY80 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(270,plain,
! [SV19: $i] :
( ( ( ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( member @ SY83 @ SV19 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY83
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(271,plain,
! [SV33: $i,SV20: $i] :
( ( ( ~ ( ilf_type @ ( sK6_SY104 @ SV20 @ SV33 ) @ ( relation_type @ SV33 @ SV20 ) ) )
= $false )
| ( ( ilf_type @ SV33 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[249]) ).
thf(272,plain,
! [SV34: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( ilf_type @ SV38 @ set_type ) )
= $true )
| ( ( ~ ~ ( ~ ( subset @ SV22 @ SV34 )
| ~ ( subset @ SV34 @ SV38 ) )
| ( subset @ SV22 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(273,plain,
! [SV2: $i,SV23: $i] :
( ( ( ~ ( empty @ SV23 ) )
= $false )
| ( ( ~ ( ilf_type @ SV23 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) )
| ~ ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(274,plain,
! [SV24: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ ( power_set @ SV24 ) )
| ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ SY93 @ SV3 )
| ( member @ SY93 @ SV24 ) ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(275,plain,
! [SV24: $i,SV3: $i] :
( ( ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ~ ( member @ SY94 @ SV3 )
| ( member @ SY94 @ SV24 ) )
| ( member @ SV3 @ ( power_set @ SV24 ) ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(276,plain,
! [SV26: $i,SV6: $i,SV35: $i] :
( ( ( ilf_type @ SV35 @ ( relation_type @ SV6 @ SV26 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( domain_of @ SV35 ) @ SV6 )
| ~ ( subset @ ( range_of @ SV35 ) @ SV26 ) ) )
= $true )
| ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(277,plain,
! [SV27: $i,SV7: $i,SV36: $i] :
( ( ( ilf_type @ SV36 @ ( subset_type @ ( cross_product @ SV7 @ SV27 ) ) )
= $false )
| ( ( relation_like @ SV36 )
= $true )
| ( ( ilf_type @ SV27 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(278,plain,
( ( subset @ sK1_B @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(279,plain,
! [SV9: $i,SV28: $i] :
( ( ( ~ ( ilf_type @ SV28 @ ( subset_type @ SV9 ) )
| ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) ) )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(280,plain,
! [SV9: $i,SV28: $i] :
( ( ( ~ ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) )
| ( ilf_type @ SV28 @ ( subset_type @ SV9 ) ) )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(281,plain,
! [SV30: $i,SV12: $i] :
( ( ( ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) )
| ( ilf_type @ SY98 @ ( relation_type @ SV12 @ SV30 ) ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(282,plain,
! [SV30: $i,SV12: $i] :
( ( ( ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ ( relation_type @ SV12 @ SV30 ) )
| ( ilf_type @ SY99 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(283,plain,
! [SV13: $i] :
( ( ( ! [SY71: $i] :
~ ( ilf_type @ SY71 @ ( member_type @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(284,plain,
! [SV15: $i,SV39: $i] :
( ( ( ~ ( ilf_type @ SV39 @ set_type )
| ~ ( member @ SV39 @ SV15 ) )
= $true )
| ( ( empty @ SV15 )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(285,plain,
! [SV15: $i] :
( ( ( ~ ( ilf_type @ ( sK7_SY73 @ SV15 ) @ set_type )
| ~ ( member @ ( sK7_SY73 @ SV15 ) @ SV15 ) )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[265]) ).
thf(286,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV31 )
| ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( member @ SY100 @ SV16 )
| ( member @ SY100 @ SV31 ) ) )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(287,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ~ ( member @ SY101 @ SV16 )
| ( member @ SY101 @ SV31 ) )
| ( subset @ SV16 @ SV31 ) )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(288,plain,
! [SV32: $i,SV18: $i,SV37: $i] :
( ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ! [SY106: $i] :
( ~ ( ilf_type @ SY106 @ ( relation_type @ SV18 @ SV37 ) )
| ~ ( subset @ ( domain_of @ SY106 ) @ SV32 )
| ( ilf_type @ SY106 @ ( relation_type @ SV32 @ SV37 ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(289,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( ilf_type @ SV40 @ set_type )
| ~ ( member @ SV40 @ SV19 )
| ~ ! [SY107: $i] :
~ ~ ( ~ ( ilf_type @ SY107 @ set_type )
| ~ ~ ! [SY108: $i] :
~ ~ ( ~ ( ilf_type @ SY108 @ set_type )
| ( SV40
!= ( ordered_pair @ SY107 @ SY108 ) ) ) ) )
= $true )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(290,plain,
! [SV19: $i] :
( ( ( ~ ( ilf_type @ ( sK8_SY83 @ SV19 ) @ set_type )
| ~ ( member @ ( sK8_SY83 @ SV19 ) @ SV19 )
| ~ ! [SY109: $i] :
~ ~ ( ~ ( ilf_type @ SY109 @ set_type )
| ~ ~ ! [SY110: $i] :
~ ~ ( ~ ( ilf_type @ SY110 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SY109 @ SY110 ) ) ) ) )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[270]) ).
thf(291,plain,
! [SV33: $i,SV20: $i] :
( ( ( ilf_type @ ( sK6_SY104 @ SV20 @ SV33 ) @ ( relation_type @ SV33 @ SV20 ) )
= $true )
| ( ( ilf_type @ SV33 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(292,plain,
! [SV34: $i,SV22: $i,SV38: $i] :
( ( ( ilf_type @ SV38 @ set_type )
= $false )
| ( ( ~ ~ ( ~ ( subset @ SV22 @ SV34 )
| ~ ( subset @ SV34 @ SV38 ) )
| ( subset @ SV22 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(293,plain,
! [SV2: $i,SV23: $i] :
( ( ( empty @ SV23 )
= $true )
| ( ( ~ ( ilf_type @ SV23 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) )
| ~ ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(294,plain,
! [SV24: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ ( power_set @ SV24 ) ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ SY93 @ SV3 )
| ( member @ SY93 @ SV24 ) ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(295,plain,
! [SV24: $i,SV3: $i] :
( ( ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ~ ( member @ SY94 @ SV3 )
| ( member @ SY94 @ SV24 ) ) )
= $true )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(296,plain,
! [SV26: $i,SV6: $i,SV35: $i] :
( ( ( ~ ( subset @ ( domain_of @ SV35 ) @ SV6 )
| ~ ( subset @ ( range_of @ SV35 ) @ SV26 ) )
= $false )
| ( ( ilf_type @ SV35 @ ( relation_type @ SV6 @ SV26 ) )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(297,plain,
! [SV9: $i,SV28: $i] :
( ( ( ~ ( ilf_type @ SV28 @ ( subset_type @ SV9 ) ) )
= $true )
| ( ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(298,plain,
! [SV9: $i,SV28: $i] :
( ( ( ~ ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) ) )
= $true )
| ( ( ilf_type @ SV28 @ ( subset_type @ SV9 ) )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(299,plain,
! [SV30: $i,SV12: $i,SV41: $i] :
( ( ( ~ ( ilf_type @ SV41 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) )
| ( ilf_type @ SV41 @ ( relation_type @ SV12 @ SV30 ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(300,plain,
! [SV30: $i,SV12: $i,SV42: $i] :
( ( ( ~ ( ilf_type @ SV42 @ ( relation_type @ SV12 @ SV30 ) )
| ( ilf_type @ SV42 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(301,plain,
! [SV13: $i] :
( ( ( ~ ( ilf_type @ ( sK9_SY71 @ SV13 ) @ ( member_type @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[283]) ).
thf(302,plain,
! [SV15: $i,SV39: $i] :
( ( ( ~ ( ilf_type @ SV39 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV39 @ SV15 ) )
= $true )
| ( ( empty @ SV15 )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(303,plain,
! [SV15: $i] :
( ( ( ~ ( ilf_type @ ( sK7_SY73 @ SV15 ) @ set_type ) )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(304,plain,
! [SV15: $i] :
( ( ( ~ ( member @ ( sK7_SY73 @ SV15 ) @ SV15 ) )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(305,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV31 ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( member @ SY100 @ SV16 )
| ( member @ SY100 @ SV31 ) ) )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(306,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ~ ( member @ SY101 @ SV16 )
| ( member @ SY101 @ SV31 ) ) )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(307,plain,
! [SV32: $i,SV37: $i,SV18: $i,SV43: $i] :
( ( ( ~ ( ilf_type @ SV43 @ ( relation_type @ SV18 @ SV37 ) )
| ~ ( subset @ ( domain_of @ SV43 ) @ SV32 )
| ( ilf_type @ SV43 @ ( relation_type @ SV32 @ SV37 ) ) )
= $true )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(308,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( ilf_type @ SV40 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV40 @ SV19 )
| ~ ! [SY107: $i] :
~ ~ ( ~ ( ilf_type @ SY107 @ set_type )
| ~ ~ ! [SY108: $i] :
~ ~ ( ~ ( ilf_type @ SY108 @ set_type )
| ( SV40
!= ( ordered_pair @ SY107 @ SY108 ) ) ) ) )
= $true )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(309,plain,
! [SV19: $i] :
( ( ( ~ ( ilf_type @ ( sK8_SY83 @ SV19 ) @ set_type ) )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(310,plain,
! [SV19: $i] :
( ( ( ~ ( member @ ( sK8_SY83 @ SV19 ) @ SV19 )
| ~ ! [SY109: $i] :
~ ~ ( ~ ( ilf_type @ SY109 @ set_type )
| ~ ~ ! [SY110: $i] :
~ ~ ( ~ ( ilf_type @ SY110 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SY109 @ SY110 ) ) ) ) )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(311,plain,
! [SV38: $i,SV34: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV22 @ SV34 )
| ~ ( subset @ SV34 @ SV38 ) ) )
= $true )
| ( ( subset @ SV22 @ SV38 )
= $true )
| ( ( ilf_type @ SV38 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(312,plain,
! [SV2: $i,SV23: $i] :
( ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( empty @ SV23 )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) )
| ~ ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(313,plain,
! [SV24: $i,SV3: $i] :
( ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $false )
| ( ( ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ SY93 @ SV3 )
| ( member @ SY93 @ SV24 ) ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(314,plain,
! [SV24: $i,SV3: $i] :
( ( ( ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ~ ( member @ SY94 @ SV3 )
| ( member @ SY94 @ SV24 ) ) )
= $false )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(315,plain,
! [SV26: $i,SV6: $i,SV35: $i] :
( ( ( ~ ( subset @ ( domain_of @ SV35 ) @ SV6 ) )
= $false )
| ( ( ilf_type @ SV35 @ ( relation_type @ SV6 @ SV26 ) )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(316,plain,
! [SV6: $i,SV26: $i,SV35: $i] :
( ( ( ~ ( subset @ ( range_of @ SV35 ) @ SV26 ) )
= $false )
| ( ( ilf_type @ SV35 @ ( relation_type @ SV6 @ SV26 ) )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(317,plain,
! [SV9: $i,SV28: $i] :
( ( ( ilf_type @ SV28 @ ( subset_type @ SV9 ) )
= $false )
| ( ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(318,plain,
! [SV9: $i,SV28: $i] :
( ( ( ilf_type @ SV28 @ ( member_type @ ( power_set @ SV9 ) ) )
= $false )
| ( ( ilf_type @ SV28 @ ( subset_type @ SV9 ) )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV9 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(319,plain,
! [SV30: $i,SV12: $i,SV41: $i] :
( ( ( ~ ( ilf_type @ SV41 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) ) )
= $true )
| ( ( ilf_type @ SV41 @ ( relation_type @ SV12 @ SV30 ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(320,plain,
! [SV30: $i,SV12: $i,SV42: $i] :
( ( ( ~ ( ilf_type @ SV42 @ ( relation_type @ SV12 @ SV30 ) ) )
= $true )
| ( ( ilf_type @ SV42 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(321,plain,
! [SV13: $i] :
( ( ( ilf_type @ ( sK9_SY71 @ SV13 ) @ ( member_type @ SV13 ) )
= $true )
| ( ( empty @ SV13 )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(322,plain,
! [SV15: $i,SV39: $i] :
( ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ~ ( member @ SV39 @ SV15 ) )
= $true )
| ( ( empty @ SV15 )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(323,plain,
! [SV15: $i] :
( ( ( ilf_type @ ( sK7_SY73 @ SV15 ) @ set_type )
= $true )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(324,plain,
! [SV15: $i] :
( ( ( member @ ( sK7_SY73 @ SV15 ) @ SV15 )
= $true )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(325,plain,
! [SV31: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV31 )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( member @ SY100 @ SV16 )
| ( member @ SY100 @ SV31 ) ) )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(326,plain,
! [SV31: $i,SV16: $i] :
( ( ( ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ~ ( member @ SY101 @ SV16 )
| ( member @ SY101 @ SV31 ) ) )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(327,plain,
! [SV32: $i,SV37: $i,SV18: $i,SV43: $i] :
( ( ( ~ ( ilf_type @ SV43 @ ( relation_type @ SV18 @ SV37 ) ) )
= $true )
| ( ( ~ ( subset @ ( domain_of @ SV43 ) @ SV32 )
| ( ilf_type @ SV43 @ ( relation_type @ SV32 @ SV37 ) ) )
= $true )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(328,plain,
! [SV19: $i,SV40: $i] :
( ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( ~ ( member @ SV40 @ SV19 )
| ~ ! [SY107: $i] :
~ ~ ( ~ ( ilf_type @ SY107 @ set_type )
| ~ ~ ! [SY108: $i] :
~ ~ ( ~ ( ilf_type @ SY108 @ set_type )
| ( SV40
!= ( ordered_pair @ SY107 @ SY108 ) ) ) ) )
= $true )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(329,plain,
! [SV19: $i] :
( ( ( ilf_type @ ( sK8_SY83 @ SV19 ) @ set_type )
= $true )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(330,plain,
! [SV19: $i] :
( ( ( ~ ( member @ ( sK8_SY83 @ SV19 ) @ SV19 ) )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(331,plain,
! [SV19: $i] :
( ( ( ~ ! [SY109: $i] :
~ ~ ( ~ ( ilf_type @ SY109 @ set_type )
| ~ ~ ! [SY110: $i] :
~ ~ ( ~ ( ilf_type @ SY110 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SY109 @ SY110 ) ) ) ) )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(332,plain,
! [SV38: $i,SV34: $i,SV22: $i] :
( ( ( ~ ( ~ ( subset @ SV22 @ SV34 )
| ~ ( subset @ SV34 @ SV38 ) ) )
= $false )
| ( ( subset @ SV22 @ SV38 )
= $true )
| ( ( ilf_type @ SV38 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(333,plain,
! [SV23: $i,SV2: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) )
| ~ ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) ) )
= $false )
| ( ( empty @ SV23 )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(334,plain,
! [SV24: $i,SV3: $i,SV44: $i] :
( ( ( ~ ( ilf_type @ SV44 @ set_type )
| ~ ( member @ SV44 @ SV3 )
| ( member @ SV44 @ SV24 ) )
= $true )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $false )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(335,plain,
! [SV3: $i,SV24: $i] :
( ( ( ~ ( ilf_type @ ( sK10_SY94 @ SV24 @ SV3 ) @ set_type )
| ~ ( member @ ( sK10_SY94 @ SV24 @ SV3 ) @ SV3 )
| ( member @ ( sK10_SY94 @ SV24 @ SV3 ) @ SV24 ) )
= $false )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[314]) ).
thf(336,plain,
! [SV26: $i,SV6: $i,SV35: $i] :
( ( ( subset @ ( domain_of @ SV35 ) @ SV6 )
= $true )
| ( ( ilf_type @ SV35 @ ( relation_type @ SV6 @ SV26 ) )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(337,plain,
! [SV6: $i,SV26: $i,SV35: $i] :
( ( ( subset @ ( range_of @ SV35 ) @ SV26 )
= $true )
| ( ( ilf_type @ SV35 @ ( relation_type @ SV6 @ SV26 ) )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(338,plain,
! [SV30: $i,SV12: $i,SV41: $i] :
( ( ( ilf_type @ SV41 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) )
= $false )
| ( ( ilf_type @ SV41 @ ( relation_type @ SV12 @ SV30 ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(339,plain,
! [SV30: $i,SV12: $i,SV42: $i] :
( ( ( ilf_type @ SV42 @ ( relation_type @ SV12 @ SV30 ) )
= $false )
| ( ( ilf_type @ SV42 @ ( subset_type @ ( cross_product @ SV12 @ SV30 ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(340,plain,
! [SV15: $i,SV39: $i] :
( ( ( member @ SV39 @ SV15 )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( empty @ SV15 )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(341,plain,
! [SV31: $i,SV16: $i,SV45: $i] :
( ( ( ~ ( ilf_type @ SV45 @ set_type )
| ~ ( member @ SV45 @ SV16 )
| ( member @ SV45 @ SV31 ) )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $false )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(342,plain,
! [SV16: $i,SV31: $i] :
( ( ( ~ ( ilf_type @ ( sK11_SY101 @ SV31 @ SV16 ) @ set_type )
| ~ ( member @ ( sK11_SY101 @ SV31 @ SV16 ) @ SV16 )
| ( member @ ( sK11_SY101 @ SV31 @ SV16 ) @ SV31 ) )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[326]) ).
thf(343,plain,
! [SV32: $i,SV37: $i,SV18: $i,SV43: $i] :
( ( ( ilf_type @ SV43 @ ( relation_type @ SV18 @ SV37 ) )
= $false )
| ( ( ~ ( subset @ ( domain_of @ SV43 ) @ SV32 )
| ( ilf_type @ SV43 @ ( relation_type @ SV32 @ SV37 ) ) )
= $true )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(344,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ SV19 ) )
= $true )
| ( ( ~ ! [SY107: $i] :
~ ~ ( ~ ( ilf_type @ SY107 @ set_type )
| ~ ~ ! [SY108: $i] :
~ ~ ( ~ ( ilf_type @ SY108 @ set_type )
| ( SV40
!= ( ordered_pair @ SY107 @ SY108 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(345,plain,
! [SV19: $i] :
( ( ( member @ ( sK8_SY83 @ SV19 ) @ SV19 )
= $true )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(346,plain,
! [SV19: $i] :
( ( ( ! [SY109: $i] :
~ ~ ( ~ ( ilf_type @ SY109 @ set_type )
| ~ ~ ! [SY110: $i] :
~ ~ ( ~ ( ilf_type @ SY110 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SY109 @ SY110 ) ) ) ) )
= $true )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(347,plain,
! [SV38: $i,SV34: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV34 )
| ~ ( subset @ SV34 @ SV38 ) )
= $true )
| ( ( subset @ SV22 @ SV38 )
= $true )
| ( ( ilf_type @ SV38 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(348,plain,
! [SV23: $i,SV2: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) ) )
= $false )
| ( ( empty @ SV23 )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(349,plain,
! [SV23: $i,SV2: $i] :
( ( ( ~ ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) ) )
= $false )
| ( ( empty @ SV23 )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(350,plain,
! [SV24: $i,SV3: $i,SV44: $i] :
( ( ( ~ ( ilf_type @ SV44 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV44 @ SV3 )
| ( member @ SV44 @ SV24 ) )
= $true )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $false )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(351,plain,
! [SV3: $i,SV24: $i] :
( ( ( ~ ( ilf_type @ ( sK10_SY94 @ SV24 @ SV3 ) @ set_type ) )
= $false )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(352,plain,
! [SV3: $i,SV24: $i] :
( ( ( ~ ( member @ ( sK10_SY94 @ SV24 @ SV3 ) @ SV3 )
| ( member @ ( sK10_SY94 @ SV24 @ SV3 ) @ SV24 ) )
= $false )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(353,plain,
! [SV31: $i,SV16: $i,SV45: $i] :
( ( ( ~ ( ilf_type @ SV45 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV45 @ SV16 )
| ( member @ SV45 @ SV31 ) )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $false )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(354,plain,
! [SV16: $i,SV31: $i] :
( ( ( ~ ( ilf_type @ ( sK11_SY101 @ SV31 @ SV16 ) @ set_type ) )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(355,plain,
! [SV16: $i,SV31: $i] :
( ( ( ~ ( member @ ( sK11_SY101 @ SV31 @ SV16 ) @ SV16 )
| ( member @ ( sK11_SY101 @ SV31 @ SV16 ) @ SV31 ) )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(356,plain,
! [SV18: $i,SV37: $i,SV32: $i,SV43: $i] :
( ( ( ~ ( subset @ ( domain_of @ SV43 ) @ SV32 ) )
= $true )
| ( ( ilf_type @ SV43 @ ( relation_type @ SV32 @ SV37 ) )
= $true )
| ( ( ilf_type @ SV43 @ ( relation_type @ SV18 @ SV37 ) )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(357,plain,
! [SV19: $i,SV40: $i] :
( ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ~ ! [SY107: $i] :
~ ~ ( ~ ( ilf_type @ SY107 @ set_type )
| ~ ~ ! [SY108: $i] :
~ ~ ( ~ ( ilf_type @ SY108 @ set_type )
| ( SV40
!= ( ordered_pair @ SY107 @ SY108 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(358,plain,
! [SV19: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ SV46 @ set_type )
| ~ ~ ! [SY111: $i] :
~ ~ ( ~ ( ilf_type @ SY111 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SY111 ) ) ) ) )
= $true )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(359,plain,
! [SV38: $i,SV34: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV34 ) )
= $true )
| ( ( ~ ( subset @ SV34 @ SV38 ) )
= $true )
| ( ( subset @ SV22 @ SV38 )
= $true )
| ( ( ilf_type @ SV38 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(360,plain,
! [SV23: $i,SV2: $i] :
( ( ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
| ( member @ SV2 @ SV23 ) )
= $true )
| ( ( empty @ SV23 )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(361,plain,
! [SV23: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV23 )
| ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(362,plain,
! [SV24: $i,SV3: $i,SV44: $i] :
( ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ~ ( member @ SV44 @ SV3 )
| ( member @ SV44 @ SV24 ) )
= $true )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $false )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(363,plain,
! [SV3: $i,SV24: $i] :
( ( ( ilf_type @ ( sK10_SY94 @ SV24 @ SV3 ) @ set_type )
= $true )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(364,plain,
! [SV3: $i,SV24: $i] :
( ( ( ~ ( member @ ( sK10_SY94 @ SV24 @ SV3 ) @ SV3 ) )
= $false )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(365,plain,
! [SV3: $i,SV24: $i] :
( ( ( member @ ( sK10_SY94 @ SV24 @ SV3 ) @ SV24 )
= $false )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(366,plain,
! [SV31: $i,SV16: $i,SV45: $i] :
( ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ~ ( member @ SV45 @ SV16 )
| ( member @ SV45 @ SV31 ) )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $false )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(367,plain,
! [SV16: $i,SV31: $i] :
( ( ( ilf_type @ ( sK11_SY101 @ SV31 @ SV16 ) @ set_type )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(368,plain,
! [SV16: $i,SV31: $i] :
( ( ( ~ ( member @ ( sK11_SY101 @ SV31 @ SV16 ) @ SV16 ) )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(369,plain,
! [SV16: $i,SV31: $i] :
( ( ( member @ ( sK11_SY101 @ SV31 @ SV16 ) @ SV31 )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(370,plain,
! [SV18: $i,SV37: $i,SV32: $i,SV43: $i] :
( ( ( subset @ ( domain_of @ SV43 ) @ SV32 )
= $false )
| ( ( ilf_type @ SV43 @ ( relation_type @ SV32 @ SV37 ) )
= $true )
| ( ( ilf_type @ SV43 @ ( relation_type @ SV18 @ SV37 ) )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(371,plain,
! [SV19: $i,SV40: $i] :
( ( ( ! [SY107: $i] :
~ ~ ( ~ ( ilf_type @ SY107 @ set_type )
| ~ ~ ! [SY108: $i] :
~ ~ ( ~ ( ilf_type @ SY108 @ set_type )
| ( SV40
!= ( ordered_pair @ SY107 @ SY108 ) ) ) ) )
= $false )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(372,plain,
! [SV19: $i,SV46: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV46 @ set_type )
| ~ ~ ! [SY111: $i] :
~ ~ ( ~ ( ilf_type @ SY111 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SY111 ) ) ) ) )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(373,plain,
! [SV38: $i,SV34: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV34 )
= $false )
| ( ( ~ ( subset @ SV34 @ SV38 ) )
= $true )
| ( ( subset @ SV22 @ SV38 )
= $true )
| ( ( ilf_type @ SV38 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(374,plain,
! [SV23: $i,SV2: $i] :
( ( ( ~ ( ilf_type @ SV2 @ ( member_type @ SV23 ) ) )
= $true )
| ( ( member @ SV2 @ SV23 )
= $true )
| ( ( empty @ SV23 )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(375,plain,
! [SV23: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV23 ) )
= $true )
| ( ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
= $true )
| ( ( empty @ SV23 )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(376,plain,
! [SV24: $i,SV3: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ SV3 ) )
= $true )
| ( ( member @ SV44 @ SV24 )
= $true )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $false )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(377,plain,
! [SV3: $i,SV24: $i] :
( ( ( member @ ( sK10_SY94 @ SV24 @ SV3 ) @ SV3 )
= $true )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(378,plain,
! [SV31: $i,SV16: $i,SV45: $i] :
( ( ( ~ ( member @ SV45 @ SV16 ) )
= $true )
| ( ( member @ SV45 @ SV31 )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $false )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(379,plain,
! [SV16: $i,SV31: $i] :
( ( ( member @ ( sK11_SY101 @ SV31 @ SV16 ) @ SV16 )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $true )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(380,plain,
! [SV40: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ ( sK12_SY107 @ SV19 @ SV40 ) @ set_type )
| ~ ~ ! [SY112: $i] :
~ ~ ( ~ ( ilf_type @ SY112 @ set_type )
| ( SV40
!= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ SY112 ) ) ) ) )
= $false )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[371]) ).
thf(381,plain,
! [SV19: $i,SV46: $i] :
( ( ( ~ ( ilf_type @ SV46 @ set_type )
| ~ ~ ! [SY111: $i] :
~ ~ ( ~ ( ilf_type @ SY111 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SY111 ) ) ) )
= $true )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(382,plain,
! [SV22: $i,SV38: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV38 )
= $false )
| ( ( subset @ SV22 @ SV34 )
= $false )
| ( ( subset @ SV22 @ SV38 )
= $true )
| ( ( ilf_type @ SV38 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(383,plain,
! [SV23: $i,SV2: $i] :
( ( ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
= $false )
| ( ( member @ SV2 @ SV23 )
= $true )
| ( ( empty @ SV23 )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(384,plain,
! [SV23: $i,SV2: $i] :
( ( ( member @ SV2 @ SV23 )
= $false )
| ( ( ilf_type @ SV2 @ ( member_type @ SV23 ) )
= $true )
| ( ( empty @ SV23 )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ilf_type @ SV2 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(385,plain,
! [SV24: $i,SV3: $i,SV44: $i] :
( ( ( member @ SV44 @ SV3 )
= $false )
| ( ( member @ SV44 @ SV24 )
= $true )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( member @ SV3 @ ( power_set @ SV24 ) )
= $false )
| ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(386,plain,
! [SV31: $i,SV16: $i,SV45: $i] :
( ( ( member @ SV45 @ SV16 )
= $false )
| ( ( member @ SV45 @ SV31 )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $false )
| ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(387,plain,
! [SV40: $i,SV19: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK12_SY107 @ SV19 @ SV40 ) @ set_type )
| ~ ~ ! [SY112: $i] :
~ ~ ( ~ ( ilf_type @ SY112 @ set_type )
| ( SV40
!= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ SY112 ) ) ) ) )
= $true )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(388,plain,
! [SV19: $i,SV46: $i] :
( ( ( ~ ( ilf_type @ SV46 @ set_type ) )
= $true )
| ( ( ~ ~ ! [SY111: $i] :
~ ~ ( ~ ( ilf_type @ SY111 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SY111 ) ) ) )
= $true )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(389,plain,
! [SV40: $i,SV19: $i] :
( ( ( ~ ( ilf_type @ ( sK12_SY107 @ SV19 @ SV40 ) @ set_type )
| ~ ~ ! [SY112: $i] :
~ ~ ( ~ ( ilf_type @ SY112 @ set_type )
| ( SV40
!= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ SY112 ) ) ) )
= $false )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(390,plain,
! [SV19: $i,SV46: $i] :
( ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( ~ ~ ! [SY111: $i] :
~ ~ ( ~ ( ilf_type @ SY111 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SY111 ) ) ) )
= $true )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(391,plain,
! [SV40: $i,SV19: $i] :
( ( ( ~ ( ilf_type @ ( sK12_SY107 @ SV19 @ SV40 ) @ set_type ) )
= $false )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(392,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ~ ! [SY112: $i] :
~ ~ ( ~ ( ilf_type @ SY112 @ set_type )
| ( SV40
!= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ SY112 ) ) ) )
= $false )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(393,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ! [SY111: $i] :
~ ~ ( ~ ( ilf_type @ SY111 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SY111 ) ) ) )
= $false )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(394,plain,
! [SV40: $i,SV19: $i] :
( ( ( ilf_type @ ( sK12_SY107 @ SV19 @ SV40 ) @ set_type )
= $true )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(395,plain,
! [SV19: $i,SV40: $i] :
( ( ( ~ ! [SY112: $i] :
~ ~ ( ~ ( ilf_type @ SY112 @ set_type )
| ( SV40
!= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ SY112 ) ) ) )
= $true )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(396,plain,
! [SV46: $i,SV19: $i] :
( ( ( ! [SY111: $i] :
~ ~ ( ~ ( ilf_type @ SY111 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SY111 ) ) ) )
= $true )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(397,plain,
! [SV19: $i,SV40: $i] :
( ( ( ! [SY112: $i] :
~ ~ ( ~ ( ilf_type @ SY112 @ set_type )
| ( SV40
!= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ SY112 ) ) ) )
= $false )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(398,plain,
! [SV46: $i,SV19: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ SV47 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SV47 ) ) ) )
= $true )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(399,plain,
! [SV40: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ ( sK13_SY112 @ SV19 @ SV40 ) @ set_type )
| ( SV40
!= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ ( sK13_SY112 @ SV19 @ SV40 ) ) ) ) )
= $false )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[397]) ).
thf(400,plain,
! [SV46: $i,SV19: $i,SV47: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV47 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SV47 ) ) ) )
= $false )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(401,plain,
! [SV40: $i,SV19: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK13_SY112 @ SV19 @ SV40 ) @ set_type )
| ( SV40
!= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ ( sK13_SY112 @ SV19 @ SV40 ) ) ) ) )
= $true )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(402,plain,
! [SV46: $i,SV19: $i,SV47: $i] :
( ( ( ~ ( ilf_type @ SV47 @ set_type )
| ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SV47 ) ) )
= $true )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(403,plain,
! [SV40: $i,SV19: $i] :
( ( ( ~ ( ilf_type @ ( sK13_SY112 @ SV19 @ SV40 ) @ set_type )
| ( SV40
!= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ ( sK13_SY112 @ SV19 @ SV40 ) ) ) )
= $false )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(404,plain,
! [SV46: $i,SV19: $i,SV47: $i] :
( ( ( ~ ( ilf_type @ SV47 @ set_type ) )
= $true )
| ( ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SV47 ) )
= $true )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(405,plain,
! [SV40: $i,SV19: $i] :
( ( ( ~ ( ilf_type @ ( sK13_SY112 @ SV19 @ SV40 ) @ set_type ) )
= $false )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(406,plain,
! [SV19: $i,SV40: $i] :
( ( ( SV40
!= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ ( sK13_SY112 @ SV19 @ SV40 ) ) )
= $false )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(407,plain,
! [SV46: $i,SV19: $i,SV47: $i] :
( ( ( ilf_type @ SV47 @ set_type )
= $false )
| ( ( ( sK8_SY83 @ SV19 )
!= ( ordered_pair @ SV46 @ SV47 ) )
= $true )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(408,plain,
! [SV40: $i,SV19: $i] :
( ( ( ilf_type @ ( sK13_SY112 @ SV19 @ SV40 ) @ set_type )
= $true )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(409,plain,
! [SV19: $i,SV40: $i] :
( ( ( SV40
= ( ordered_pair @ ( sK12_SY107 @ SV19 @ SV40 ) @ ( sK13_SY112 @ SV19 @ SV40 ) ) )
= $true )
| ( ( member @ SV40 @ SV19 )
= $false )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(410,plain,
! [SV47: $i,SV46: $i,SV19: $i] :
( ( ( ( sK8_SY83 @ SV19 )
= ( ordered_pair @ SV46 @ SV47 ) )
= $false )
| ( ( ilf_type @ SV47 @ set_type )
= $false )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( relation_like @ SV19 )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(411,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[74,410,409,408,394,386,385,384,383,382,379,377,370,369,367,365,363,345,340,339,338,337,336,329,324,323,321,318,317,291,278,277,258,256,245,234,230,219,216,213,211,172,157,154,151,98]) ).
thf(412,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[411]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET653+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n011.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 14:48:06 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.55/0.53
% 1.55/0.53 No.of.Axioms: 22
% 1.55/0.53
% 1.55/0.53 Length.of.Defs: 0
% 1.55/0.53
% 1.55/0.53 Contains.Choice.Funs: false
% 1.55/0.53 .............
% 1.55/0.53
% 1.55/0.53 ********************************
% 1.55/0.53 * All subproblems solved! *
% 1.55/0.53 ********************************
% 1.55/0.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:411,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.55/0.53
% 1.55/0.53 %**** Beginning of derivation protocol ****
% 1.55/0.53 % SZS output start CNFRefutation
% See solution above
% 1.55/0.53
% 1.55/0.53 %**** End of derivation protocol ****
% 1.55/0.53 %**** no. of clauses in derivation: 412 ****
% 1.55/0.53 %**** clause counter: 411 ****
% 1.55/0.53
% 1.55/0.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:411,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------