%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET678+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:40:49 AM UTC 2026
% Result : Theorem 5.63s 1.19s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 39
% Syntax : Number of formulae : 697 ( 172 unt; 0 typ; 0 def)
% Number of atoms : 7430 (2202 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 15005 (2598 ~;2559 |; 40 &;9500 @)
% ( 36 <=>; 272 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 7 con; 0-5 aty)
% Number of variables : 1891 ( 0 ^;1867 !; 24 ?;1891 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binary_relation_type,type,
binary_relation_type: $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_compose5,type,
compose5: $i > $i > $i > $i > $i > $i ).
thf(tp_cross_product,type,
cross_product: $i > $i > $i ).
thf(tp_domain,type,
domain: $i > $i > $i > $i ).
thf(tp_domain_of,type,
domain_of: $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_identity_relation_of,type,
identity_relation_of: $i > $i ).
thf(tp_identity_relation_of_type,type,
identity_relation_of_type: $i > $i ).
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,type,
range: $i > $i > $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_SY162,type,
sK10_SY162: $i > $i > $i ).
thf(tp_sK11_SY176,type,
sK11_SY176: $i > $i > $i ).
thf(tp_sK12_SY179,type,
sK12_SY179: $i > $i > $i ).
thf(tp_sK13_SY197,type,
sK13_SY197: $i > $i > $i ).
thf(tp_sK14_SY188,type,
sK14_SY188: $i > $i > $i ).
thf(tp_sK15_SY192,type,
sK15_SY192: $i > $i > $i > $i > $i ).
thf(tp_sK16_SY199,type,
sK16_SY199: $i > $i > $i ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY118,type,
sK4_SY118: $i > $i ).
thf(tp_sK5_SY147,type,
sK5_SY147: $i > $i ).
thf(tp_sK6_SY167,type,
sK6_SY167: $i > $i > $i ).
thf(tp_sK7_SY122,type,
sK7_SY122: $i > $i ).
thf(tp_sK8_SY132,type,
sK8_SY132: $i > $i ).
thf(tp_sK9_SY119,type,
sK9_SY119: $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/sandbox/benchmark/theBenchmark.p',p38) ).
thf(2,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 @ C ) )
=> ! [F: $i] :
( ( ilf_type @ F @ ( relation_type @ C @ D ) )
=> ( ilf_type @ ( compose5 @ B @ C @ D @ E @ F ) @ ( relation_type @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p37) ).
thf(3,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 @ C ) )
=> ! [F: $i] :
( ( ilf_type @ F @ ( relation_type @ C @ D ) )
=> ( ( compose5 @ B @ C @ D @ E @ F )
= ( compose @ E @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p36) ).
thf(4,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ilf_type @ ( range @ B @ C @ D ) @ ( subset_type @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p35) ).
thf(5,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( range @ B @ C @ D )
= ( range_of @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).
thf(6,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ilf_type @ ( domain @ B @ C @ D ) @ ( subset_type @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
thf(7,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( domain @ B @ C @ D )
= ( domain_of @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p32) ).
thf(8,axiom,
! [B: $i] :
( ( ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( relation_like @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
thf(9,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( empty @ B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ~ ( member @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
thf(10,axiom,
! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ? [C: $i] : ( ilf_type @ C @ ( member_type @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',p28) ).
thf(12,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ~ ( empty @ ( power_set @ B ) )
& ( ilf_type @ ( power_set @ B ) @ set_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',p26) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',p25) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',p24) ).
thf(16,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',p22) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',p21) ).
thf(19,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',p19) ).
thf(21,axiom,
! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( B = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
thf(22,axiom,
! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( B = C )
=> ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',p16) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',p15) ).
thf(25,axiom,
? [B: $i] : ( ilf_type @ B @ binary_relation_type ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
thf(26,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ilf_type @ B @ binary_relation_type )
<=> ( ( relation_like @ B )
& ( ilf_type @ B @ set_type ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',p12) ).
thf(28,axiom,
! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( range_of @ B ) @ set_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
thf(29,axiom,
! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ B ) @ set_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
thf(30,axiom,
! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( B = C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ set_type )
=> ( ( member @ ( ordered_pair @ D @ E ) @ B )
<=> ( member @ ( ordered_pair @ D @ E ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
thf(31,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( identity_relation_of_type @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
thf(32,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
<=> ( ilf_type @ C @ ( relation_type @ B @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
thf(33,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( identity_relation_of @ B ) @ binary_relation_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
thf(34,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ ( ordered_pair @ C @ D ) @ ( identity_relation_of @ B ) )
<=> ( ( member @ C @ B )
& ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
thf(35,axiom,
! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ilf_type @ ( compose @ B @ C ) @ binary_relation_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
thf(36,axiom,
! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ set_type )
=> ( ( member @ ( ordered_pair @ D @ E ) @ ( compose @ B @ C ) )
<=> ? [F: $i] :
( ( ilf_type @ F @ set_type )
& ( member @ ( ordered_pair @ D @ F ) @ B )
& ( member @ ( ordered_pair @ F @ E ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
thf(37,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( subset @ ( range_of @ C ) @ B )
=> ( ( compose @ C @ ( identity_relation_of @ B ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
thf(38,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( subset @ ( domain_of @ C ) @ B )
=> ( ( compose @ ( identity_relation_of @ B ) @ C )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
thf(39,conjecture,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
=> ( ( ( compose @ C @ ( identity_relation_of @ B ) )
= C )
& ( ( compose @ ( identity_relation_of @ B ) @ C )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_45) ).
thf(40,negated_conjecture,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
=> ( ( ( compose @ C @ ( identity_relation_of @ B ) )
= C )
& ( ( compose @ ( identity_relation_of @ B ) @ C )
= C ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[39]) ).
thf(41,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
=> ( ( ( compose @ C @ ( identity_relation_of @ B ) )
= C )
& ( ( compose @ ( identity_relation_of @ B ) @ C )
= C ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[40]) ).
thf(42,plain,
( ( ! [B: $i] : ( ilf_type @ B @ set_type ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(43,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 @ C ) )
=> ! [F: $i] :
( ( ilf_type @ F @ ( relation_type @ C @ D ) )
=> ( ilf_type @ ( compose5 @ B @ C @ D @ E @ F ) @ ( relation_type @ B @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(44,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 @ C ) )
=> ! [F: $i] :
( ( ilf_type @ F @ ( relation_type @ C @ D ) )
=> ( ( compose5 @ B @ C @ D @ E @ F )
= ( compose @ E @ F ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ilf_type @ ( range @ B @ C @ D ) @ ( subset_type @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
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 ) )
=> ( ( range @ B @ C @ D )
= ( range_of @ D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(47,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ilf_type @ ( domain @ B @ C @ D ) @ ( subset_type @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(48,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( domain @ B @ C @ D )
= ( domain_of @ D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(49,plain,
( ( ! [B: $i] :
( ( ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( relation_like @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(50,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)],[9]) ).
thf(51,plain,
( ( ! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ? [C: $i] : ( ilf_type @ C @ ( member_type @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(52,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)],[11]) ).
thf(53,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)],[12]) ).
thf(54,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)],[13]) ).
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 ) ) )
=> ( relation_like @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(56,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)],[15]) ).
thf(57,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(58,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)],[17]) ).
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(unfold_def,[status(thm)],[18]) ).
thf(60,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(61,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)],[20]) ).
thf(62,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( B = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(63,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( B = C )
=> ( C = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(64,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)],[23]) ).
thf(65,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)],[24]) ).
thf(66,plain,
( ( ? [B: $i] : ( ilf_type @ B @ binary_relation_type ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(67,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ilf_type @ B @ binary_relation_type )
<=> ( ( relation_like @ B )
& ( ilf_type @ B @ set_type ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(68,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)],[27]) ).
thf(69,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( range_of @ B ) @ set_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(70,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ B ) @ set_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(71,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( B = C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ set_type )
=> ( ( member @ ( ordered_pair @ D @ E ) @ B )
<=> ( member @ ( ordered_pair @ D @ E ) @ C ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(72,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( identity_relation_of_type @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(73,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
<=> ( ilf_type @ C @ ( relation_type @ B @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(74,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( identity_relation_of @ B ) @ binary_relation_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(75,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ ( ordered_pair @ C @ D ) @ ( identity_relation_of @ B ) )
<=> ( ( member @ C @ B )
& ( C = D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(76,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ilf_type @ ( compose @ B @ C ) @ binary_relation_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(77,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ set_type )
=> ( ( member @ ( ordered_pair @ D @ E ) @ ( compose @ B @ C ) )
<=> ? [F: $i] :
( ( ilf_type @ F @ set_type )
& ( member @ ( ordered_pair @ D @ F ) @ B )
& ( member @ ( ordered_pair @ F @ E ) @ C ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(78,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( subset @ ( range_of @ C ) @ B )
=> ( ( compose @ C @ ( identity_relation_of @ B ) )
= C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(79,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( subset @ ( domain_of @ C ) @ B )
=> ( ( compose @ ( identity_relation_of @ B ) @ C )
= C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(80,plain,
( ( ( ilf_type @ sK1_B @ set_type )
=> ! [SY92: $i] :
( ( ilf_type @ SY92 @ ( identity_relation_of_type @ sK1_B ) )
=> ( ( ( compose @ SY92 @ ( identity_relation_of @ sK1_B ) )
= SY92 )
& ( ( compose @ ( identity_relation_of @ sK1_B ) @ SY92 )
= SY92 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(81,plain,
( ( ilf_type @ sK1_B @ set_type )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(82,plain,
( ( ! [SY92: $i] :
( ( ilf_type @ SY92 @ ( identity_relation_of_type @ sK1_B ) )
=> ( ( ( compose @ SY92 @ ( identity_relation_of @ sK1_B ) )
= SY92 )
& ( ( compose @ ( identity_relation_of @ sK1_B ) @ SY92 )
= SY92 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(83,plain,
( ( ~ ! [SY92: $i] :
( ( ilf_type @ SY92 @ ( identity_relation_of_type @ sK1_B ) )
=> ( ( ( compose @ SY92 @ ( identity_relation_of @ sK1_B ) )
= SY92 )
& ( ( compose @ ( identity_relation_of @ sK1_B ) @ SY92 )
= SY92 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[82]) ).
thf(84,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( subset @ ( domain_of @ C ) @ B )
=> ( ( compose @ ( identity_relation_of @ B ) @ C )
= C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(85,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( subset @ ( range_of @ C ) @ B )
=> ( ( compose @ C @ ( identity_relation_of @ B ) )
= C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(86,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ set_type )
=> ( ( member @ ( ordered_pair @ D @ E ) @ ( compose @ B @ C ) )
<=> ? [F: $i] :
( ( ilf_type @ F @ set_type )
& ( member @ ( ordered_pair @ D @ F ) @ B )
& ( member @ ( ordered_pair @ F @ E ) @ C ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(87,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ilf_type @ ( compose @ B @ C ) @ binary_relation_type ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(88,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ ( ordered_pair @ C @ D ) @ ( identity_relation_of @ B ) )
<=> ( ( member @ C @ B )
& ( C = D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(89,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( identity_relation_of @ B ) @ binary_relation_type ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(90,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
<=> ( ilf_type @ C @ ( relation_type @ B @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(91,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( identity_relation_of_type @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(92,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( B = C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ set_type )
=> ( ( member @ ( ordered_pair @ D @ E ) @ B )
<=> ( member @ ( ordered_pair @ D @ E ) @ C ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(93,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ B ) @ set_type ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(94,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ilf_type @ ( range_of @ B ) @ set_type ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(95,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)],[68]) ).
thf(96,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ilf_type @ B @ binary_relation_type )
<=> ( ( relation_like @ B )
& ( ilf_type @ B @ set_type ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(97,plain,
( ( ? [B: $i] : ( ilf_type @ B @ binary_relation_type ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(98,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)],[65]) ).
thf(99,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)],[64]) ).
thf(100,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( B = C )
=> ( C = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(101,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( B = B ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(102,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)],[61]) ).
thf(103,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(104,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)],[59]) ).
thf(105,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)],[58]) ).
thf(106,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(107,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)],[56]) ).
thf(108,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)],[55]) ).
thf(109,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)],[54]) ).
thf(110,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ~ ( empty @ ( power_set @ B ) )
& ( ilf_type @ ( power_set @ B ) @ set_type ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(111,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)],[52]) ).
thf(112,plain,
( ( ! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ? [C: $i] : ( ilf_type @ C @ ( member_type @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(113,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)],[50]) ).
thf(114,plain,
( ( ! [B: $i] :
( ( ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( relation_like @ B ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(115,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( domain @ B @ C @ D )
= ( domain_of @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(116,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ilf_type @ ( domain @ B @ C @ D ) @ ( subset_type @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(117,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ( range @ B @ C @ D )
= ( range_of @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(118,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
=> ( ilf_type @ ( range @ B @ C @ D ) @ ( subset_type @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(119,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 @ C ) )
=> ! [F: $i] :
( ( ilf_type @ F @ ( relation_type @ C @ D ) )
=> ( ( compose5 @ B @ C @ D @ E @ F )
= ( compose @ E @ F ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(120,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 @ C ) )
=> ! [F: $i] :
( ( ilf_type @ F @ ( relation_type @ C @ D ) )
=> ( ilf_type @ ( compose5 @ B @ C @ D @ E @ F ) @ ( relation_type @ B @ D ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(121,plain,
( ( ! [B: $i] : ( ilf_type @ B @ set_type ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(122,plain,
( ( ilf_type @ sK1_B @ set_type )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(123,plain,
( ( ~ ! [SY92: $i] :
( ( ilf_type @ SY92 @ ( identity_relation_of_type @ sK1_B ) )
=> ( ( ( compose @ SY92 @ ( identity_relation_of @ sK1_B ) )
= SY92 )
& ( ( compose @ ( identity_relation_of @ sK1_B ) @ SY92 )
= SY92 ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(124,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ binary_relation_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ! [SX3: $i] :
( ~ ( ilf_type @ SX3 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SX2 @ SX3 ) @ ( compose @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SX4 @ set_type )
| ~ ( member @ ( ordered_pair @ SX2 @ SX4 ) @ SX0 ) )
| ~ ( member @ ( ordered_pair @ SX4 @ SX3 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SX4 @ set_type )
| ~ ( member @ ( ordered_pair @ SX2 @ SX4 ) @ SX0 ) )
| ~ ( member @ ( ordered_pair @ SX4 @ SX3 ) @ SX1 ) )
| ( member @ ( ordered_pair @ SX2 @ SX3 ) @ ( compose @ SX0 @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(125,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SX1 @ SX2 ) @ ( identity_relation_of @ SX0 ) )
| ~ ( ~ ( member @ SX1 @ SX0 )
| ( SX1 != SX2 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX1 @ SX0 )
| ( SX1 != SX2 ) )
| ( member @ ( ordered_pair @ SX1 @ SX2 ) @ ( identity_relation_of @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(126,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) )
| ( ( domain @ SX0 @ SX1 @ SX2 )
= ( domain_of @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(127,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ binary_relation_type )
| ~ ( ~ ( ( SX0 != SX1 )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ! [SX3: $i] :
( ~ ( ilf_type @ SX3 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( member @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( member @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ! [SX3: $i] :
( ~ ( ilf_type @ SX3 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( member @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( member @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) ) )
| ( SX0 = SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(128,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)],[95]) ).
thf(129,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 @ SX1 ) )
| ! [SX4: $i] :
( ~ ( ilf_type @ SX4 @ ( relation_type @ SX1 @ SX2 ) )
| ( ( compose5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
= ( compose @ SX3 @ SX4 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(130,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ( ilf_type @ ( domain_of @ SX0 ) @ set_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(131,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( empty @ SX0 )
| ~ ( ilf_type @ SX0 @ set_type ) )
| ( relation_like @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(132,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)],[99]) ).
thf(133,plain,
( ( ~ ! [SX0: $i] :
~ ( ilf_type @ SX0 @ binary_relation_type ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(134,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 @ SX1 ) )
| ! [SX4: $i] :
( ~ ( ilf_type @ SX4 @ ( relation_type @ SX1 @ SX2 ) )
| ( ilf_type @ ( compose5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) @ ( relation_type @ SX0 @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(135,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ! [SX1: $i] :
~ ( ilf_type @ SX1 @ ( identity_relation_of_type @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(136,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ ( identity_relation_of_type @ sK1_B ) )
| ~ ( ( ( compose @ SX0 @ ( identity_relation_of @ sK1_B ) )
!= SX0 )
| ( ( compose @ ( identity_relation_of @ sK1_B ) @ SX0 )
!= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(137,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( ilf_type @ SX0 @ set_type ) )
| ~ ! [SX1: $i] :
~ ( ilf_type @ SX1 @ ( member_type @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(138,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ binary_relation_type )
| ~ ( subset @ ( domain_of @ SX1 ) @ SX0 )
| ( ( compose @ ( identity_relation_of @ SX0 ) @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(139,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)],[113]) ).
thf(140,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ binary_relation_type )
| ( ilf_type @ ( compose @ SX0 @ SX1 ) @ binary_relation_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(141,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) )
| ( ilf_type @ ( domain @ SX0 @ SX1 @ SX2 ) @ ( subset_type @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(142,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)],[110]) ).
thf(143,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) )
| ( ( range @ SX0 @ SX1 @ SX2 )
= ( range_of @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(144,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SX1 @ ( identity_relation_of_type @ SX0 ) )
| ( ilf_type @ SX1 @ ( relation_type @ SX0 @ SX0 ) ) )
| ~ ( ~ ( ilf_type @ SX1 @ ( relation_type @ SX0 @ SX0 ) )
| ( ilf_type @ SX1 @ ( identity_relation_of_type @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(145,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)],[107]) ).
thf(146,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)],[105]) ).
thf(147,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)],[98]) ).
thf(148,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ binary_relation_type )
| ( SX0 != SX1 )
| ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(149,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ binary_relation_type )
| ~ ( subset @ ( range_of @ SX1 ) @ SX0 )
| ( ( compose @ SX1 @ ( identity_relation_of @ SX0 ) )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(150,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)],[109]) ).
thf(151,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ( ilf_type @ ( range_of @ SX0 ) @ set_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(152,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) )
| ( ilf_type @ ( range @ SX0 @ SX1 @ SX2 ) @ ( subset_type @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(153,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ~ ( ~ ( relation_like @ SX0 )
| ~ ( ilf_type @ SX0 @ set_type ) ) )
| ~ ( ~ ~ ( ~ ( relation_like @ SX0 )
| ~ ( ilf_type @ SX0 @ set_type ) )
| ( ilf_type @ SX0 @ binary_relation_type ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(154,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ binary_relation_type )
| ( SX0 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(155,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ( ilf_type @ ( identity_relation_of @ SX0 ) @ binary_relation_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(156,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)],[111]) ).
thf(157,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ! [SX1: $i] :
~ ( ilf_type @ SX1 @ ( subset_type @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(158,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)],[102]) ).
thf(159,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ( subset @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(160,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)],[104]) ).
thf(161,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)],[108]) ).
thf(162,plain,
! [SV1: $i] :
( ( ilf_type @ SV1 @ set_type )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(163,plain,
! [SV2: $i] :
( ( ~ ( ilf_type @ SV2 @ binary_relation_type )
| ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ binary_relation_type )
| ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY94 @ SY95 ) @ ( compose @ SV2 @ SY93 ) )
| ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY96 @ set_type )
| ~ ( member @ ( ordered_pair @ SY94 @ SY96 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY96 @ SY95 ) @ SY93 ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY97 @ set_type )
| ~ ( member @ ( ordered_pair @ SY94 @ SY97 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY97 @ SY95 ) @ SY93 ) )
| ( member @ ( ordered_pair @ SY94 @ SY95 ) @ ( compose @ SV2 @ SY93 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(164,plain,
! [SV3: $i] :
( ( ~ ( ilf_type @ SV3 @ set_type )
| ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ set_type )
| ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY98 @ SY99 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SY98 @ SV3 )
| ( SY98 != SY99 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY98 @ SV3 )
| ( SY98 != SY99 ) )
| ( member @ ( ordered_pair @ SY98 @ SY99 ) @ ( identity_relation_of @ SV3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(165,plain,
! [SV4: $i] :
( ( ~ ( ilf_type @ SV4 @ set_type )
| ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ ( relation_type @ SV4 @ SY100 ) )
| ( ( domain @ SV4 @ SY100 @ SY101 )
= ( domain_of @ SY101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(166,plain,
! [SV5: $i] :
( ( ~ ( ilf_type @ SV5 @ binary_relation_type )
| ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ binary_relation_type )
| ~ ( ~ ( ( SV5 != SY102 )
| ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ set_type )
| ! [SY104: $i] :
( ~ ( ilf_type @ SY104 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SV5 )
| ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SY102 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SY102 )
| ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SV5 ) ) ) ) ) )
| ~ ( ~ ! [SY105: $i] :
( ~ ( ilf_type @ SY105 @ set_type )
| ! [SY106: $i] :
( ~ ( ilf_type @ SY106 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SV5 )
| ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SY102 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SY102 )
| ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SV5 ) ) ) ) )
| ( SV5 = SY102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(167,plain,
! [SV6: $i] :
( ( ~ ( ilf_type @ SV6 @ set_type )
| ! [SY107: $i] :
( ~ ( ilf_type @ SY107 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV6 @ SY107 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(168,plain,
! [SV7: $i] :
( ( ~ ( ilf_type @ SV7 @ set_type )
| ! [SY108: $i] :
( ~ ( ilf_type @ SY108 @ set_type )
| ! [SY109: $i] :
( ~ ( ilf_type @ SY109 @ set_type )
| ! [SY110: $i] :
( ~ ( ilf_type @ SY110 @ ( relation_type @ SV7 @ SY108 ) )
| ! [SY111: $i] :
( ~ ( ilf_type @ SY111 @ ( relation_type @ SY108 @ SY109 ) )
| ( ( compose5 @ SV7 @ SY108 @ SY109 @ SY110 @ SY111 )
= ( compose @ SY110 @ SY111 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(169,plain,
! [SV8: $i] :
( ( ~ ( ilf_type @ SV8 @ binary_relation_type )
| ( ilf_type @ ( domain_of @ SV8 ) @ set_type ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(170,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ( empty @ SV9 )
| ~ ( ilf_type @ SV9 @ set_type ) )
| ( relation_like @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(171,plain,
! [SV10: $i] :
( ( ~ ( ilf_type @ SV10 @ set_type )
| ! [SY112: $i] :
( ~ ( ilf_type @ SY112 @ set_type )
| ~ ! [SY113: $i] :
~ ( ilf_type @ SY113 @ ( relation_type @ SY112 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(172,plain,
( ( ! [SX0: $i] :
~ ( ilf_type @ SX0 @ binary_relation_type ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(173,plain,
! [SV11: $i] :
( ( ~ ( ilf_type @ SV11 @ set_type )
| ! [SY114: $i] :
( ~ ( ilf_type @ SY114 @ set_type )
| ! [SY115: $i] :
( ~ ( ilf_type @ SY115 @ set_type )
| ! [SY116: $i] :
( ~ ( ilf_type @ SY116 @ ( relation_type @ SV11 @ SY114 ) )
| ! [SY117: $i] :
( ~ ( ilf_type @ SY117 @ ( relation_type @ SY114 @ SY115 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SY114 @ SY115 @ SY116 @ SY117 ) @ ( relation_type @ SV11 @ SY115 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(174,plain,
! [SV12: $i] :
( ( ~ ( ilf_type @ SV12 @ set_type )
| ~ ! [SY118: $i] :
~ ( ilf_type @ SY118 @ ( identity_relation_of_type @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(175,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ ( identity_relation_of_type @ sK1_B ) )
| ~ ( ( ( compose @ SX0 @ ( identity_relation_of @ sK1_B ) )
!= SX0 )
| ( ( compose @ ( identity_relation_of @ sK1_B ) @ SX0 )
!= SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(176,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV13 )
| ~ ( ilf_type @ SV13 @ set_type ) )
| ~ ! [SY119: $i] :
~ ( ilf_type @ SY119 @ ( member_type @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(177,plain,
! [SV14: $i] :
( ( ~ ( ilf_type @ SV14 @ set_type )
| ! [SY120: $i] :
( ~ ( ilf_type @ SY120 @ binary_relation_type )
| ~ ( subset @ ( domain_of @ SY120 ) @ SV14 )
| ( ( compose @ ( identity_relation_of @ SV14 ) @ SY120 )
= SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(178,plain,
! [SV15: $i] :
( ( ~ ( ilf_type @ SV15 @ set_type )
| ~ ( ~ ( ~ ( empty @ SV15 )
| ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SY121 @ SV15 ) ) )
| ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ SY122 @ SV15 ) )
| ( empty @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(179,plain,
! [SV16: $i] :
( ( ~ ( ilf_type @ SV16 @ binary_relation_type )
| ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ binary_relation_type )
| ( ilf_type @ ( compose @ SV16 @ SY123 ) @ binary_relation_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(180,plain,
! [SV17: $i] :
( ( ~ ( ilf_type @ SV17 @ set_type )
| ! [SY124: $i] :
( ~ ( ilf_type @ SY124 @ set_type )
| ! [SY125: $i] :
( ~ ( ilf_type @ SY125 @ ( relation_type @ SV17 @ SY124 ) )
| ( ilf_type @ ( domain @ SV17 @ SY124 @ SY125 ) @ ( subset_type @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(181,plain,
! [SV18: $i] :
( ( ~ ( ilf_type @ SV18 @ set_type )
| ~ ( ~ ~ ( empty @ ( power_set @ SV18 ) )
| ~ ( ilf_type @ ( power_set @ SV18 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(182,plain,
! [SV19: $i] :
( ( ~ ( ilf_type @ SV19 @ set_type )
| ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ ( relation_type @ SV19 @ SY126 ) )
| ( ( range @ SV19 @ SY126 @ SY127 )
= ( range_of @ SY127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(183,plain,
! [SV20: $i] :
( ( ~ ( ilf_type @ SV20 @ set_type )
| ! [SY128: $i] :
( ~ ( ilf_type @ SY128 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY128 @ ( identity_relation_of_type @ SV20 ) )
| ( ilf_type @ SY128 @ ( relation_type @ SV20 @ SV20 ) ) )
| ~ ( ~ ( ilf_type @ SY128 @ ( relation_type @ SV20 @ SV20 ) )
| ( ilf_type @ SY128 @ ( identity_relation_of_type @ SV20 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(184,plain,
! [SV21: $i] :
( ( ~ ( ilf_type @ SV21 @ set_type )
| ~ ( ~ ( ~ ( relation_like @ SV21 )
| ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ~ ( member @ SY129 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY129
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
| ~ ( ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY132
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(185,plain,
! [SV22: $i] :
( ( ~ ( ilf_type @ SV22 @ set_type )
| ! [SY135: $i] :
( ~ ( ilf_type @ SY135 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY135 @ ( subset_type @ SV22 ) )
| ( ilf_type @ SY135 @ ( member_type @ ( power_set @ SV22 ) ) ) )
| ~ ( ~ ( ilf_type @ SY135 @ ( member_type @ ( power_set @ SV22 ) ) )
| ( ilf_type @ SY135 @ ( subset_type @ SV22 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(186,plain,
! [SV23: $i] :
( ( ~ ( ilf_type @ SV23 @ set_type )
| ! [SY136: $i] :
( ~ ( ilf_type @ SY136 @ set_type )
| ~ ( ~ ! [SY137: $i] :
( ~ ( ilf_type @ SY137 @ ( subset_type @ ( cross_product @ SV23 @ SY136 ) ) )
| ( ilf_type @ SY137 @ ( relation_type @ SV23 @ SY136 ) ) )
| ~ ! [SY138: $i] :
( ~ ( ilf_type @ SY138 @ ( relation_type @ SV23 @ SY136 ) )
| ( ilf_type @ SY138 @ ( subset_type @ ( cross_product @ SV23 @ SY136 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(187,plain,
! [SV24: $i] :
( ( ~ ( ilf_type @ SV24 @ binary_relation_type )
| ! [SY139: $i] :
( ~ ( ilf_type @ SY139 @ binary_relation_type )
| ( SV24 != SY139 )
| ( SY139 = SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(188,plain,
! [SV25: $i] :
( ( ~ ( ilf_type @ SV25 @ set_type )
| ! [SY140: $i] :
( ~ ( ilf_type @ SY140 @ binary_relation_type )
| ~ ( subset @ ( range_of @ SY140 ) @ SV25 )
| ( ( compose @ SY140 @ ( identity_relation_of @ SV25 ) )
= SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(189,plain,
! [SV26: $i] :
( ( ~ ( ilf_type @ SV26 @ set_type )
| ! [SY141: $i] :
( ~ ( ilf_type @ SY141 @ set_type )
| ~ ( ~ ( ~ ( member @ SV26 @ ( power_set @ SY141 ) )
| ! [SY142: $i] :
( ~ ( ilf_type @ SY142 @ set_type )
| ~ ( member @ SY142 @ SV26 )
| ( member @ SY142 @ SY141 ) ) )
| ~ ( ~ ! [SY143: $i] :
( ~ ( ilf_type @ SY143 @ set_type )
| ~ ( member @ SY143 @ SV26 )
| ( member @ SY143 @ SY141 ) )
| ( member @ SV26 @ ( power_set @ SY141 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(190,plain,
! [SV27: $i] :
( ( ~ ( ilf_type @ SV27 @ binary_relation_type )
| ( ilf_type @ ( range_of @ SV27 ) @ set_type ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(191,plain,
! [SV28: $i] :
( ( ~ ( ilf_type @ SV28 @ set_type )
| ! [SY144: $i] :
( ~ ( ilf_type @ SY144 @ set_type )
| ! [SY145: $i] :
( ~ ( ilf_type @ SY145 @ ( relation_type @ SV28 @ SY144 ) )
| ( ilf_type @ ( range @ SV28 @ SY144 @ SY145 ) @ ( subset_type @ SY144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(192,plain,
! [SV29: $i] :
( ( ~ ( ilf_type @ SV29 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SV29 @ binary_relation_type )
| ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) ) )
| ~ ( ~ ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) )
| ( ilf_type @ SV29 @ binary_relation_type ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(193,plain,
! [SV30: $i] :
( ( ~ ( ilf_type @ SV30 @ binary_relation_type )
| ( SV30 = SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(194,plain,
! [SV31: $i] :
( ( ~ ( ilf_type @ SV31 @ set_type )
| ( ilf_type @ ( identity_relation_of @ SV31 ) @ binary_relation_type ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(195,plain,
! [SV32: $i] :
( ( ~ ( ilf_type @ SV32 @ set_type )
| ! [SY146: $i] :
( ~ ~ ( ~ ~ ( empty @ SY146 )
| ~ ( ilf_type @ SY146 @ set_type ) )
| ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SY146 ) )
| ( member @ SV32 @ SY146 ) )
| ~ ( ~ ( member @ SV32 @ SY146 )
| ( ilf_type @ SV32 @ ( member_type @ SY146 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(196,plain,
! [SV33: $i] :
( ( ~ ( ilf_type @ SV33 @ set_type )
| ~ ! [SY147: $i] :
~ ( ilf_type @ SY147 @ ( subset_type @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(197,plain,
! [SV34: $i] :
( ( ~ ( ilf_type @ SV34 @ set_type )
| ! [SY148: $i] :
( ~ ( ilf_type @ SY148 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV34 @ SY148 )
| ! [SY149: $i] :
( ~ ( ilf_type @ SY149 @ set_type )
| ~ ( member @ SY149 @ SV34 )
| ( member @ SY149 @ SY148 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( ilf_type @ SY150 @ set_type )
| ~ ( member @ SY150 @ SV34 )
| ( member @ SY150 @ SY148 ) )
| ( subset @ SV34 @ SY148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(198,plain,
! [SV35: $i] :
( ( ~ ( ilf_type @ SV35 @ set_type )
| ( subset @ SV35 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(199,plain,
! [SV36: $i] :
( ( ~ ( ilf_type @ SV36 @ set_type )
| ! [SY151: $i] :
( ~ ( ilf_type @ SY151 @ set_type )
| ( ilf_type @ ( cross_product @ SV36 @ SY151 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(200,plain,
! [SV37: $i] :
( ( ~ ( ilf_type @ SV37 @ set_type )
| ! [SY152: $i] :
( ~ ( ilf_type @ SY152 @ set_type )
| ! [SY153: $i] :
( ~ ( ilf_type @ SY153 @ ( subset_type @ ( cross_product @ SV37 @ SY152 ) ) )
| ( relation_like @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(201,plain,
! [SV2: $i] :
( ( ( ~ ( ilf_type @ SV2 @ binary_relation_type ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ binary_relation_type )
| ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY94 @ SY95 ) @ ( compose @ SV2 @ SY93 ) )
| ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY96 @ set_type )
| ~ ( member @ ( ordered_pair @ SY94 @ SY96 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY96 @ SY95 ) @ SY93 ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY97 @ set_type )
| ~ ( member @ ( ordered_pair @ SY94 @ SY97 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY97 @ SY95 ) @ SY93 ) )
| ( member @ ( ordered_pair @ SY94 @ SY95 ) @ ( compose @ SV2 @ SY93 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(202,plain,
! [SV3: $i] :
( ( ( ~ ( ilf_type @ SV3 @ set_type ) )
= $true )
| ( ( ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ set_type )
| ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY98 @ SY99 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SY98 @ SV3 )
| ( SY98 != SY99 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY98 @ SV3 )
| ( SY98 != SY99 ) )
| ( member @ ( ordered_pair @ SY98 @ SY99 ) @ ( identity_relation_of @ SV3 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(203,plain,
! [SV4: $i] :
( ( ( ~ ( ilf_type @ SV4 @ set_type ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ ( relation_type @ SV4 @ SY100 ) )
| ( ( domain @ SV4 @ SY100 @ SY101 )
= ( domain_of @ SY101 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(204,plain,
! [SV5: $i] :
( ( ( ~ ( ilf_type @ SV5 @ binary_relation_type ) )
= $true )
| ( ( ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ binary_relation_type )
| ~ ( ~ ( ( SV5 != SY102 )
| ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ set_type )
| ! [SY104: $i] :
( ~ ( ilf_type @ SY104 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SV5 )
| ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SY102 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SY102 )
| ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SV5 ) ) ) ) ) )
| ~ ( ~ ! [SY105: $i] :
( ~ ( ilf_type @ SY105 @ set_type )
| ! [SY106: $i] :
( ~ ( ilf_type @ SY106 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SV5 )
| ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SY102 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SY102 )
| ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SV5 ) ) ) ) )
| ( SV5 = SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(205,plain,
! [SV6: $i] :
( ( ( ~ ( ilf_type @ SV6 @ set_type ) )
= $true )
| ( ( ! [SY107: $i] :
( ~ ( ilf_type @ SY107 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV6 @ SY107 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(206,plain,
! [SV7: $i] :
( ( ( ~ ( ilf_type @ SV7 @ set_type ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( ilf_type @ SY108 @ set_type )
| ! [SY109: $i] :
( ~ ( ilf_type @ SY109 @ set_type )
| ! [SY110: $i] :
( ~ ( ilf_type @ SY110 @ ( relation_type @ SV7 @ SY108 ) )
| ! [SY111: $i] :
( ~ ( ilf_type @ SY111 @ ( relation_type @ SY108 @ SY109 ) )
| ( ( compose5 @ SV7 @ SY108 @ SY109 @ SY110 @ SY111 )
= ( compose @ SY110 @ SY111 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(207,plain,
! [SV8: $i] :
( ( ( ~ ( ilf_type @ SV8 @ binary_relation_type ) )
= $true )
| ( ( ilf_type @ ( domain_of @ SV8 ) @ set_type )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(208,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( empty @ SV9 )
| ~ ( ilf_type @ SV9 @ set_type ) ) )
= $true )
| ( ( relation_like @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(209,plain,
! [SV10: $i] :
( ( ( ~ ( ilf_type @ SV10 @ set_type ) )
= $true )
| ( ( ! [SY112: $i] :
( ~ ( ilf_type @ SY112 @ set_type )
| ~ ! [SY113: $i] :
~ ( ilf_type @ SY113 @ ( relation_type @ SY112 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(210,plain,
( ( ~ ( ilf_type @ sK2_SX0 @ binary_relation_type ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[172]) ).
thf(211,plain,
! [SV11: $i] :
( ( ( ~ ( ilf_type @ SV11 @ set_type ) )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( ilf_type @ SY114 @ set_type )
| ! [SY115: $i] :
( ~ ( ilf_type @ SY115 @ set_type )
| ! [SY116: $i] :
( ~ ( ilf_type @ SY116 @ ( relation_type @ SV11 @ SY114 ) )
| ! [SY117: $i] :
( ~ ( ilf_type @ SY117 @ ( relation_type @ SY114 @ SY115 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SY114 @ SY115 @ SY116 @ SY117 ) @ ( relation_type @ SV11 @ SY115 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(212,plain,
! [SV12: $i] :
( ( ( ~ ( ilf_type @ SV12 @ set_type ) )
= $true )
| ( ( ~ ! [SY118: $i] :
~ ( ilf_type @ SY118 @ ( identity_relation_of_type @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(213,plain,
( ( ~ ( ilf_type @ sK3_SX0 @ ( identity_relation_of_type @ sK1_B ) )
| ~ ( ( ( compose @ sK3_SX0 @ ( identity_relation_of @ sK1_B ) )
!= sK3_SX0 )
| ( ( compose @ ( identity_relation_of @ sK1_B ) @ sK3_SX0 )
!= sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[175]) ).
thf(214,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV13 )
| ~ ( ilf_type @ SV13 @ set_type ) ) )
= $true )
| ( ( ~ ! [SY119: $i] :
~ ( ilf_type @ SY119 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(215,plain,
! [SV14: $i] :
( ( ( ~ ( ilf_type @ SV14 @ set_type ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( ilf_type @ SY120 @ binary_relation_type )
| ~ ( subset @ ( domain_of @ SY120 ) @ SV14 )
| ( ( compose @ ( identity_relation_of @ SV14 ) @ SY120 )
= SY120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(216,plain,
! [SV15: $i] :
( ( ( ~ ( ilf_type @ SV15 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( empty @ SV15 )
| ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SY121 @ SV15 ) ) )
| ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ SY122 @ SV15 ) )
| ( empty @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(217,plain,
! [SV16: $i] :
( ( ( ~ ( ilf_type @ SV16 @ binary_relation_type ) )
= $true )
| ( ( ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ binary_relation_type )
| ( ilf_type @ ( compose @ SV16 @ SY123 ) @ binary_relation_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(218,plain,
! [SV17: $i] :
( ( ( ~ ( ilf_type @ SV17 @ set_type ) )
= $true )
| ( ( ! [SY124: $i] :
( ~ ( ilf_type @ SY124 @ set_type )
| ! [SY125: $i] :
( ~ ( ilf_type @ SY125 @ ( relation_type @ SV17 @ SY124 ) )
| ( ilf_type @ ( domain @ SV17 @ SY124 @ SY125 ) @ ( subset_type @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(219,plain,
! [SV18: $i] :
( ( ( ~ ( ilf_type @ SV18 @ set_type ) )
= $true )
| ( ( ~ ( ~ ~ ( empty @ ( power_set @ SV18 ) )
| ~ ( ilf_type @ ( power_set @ SV18 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(220,plain,
! [SV19: $i] :
( ( ( ~ ( ilf_type @ SV19 @ set_type ) )
= $true )
| ( ( ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ ( relation_type @ SV19 @ SY126 ) )
| ( ( range @ SV19 @ SY126 @ SY127 )
= ( range_of @ SY127 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(221,plain,
! [SV20: $i] :
( ( ( ~ ( ilf_type @ SV20 @ set_type ) )
= $true )
| ( ( ! [SY128: $i] :
( ~ ( ilf_type @ SY128 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY128 @ ( identity_relation_of_type @ SV20 ) )
| ( ilf_type @ SY128 @ ( relation_type @ SV20 @ SV20 ) ) )
| ~ ( ~ ( ilf_type @ SY128 @ ( relation_type @ SV20 @ SV20 ) )
| ( ilf_type @ SY128 @ ( identity_relation_of_type @ SV20 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(222,plain,
! [SV21: $i] :
( ( ( ~ ( ilf_type @ SV21 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( relation_like @ SV21 )
| ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ~ ( member @ SY129 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY129
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
| ~ ( ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY132
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(223,plain,
! [SV22: $i] :
( ( ( ~ ( ilf_type @ SV22 @ set_type ) )
= $true )
| ( ( ! [SY135: $i] :
( ~ ( ilf_type @ SY135 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY135 @ ( subset_type @ SV22 ) )
| ( ilf_type @ SY135 @ ( member_type @ ( power_set @ SV22 ) ) ) )
| ~ ( ~ ( ilf_type @ SY135 @ ( member_type @ ( power_set @ SV22 ) ) )
| ( ilf_type @ SY135 @ ( subset_type @ SV22 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(224,plain,
! [SV23: $i] :
( ( ( ~ ( ilf_type @ SV23 @ set_type ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( ilf_type @ SY136 @ set_type )
| ~ ( ~ ! [SY137: $i] :
( ~ ( ilf_type @ SY137 @ ( subset_type @ ( cross_product @ SV23 @ SY136 ) ) )
| ( ilf_type @ SY137 @ ( relation_type @ SV23 @ SY136 ) ) )
| ~ ! [SY138: $i] :
( ~ ( ilf_type @ SY138 @ ( relation_type @ SV23 @ SY136 ) )
| ( ilf_type @ SY138 @ ( subset_type @ ( cross_product @ SV23 @ SY136 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(225,plain,
! [SV24: $i] :
( ( ( ~ ( ilf_type @ SV24 @ binary_relation_type ) )
= $true )
| ( ( ! [SY139: $i] :
( ~ ( ilf_type @ SY139 @ binary_relation_type )
| ( SV24 != SY139 )
| ( SY139 = SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(226,plain,
! [SV25: $i] :
( ( ( ~ ( ilf_type @ SV25 @ set_type ) )
= $true )
| ( ( ! [SY140: $i] :
( ~ ( ilf_type @ SY140 @ binary_relation_type )
| ~ ( subset @ ( range_of @ SY140 ) @ SV25 )
| ( ( compose @ SY140 @ ( identity_relation_of @ SV25 ) )
= SY140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(227,plain,
! [SV26: $i] :
( ( ( ~ ( ilf_type @ SV26 @ set_type ) )
= $true )
| ( ( ! [SY141: $i] :
( ~ ( ilf_type @ SY141 @ set_type )
| ~ ( ~ ( ~ ( member @ SV26 @ ( power_set @ SY141 ) )
| ! [SY142: $i] :
( ~ ( ilf_type @ SY142 @ set_type )
| ~ ( member @ SY142 @ SV26 )
| ( member @ SY142 @ SY141 ) ) )
| ~ ( ~ ! [SY143: $i] :
( ~ ( ilf_type @ SY143 @ set_type )
| ~ ( member @ SY143 @ SV26 )
| ( member @ SY143 @ SY141 ) )
| ( member @ SV26 @ ( power_set @ SY141 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(228,plain,
! [SV27: $i] :
( ( ( ~ ( ilf_type @ SV27 @ binary_relation_type ) )
= $true )
| ( ( ilf_type @ ( range_of @ SV27 ) @ set_type )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(229,plain,
! [SV28: $i] :
( ( ( ~ ( ilf_type @ SV28 @ set_type ) )
= $true )
| ( ( ! [SY144: $i] :
( ~ ( ilf_type @ SY144 @ set_type )
| ! [SY145: $i] :
( ~ ( ilf_type @ SY145 @ ( relation_type @ SV28 @ SY144 ) )
| ( ilf_type @ ( range @ SV28 @ SY144 @ SY145 ) @ ( subset_type @ SY144 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(230,plain,
! [SV29: $i] :
( ( ( ~ ( ilf_type @ SV29 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV29 @ binary_relation_type )
| ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) ) )
| ~ ( ~ ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) )
| ( ilf_type @ SV29 @ binary_relation_type ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(231,plain,
! [SV30: $i] :
( ( ( ~ ( ilf_type @ SV30 @ binary_relation_type ) )
= $true )
| ( ( SV30 = SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(232,plain,
! [SV31: $i] :
( ( ( ~ ( ilf_type @ SV31 @ set_type ) )
= $true )
| ( ( ilf_type @ ( identity_relation_of @ SV31 ) @ binary_relation_type )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(233,plain,
! [SV32: $i] :
( ( ( ~ ( ilf_type @ SV32 @ set_type ) )
= $true )
| ( ( ! [SY146: $i] :
( ~ ~ ( ~ ~ ( empty @ SY146 )
| ~ ( ilf_type @ SY146 @ set_type ) )
| ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SY146 ) )
| ( member @ SV32 @ SY146 ) )
| ~ ( ~ ( member @ SV32 @ SY146 )
| ( ilf_type @ SV32 @ ( member_type @ SY146 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(234,plain,
! [SV33: $i] :
( ( ( ~ ( ilf_type @ SV33 @ set_type ) )
= $true )
| ( ( ~ ! [SY147: $i] :
~ ( ilf_type @ SY147 @ ( subset_type @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(235,plain,
! [SV34: $i] :
( ( ( ~ ( ilf_type @ SV34 @ set_type ) )
= $true )
| ( ( ! [SY148: $i] :
( ~ ( ilf_type @ SY148 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV34 @ SY148 )
| ! [SY149: $i] :
( ~ ( ilf_type @ SY149 @ set_type )
| ~ ( member @ SY149 @ SV34 )
| ( member @ SY149 @ SY148 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( ilf_type @ SY150 @ set_type )
| ~ ( member @ SY150 @ SV34 )
| ( member @ SY150 @ SY148 ) )
| ( subset @ SV34 @ SY148 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(236,plain,
! [SV35: $i] :
( ( ( ~ ( ilf_type @ SV35 @ set_type ) )
= $true )
| ( ( subset @ SV35 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(237,plain,
! [SV36: $i] :
( ( ( ~ ( ilf_type @ SV36 @ set_type ) )
= $true )
| ( ( ! [SY151: $i] :
( ~ ( ilf_type @ SY151 @ set_type )
| ( ilf_type @ ( cross_product @ SV36 @ SY151 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(238,plain,
! [SV37: $i] :
( ( ( ~ ( ilf_type @ SV37 @ set_type ) )
= $true )
| ( ( ! [SY152: $i] :
( ~ ( ilf_type @ SY152 @ set_type )
| ! [SY153: $i] :
( ~ ( ilf_type @ SY153 @ ( subset_type @ ( cross_product @ SV37 @ SY152 ) ) )
| ( relation_like @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(239,plain,
! [SV2: $i] :
( ( ( ilf_type @ SV2 @ binary_relation_type )
= $false )
| ( ( ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ binary_relation_type )
| ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY94 @ SY95 ) @ ( compose @ SV2 @ SY93 ) )
| ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY96 @ set_type )
| ~ ( member @ ( ordered_pair @ SY94 @ SY96 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY96 @ SY95 ) @ SY93 ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY97 @ set_type )
| ~ ( member @ ( ordered_pair @ SY94 @ SY97 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY97 @ SY95 ) @ SY93 ) )
| ( member @ ( ordered_pair @ SY94 @ SY95 ) @ ( compose @ SV2 @ SY93 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(240,plain,
! [SV3: $i] :
( ( ( ilf_type @ SV3 @ set_type )
= $false )
| ( ( ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ set_type )
| ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY98 @ SY99 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SY98 @ SV3 )
| ( SY98 != SY99 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY98 @ SV3 )
| ( SY98 != SY99 ) )
| ( member @ ( ordered_pair @ SY98 @ SY99 ) @ ( identity_relation_of @ SV3 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(241,plain,
! [SV4: $i] :
( ( ( ilf_type @ SV4 @ set_type )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ ( relation_type @ SV4 @ SY100 ) )
| ( ( domain @ SV4 @ SY100 @ SY101 )
= ( domain_of @ SY101 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(242,plain,
! [SV5: $i] :
( ( ( ilf_type @ SV5 @ binary_relation_type )
= $false )
| ( ( ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ binary_relation_type )
| ~ ( ~ ( ( SV5 != SY102 )
| ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ set_type )
| ! [SY104: $i] :
( ~ ( ilf_type @ SY104 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SV5 )
| ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SY102 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SY102 )
| ( member @ ( ordered_pair @ SY103 @ SY104 ) @ SV5 ) ) ) ) ) )
| ~ ( ~ ! [SY105: $i] :
( ~ ( ilf_type @ SY105 @ set_type )
| ! [SY106: $i] :
( ~ ( ilf_type @ SY106 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SV5 )
| ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SY102 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SY102 )
| ( member @ ( ordered_pair @ SY105 @ SY106 ) @ SV5 ) ) ) ) )
| ( SV5 = SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(243,plain,
! [SV6: $i] :
( ( ( ilf_type @ SV6 @ set_type )
= $false )
| ( ( ! [SY107: $i] :
( ~ ( ilf_type @ SY107 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV6 @ SY107 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(244,plain,
! [SV7: $i] :
( ( ( ilf_type @ SV7 @ set_type )
= $false )
| ( ( ! [SY108: $i] :
( ~ ( ilf_type @ SY108 @ set_type )
| ! [SY109: $i] :
( ~ ( ilf_type @ SY109 @ set_type )
| ! [SY110: $i] :
( ~ ( ilf_type @ SY110 @ ( relation_type @ SV7 @ SY108 ) )
| ! [SY111: $i] :
( ~ ( ilf_type @ SY111 @ ( relation_type @ SY108 @ SY109 ) )
| ( ( compose5 @ SV7 @ SY108 @ SY109 @ SY110 @ SY111 )
= ( compose @ SY110 @ SY111 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(245,plain,
! [SV8: $i] :
( ( ( ilf_type @ SV8 @ binary_relation_type )
= $false )
| ( ( ilf_type @ ( domain_of @ SV8 ) @ set_type )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(246,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( empty @ SV9 )
| ~ ( ilf_type @ SV9 @ set_type ) ) )
= $false )
| ( ( relation_like @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(247,plain,
! [SV10: $i] :
( ( ( ilf_type @ SV10 @ set_type )
= $false )
| ( ( ! [SY112: $i] :
( ~ ( ilf_type @ SY112 @ set_type )
| ~ ! [SY113: $i] :
~ ( ilf_type @ SY113 @ ( relation_type @ SY112 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(248,plain,
( ( ilf_type @ sK2_SX0 @ binary_relation_type )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(249,plain,
! [SV11: $i] :
( ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ! [SY114: $i] :
( ~ ( ilf_type @ SY114 @ set_type )
| ! [SY115: $i] :
( ~ ( ilf_type @ SY115 @ set_type )
| ! [SY116: $i] :
( ~ ( ilf_type @ SY116 @ ( relation_type @ SV11 @ SY114 ) )
| ! [SY117: $i] :
( ~ ( ilf_type @ SY117 @ ( relation_type @ SY114 @ SY115 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SY114 @ SY115 @ SY116 @ SY117 ) @ ( relation_type @ SV11 @ SY115 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(250,plain,
! [SV12: $i] :
( ( ( ilf_type @ SV12 @ set_type )
= $false )
| ( ( ~ ! [SY118: $i] :
~ ( ilf_type @ SY118 @ ( identity_relation_of_type @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(251,plain,
( ( ~ ( ilf_type @ sK3_SX0 @ ( identity_relation_of_type @ sK1_B ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(252,plain,
( ( ~ ( ( ( compose @ sK3_SX0 @ ( identity_relation_of @ sK1_B ) )
!= sK3_SX0 )
| ( ( compose @ ( identity_relation_of @ sK1_B ) @ sK3_SX0 )
!= sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(253,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV13 )
| ~ ( ilf_type @ SV13 @ set_type ) ) )
= $false )
| ( ( ~ ! [SY119: $i] :
~ ( ilf_type @ SY119 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(254,plain,
! [SV14: $i] :
( ( ( ilf_type @ SV14 @ set_type )
= $false )
| ( ( ! [SY120: $i] :
( ~ ( ilf_type @ SY120 @ binary_relation_type )
| ~ ( subset @ ( domain_of @ SY120 ) @ SV14 )
| ( ( compose @ ( identity_relation_of @ SV14 ) @ SY120 )
= SY120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(255,plain,
! [SV15: $i] :
( ( ( ilf_type @ SV15 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( empty @ SV15 )
| ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SY121 @ SV15 ) ) )
| ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ SY122 @ SV15 ) )
| ( empty @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(256,plain,
! [SV16: $i] :
( ( ( ilf_type @ SV16 @ binary_relation_type )
= $false )
| ( ( ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ binary_relation_type )
| ( ilf_type @ ( compose @ SV16 @ SY123 ) @ binary_relation_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(257,plain,
! [SV17: $i] :
( ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ! [SY124: $i] :
( ~ ( ilf_type @ SY124 @ set_type )
| ! [SY125: $i] :
( ~ ( ilf_type @ SY125 @ ( relation_type @ SV17 @ SY124 ) )
| ( ilf_type @ ( domain @ SV17 @ SY124 @ SY125 ) @ ( subset_type @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(258,plain,
! [SV18: $i] :
( ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ~ ( ~ ~ ( empty @ ( power_set @ SV18 ) )
| ~ ( ilf_type @ ( power_set @ SV18 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(259,plain,
! [SV19: $i] :
( ( ( ilf_type @ SV19 @ set_type )
= $false )
| ( ( ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ ( relation_type @ SV19 @ SY126 ) )
| ( ( range @ SV19 @ SY126 @ SY127 )
= ( range_of @ SY127 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(260,plain,
! [SV20: $i] :
( ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ! [SY128: $i] :
( ~ ( ilf_type @ SY128 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY128 @ ( identity_relation_of_type @ SV20 ) )
| ( ilf_type @ SY128 @ ( relation_type @ SV20 @ SV20 ) ) )
| ~ ( ~ ( ilf_type @ SY128 @ ( relation_type @ SV20 @ SV20 ) )
| ( ilf_type @ SY128 @ ( identity_relation_of_type @ SV20 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(261,plain,
! [SV21: $i] :
( ( ( ilf_type @ SV21 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( relation_like @ SV21 )
| ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ~ ( member @ SY129 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY129
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
| ~ ( ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY132
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(262,plain,
! [SV22: $i] :
( ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ! [SY135: $i] :
( ~ ( ilf_type @ SY135 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SY135 @ ( subset_type @ SV22 ) )
| ( ilf_type @ SY135 @ ( member_type @ ( power_set @ SV22 ) ) ) )
| ~ ( ~ ( ilf_type @ SY135 @ ( member_type @ ( power_set @ SV22 ) ) )
| ( ilf_type @ SY135 @ ( subset_type @ SV22 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(263,plain,
! [SV23: $i] :
( ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ! [SY136: $i] :
( ~ ( ilf_type @ SY136 @ set_type )
| ~ ( ~ ! [SY137: $i] :
( ~ ( ilf_type @ SY137 @ ( subset_type @ ( cross_product @ SV23 @ SY136 ) ) )
| ( ilf_type @ SY137 @ ( relation_type @ SV23 @ SY136 ) ) )
| ~ ! [SY138: $i] :
( ~ ( ilf_type @ SY138 @ ( relation_type @ SV23 @ SY136 ) )
| ( ilf_type @ SY138 @ ( subset_type @ ( cross_product @ SV23 @ SY136 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(264,plain,
! [SV24: $i] :
( ( ( ilf_type @ SV24 @ binary_relation_type )
= $false )
| ( ( ! [SY139: $i] :
( ~ ( ilf_type @ SY139 @ binary_relation_type )
| ( SV24 != SY139 )
| ( SY139 = SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(265,plain,
! [SV25: $i] :
( ( ( ilf_type @ SV25 @ set_type )
= $false )
| ( ( ! [SY140: $i] :
( ~ ( ilf_type @ SY140 @ binary_relation_type )
| ~ ( subset @ ( range_of @ SY140 ) @ SV25 )
| ( ( compose @ SY140 @ ( identity_relation_of @ SV25 ) )
= SY140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(266,plain,
! [SV26: $i] :
( ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ! [SY141: $i] :
( ~ ( ilf_type @ SY141 @ set_type )
| ~ ( ~ ( ~ ( member @ SV26 @ ( power_set @ SY141 ) )
| ! [SY142: $i] :
( ~ ( ilf_type @ SY142 @ set_type )
| ~ ( member @ SY142 @ SV26 )
| ( member @ SY142 @ SY141 ) ) )
| ~ ( ~ ! [SY143: $i] :
( ~ ( ilf_type @ SY143 @ set_type )
| ~ ( member @ SY143 @ SV26 )
| ( member @ SY143 @ SY141 ) )
| ( member @ SV26 @ ( power_set @ SY141 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(267,plain,
! [SV27: $i] :
( ( ( ilf_type @ SV27 @ binary_relation_type )
= $false )
| ( ( ilf_type @ ( range_of @ SV27 ) @ set_type )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(268,plain,
! [SV28: $i] :
( ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ! [SY144: $i] :
( ~ ( ilf_type @ SY144 @ set_type )
| ! [SY145: $i] :
( ~ ( ilf_type @ SY145 @ ( relation_type @ SV28 @ SY144 ) )
| ( ilf_type @ ( range @ SV28 @ SY144 @ SY145 ) @ ( subset_type @ SY144 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(269,plain,
! [SV29: $i] :
( ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV29 @ binary_relation_type )
| ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) ) )
| ~ ( ~ ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) )
| ( ilf_type @ SV29 @ binary_relation_type ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(270,plain,
! [SV30: $i] :
( ( ( ilf_type @ SV30 @ binary_relation_type )
= $false )
| ( ( SV30 = SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(271,plain,
! [SV31: $i] :
( ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ilf_type @ ( identity_relation_of @ SV31 ) @ binary_relation_type )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(272,plain,
! [SV32: $i] :
( ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ! [SY146: $i] :
( ~ ~ ( ~ ~ ( empty @ SY146 )
| ~ ( ilf_type @ SY146 @ set_type ) )
| ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SY146 ) )
| ( member @ SV32 @ SY146 ) )
| ~ ( ~ ( member @ SV32 @ SY146 )
| ( ilf_type @ SV32 @ ( member_type @ SY146 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(273,plain,
! [SV33: $i] :
( ( ( ilf_type @ SV33 @ set_type )
= $false )
| ( ( ~ ! [SY147: $i] :
~ ( ilf_type @ SY147 @ ( subset_type @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(274,plain,
! [SV34: $i] :
( ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ! [SY148: $i] :
( ~ ( ilf_type @ SY148 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV34 @ SY148 )
| ! [SY149: $i] :
( ~ ( ilf_type @ SY149 @ set_type )
| ~ ( member @ SY149 @ SV34 )
| ( member @ SY149 @ SY148 ) ) )
| ~ ( ~ ! [SY150: $i] :
( ~ ( ilf_type @ SY150 @ set_type )
| ~ ( member @ SY150 @ SV34 )
| ( member @ SY150 @ SY148 ) )
| ( subset @ SV34 @ SY148 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(275,plain,
! [SV35: $i] :
( ( ( ilf_type @ SV35 @ set_type )
= $false )
| ( ( subset @ SV35 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(276,plain,
! [SV36: $i] :
( ( ( ilf_type @ SV36 @ set_type )
= $false )
| ( ( ! [SY151: $i] :
( ~ ( ilf_type @ SY151 @ set_type )
| ( ilf_type @ ( cross_product @ SV36 @ SY151 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(277,plain,
! [SV37: $i] :
( ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ! [SY152: $i] :
( ~ ( ilf_type @ SY152 @ set_type )
| ! [SY153: $i] :
( ~ ( ilf_type @ SY153 @ ( subset_type @ ( cross_product @ SV37 @ SY152 ) ) )
| ( relation_like @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(278,plain,
! [SV2: $i,SV38: $i] :
( ( ( ~ ( ilf_type @ SV38 @ binary_relation_type )
| ! [SY154: $i] :
( ~ ( ilf_type @ SY154 @ set_type )
| ! [SY155: $i] :
( ~ ( ilf_type @ SY155 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY154 @ SY155 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY156: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY156 @ set_type )
| ~ ( member @ ( ordered_pair @ SY154 @ SY156 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY156 @ SY155 ) @ SV38 ) ) )
| ~ ( ~ ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY157 @ set_type )
| ~ ( member @ ( ordered_pair @ SY154 @ SY157 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY157 @ SY155 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SY154 @ SY155 ) @ ( compose @ SV2 @ SV38 ) ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(279,plain,
! [SV3: $i,SV39: $i] :
( ( ( ~ ( ilf_type @ SV39 @ set_type )
| ! [SY158: $i] :
( ~ ( ilf_type @ SY158 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SY158 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SY158 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SY158 ) )
| ( member @ ( ordered_pair @ SV39 @ SY158 ) @ ( identity_relation_of @ SV3 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(280,plain,
! [SV4: $i,SV40: $i] :
( ( ( ~ ( ilf_type @ SV40 @ set_type )
| ! [SY159: $i] :
( ~ ( ilf_type @ SY159 @ ( relation_type @ SV4 @ SV40 ) )
| ( ( domain @ SV4 @ SV40 @ SY159 )
= ( domain_of @ SY159 ) ) ) )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(281,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( ilf_type @ SV41 @ binary_relation_type )
| ~ ( ~ ( ( SV5 != SV41 )
| ! [SY160: $i] :
( ~ ( ilf_type @ SY160 @ set_type )
| ! [SY161: $i] :
( ~ ( ilf_type @ SY161 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 ) ) ) ) ) )
| ~ ( ~ ! [SY162: $i] :
( ~ ( ilf_type @ SY162 @ set_type )
| ! [SY163: $i] :
( ~ ( ilf_type @ SY163 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 ) ) ) ) )
| ( SV5 = SV41 ) ) ) )
= $true )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(282,plain,
! [SV6: $i,SV42: $i] :
( ( ( ~ ( ilf_type @ SV42 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV6 @ SV42 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(283,plain,
! [SV7: $i,SV43: $i] :
( ( ( ~ ( ilf_type @ SV43 @ set_type )
| ! [SY164: $i] :
( ~ ( ilf_type @ SY164 @ set_type )
| ! [SY165: $i] :
( ~ ( ilf_type @ SY165 @ ( relation_type @ SV7 @ SV43 ) )
| ! [SY166: $i] :
( ~ ( ilf_type @ SY166 @ ( relation_type @ SV43 @ SY164 ) )
| ( ( compose5 @ SV7 @ SV43 @ SY164 @ SY165 @ SY166 )
= ( compose @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(284,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 )
| ~ ( ilf_type @ SV9 @ set_type ) )
= $true )
| ( ( relation_like @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(285,plain,
! [SV10: $i,SV44: $i] :
( ( ( ~ ( ilf_type @ SV44 @ set_type )
| ~ ! [SY167: $i] :
~ ( ilf_type @ SY167 @ ( relation_type @ SV44 @ SV10 ) ) )
= $true )
| ( ( ilf_type @ SV10 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(286,plain,
! [SV11: $i,SV45: $i] :
( ( ( ~ ( ilf_type @ SV45 @ set_type )
| ! [SY168: $i] :
( ~ ( ilf_type @ SY168 @ set_type )
| ! [SY169: $i] :
( ~ ( ilf_type @ SY169 @ ( relation_type @ SV11 @ SV45 ) )
| ! [SY170: $i] :
( ~ ( ilf_type @ SY170 @ ( relation_type @ SV45 @ SY168 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SY168 @ SY169 @ SY170 ) @ ( relation_type @ SV11 @ SY168 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(287,plain,
! [SV12: $i] :
( ( ( ! [SY118: $i] :
~ ( ilf_type @ SY118 @ ( identity_relation_of_type @ SV12 ) ) )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(288,plain,
( ( ilf_type @ sK3_SX0 @ ( identity_relation_of_type @ sK1_B ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(289,plain,
( ( ( ( compose @ sK3_SX0 @ ( identity_relation_of @ sK1_B ) )
!= sK3_SX0 )
| ( ( compose @ ( identity_relation_of @ sK1_B ) @ sK3_SX0 )
!= sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(290,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ SV13 )
| ~ ( ilf_type @ SV13 @ set_type ) )
= $true )
| ( ( ~ ! [SY119: $i] :
~ ( ilf_type @ SY119 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(291,plain,
! [SV14: $i,SV46: $i] :
( ( ( ~ ( ilf_type @ SV46 @ binary_relation_type )
| ~ ( subset @ ( domain_of @ SV46 ) @ SV14 )
| ( ( compose @ ( identity_relation_of @ SV14 ) @ SV46 )
= SV46 ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(292,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( empty @ SV15 )
| ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SY121 @ SV15 ) ) )
| ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ SY122 @ SV15 ) )
| ( empty @ SV15 ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(293,plain,
! [SV16: $i,SV47: $i] :
( ( ( ~ ( ilf_type @ SV47 @ binary_relation_type )
| ( ilf_type @ ( compose @ SV16 @ SV47 ) @ binary_relation_type ) )
= $true )
| ( ( ilf_type @ SV16 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(294,plain,
! [SV17: $i,SV48: $i] :
( ( ( ~ ( ilf_type @ SV48 @ set_type )
| ! [SY171: $i] :
( ~ ( ilf_type @ SY171 @ ( relation_type @ SV17 @ SV48 ) )
| ( ilf_type @ ( domain @ SV17 @ SV48 @ SY171 ) @ ( subset_type @ SV17 ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(295,plain,
! [SV18: $i] :
( ( ( ~ ~ ( empty @ ( power_set @ SV18 ) )
| ~ ( ilf_type @ ( power_set @ SV18 ) @ set_type ) )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(296,plain,
! [SV19: $i,SV49: $i] :
( ( ( ~ ( ilf_type @ SV49 @ set_type )
| ! [SY172: $i] :
( ~ ( ilf_type @ SY172 @ ( relation_type @ SV19 @ SV49 ) )
| ( ( range @ SV19 @ SV49 @ SY172 )
= ( range_of @ SY172 ) ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(297,plain,
! [SV20: $i,SV50: $i] :
( ( ( ~ ( ilf_type @ SV50 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) )
| ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) ) )
| ~ ( ~ ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) )
| ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(298,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( relation_like @ SV21 )
| ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ~ ( member @ SY129 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY129
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
| ~ ( ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY132
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV21 ) ) )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(299,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ilf_type @ SV51 @ set_type )
| ~ ( ~ ( ~ ( ilf_type @ SV51 @ ( subset_type @ SV22 ) )
| ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) ) )
| ~ ( ~ ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) )
| ( ilf_type @ SV51 @ ( subset_type @ SV22 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(300,plain,
! [SV23: $i,SV52: $i] :
( ( ( ~ ( ilf_type @ SV52 @ set_type )
| ~ ( ~ ! [SY173: $i] :
( ~ ( ilf_type @ SY173 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) )
| ( ilf_type @ SY173 @ ( relation_type @ SV23 @ SV52 ) ) )
| ~ ! [SY174: $i] :
( ~ ( ilf_type @ SY174 @ ( relation_type @ SV23 @ SV52 ) )
| ( ilf_type @ SY174 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(301,plain,
! [SV24: $i,SV53: $i] :
( ( ( ~ ( ilf_type @ SV53 @ binary_relation_type )
| ( SV24 != SV53 )
| ( SV53 = SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(302,plain,
! [SV25: $i,SV54: $i] :
( ( ( ~ ( ilf_type @ SV54 @ binary_relation_type )
| ~ ( subset @ ( range_of @ SV54 ) @ SV25 )
| ( ( compose @ SV54 @ ( identity_relation_of @ SV25 ) )
= SV54 ) )
= $true )
| ( ( ilf_type @ SV25 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(303,plain,
! [SV26: $i,SV55: $i] :
( ( ( ~ ( ilf_type @ SV55 @ set_type )
| ~ ( ~ ( ~ ( member @ SV26 @ ( power_set @ SV55 ) )
| ! [SY175: $i] :
( ~ ( ilf_type @ SY175 @ set_type )
| ~ ( member @ SY175 @ SV26 )
| ( member @ SY175 @ SV55 ) ) )
| ~ ( ~ ! [SY176: $i] :
( ~ ( ilf_type @ SY176 @ set_type )
| ~ ( member @ SY176 @ SV26 )
| ( member @ SY176 @ SV55 ) )
| ( member @ SV26 @ ( power_set @ SV55 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(304,plain,
! [SV28: $i,SV56: $i] :
( ( ( ~ ( ilf_type @ SV56 @ set_type )
| ! [SY177: $i] :
( ~ ( ilf_type @ SY177 @ ( relation_type @ SV28 @ SV56 ) )
| ( ilf_type @ ( range @ SV28 @ SV56 @ SY177 ) @ ( subset_type @ SV56 ) ) ) )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(305,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV29 @ binary_relation_type )
| ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) ) )
| ~ ( ~ ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) )
| ( ilf_type @ SV29 @ binary_relation_type ) ) )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(306,plain,
! [SV32: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV57 )
| ~ ( ilf_type @ SV57 @ set_type ) )
| ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) )
| ~ ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(307,plain,
! [SV33: $i] :
( ( ( ! [SY147: $i] :
~ ( ilf_type @ SY147 @ ( subset_type @ SV33 ) ) )
= $false )
| ( ( ilf_type @ SV33 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(308,plain,
! [SV34: $i,SV58: $i] :
( ( ( ~ ( ilf_type @ SV58 @ set_type )
| ~ ( ~ ( ~ ( subset @ SV34 @ SV58 )
| ! [SY178: $i] :
( ~ ( ilf_type @ SY178 @ set_type )
| ~ ( member @ SY178 @ SV34 )
| ( member @ SY178 @ SV58 ) ) )
| ~ ( ~ ! [SY179: $i] :
( ~ ( ilf_type @ SY179 @ set_type )
| ~ ( member @ SY179 @ SV34 )
| ( member @ SY179 @ SV58 ) )
| ( subset @ SV34 @ SV58 ) ) ) )
= $true )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(309,plain,
! [SV36: $i,SV59: $i] :
( ( ( ~ ( ilf_type @ SV59 @ set_type )
| ( ilf_type @ ( cross_product @ SV36 @ SV59 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(310,plain,
! [SV37: $i,SV60: $i] :
( ( ( ~ ( ilf_type @ SV60 @ set_type )
| ! [SY180: $i] :
( ~ ( ilf_type @ SY180 @ ( subset_type @ ( cross_product @ SV37 @ SV60 ) ) )
| ( relation_like @ SY180 ) ) )
= $true )
| ( ( ilf_type @ SV37 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(311,plain,
! [SV2: $i,SV38: $i] :
( ( ( ~ ( ilf_type @ SV38 @ binary_relation_type ) )
= $true )
| ( ( ! [SY154: $i] :
( ~ ( ilf_type @ SY154 @ set_type )
| ! [SY155: $i] :
( ~ ( ilf_type @ SY155 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY154 @ SY155 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY156: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY156 @ set_type )
| ~ ( member @ ( ordered_pair @ SY154 @ SY156 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY156 @ SY155 ) @ SV38 ) ) )
| ~ ( ~ ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY157 @ set_type )
| ~ ( member @ ( ordered_pair @ SY154 @ SY157 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY157 @ SY155 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SY154 @ SY155 ) @ ( compose @ SV2 @ SV38 ) ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(312,plain,
! [SV3: $i,SV39: $i] :
( ( ( ~ ( ilf_type @ SV39 @ set_type ) )
= $true )
| ( ( ! [SY158: $i] :
( ~ ( ilf_type @ SY158 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SY158 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SY158 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SY158 ) )
| ( member @ ( ordered_pair @ SV39 @ SY158 ) @ ( identity_relation_of @ SV3 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(313,plain,
! [SV4: $i,SV40: $i] :
( ( ( ~ ( ilf_type @ SV40 @ set_type ) )
= $true )
| ( ( ! [SY159: $i] :
( ~ ( ilf_type @ SY159 @ ( relation_type @ SV4 @ SV40 ) )
| ( ( domain @ SV4 @ SV40 @ SY159 )
= ( domain_of @ SY159 ) ) ) )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(314,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( ilf_type @ SV41 @ binary_relation_type ) )
= $true )
| ( ( ~ ( ~ ( ( SV5 != SV41 )
| ! [SY160: $i] :
( ~ ( ilf_type @ SY160 @ set_type )
| ! [SY161: $i] :
( ~ ( ilf_type @ SY161 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 ) ) ) ) ) )
| ~ ( ~ ! [SY162: $i] :
( ~ ( ilf_type @ SY162 @ set_type )
| ! [SY163: $i] :
( ~ ( ilf_type @ SY163 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 ) ) ) ) )
| ( SV5 = SV41 ) ) ) )
= $true )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(315,plain,
! [SV6: $i,SV42: $i] :
( ( ( ~ ( ilf_type @ SV42 @ set_type ) )
= $true )
| ( ( ilf_type @ ( ordered_pair @ SV6 @ SV42 ) @ set_type )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(316,plain,
! [SV7: $i,SV43: $i] :
( ( ( ~ ( ilf_type @ SV43 @ set_type ) )
= $true )
| ( ( ! [SY164: $i] :
( ~ ( ilf_type @ SY164 @ set_type )
| ! [SY165: $i] :
( ~ ( ilf_type @ SY165 @ ( relation_type @ SV7 @ SV43 ) )
| ! [SY166: $i] :
( ~ ( ilf_type @ SY166 @ ( relation_type @ SV43 @ SY164 ) )
| ( ( compose5 @ SV7 @ SV43 @ SY164 @ SY165 @ SY166 )
= ( compose @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(317,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ( ilf_type @ SV9 @ set_type ) )
= $true )
| ( ( relation_like @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(318,plain,
! [SV10: $i,SV44: $i] :
( ( ( ~ ( ilf_type @ SV44 @ set_type ) )
= $true )
| ( ( ~ ! [SY167: $i] :
~ ( ilf_type @ SY167 @ ( relation_type @ SV44 @ SV10 ) ) )
= $true )
| ( ( ilf_type @ SV10 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(319,plain,
! [SV11: $i,SV45: $i] :
( ( ( ~ ( ilf_type @ SV45 @ set_type ) )
= $true )
| ( ( ! [SY168: $i] :
( ~ ( ilf_type @ SY168 @ set_type )
| ! [SY169: $i] :
( ~ ( ilf_type @ SY169 @ ( relation_type @ SV11 @ SV45 ) )
| ! [SY170: $i] :
( ~ ( ilf_type @ SY170 @ ( relation_type @ SV45 @ SY168 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SY168 @ SY169 @ SY170 ) @ ( relation_type @ SV11 @ SY168 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(320,plain,
! [SV12: $i] :
( ( ( ~ ( ilf_type @ ( sK4_SY118 @ SV12 ) @ ( identity_relation_of_type @ SV12 ) ) )
= $false )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[287]) ).
thf(321,plain,
( ( ( ( compose @ sK3_SX0 @ ( identity_relation_of @ sK1_B ) )
!= sK3_SX0 )
= $true )
| ( ( ( compose @ ( identity_relation_of @ sK1_B ) @ sK3_SX0 )
!= sK3_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(322,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ( ilf_type @ SV13 @ set_type ) )
= $true )
| ( ( ~ ! [SY119: $i] :
~ ( ilf_type @ SY119 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(323,plain,
! [SV14: $i,SV46: $i] :
( ( ( ~ ( ilf_type @ SV46 @ binary_relation_type ) )
= $true )
| ( ( ~ ( subset @ ( domain_of @ SV46 ) @ SV14 )
| ( ( compose @ ( identity_relation_of @ SV14 ) @ SV46 )
= SV46 ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(324,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( empty @ SV15 )
| ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SY121 @ SV15 ) ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(325,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ SY122 @ SV15 ) )
| ( empty @ SV15 ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(326,plain,
! [SV16: $i,SV47: $i] :
( ( ( ~ ( ilf_type @ SV47 @ binary_relation_type ) )
= $true )
| ( ( ilf_type @ ( compose @ SV16 @ SV47 ) @ binary_relation_type )
= $true )
| ( ( ilf_type @ SV16 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(327,plain,
! [SV17: $i,SV48: $i] :
( ( ( ~ ( ilf_type @ SV48 @ set_type ) )
= $true )
| ( ( ! [SY171: $i] :
( ~ ( ilf_type @ SY171 @ ( relation_type @ SV17 @ SV48 ) )
| ( ilf_type @ ( domain @ SV17 @ SV48 @ SY171 ) @ ( subset_type @ SV17 ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(328,plain,
! [SV18: $i] :
( ( ( ~ ~ ( empty @ ( power_set @ SV18 ) ) )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(329,plain,
! [SV18: $i] :
( ( ( ~ ( ilf_type @ ( power_set @ SV18 ) @ set_type ) )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(330,plain,
! [SV19: $i,SV49: $i] :
( ( ( ~ ( ilf_type @ SV49 @ set_type ) )
= $true )
| ( ( ! [SY172: $i] :
( ~ ( ilf_type @ SY172 @ ( relation_type @ SV19 @ SV49 ) )
| ( ( range @ SV19 @ SV49 @ SY172 )
= ( range_of @ SY172 ) ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(331,plain,
! [SV20: $i,SV50: $i] :
( ( ( ~ ( ilf_type @ SV50 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) )
| ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) ) )
| ~ ( ~ ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) )
| ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(332,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( relation_like @ SV21 )
| ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ~ ( member @ SY129 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY129
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) ) )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(333,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY132
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV21 ) ) )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(334,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ilf_type @ SV51 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV51 @ ( subset_type @ SV22 ) )
| ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) ) )
| ~ ( ~ ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) )
| ( ilf_type @ SV51 @ ( subset_type @ SV22 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(335,plain,
! [SV23: $i,SV52: $i] :
( ( ( ~ ( ilf_type @ SV52 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY173: $i] :
( ~ ( ilf_type @ SY173 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) )
| ( ilf_type @ SY173 @ ( relation_type @ SV23 @ SV52 ) ) )
| ~ ! [SY174: $i] :
( ~ ( ilf_type @ SY174 @ ( relation_type @ SV23 @ SV52 ) )
| ( ilf_type @ SY174 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(336,plain,
! [SV24: $i,SV53: $i] :
( ( ( ~ ( ilf_type @ SV53 @ binary_relation_type ) )
= $true )
| ( ( ( SV24 != SV53 )
| ( SV53 = SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(337,plain,
! [SV25: $i,SV54: $i] :
( ( ( ~ ( ilf_type @ SV54 @ binary_relation_type ) )
= $true )
| ( ( ~ ( subset @ ( range_of @ SV54 ) @ SV25 )
| ( ( compose @ SV54 @ ( identity_relation_of @ SV25 ) )
= SV54 ) )
= $true )
| ( ( ilf_type @ SV25 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(338,plain,
! [SV26: $i,SV55: $i] :
( ( ( ~ ( ilf_type @ SV55 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV26 @ ( power_set @ SV55 ) )
| ! [SY175: $i] :
( ~ ( ilf_type @ SY175 @ set_type )
| ~ ( member @ SY175 @ SV26 )
| ( member @ SY175 @ SV55 ) ) )
| ~ ( ~ ! [SY176: $i] :
( ~ ( ilf_type @ SY176 @ set_type )
| ~ ( member @ SY176 @ SV26 )
| ( member @ SY176 @ SV55 ) )
| ( member @ SV26 @ ( power_set @ SV55 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(339,plain,
! [SV28: $i,SV56: $i] :
( ( ( ~ ( ilf_type @ SV56 @ set_type ) )
= $true )
| ( ( ! [SY177: $i] :
( ~ ( ilf_type @ SY177 @ ( relation_type @ SV28 @ SV56 ) )
| ( ilf_type @ ( range @ SV28 @ SV56 @ SY177 ) @ ( subset_type @ SV56 ) ) ) )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(340,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV29 @ binary_relation_type )
| ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) ) ) )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(341,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) )
| ( ilf_type @ SV29 @ binary_relation_type ) ) )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(342,plain,
! [SV32: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV57 )
| ~ ( ilf_type @ SV57 @ set_type ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) )
| ~ ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(343,plain,
! [SV33: $i] :
( ( ( ~ ( ilf_type @ ( sK5_SY147 @ SV33 ) @ ( subset_type @ SV33 ) ) )
= $false )
| ( ( ilf_type @ SV33 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[307]) ).
thf(344,plain,
! [SV34: $i,SV58: $i] :
( ( ( ~ ( ilf_type @ SV58 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV34 @ SV58 )
| ! [SY178: $i] :
( ~ ( ilf_type @ SY178 @ set_type )
| ~ ( member @ SY178 @ SV34 )
| ( member @ SY178 @ SV58 ) ) )
| ~ ( ~ ! [SY179: $i] :
( ~ ( ilf_type @ SY179 @ set_type )
| ~ ( member @ SY179 @ SV34 )
| ( member @ SY179 @ SV58 ) )
| ( subset @ SV34 @ SV58 ) ) ) )
= $true )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(345,plain,
! [SV36: $i,SV59: $i] :
( ( ( ~ ( ilf_type @ SV59 @ set_type ) )
= $true )
| ( ( ilf_type @ ( cross_product @ SV36 @ SV59 ) @ set_type )
= $true )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(346,plain,
! [SV37: $i,SV60: $i] :
( ( ( ~ ( ilf_type @ SV60 @ set_type ) )
= $true )
| ( ( ! [SY180: $i] :
( ~ ( ilf_type @ SY180 @ ( subset_type @ ( cross_product @ SV37 @ SV60 ) ) )
| ( relation_like @ SY180 ) ) )
= $true )
| ( ( ilf_type @ SV37 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(347,plain,
! [SV2: $i,SV38: $i] :
( ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ! [SY154: $i] :
( ~ ( ilf_type @ SY154 @ set_type )
| ! [SY155: $i] :
( ~ ( ilf_type @ SY155 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY154 @ SY155 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY156: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY156 @ set_type )
| ~ ( member @ ( ordered_pair @ SY154 @ SY156 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY156 @ SY155 ) @ SV38 ) ) )
| ~ ( ~ ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY157 @ set_type )
| ~ ( member @ ( ordered_pair @ SY154 @ SY157 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY157 @ SY155 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SY154 @ SY155 ) @ ( compose @ SV2 @ SV38 ) ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(348,plain,
! [SV3: $i,SV39: $i] :
( ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ! [SY158: $i] :
( ~ ( ilf_type @ SY158 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SY158 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SY158 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SY158 ) )
| ( member @ ( ordered_pair @ SV39 @ SY158 ) @ ( identity_relation_of @ SV3 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(349,plain,
! [SV4: $i,SV40: $i] :
( ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( ! [SY159: $i] :
( ~ ( ilf_type @ SY159 @ ( relation_type @ SV4 @ SV40 ) )
| ( ( domain @ SV4 @ SV40 @ SY159 )
= ( domain_of @ SY159 ) ) ) )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(350,plain,
! [SV5: $i,SV41: $i] :
( ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ~ ( ~ ( ( SV5 != SV41 )
| ! [SY160: $i] :
( ~ ( ilf_type @ SY160 @ set_type )
| ! [SY161: $i] :
( ~ ( ilf_type @ SY161 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 ) ) ) ) ) )
| ~ ( ~ ! [SY162: $i] :
( ~ ( ilf_type @ SY162 @ set_type )
| ! [SY163: $i] :
( ~ ( ilf_type @ SY163 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 ) ) ) ) )
| ( SV5 = SV41 ) ) ) )
= $true )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(351,plain,
! [SV6: $i,SV42: $i] :
( ( ( ilf_type @ SV42 @ set_type )
= $false )
| ( ( ilf_type @ ( ordered_pair @ SV6 @ SV42 ) @ set_type )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(352,plain,
! [SV7: $i,SV43: $i] :
( ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ! [SY164: $i] :
( ~ ( ilf_type @ SY164 @ set_type )
| ! [SY165: $i] :
( ~ ( ilf_type @ SY165 @ ( relation_type @ SV7 @ SV43 ) )
| ! [SY166: $i] :
( ~ ( ilf_type @ SY166 @ ( relation_type @ SV43 @ SY164 ) )
| ( ( compose5 @ SV7 @ SV43 @ SY164 @ SY165 @ SY166 )
= ( compose @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(353,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $false )
| ( ( ~ ( ilf_type @ SV9 @ set_type ) )
= $true )
| ( ( relation_like @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(354,plain,
! [SV10: $i,SV44: $i] :
( ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ~ ! [SY167: $i] :
~ ( ilf_type @ SY167 @ ( relation_type @ SV44 @ SV10 ) ) )
= $true )
| ( ( ilf_type @ SV10 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(355,plain,
! [SV11: $i,SV45: $i] :
( ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ! [SY168: $i] :
( ~ ( ilf_type @ SY168 @ set_type )
| ! [SY169: $i] :
( ~ ( ilf_type @ SY169 @ ( relation_type @ SV11 @ SV45 ) )
| ! [SY170: $i] :
( ~ ( ilf_type @ SY170 @ ( relation_type @ SV45 @ SY168 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SY168 @ SY169 @ SY170 ) @ ( relation_type @ SV11 @ SY168 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(356,plain,
! [SV12: $i] :
( ( ( ilf_type @ ( sK4_SY118 @ SV12 ) @ ( identity_relation_of_type @ SV12 ) )
= $true )
| ( ( ilf_type @ SV12 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(357,plain,
( ( ( ( compose @ sK3_SX0 @ ( identity_relation_of @ sK1_B ) )
= sK3_SX0 )
= $false )
| ( ( ( compose @ ( identity_relation_of @ sK1_B ) @ sK3_SX0 )
!= sK3_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(358,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $false )
| ( ( ~ ( ilf_type @ SV13 @ set_type ) )
= $true )
| ( ( ~ ! [SY119: $i] :
~ ( ilf_type @ SY119 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(359,plain,
! [SV14: $i,SV46: $i] :
( ( ( ilf_type @ SV46 @ binary_relation_type )
= $false )
| ( ( ~ ( subset @ ( domain_of @ SV46 ) @ SV14 )
| ( ( compose @ ( identity_relation_of @ SV14 ) @ SV46 )
= SV46 ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(360,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ SV15 )
| ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SY121 @ SV15 ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(361,plain,
! [SV15: $i] :
( ( ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ SY122 @ SV15 ) )
| ( empty @ SV15 ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(362,plain,
! [SV16: $i,SV47: $i] :
( ( ( ilf_type @ SV47 @ binary_relation_type )
= $false )
| ( ( ilf_type @ ( compose @ SV16 @ SV47 ) @ binary_relation_type )
= $true )
| ( ( ilf_type @ SV16 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(363,plain,
! [SV17: $i,SV48: $i] :
( ( ( ilf_type @ SV48 @ set_type )
= $false )
| ( ( ! [SY171: $i] :
( ~ ( ilf_type @ SY171 @ ( relation_type @ SV17 @ SV48 ) )
| ( ilf_type @ ( domain @ SV17 @ SV48 @ SY171 ) @ ( subset_type @ SV17 ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(364,plain,
! [SV18: $i] :
( ( ( ~ ( empty @ ( power_set @ SV18 ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(365,plain,
! [SV18: $i] :
( ( ( ilf_type @ ( power_set @ SV18 ) @ set_type )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(366,plain,
! [SV19: $i,SV49: $i] :
( ( ( ilf_type @ SV49 @ set_type )
= $false )
| ( ( ! [SY172: $i] :
( ~ ( ilf_type @ SY172 @ ( relation_type @ SV19 @ SV49 ) )
| ( ( range @ SV19 @ SV49 @ SY172 )
= ( range_of @ SY172 ) ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(367,plain,
! [SV20: $i,SV50: $i] :
( ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) )
| ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) ) )
| ~ ( ~ ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) )
| ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(368,plain,
! [SV21: $i] :
( ( ( ~ ( relation_like @ SV21 )
| ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ~ ( member @ SY129 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY129
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(369,plain,
! [SV21: $i] :
( ( ( ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY132
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
| ( relation_like @ SV21 ) )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(370,plain,
! [SV22: $i,SV51: $i] :
( ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV51 @ ( subset_type @ SV22 ) )
| ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) ) )
| ~ ( ~ ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) )
| ( ilf_type @ SV51 @ ( subset_type @ SV22 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(371,plain,
! [SV23: $i,SV52: $i] :
( ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY173: $i] :
( ~ ( ilf_type @ SY173 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) )
| ( ilf_type @ SY173 @ ( relation_type @ SV23 @ SV52 ) ) )
| ~ ! [SY174: $i] :
( ~ ( ilf_type @ SY174 @ ( relation_type @ SV23 @ SV52 ) )
| ( ilf_type @ SY174 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(372,plain,
! [SV24: $i,SV53: $i] :
( ( ( ilf_type @ SV53 @ binary_relation_type )
= $false )
| ( ( ( SV24 != SV53 )
| ( SV53 = SV24 ) )
= $true )
| ( ( ilf_type @ SV24 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(373,plain,
! [SV25: $i,SV54: $i] :
( ( ( ilf_type @ SV54 @ binary_relation_type )
= $false )
| ( ( ~ ( subset @ ( range_of @ SV54 ) @ SV25 )
| ( ( compose @ SV54 @ ( identity_relation_of @ SV25 ) )
= SV54 ) )
= $true )
| ( ( ilf_type @ SV25 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(374,plain,
! [SV26: $i,SV55: $i] :
( ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV26 @ ( power_set @ SV55 ) )
| ! [SY175: $i] :
( ~ ( ilf_type @ SY175 @ set_type )
| ~ ( member @ SY175 @ SV26 )
| ( member @ SY175 @ SV55 ) ) )
| ~ ( ~ ! [SY176: $i] :
( ~ ( ilf_type @ SY176 @ set_type )
| ~ ( member @ SY176 @ SV26 )
| ( member @ SY176 @ SV55 ) )
| ( member @ SV26 @ ( power_set @ SV55 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(375,plain,
! [SV28: $i,SV56: $i] :
( ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( ! [SY177: $i] :
( ~ ( ilf_type @ SY177 @ ( relation_type @ SV28 @ SV56 ) )
| ( ilf_type @ ( range @ SV28 @ SV56 @ SY177 ) @ ( subset_type @ SV56 ) ) ) )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(376,plain,
! [SV29: $i] :
( ( ( ~ ( ilf_type @ SV29 @ binary_relation_type )
| ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) ) )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(377,plain,
! [SV29: $i] :
( ( ( ~ ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) )
| ( ilf_type @ SV29 @ binary_relation_type ) )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(378,plain,
! [SV32: $i,SV57: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV57 )
| ~ ( ilf_type @ SV57 @ set_type ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) )
| ~ ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(379,plain,
! [SV33: $i] :
( ( ( ilf_type @ ( sK5_SY147 @ SV33 ) @ ( subset_type @ SV33 ) )
= $true )
| ( ( ilf_type @ SV33 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(380,plain,
! [SV34: $i,SV58: $i] :
( ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV34 @ SV58 )
| ! [SY178: $i] :
( ~ ( ilf_type @ SY178 @ set_type )
| ~ ( member @ SY178 @ SV34 )
| ( member @ SY178 @ SV58 ) ) )
| ~ ( ~ ! [SY179: $i] :
( ~ ( ilf_type @ SY179 @ set_type )
| ~ ( member @ SY179 @ SV34 )
| ( member @ SY179 @ SV58 ) )
| ( subset @ SV34 @ SV58 ) ) ) )
= $true )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(381,plain,
! [SV36: $i,SV59: $i] :
( ( ( ilf_type @ SV59 @ set_type )
= $false )
| ( ( ilf_type @ ( cross_product @ SV36 @ SV59 ) @ set_type )
= $true )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(382,plain,
! [SV37: $i,SV60: $i] :
( ( ( ilf_type @ SV60 @ set_type )
= $false )
| ( ( ! [SY180: $i] :
( ~ ( ilf_type @ SY180 @ ( subset_type @ ( cross_product @ SV37 @ SV60 ) ) )
| ( relation_like @ SY180 ) ) )
= $true )
| ( ( ilf_type @ SV37 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(383,plain,
! [SV38: $i,SV2: $i,SV61: $i] :
( ( ( ~ ( ilf_type @ SV61 @ set_type )
| ! [SY181: $i] :
( ~ ( ilf_type @ SY181 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV61 @ SY181 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY182: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY182 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY182 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY182 @ SY181 ) @ SV38 ) ) )
| ~ ( ~ ~ ! [SY183: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY183 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY183 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY183 @ SY181 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SV61 @ SY181 ) @ ( compose @ SV2 @ SV38 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(384,plain,
! [SV3: $i,SV39: $i,SV62: $i] :
( ( ( ~ ( ilf_type @ SV62 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) )
| ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(385,plain,
! [SV40: $i,SV4: $i,SV63: $i] :
( ( ( ~ ( ilf_type @ SV63 @ ( relation_type @ SV4 @ SV40 ) )
| ( ( domain @ SV4 @ SV40 @ SV63 )
= ( domain_of @ SV63 ) ) )
= $true )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(386,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV41 )
| ! [SY160: $i] :
( ~ ( ilf_type @ SY160 @ set_type )
| ! [SY161: $i] :
( ~ ( ilf_type @ SY161 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 ) ) ) ) ) )
| ~ ( ~ ! [SY162: $i] :
( ~ ( ilf_type @ SY162 @ set_type )
| ! [SY163: $i] :
( ~ ( ilf_type @ SY163 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 ) ) ) ) )
| ( SV5 = SV41 ) ) )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(387,plain,
! [SV43: $i,SV7: $i,SV64: $i] :
( ( ( ~ ( ilf_type @ SV64 @ set_type )
| ! [SY184: $i] :
( ~ ( ilf_type @ SY184 @ ( relation_type @ SV7 @ SV43 ) )
| ! [SY185: $i] :
( ~ ( ilf_type @ SY185 @ ( relation_type @ SV43 @ SV64 ) )
| ( ( compose5 @ SV7 @ SV43 @ SV64 @ SY184 @ SY185 )
= ( compose @ SY184 @ SY185 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(388,plain,
! [SV9: $i] :
( ( ( ilf_type @ SV9 @ set_type )
= $false )
| ( ( empty @ SV9 )
= $false )
| ( ( relation_like @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(389,plain,
! [SV10: $i,SV44: $i] :
( ( ( ! [SY167: $i] :
~ ( ilf_type @ SY167 @ ( relation_type @ SV44 @ SV10 ) ) )
= $false )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ilf_type @ SV10 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(390,plain,
! [SV45: $i,SV11: $i,SV65: $i] :
( ( ( ~ ( ilf_type @ SV65 @ set_type )
| ! [SY186: $i] :
( ~ ( ilf_type @ SY186 @ ( relation_type @ SV11 @ SV45 ) )
| ! [SY187: $i] :
( ~ ( ilf_type @ SY187 @ ( relation_type @ SV45 @ SV65 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SV65 @ SY186 @ SY187 ) @ ( relation_type @ SV11 @ SV65 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(391,plain,
( ( ( ( compose @ ( identity_relation_of @ sK1_B ) @ sK3_SX0 )
= sK3_SX0 )
= $false )
| ( ( ( compose @ sK3_SX0 @ ( identity_relation_of @ sK1_B ) )
= sK3_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(392,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
= $true )
| ( ( ~ ( ilf_type @ SV13 @ set_type ) )
= $true )
| ( ( ~ ! [SY119: $i] :
~ ( ilf_type @ SY119 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(393,plain,
! [SV14: $i,SV46: $i] :
( ( ( ~ ( subset @ ( domain_of @ SV46 ) @ SV14 ) )
= $true )
| ( ( ( compose @ ( identity_relation_of @ SV14 ) @ SV46 )
= SV46 )
= $true )
| ( ( ilf_type @ SV46 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(394,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ SV15 ) )
= $true )
| ( ( ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SY121 @ SV15 ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(395,plain,
! [SV15: $i] :
( ( ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ SY122 @ SV15 ) ) )
= $true )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(396,plain,
! [SV48: $i,SV17: $i,SV66: $i] :
( ( ( ~ ( ilf_type @ SV66 @ ( relation_type @ SV17 @ SV48 ) )
| ( ilf_type @ ( domain @ SV17 @ SV48 @ SV66 ) @ ( subset_type @ SV17 ) ) )
= $true )
| ( ( ilf_type @ SV48 @ set_type )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(397,plain,
! [SV18: $i] :
( ( ( empty @ ( power_set @ SV18 ) )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(398,plain,
! [SV49: $i,SV19: $i,SV67: $i] :
( ( ( ~ ( ilf_type @ SV67 @ ( relation_type @ SV19 @ SV49 ) )
| ( ( range @ SV19 @ SV49 @ SV67 )
= ( range_of @ SV67 ) ) )
= $true )
| ( ( ilf_type @ SV49 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(399,plain,
! [SV20: $i,SV50: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) )
| ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) ) )
| ~ ( ~ ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) )
| ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) ) ) )
= $false )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(400,plain,
! [SV21: $i] :
( ( ( ~ ( relation_like @ SV21 ) )
= $true )
| ( ( ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ~ ( member @ SY129 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY129
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(401,plain,
! [SV21: $i] :
( ( ( ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY132
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(402,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV51 @ ( subset_type @ SV22 ) )
| ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) ) )
| ~ ( ~ ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) )
| ( ilf_type @ SV51 @ ( subset_type @ SV22 ) ) ) )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(403,plain,
! [SV52: $i,SV23: $i] :
( ( ( ~ ! [SY173: $i] :
( ~ ( ilf_type @ SY173 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) )
| ( ilf_type @ SY173 @ ( relation_type @ SV23 @ SV52 ) ) )
| ~ ! [SY174: $i] :
( ~ ( ilf_type @ SY174 @ ( relation_type @ SV23 @ SV52 ) )
| ( ilf_type @ SY174 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(404,plain,
! [SV53: $i,SV24: $i] :
( ( ( SV24 != SV53 )
= $true )
| ( ( SV53 = SV24 )
= $true )
| ( ( ilf_type @ SV53 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV24 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(405,plain,
! [SV25: $i,SV54: $i] :
( ( ( ~ ( subset @ ( range_of @ SV54 ) @ SV25 ) )
= $true )
| ( ( ( compose @ SV54 @ ( identity_relation_of @ SV25 ) )
= SV54 )
= $true )
| ( ( ilf_type @ SV54 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV25 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(406,plain,
! [SV55: $i,SV26: $i] :
( ( ( ~ ( ~ ( member @ SV26 @ ( power_set @ SV55 ) )
| ! [SY175: $i] :
( ~ ( ilf_type @ SY175 @ set_type )
| ~ ( member @ SY175 @ SV26 )
| ( member @ SY175 @ SV55 ) ) )
| ~ ( ~ ! [SY176: $i] :
( ~ ( ilf_type @ SY176 @ set_type )
| ~ ( member @ SY176 @ SV26 )
| ( member @ SY176 @ SV55 ) )
| ( member @ SV26 @ ( power_set @ SV55 ) ) ) )
= $false )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(407,plain,
! [SV56: $i,SV28: $i,SV68: $i] :
( ( ( ~ ( ilf_type @ SV68 @ ( relation_type @ SV28 @ SV56 ) )
| ( ilf_type @ ( range @ SV28 @ SV56 @ SV68 ) @ ( subset_type @ SV56 ) ) )
= $true )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( ilf_type @ SV28 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(408,plain,
! [SV29: $i] :
( ( ( ~ ( ilf_type @ SV29 @ binary_relation_type ) )
= $true )
| ( ( ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) ) )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(409,plain,
! [SV29: $i] :
( ( ( ~ ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) ) )
= $true )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(410,plain,
! [SV32: $i,SV57: $i] :
( ( ( ~ ~ ( empty @ SV57 )
| ~ ( ilf_type @ SV57 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) )
| ~ ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(411,plain,
! [SV58: $i,SV34: $i] :
( ( ( ~ ( ~ ( subset @ SV34 @ SV58 )
| ! [SY178: $i] :
( ~ ( ilf_type @ SY178 @ set_type )
| ~ ( member @ SY178 @ SV34 )
| ( member @ SY178 @ SV58 ) ) )
| ~ ( ~ ! [SY179: $i] :
( ~ ( ilf_type @ SY179 @ set_type )
| ~ ( member @ SY179 @ SV34 )
| ( member @ SY179 @ SV58 ) )
| ( subset @ SV34 @ SV58 ) ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(412,plain,
! [SV60: $i,SV37: $i,SV69: $i] :
( ( ( ~ ( ilf_type @ SV69 @ ( subset_type @ ( cross_product @ SV37 @ SV60 ) ) )
| ( relation_like @ SV69 ) )
= $true )
| ( ( ilf_type @ SV60 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(413,plain,
! [SV38: $i,SV2: $i,SV61: $i] :
( ( ( ~ ( ilf_type @ SV61 @ set_type ) )
= $true )
| ( ( ! [SY181: $i] :
( ~ ( ilf_type @ SY181 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV61 @ SY181 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY182: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY182 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY182 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY182 @ SY181 ) @ SV38 ) ) )
| ~ ( ~ ~ ! [SY183: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY183 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY183 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY183 @ SY181 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SV61 @ SY181 ) @ ( compose @ SV2 @ SV38 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(414,plain,
! [SV3: $i,SV39: $i,SV62: $i] :
( ( ( ~ ( ilf_type @ SV62 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) )
| ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(415,plain,
! [SV40: $i,SV4: $i,SV63: $i] :
( ( ( ~ ( ilf_type @ SV63 @ ( relation_type @ SV4 @ SV40 ) ) )
= $true )
| ( ( ( domain @ SV4 @ SV40 @ SV63 )
= ( domain_of @ SV63 ) )
= $true )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(416,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV41 )
| ! [SY160: $i] :
( ~ ( ilf_type @ SY160 @ set_type )
| ! [SY161: $i] :
( ~ ( ilf_type @ SY161 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(417,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ( ~ ! [SY162: $i] :
( ~ ( ilf_type @ SY162 @ set_type )
| ! [SY163: $i] :
( ~ ( ilf_type @ SY163 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 ) ) ) ) )
| ( SV5 = SV41 ) ) )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(418,plain,
! [SV43: $i,SV7: $i,SV64: $i] :
( ( ( ~ ( ilf_type @ SV64 @ set_type ) )
= $true )
| ( ( ! [SY184: $i] :
( ~ ( ilf_type @ SY184 @ ( relation_type @ SV7 @ SV43 ) )
| ! [SY185: $i] :
( ~ ( ilf_type @ SY185 @ ( relation_type @ SV43 @ SV64 ) )
| ( ( compose5 @ SV7 @ SV43 @ SV64 @ SY184 @ SY185 )
= ( compose @ SY184 @ SY185 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(419,plain,
! [SV44: $i,SV10: $i] :
( ( ( ~ ( ilf_type @ ( sK6_SY167 @ SV10 @ SV44 ) @ ( relation_type @ SV44 @ SV10 ) ) )
= $false )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ilf_type @ SV10 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[389]) ).
thf(420,plain,
! [SV45: $i,SV11: $i,SV65: $i] :
( ( ( ~ ( ilf_type @ SV65 @ set_type ) )
= $true )
| ( ( ! [SY186: $i] :
( ~ ( ilf_type @ SY186 @ ( relation_type @ SV11 @ SV45 ) )
| ! [SY187: $i] :
( ~ ( ilf_type @ SY187 @ ( relation_type @ SV45 @ SV65 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SV65 @ SY186 @ SY187 ) @ ( relation_type @ SV11 @ SV65 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(421,plain,
! [SV13: $i] :
( ( ( ilf_type @ SV13 @ set_type )
= $false )
| ( ( empty @ SV13 )
= $true )
| ( ( ~ ! [SY119: $i] :
~ ( ilf_type @ SY119 @ ( member_type @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(422,plain,
! [SV14: $i,SV46: $i] :
( ( ( subset @ ( domain_of @ SV46 ) @ SV14 )
= $false )
| ( ( ( compose @ ( identity_relation_of @ SV14 ) @ SV46 )
= SV46 )
= $true )
| ( ( ilf_type @ SV46 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(423,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
= $false )
| ( ( ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SY121 @ SV15 ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(424,plain,
! [SV15: $i] :
( ( ( ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ SY122 @ SV15 ) ) )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(425,plain,
! [SV48: $i,SV17: $i,SV66: $i] :
( ( ( ~ ( ilf_type @ SV66 @ ( relation_type @ SV17 @ SV48 ) ) )
= $true )
| ( ( ilf_type @ ( domain @ SV17 @ SV48 @ SV66 ) @ ( subset_type @ SV17 ) )
= $true )
| ( ( ilf_type @ SV48 @ set_type )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(426,plain,
! [SV49: $i,SV19: $i,SV67: $i] :
( ( ( ~ ( ilf_type @ SV67 @ ( relation_type @ SV19 @ SV49 ) ) )
= $true )
| ( ( ( range @ SV19 @ SV49 @ SV67 )
= ( range_of @ SV67 ) )
= $true )
| ( ( ilf_type @ SV49 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(427,plain,
! [SV20: $i,SV50: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) )
| ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) ) ) )
= $false )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(428,plain,
! [SV20: $i,SV50: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) )
| ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) ) ) )
= $false )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(429,plain,
! [SV21: $i] :
( ( ( relation_like @ SV21 )
= $false )
| ( ( ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ~ ( member @ SY129 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY129
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(430,plain,
! [SV21: $i] :
( ( ( ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV21 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ilf_type @ SX2 @ set_type )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( ilf_type @ SX3 @ set_type )
| ( SY132
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) ) )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(431,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV51 @ ( subset_type @ SV22 ) )
| ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(432,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) )
| ( ilf_type @ SV51 @ ( subset_type @ SV22 ) ) ) )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(433,plain,
! [SV52: $i,SV23: $i] :
( ( ( ~ ! [SY173: $i] :
( ~ ( ilf_type @ SY173 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) )
| ( ilf_type @ SY173 @ ( relation_type @ SV23 @ SV52 ) ) ) )
= $false )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(434,plain,
! [SV52: $i,SV23: $i] :
( ( ( ~ ! [SY174: $i] :
( ~ ( ilf_type @ SY174 @ ( relation_type @ SV23 @ SV52 ) )
| ( ilf_type @ SY174 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(435,plain,
! [SV53: $i,SV24: $i] :
( ( ( SV24 = SV53 )
= $false )
| ( ( SV53 = SV24 )
= $true )
| ( ( ilf_type @ SV53 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV24 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(436,plain,
! [SV25: $i,SV54: $i] :
( ( ( subset @ ( range_of @ SV54 ) @ SV25 )
= $false )
| ( ( ( compose @ SV54 @ ( identity_relation_of @ SV25 ) )
= SV54 )
= $true )
| ( ( ilf_type @ SV54 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV25 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(437,plain,
! [SV55: $i,SV26: $i] :
( ( ( ~ ( ~ ( member @ SV26 @ ( power_set @ SV55 ) )
| ! [SY175: $i] :
( ~ ( ilf_type @ SY175 @ set_type )
| ~ ( member @ SY175 @ SV26 )
| ( member @ SY175 @ SV55 ) ) ) )
= $false )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(438,plain,
! [SV55: $i,SV26: $i] :
( ( ( ~ ( ~ ! [SY176: $i] :
( ~ ( ilf_type @ SY176 @ set_type )
| ~ ( member @ SY176 @ SV26 )
| ( member @ SY176 @ SV55 ) )
| ( member @ SV26 @ ( power_set @ SV55 ) ) ) )
= $false )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(439,plain,
! [SV56: $i,SV28: $i,SV68: $i] :
( ( ( ~ ( ilf_type @ SV68 @ ( relation_type @ SV28 @ SV56 ) ) )
= $true )
| ( ( ilf_type @ ( range @ SV28 @ SV56 @ SV68 ) @ ( subset_type @ SV56 ) )
= $true )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( ilf_type @ SV28 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(440,plain,
! [SV29: $i] :
( ( ( ilf_type @ SV29 @ binary_relation_type )
= $false )
| ( ( ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) ) )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(441,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) ) )
= $false )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(442,plain,
! [SV32: $i,SV57: $i] :
( ( ( ~ ~ ( empty @ SV57 ) )
= $true )
| ( ( ~ ( ilf_type @ SV57 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) )
| ~ ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(443,plain,
! [SV58: $i,SV34: $i] :
( ( ( ~ ( ~ ( subset @ SV34 @ SV58 )
| ! [SY178: $i] :
( ~ ( ilf_type @ SY178 @ set_type )
| ~ ( member @ SY178 @ SV34 )
| ( member @ SY178 @ SV58 ) ) ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(444,plain,
! [SV58: $i,SV34: $i] :
( ( ( ~ ( ~ ! [SY179: $i] :
( ~ ( ilf_type @ SY179 @ set_type )
| ~ ( member @ SY179 @ SV34 )
| ( member @ SY179 @ SV58 ) )
| ( subset @ SV34 @ SV58 ) ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(445,plain,
! [SV60: $i,SV37: $i,SV69: $i] :
( ( ( ~ ( ilf_type @ SV69 @ ( subset_type @ ( cross_product @ SV37 @ SV60 ) ) ) )
= $true )
| ( ( relation_like @ SV69 )
= $true )
| ( ( ilf_type @ SV60 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(446,plain,
! [SV38: $i,SV2: $i,SV61: $i] :
( ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ! [SY181: $i] :
( ~ ( ilf_type @ SY181 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV61 @ SY181 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY182: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY182 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY182 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY182 @ SY181 ) @ SV38 ) ) )
| ~ ( ~ ~ ! [SY183: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY183 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY183 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY183 @ SY181 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SV61 @ SY181 ) @ ( compose @ SV2 @ SV38 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(447,plain,
! [SV3: $i,SV39: $i,SV62: $i] :
( ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) )
| ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(448,plain,
! [SV40: $i,SV4: $i,SV63: $i] :
( ( ( ilf_type @ SV63 @ ( relation_type @ SV4 @ SV40 ) )
= $false )
| ( ( ( domain @ SV4 @ SV40 @ SV63 )
= ( domain_of @ SV63 ) )
= $true )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(449,plain,
! [SV41: $i,SV5: $i] :
( ( ( ( SV5 != SV41 )
| ! [SY160: $i] :
( ~ ( ilf_type @ SY160 @ set_type )
| ! [SY161: $i] :
( ~ ( ilf_type @ SY161 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(450,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ! [SY162: $i] :
( ~ ( ilf_type @ SY162 @ set_type )
| ! [SY163: $i] :
( ~ ( ilf_type @ SY163 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 ) ) ) ) )
| ( SV5 = SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(451,plain,
! [SV43: $i,SV7: $i,SV64: $i] :
( ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ! [SY184: $i] :
( ~ ( ilf_type @ SY184 @ ( relation_type @ SV7 @ SV43 ) )
| ! [SY185: $i] :
( ~ ( ilf_type @ SY185 @ ( relation_type @ SV43 @ SV64 ) )
| ( ( compose5 @ SV7 @ SV43 @ SV64 @ SY184 @ SY185 )
= ( compose @ SY184 @ SY185 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(452,plain,
! [SV44: $i,SV10: $i] :
( ( ( ilf_type @ ( sK6_SY167 @ SV10 @ SV44 ) @ ( relation_type @ SV44 @ SV10 ) )
= $true )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ilf_type @ SV10 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(453,plain,
! [SV45: $i,SV11: $i,SV65: $i] :
( ( ( ilf_type @ SV65 @ set_type )
= $false )
| ( ( ! [SY186: $i] :
( ~ ( ilf_type @ SY186 @ ( relation_type @ SV11 @ SV45 ) )
| ! [SY187: $i] :
( ~ ( ilf_type @ SY187 @ ( relation_type @ SV45 @ SV65 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SV65 @ SY186 @ SY187 ) @ ( relation_type @ SV11 @ SV65 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(454,plain,
! [SV13: $i] :
( ( ( ! [SY119: $i] :
~ ( ilf_type @ SY119 @ ( member_type @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(455,plain,
! [SV15: $i,SV70: $i] :
( ( ( ~ ( ilf_type @ SV70 @ set_type )
| ~ ( member @ SV70 @ SV15 ) )
= $true )
| ( ( empty @ SV15 )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(456,plain,
! [SV15: $i] :
( ( ( ~ ( ilf_type @ ( sK7_SY122 @ SV15 ) @ set_type )
| ~ ( member @ ( sK7_SY122 @ SV15 ) @ SV15 ) )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[424]) ).
thf(457,plain,
! [SV48: $i,SV17: $i,SV66: $i] :
( ( ( ilf_type @ SV66 @ ( relation_type @ SV17 @ SV48 ) )
= $false )
| ( ( ilf_type @ ( domain @ SV17 @ SV48 @ SV66 ) @ ( subset_type @ SV17 ) )
= $true )
| ( ( ilf_type @ SV48 @ set_type )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(458,plain,
! [SV49: $i,SV19: $i,SV67: $i] :
( ( ( ilf_type @ SV67 @ ( relation_type @ SV19 @ SV49 ) )
= $false )
| ( ( ( range @ SV19 @ SV49 @ SV67 )
= ( range_of @ SV67 ) )
= $true )
| ( ( ilf_type @ SV49 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(459,plain,
! [SV20: $i,SV50: $i] :
( ( ( ~ ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) )
| ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) ) )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(460,plain,
! [SV20: $i,SV50: $i] :
( ( ( ~ ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) )
| ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) ) )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(461,plain,
! [SV21: $i,SV71: $i] :
( ( ( ~ ( ilf_type @ SV71 @ set_type )
| ~ ( member @ SV71 @ SV21 )
| ~ ! [SY188: $i] :
~ ~ ( ~ ( ilf_type @ SY188 @ set_type )
| ~ ~ ! [SY189: $i] :
~ ~ ( ~ ( ilf_type @ SY189 @ set_type )
| ( SV71
!= ( ordered_pair @ SY188 @ SY189 ) ) ) ) )
= $true )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(462,plain,
! [SV21: $i] :
( ( ( ~ ( ilf_type @ ( sK8_SY132 @ SV21 ) @ set_type )
| ~ ( member @ ( sK8_SY132 @ SV21 ) @ SV21 )
| ~ ! [SY190: $i] :
~ ~ ( ~ ( ilf_type @ SY190 @ set_type )
| ~ ~ ! [SY191: $i] :
~ ~ ( ~ ( ilf_type @ SY191 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SY190 @ SY191 ) ) ) ) )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[430]) ).
thf(463,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ilf_type @ SV51 @ ( subset_type @ SV22 ) )
| ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) ) )
= $true )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(464,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) )
| ( ilf_type @ SV51 @ ( subset_type @ SV22 ) ) )
= $true )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(465,plain,
! [SV52: $i,SV23: $i] :
( ( ( ! [SY173: $i] :
( ~ ( ilf_type @ SY173 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) )
| ( ilf_type @ SY173 @ ( relation_type @ SV23 @ SV52 ) ) ) )
= $true )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(466,plain,
! [SV52: $i,SV23: $i] :
( ( ( ! [SY174: $i] :
( ~ ( ilf_type @ SY174 @ ( relation_type @ SV23 @ SV52 ) )
| ( ilf_type @ SY174 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(467,plain,
! [SV55: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ ( power_set @ SV55 ) )
| ! [SY175: $i] :
( ~ ( ilf_type @ SY175 @ set_type )
| ~ ( member @ SY175 @ SV26 )
| ( member @ SY175 @ SV55 ) ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(468,plain,
! [SV55: $i,SV26: $i] :
( ( ( ~ ! [SY176: $i] :
( ~ ( ilf_type @ SY176 @ set_type )
| ~ ( member @ SY176 @ SV26 )
| ( member @ SY176 @ SV55 ) )
| ( member @ SV26 @ ( power_set @ SV55 ) ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(469,plain,
! [SV56: $i,SV28: $i,SV68: $i] :
( ( ( ilf_type @ SV68 @ ( relation_type @ SV28 @ SV56 ) )
= $false )
| ( ( ilf_type @ ( range @ SV28 @ SV56 @ SV68 ) @ ( subset_type @ SV56 ) )
= $true )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( ilf_type @ SV28 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(470,plain,
! [SV29: $i] :
( ( ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) )
= $false )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(471,plain,
! [SV29: $i] :
( ( ( ~ ( relation_like @ SV29 )
| ~ ( ilf_type @ SV29 @ set_type ) )
= $true )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(472,plain,
! [SV32: $i,SV57: $i] :
( ( ( ~ ( empty @ SV57 ) )
= $false )
| ( ( ~ ( ilf_type @ SV57 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) )
| ~ ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(473,plain,
! [SV58: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV58 )
| ! [SY178: $i] :
( ~ ( ilf_type @ SY178 @ set_type )
| ~ ( member @ SY178 @ SV34 )
| ( member @ SY178 @ SV58 ) ) )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(474,plain,
! [SV58: $i,SV34: $i] :
( ( ( ~ ! [SY179: $i] :
( ~ ( ilf_type @ SY179 @ set_type )
| ~ ( member @ SY179 @ SV34 )
| ( member @ SY179 @ SV58 ) )
| ( subset @ SV34 @ SV58 ) )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(475,plain,
! [SV60: $i,SV37: $i,SV69: $i] :
( ( ( ilf_type @ SV69 @ ( subset_type @ ( cross_product @ SV37 @ SV60 ) ) )
= $false )
| ( ( relation_like @ SV69 )
= $true )
| ( ( ilf_type @ SV60 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(476,plain,
! [SV38: $i,SV2: $i,SV61: $i,SV72: $i] :
( ( ( ~ ( ilf_type @ SV72 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY192: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY192 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY192 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY192 @ SV72 ) @ SV38 ) ) )
| ~ ( ~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY193 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY193 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY193 @ SV72 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(477,plain,
! [SV3: $i,SV62: $i,SV39: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) )
| ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) ) ) )
= $false )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(478,plain,
! [SV41: $i,SV5: $i] :
( ( ( SV5 != SV41 )
= $true )
| ( ( ! [SY160: $i] :
( ~ ( ilf_type @ SY160 @ set_type )
| ! [SY161: $i] :
( ~ ( ilf_type @ SY161 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(479,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ! [SY162: $i] :
( ~ ( ilf_type @ SY162 @ set_type )
| ! [SY163: $i] :
( ~ ( ilf_type @ SY163 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 ) ) ) ) ) )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(480,plain,
! [SV64: $i,SV43: $i,SV7: $i,SV73: $i] :
( ( ( ~ ( ilf_type @ SV73 @ ( relation_type @ SV7 @ SV43 ) )
| ! [SY194: $i] :
( ~ ( ilf_type @ SY194 @ ( relation_type @ SV43 @ SV64 ) )
| ( ( compose5 @ SV7 @ SV43 @ SV64 @ SV73 @ SY194 )
= ( compose @ SV73 @ SY194 ) ) ) )
= $true )
| ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(481,plain,
! [SV65: $i,SV45: $i,SV11: $i,SV74: $i] :
( ( ( ~ ( ilf_type @ SV74 @ ( relation_type @ SV11 @ SV45 ) )
| ! [SY195: $i] :
( ~ ( ilf_type @ SY195 @ ( relation_type @ SV45 @ SV65 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SV65 @ SV74 @ SY195 ) @ ( relation_type @ SV11 @ SV65 ) ) ) )
= $true )
| ( ( ilf_type @ SV65 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(482,plain,
! [SV13: $i] :
( ( ( ~ ( ilf_type @ ( sK9_SY119 @ SV13 ) @ ( member_type @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[454]) ).
thf(483,plain,
! [SV15: $i,SV70: $i] :
( ( ( ~ ( ilf_type @ SV70 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV70 @ SV15 ) )
= $true )
| ( ( empty @ SV15 )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(484,plain,
! [SV15: $i] :
( ( ( ~ ( ilf_type @ ( sK7_SY122 @ SV15 ) @ set_type ) )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(485,plain,
! [SV15: $i] :
( ( ( ~ ( member @ ( sK7_SY122 @ SV15 ) @ SV15 ) )
= $false )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(486,plain,
! [SV20: $i,SV50: $i] :
( ( ( ~ ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) ) )
= $true )
| ( ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(487,plain,
! [SV20: $i,SV50: $i] :
( ( ( ~ ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) ) )
= $true )
| ( ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(488,plain,
! [SV21: $i,SV71: $i] :
( ( ( ~ ( ilf_type @ SV71 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV71 @ SV21 )
| ~ ! [SY188: $i] :
~ ~ ( ~ ( ilf_type @ SY188 @ set_type )
| ~ ~ ! [SY189: $i] :
~ ~ ( ~ ( ilf_type @ SY189 @ set_type )
| ( SV71
!= ( ordered_pair @ SY188 @ SY189 ) ) ) ) )
= $true )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(489,plain,
! [SV21: $i] :
( ( ( ~ ( ilf_type @ ( sK8_SY132 @ SV21 ) @ set_type ) )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(490,plain,
! [SV21: $i] :
( ( ( ~ ( member @ ( sK8_SY132 @ SV21 ) @ SV21 )
| ~ ! [SY190: $i] :
~ ~ ( ~ ( ilf_type @ SY190 @ set_type )
| ~ ~ ! [SY191: $i] :
~ ~ ( ~ ( ilf_type @ SY191 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SY190 @ SY191 ) ) ) ) )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(491,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ilf_type @ SV51 @ ( subset_type @ SV22 ) ) )
= $true )
| ( ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) )
= $true )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(492,plain,
! [SV22: $i,SV51: $i] :
( ( ( ~ ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) ) )
= $true )
| ( ( ilf_type @ SV51 @ ( subset_type @ SV22 ) )
= $true )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(493,plain,
! [SV52: $i,SV23: $i,SV75: $i] :
( ( ( ~ ( ilf_type @ SV75 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) )
| ( ilf_type @ SV75 @ ( relation_type @ SV23 @ SV52 ) ) )
= $true )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(494,plain,
! [SV52: $i,SV23: $i,SV76: $i] :
( ( ( ~ ( ilf_type @ SV76 @ ( relation_type @ SV23 @ SV52 ) )
| ( ilf_type @ SV76 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) ) )
= $true )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(495,plain,
! [SV55: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ ( power_set @ SV55 ) ) )
= $true )
| ( ( ! [SY175: $i] :
( ~ ( ilf_type @ SY175 @ set_type )
| ~ ( member @ SY175 @ SV26 )
| ( member @ SY175 @ SV55 ) ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(496,plain,
! [SV55: $i,SV26: $i] :
( ( ( ~ ! [SY176: $i] :
( ~ ( ilf_type @ SY176 @ set_type )
| ~ ( member @ SY176 @ SV26 )
| ( member @ SY176 @ SV55 ) ) )
= $true )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(497,plain,
! [SV29: $i] :
( ( ( ~ ( relation_like @ SV29 ) )
= $false )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(498,plain,
! [SV29: $i] :
( ( ( ~ ( ilf_type @ SV29 @ set_type ) )
= $false )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(499,plain,
! [SV29: $i] :
( ( ( ~ ( relation_like @ SV29 ) )
= $true )
| ( ( ~ ( ilf_type @ SV29 @ set_type ) )
= $true )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(500,plain,
! [SV32: $i,SV57: $i] :
( ( ( empty @ SV57 )
= $true )
| ( ( ~ ( ilf_type @ SV57 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) )
| ~ ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(501,plain,
! [SV58: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV58 ) )
= $true )
| ( ( ! [SY178: $i] :
( ~ ( ilf_type @ SY178 @ set_type )
| ~ ( member @ SY178 @ SV34 )
| ( member @ SY178 @ SV58 ) ) )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(502,plain,
! [SV58: $i,SV34: $i] :
( ( ( ~ ! [SY179: $i] :
( ~ ( ilf_type @ SY179 @ set_type )
| ~ ( member @ SY179 @ SV34 )
| ( member @ SY179 @ SV58 ) ) )
= $true )
| ( ( subset @ SV34 @ SV58 )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(503,plain,
! [SV38: $i,SV2: $i,SV61: $i,SV72: $i] :
( ( ( ~ ( ilf_type @ SV72 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY192: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY192 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY192 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY192 @ SV72 ) @ SV38 ) ) )
| ~ ( ~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY193 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY193 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY193 @ SV72 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(504,plain,
! [SV3: $i,SV62: $i,SV39: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) ) ) )
= $false )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(505,plain,
! [SV62: $i,SV3: $i,SV39: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) )
| ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) ) ) )
= $false )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(506,plain,
! [SV41: $i,SV5: $i] :
( ( ( SV5 = SV41 )
= $false )
| ( ( ! [SY160: $i] :
( ~ ( ilf_type @ SY160 @ set_type )
| ! [SY161: $i] :
( ~ ( ilf_type @ SY161 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV41 )
| ( member @ ( ordered_pair @ SY160 @ SY161 ) @ SV5 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(507,plain,
! [SV41: $i,SV5: $i] :
( ( ( ! [SY162: $i] :
( ~ ( ilf_type @ SY162 @ set_type )
| ! [SY163: $i] :
( ~ ( ilf_type @ SY163 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV41 )
| ( member @ ( ordered_pair @ SY162 @ SY163 ) @ SV5 ) ) ) ) ) )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(508,plain,
! [SV64: $i,SV43: $i,SV7: $i,SV73: $i] :
( ( ( ~ ( ilf_type @ SV73 @ ( relation_type @ SV7 @ SV43 ) ) )
= $true )
| ( ( ! [SY194: $i] :
( ~ ( ilf_type @ SY194 @ ( relation_type @ SV43 @ SV64 ) )
| ( ( compose5 @ SV7 @ SV43 @ SV64 @ SV73 @ SY194 )
= ( compose @ SV73 @ SY194 ) ) ) )
= $true )
| ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(509,plain,
! [SV65: $i,SV45: $i,SV11: $i,SV74: $i] :
( ( ( ~ ( ilf_type @ SV74 @ ( relation_type @ SV11 @ SV45 ) ) )
= $true )
| ( ( ! [SY195: $i] :
( ~ ( ilf_type @ SY195 @ ( relation_type @ SV45 @ SV65 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SV65 @ SV74 @ SY195 ) @ ( relation_type @ SV11 @ SV65 ) ) ) )
= $true )
| ( ( ilf_type @ SV65 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(510,plain,
! [SV13: $i] :
( ( ( ilf_type @ ( sK9_SY119 @ SV13 ) @ ( member_type @ SV13 ) )
= $true )
| ( ( empty @ SV13 )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(511,plain,
! [SV15: $i,SV70: $i] :
( ( ( ilf_type @ SV70 @ set_type )
= $false )
| ( ( ~ ( member @ SV70 @ SV15 ) )
= $true )
| ( ( empty @ SV15 )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(512,plain,
! [SV15: $i] :
( ( ( ilf_type @ ( sK7_SY122 @ SV15 ) @ set_type )
= $true )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(513,plain,
! [SV15: $i] :
( ( ( member @ ( sK7_SY122 @ SV15 ) @ SV15 )
= $true )
| ( ( empty @ SV15 )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(514,plain,
! [SV20: $i,SV50: $i] :
( ( ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) )
= $false )
| ( ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(515,plain,
! [SV20: $i,SV50: $i] :
( ( ( ilf_type @ SV50 @ ( relation_type @ SV20 @ SV20 ) )
= $false )
| ( ( ilf_type @ SV50 @ ( identity_relation_of_type @ SV20 ) )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(516,plain,
! [SV21: $i,SV71: $i] :
( ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( ~ ( member @ SV71 @ SV21 )
| ~ ! [SY188: $i] :
~ ~ ( ~ ( ilf_type @ SY188 @ set_type )
| ~ ~ ! [SY189: $i] :
~ ~ ( ~ ( ilf_type @ SY189 @ set_type )
| ( SV71
!= ( ordered_pair @ SY188 @ SY189 ) ) ) ) )
= $true )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(517,plain,
! [SV21: $i] :
( ( ( ilf_type @ ( sK8_SY132 @ SV21 ) @ set_type )
= $true )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(518,plain,
! [SV21: $i] :
( ( ( ~ ( member @ ( sK8_SY132 @ SV21 ) @ SV21 ) )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(519,plain,
! [SV21: $i] :
( ( ( ~ ! [SY190: $i] :
~ ~ ( ~ ( ilf_type @ SY190 @ set_type )
| ~ ~ ! [SY191: $i] :
~ ~ ( ~ ( ilf_type @ SY191 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SY190 @ SY191 ) ) ) ) )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(520,plain,
! [SV22: $i,SV51: $i] :
( ( ( ilf_type @ SV51 @ ( subset_type @ SV22 ) )
= $false )
| ( ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) )
= $true )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(521,plain,
! [SV22: $i,SV51: $i] :
( ( ( ilf_type @ SV51 @ ( member_type @ ( power_set @ SV22 ) ) )
= $false )
| ( ( ilf_type @ SV51 @ ( subset_type @ SV22 ) )
= $true )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(522,plain,
! [SV52: $i,SV23: $i,SV75: $i] :
( ( ( ~ ( ilf_type @ SV75 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) ) )
= $true )
| ( ( ilf_type @ SV75 @ ( relation_type @ SV23 @ SV52 ) )
= $true )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(523,plain,
! [SV52: $i,SV23: $i,SV76: $i] :
( ( ( ~ ( ilf_type @ SV76 @ ( relation_type @ SV23 @ SV52 ) ) )
= $true )
| ( ( ilf_type @ SV76 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) )
= $true )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(524,plain,
! [SV55: $i,SV26: $i] :
( ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $false )
| ( ( ! [SY175: $i] :
( ~ ( ilf_type @ SY175 @ set_type )
| ~ ( member @ SY175 @ SV26 )
| ( member @ SY175 @ SV55 ) ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(525,plain,
! [SV55: $i,SV26: $i] :
( ( ( ! [SY176: $i] :
( ~ ( ilf_type @ SY176 @ set_type )
| ~ ( member @ SY176 @ SV26 )
| ( member @ SY176 @ SV55 ) ) )
= $false )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(526,plain,
! [SV29: $i] :
( ( ( relation_like @ SV29 )
= $true )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(527,plain,
! [SV29: $i] :
( ( ( ilf_type @ SV29 @ set_type )
= $true )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(528,plain,
! [SV29: $i] :
( ( ( relation_like @ SV29 )
= $false )
| ( ( ~ ( ilf_type @ SV29 @ set_type ) )
= $true )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(529,plain,
! [SV32: $i,SV57: $i] :
( ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( empty @ SV57 )
= $true )
| ( ( ~ ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) )
| ~ ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(530,plain,
! [SV58: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV58 )
= $false )
| ( ( ! [SY178: $i] :
( ~ ( ilf_type @ SY178 @ set_type )
| ~ ( member @ SY178 @ SV34 )
| ( member @ SY178 @ SV58 ) ) )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(531,plain,
! [SV58: $i,SV34: $i] :
( ( ( ! [SY179: $i] :
( ~ ( ilf_type @ SY179 @ set_type )
| ~ ( member @ SY179 @ SV34 )
| ( member @ SY179 @ SV58 ) ) )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(532,plain,
! [SV38: $i,SV2: $i,SV61: $i,SV72: $i] :
( ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY192: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY192 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY192 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY192 @ SV72 ) @ SV38 ) ) )
| ~ ( ~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY193 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY193 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY193 @ SV72 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(533,plain,
! [SV3: $i,SV62: $i,SV39: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
| ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) ) )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(534,plain,
! [SV62: $i,SV3: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) )
| ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) ) )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(535,plain,
! [SV41: $i,SV5: $i,SV77: $i] :
( ( ( ~ ( ilf_type @ SV77 @ set_type )
| ! [SY196: $i] :
( ~ ( ilf_type @ SY196 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV5 )
| ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV41 )
| ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV5 ) ) ) ) )
= $true )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(536,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( ilf_type @ ( sK10_SY162 @ SV41 @ SV5 ) @ set_type )
| ! [SY197: $i] :
( ~ ( ilf_type @ SY197 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ SY197 ) @ SV5 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ SY197 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ SY197 ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ SY197 ) @ SV5 ) ) ) ) )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[507]) ).
thf(537,plain,
! [SV64: $i,SV43: $i,SV7: $i,SV73: $i] :
( ( ( ilf_type @ SV73 @ ( relation_type @ SV7 @ SV43 ) )
= $false )
| ( ( ! [SY194: $i] :
( ~ ( ilf_type @ SY194 @ ( relation_type @ SV43 @ SV64 ) )
| ( ( compose5 @ SV7 @ SV43 @ SV64 @ SV73 @ SY194 )
= ( compose @ SV73 @ SY194 ) ) ) )
= $true )
| ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(538,plain,
! [SV65: $i,SV45: $i,SV11: $i,SV74: $i] :
( ( ( ilf_type @ SV74 @ ( relation_type @ SV11 @ SV45 ) )
= $false )
| ( ( ! [SY195: $i] :
( ~ ( ilf_type @ SY195 @ ( relation_type @ SV45 @ SV65 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SV65 @ SV74 @ SY195 ) @ ( relation_type @ SV11 @ SV65 ) ) ) )
= $true )
| ( ( ilf_type @ SV65 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(539,plain,
! [SV15: $i,SV70: $i] :
( ( ( member @ SV70 @ SV15 )
= $false )
| ( ( ilf_type @ SV70 @ set_type )
= $false )
| ( ( empty @ SV15 )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(540,plain,
! [SV21: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ SV21 ) )
= $true )
| ( ( ~ ! [SY188: $i] :
~ ~ ( ~ ( ilf_type @ SY188 @ set_type )
| ~ ~ ! [SY189: $i] :
~ ~ ( ~ ( ilf_type @ SY189 @ set_type )
| ( SV71
!= ( ordered_pair @ SY188 @ SY189 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(541,plain,
! [SV21: $i] :
( ( ( member @ ( sK8_SY132 @ SV21 ) @ SV21 )
= $true )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(542,plain,
! [SV21: $i] :
( ( ( ! [SY190: $i] :
~ ~ ( ~ ( ilf_type @ SY190 @ set_type )
| ~ ~ ! [SY191: $i] :
~ ~ ( ~ ( ilf_type @ SY191 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SY190 @ SY191 ) ) ) ) )
= $true )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(543,plain,
! [SV52: $i,SV23: $i,SV75: $i] :
( ( ( ilf_type @ SV75 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) )
= $false )
| ( ( ilf_type @ SV75 @ ( relation_type @ SV23 @ SV52 ) )
= $true )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(544,plain,
! [SV52: $i,SV23: $i,SV76: $i] :
( ( ( ilf_type @ SV76 @ ( relation_type @ SV23 @ SV52 ) )
= $false )
| ( ( ilf_type @ SV76 @ ( subset_type @ ( cross_product @ SV23 @ SV52 ) ) )
= $true )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV23 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(545,plain,
! [SV55: $i,SV26: $i,SV78: $i] :
( ( ( ~ ( ilf_type @ SV78 @ set_type )
| ~ ( member @ SV78 @ SV26 )
| ( member @ SV78 @ SV55 ) )
= $true )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $false )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(546,plain,
! [SV26: $i,SV55: $i] :
( ( ( ~ ( ilf_type @ ( sK11_SY176 @ SV55 @ SV26 ) @ set_type )
| ~ ( member @ ( sK11_SY176 @ SV55 @ SV26 ) @ SV26 )
| ( member @ ( sK11_SY176 @ SV55 @ SV26 ) @ SV55 ) )
= $false )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[525]) ).
thf(547,plain,
! [SV29: $i] :
( ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( relation_like @ SV29 )
= $false )
| ( ( ilf_type @ SV29 @ binary_relation_type )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(548,plain,
! [SV57: $i,SV32: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) )
| ~ ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) ) )
= $false )
| ( ( empty @ SV57 )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(549,plain,
! [SV58: $i,SV34: $i,SV79: $i] :
( ( ( ~ ( ilf_type @ SV79 @ set_type )
| ~ ( member @ SV79 @ SV34 )
| ( member @ SV79 @ SV58 ) )
= $true )
| ( ( subset @ SV34 @ SV58 )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(550,plain,
! [SV34: $i,SV58: $i] :
( ( ( ~ ( ilf_type @ ( sK12_SY179 @ SV58 @ SV34 ) @ set_type )
| ~ ( member @ ( sK12_SY179 @ SV58 @ SV34 ) @ SV34 )
| ( member @ ( sK12_SY179 @ SV58 @ SV34 ) @ SV58 ) )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[531]) ).
thf(551,plain,
! [SV38: $i,SV2: $i,SV72: $i,SV61: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY192: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY192 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY192 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY192 @ SV72 ) @ SV38 ) ) )
| ~ ( ~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY193 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY193 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY193 @ SV72 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) ) ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(552,plain,
! [SV3: $i,SV62: $i,SV39: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) ) )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(553,plain,
! [SV62: $i,SV3: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(554,plain,
! [SV41: $i,SV5: $i,SV77: $i] :
( ( ( ~ ( ilf_type @ SV77 @ set_type ) )
= $true )
| ( ( ! [SY196: $i] :
( ~ ( ilf_type @ SY196 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV5 )
| ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV41 )
| ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV5 ) ) ) ) )
= $true )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(555,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( ilf_type @ ( sK10_SY162 @ SV41 @ SV5 ) @ set_type ) )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(556,plain,
! [SV5: $i,SV41: $i] :
( ( ( ! [SY197: $i] :
( ~ ( ilf_type @ SY197 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ SY197 ) @ SV5 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ SY197 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ SY197 ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ SY197 ) @ SV5 ) ) ) ) )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(557,plain,
! [SV73: $i,SV7: $i,SV64: $i,SV43: $i,SV80: $i] :
( ( ( ~ ( ilf_type @ SV80 @ ( relation_type @ SV43 @ SV64 ) )
| ( ( compose5 @ SV7 @ SV43 @ SV64 @ SV73 @ SV80 )
= ( compose @ SV73 @ SV80 ) ) )
= $true )
| ( ( ilf_type @ SV73 @ ( relation_type @ SV7 @ SV43 ) )
= $false )
| ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(558,plain,
! [SV74: $i,SV11: $i,SV65: $i,SV45: $i,SV81: $i] :
( ( ( ~ ( ilf_type @ SV81 @ ( relation_type @ SV45 @ SV65 ) )
| ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SV65 @ SV74 @ SV81 ) @ ( relation_type @ SV11 @ SV65 ) ) )
= $true )
| ( ( ilf_type @ SV74 @ ( relation_type @ SV11 @ SV45 ) )
= $false )
| ( ( ilf_type @ SV65 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(559,plain,
! [SV21: $i,SV71: $i] :
( ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ~ ! [SY188: $i] :
~ ~ ( ~ ( ilf_type @ SY188 @ set_type )
| ~ ~ ! [SY189: $i] :
~ ~ ( ~ ( ilf_type @ SY189 @ set_type )
| ( SV71
!= ( ordered_pair @ SY188 @ SY189 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(560,plain,
! [SV21: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ SV82 @ set_type )
| ~ ~ ! [SY198: $i] :
~ ~ ( ~ ( ilf_type @ SY198 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SY198 ) ) ) ) )
= $true )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(561,plain,
! [SV55: $i,SV26: $i,SV78: $i] :
( ( ( ~ ( ilf_type @ SV78 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV78 @ SV26 )
| ( member @ SV78 @ SV55 ) )
= $true )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $false )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(562,plain,
! [SV26: $i,SV55: $i] :
( ( ( ~ ( ilf_type @ ( sK11_SY176 @ SV55 @ SV26 ) @ set_type ) )
= $false )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(563,plain,
! [SV26: $i,SV55: $i] :
( ( ( ~ ( member @ ( sK11_SY176 @ SV55 @ SV26 ) @ SV26 )
| ( member @ ( sK11_SY176 @ SV55 @ SV26 ) @ SV55 ) )
= $false )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(564,plain,
! [SV57: $i,SV32: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) ) )
= $false )
| ( ( empty @ SV57 )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(565,plain,
! [SV57: $i,SV32: $i] :
( ( ( ~ ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) ) )
= $false )
| ( ( empty @ SV57 )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(566,plain,
! [SV58: $i,SV34: $i,SV79: $i] :
( ( ( ~ ( ilf_type @ SV79 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV79 @ SV34 )
| ( member @ SV79 @ SV58 ) )
= $true )
| ( ( subset @ SV34 @ SV58 )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(567,plain,
! [SV34: $i,SV58: $i] :
( ( ( ~ ( ilf_type @ ( sK12_SY179 @ SV58 @ SV34 ) @ set_type ) )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(568,plain,
! [SV34: $i,SV58: $i] :
( ( ( ~ ( member @ ( sK12_SY179 @ SV58 @ SV34 ) @ SV34 )
| ( member @ ( sK12_SY179 @ SV58 @ SV34 ) @ SV58 ) )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(569,plain,
! [SV38: $i,SV2: $i,SV72: $i,SV61: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY192: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY192 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY192 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY192 @ SV72 ) @ SV38 ) ) ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(570,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i] :
( ( ( ~ ( ~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY193 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY193 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY193 @ SV72 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) ) ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(571,plain,
! [SV3: $i,SV62: $i,SV39: $i] :
( ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) ) )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(572,plain,
! [SV62: $i,SV3: $i,SV39: $i] :
( ( ( ~ ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(573,plain,
! [SV41: $i,SV5: $i,SV77: $i] :
( ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( ! [SY196: $i] :
( ~ ( ilf_type @ SY196 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV5 )
| ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV41 )
| ( member @ ( ordered_pair @ SV77 @ SY196 ) @ SV5 ) ) ) ) )
= $true )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(574,plain,
! [SV5: $i,SV41: $i] :
( ( ( ilf_type @ ( sK10_SY162 @ SV41 @ SV5 ) @ set_type )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(575,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ( ilf_type @ ( sK13_SY197 @ SV5 @ SV41 ) @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) ) ) )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[556]) ).
thf(576,plain,
! [SV73: $i,SV7: $i,SV64: $i,SV43: $i,SV80: $i] :
( ( ( ~ ( ilf_type @ SV80 @ ( relation_type @ SV43 @ SV64 ) ) )
= $true )
| ( ( ( compose5 @ SV7 @ SV43 @ SV64 @ SV73 @ SV80 )
= ( compose @ SV73 @ SV80 ) )
= $true )
| ( ( ilf_type @ SV73 @ ( relation_type @ SV7 @ SV43 ) )
= $false )
| ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(577,plain,
! [SV74: $i,SV11: $i,SV65: $i,SV45: $i,SV81: $i] :
( ( ( ~ ( ilf_type @ SV81 @ ( relation_type @ SV45 @ SV65 ) ) )
= $true )
| ( ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SV65 @ SV74 @ SV81 ) @ ( relation_type @ SV11 @ SV65 ) )
= $true )
| ( ( ilf_type @ SV74 @ ( relation_type @ SV11 @ SV45 ) )
= $false )
| ( ( ilf_type @ SV65 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(578,plain,
! [SV21: $i,SV71: $i] :
( ( ( ! [SY188: $i] :
~ ~ ( ~ ( ilf_type @ SY188 @ set_type )
| ~ ~ ! [SY189: $i] :
~ ~ ( ~ ( ilf_type @ SY189 @ set_type )
| ( SV71
!= ( ordered_pair @ SY188 @ SY189 ) ) ) ) )
= $false )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(579,plain,
! [SV21: $i,SV82: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV82 @ set_type )
| ~ ~ ! [SY198: $i] :
~ ~ ( ~ ( ilf_type @ SY198 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SY198 ) ) ) ) )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(580,plain,
! [SV55: $i,SV26: $i,SV78: $i] :
( ( ( ilf_type @ SV78 @ set_type )
= $false )
| ( ( ~ ( member @ SV78 @ SV26 )
| ( member @ SV78 @ SV55 ) )
= $true )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $false )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(581,plain,
! [SV26: $i,SV55: $i] :
( ( ( ilf_type @ ( sK11_SY176 @ SV55 @ SV26 ) @ set_type )
= $true )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(582,plain,
! [SV26: $i,SV55: $i] :
( ( ( ~ ( member @ ( sK11_SY176 @ SV55 @ SV26 ) @ SV26 ) )
= $false )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(583,plain,
! [SV26: $i,SV55: $i] :
( ( ( member @ ( sK11_SY176 @ SV55 @ SV26 ) @ SV55 )
= $false )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(584,plain,
! [SV57: $i,SV32: $i] :
( ( ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
| ( member @ SV32 @ SV57 ) )
= $true )
| ( ( empty @ SV57 )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(585,plain,
! [SV57: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV57 )
| ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) )
= $true )
| ( ( empty @ SV57 )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(586,plain,
! [SV58: $i,SV34: $i,SV79: $i] :
( ( ( ilf_type @ SV79 @ set_type )
= $false )
| ( ( ~ ( member @ SV79 @ SV34 )
| ( member @ SV79 @ SV58 ) )
= $true )
| ( ( subset @ SV34 @ SV58 )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(587,plain,
! [SV34: $i,SV58: $i] :
( ( ( ilf_type @ ( sK12_SY179 @ SV58 @ SV34 ) @ set_type )
= $true )
| ( ( subset @ SV34 @ SV58 )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(588,plain,
! [SV34: $i,SV58: $i] :
( ( ( ~ ( member @ ( sK12_SY179 @ SV58 @ SV34 ) @ SV34 ) )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(589,plain,
! [SV34: $i,SV58: $i] :
( ( ( member @ ( sK12_SY179 @ SV58 @ SV34 ) @ SV58 )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(590,plain,
! [SV38: $i,SV2: $i,SV72: $i,SV61: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
| ~ ! [SY192: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY192 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY192 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY192 @ SV72 ) @ SV38 ) ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(591,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i] :
( ( ( ~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY193 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY193 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY193 @ SV72 ) @ SV38 ) )
| ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(592,plain,
! [SV62: $i,SV3: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $false )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(593,plain,
! [SV62: $i,SV3: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ SV3 )
| ( SV39 != SV62 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(594,plain,
! [SV41: $i,SV5: $i,SV77: $i,SV83: $i] :
( ( ( ~ ( ilf_type @ SV83 @ set_type )
| ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 ) ) ) )
= $true )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(595,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ( ilf_type @ ( sK13_SY197 @ SV5 @ SV41 ) @ set_type ) )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[575]) ).
thf(596,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) ) ) )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[575]) ).
thf(597,plain,
! [SV73: $i,SV7: $i,SV64: $i,SV43: $i,SV80: $i] :
( ( ( ilf_type @ SV80 @ ( relation_type @ SV43 @ SV64 ) )
= $false )
| ( ( ( compose5 @ SV7 @ SV43 @ SV64 @ SV73 @ SV80 )
= ( compose @ SV73 @ SV80 ) )
= $true )
| ( ( ilf_type @ SV73 @ ( relation_type @ SV7 @ SV43 ) )
= $false )
| ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV7 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(598,plain,
! [SV74: $i,SV11: $i,SV65: $i,SV45: $i,SV81: $i] :
( ( ( ilf_type @ SV81 @ ( relation_type @ SV45 @ SV65 ) )
= $false )
| ( ( ilf_type @ ( compose5 @ SV11 @ SV45 @ SV65 @ SV74 @ SV81 ) @ ( relation_type @ SV11 @ SV65 ) )
= $true )
| ( ( ilf_type @ SV74 @ ( relation_type @ SV11 @ SV45 ) )
= $false )
| ( ( ilf_type @ SV65 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(599,plain,
! [SV71: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ ( sK14_SY188 @ SV21 @ SV71 ) @ set_type )
| ~ ~ ! [SY199: $i] :
~ ~ ( ~ ( ilf_type @ SY199 @ set_type )
| ( SV71
!= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ SY199 ) ) ) ) )
= $false )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[578]) ).
thf(600,plain,
! [SV21: $i,SV82: $i] :
( ( ( ~ ( ilf_type @ SV82 @ set_type )
| ~ ~ ! [SY198: $i] :
~ ~ ( ~ ( ilf_type @ SY198 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SY198 ) ) ) )
= $true )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(601,plain,
! [SV55: $i,SV26: $i,SV78: $i] :
( ( ( ~ ( member @ SV78 @ SV26 ) )
= $true )
| ( ( member @ SV78 @ SV55 )
= $true )
| ( ( ilf_type @ SV78 @ set_type )
= $false )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $false )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(602,plain,
! [SV26: $i,SV55: $i] :
( ( ( member @ ( sK11_SY176 @ SV55 @ SV26 ) @ SV26 )
= $true )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $true )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(603,plain,
! [SV57: $i,SV32: $i] :
( ( ( ~ ( ilf_type @ SV32 @ ( member_type @ SV57 ) ) )
= $true )
| ( ( member @ SV32 @ SV57 )
= $true )
| ( ( empty @ SV57 )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(604,plain,
! [SV57: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV57 ) )
= $true )
| ( ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
= $true )
| ( ( empty @ SV57 )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(605,plain,
! [SV58: $i,SV34: $i,SV79: $i] :
( ( ( ~ ( member @ SV79 @ SV34 ) )
= $true )
| ( ( member @ SV79 @ SV58 )
= $true )
| ( ( ilf_type @ SV79 @ set_type )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(606,plain,
! [SV34: $i,SV58: $i] :
( ( ( member @ ( sK12_SY179 @ SV58 @ SV34 ) @ SV34 )
= $true )
| ( ( subset @ SV34 @ SV58 )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(607,plain,
! [SV38: $i,SV2: $i,SV72: $i,SV61: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) ) )
= $true )
| ( ( ~ ! [SY192: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY192 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY192 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY192 @ SV72 ) @ SV38 ) ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(608,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i] :
( ( ( ~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY193 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY193 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY193 @ SV72 ) @ SV38 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(609,plain,
! [SV62: $i,SV3: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ SV3 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $false )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(610,plain,
! [SV3: $i,SV62: $i,SV39: $i] :
( ( ( SV39 != SV62 )
= $false )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $false )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(611,plain,
! [SV62: $i,SV3: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ SV3 ) )
= $true )
| ( ( SV39 != SV62 )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(612,plain,
! [SV41: $i,SV5: $i,SV77: $i,SV83: $i] :
( ( ( ~ ( ilf_type @ SV83 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 ) ) ) )
= $true )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(613,plain,
! [SV41: $i,SV5: $i] :
( ( ( ilf_type @ ( sK13_SY197 @ SV5 @ SV41 ) @ set_type )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(614,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(615,plain,
! [SV71: $i,SV21: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK14_SY188 @ SV21 @ SV71 ) @ set_type )
| ~ ~ ! [SY199: $i] :
~ ~ ( ~ ( ilf_type @ SY199 @ set_type )
| ( SV71
!= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ SY199 ) ) ) ) )
= $true )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(616,plain,
! [SV21: $i,SV82: $i] :
( ( ( ~ ( ilf_type @ SV82 @ set_type ) )
= $true )
| ( ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ( ilf_type @ SY198 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SY198 ) ) ) )
= $true )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(617,plain,
! [SV55: $i,SV26: $i,SV78: $i] :
( ( ( member @ SV78 @ SV26 )
= $false )
| ( ( member @ SV78 @ SV55 )
= $true )
| ( ( ilf_type @ SV78 @ set_type )
= $false )
| ( ( member @ SV26 @ ( power_set @ SV55 ) )
= $false )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ilf_type @ SV26 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(618,plain,
! [SV57: $i,SV32: $i] :
( ( ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
= $false )
| ( ( member @ SV32 @ SV57 )
= $true )
| ( ( empty @ SV57 )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(619,plain,
! [SV57: $i,SV32: $i] :
( ( ( member @ SV32 @ SV57 )
= $false )
| ( ( ilf_type @ SV32 @ ( member_type @ SV57 ) )
= $true )
| ( ( empty @ SV57 )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV32 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(620,plain,
! [SV58: $i,SV34: $i,SV79: $i] :
( ( ( member @ SV79 @ SV34 )
= $false )
| ( ( member @ SV79 @ SV58 )
= $true )
| ( ( ilf_type @ SV79 @ set_type )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(621,plain,
! [SV38: $i,SV2: $i,SV72: $i,SV61: $i] :
( ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ~ ! [SY192: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY192 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY192 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY192 @ SV72 ) @ SV38 ) ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(622,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i] :
( ( ( ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY193 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY193 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY193 @ SV72 ) @ SV38 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(623,plain,
! [SV62: $i,SV3: $i,SV39: $i] :
( ( ( member @ SV39 @ SV3 )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $false )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(624,plain,
! [SV3: $i,SV62: $i,SV39: $i] :
( ( ( SV39 = SV62 )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $false )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(625,plain,
! [SV62: $i,SV3: $i,SV39: $i] :
( ( ( member @ SV39 @ SV3 )
= $false )
| ( ( SV39 != SV62 )
= $true )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(626,plain,
! [SV41: $i,SV5: $i,SV77: $i,SV83: $i] :
( ( ( ilf_type @ SV83 @ set_type )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 ) ) ) )
= $true )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(627,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(628,plain,
! [SV71: $i,SV21: $i] :
( ( ( ~ ( ilf_type @ ( sK14_SY188 @ SV21 @ SV71 ) @ set_type )
| ~ ~ ! [SY199: $i] :
~ ~ ( ~ ( ilf_type @ SY199 @ set_type )
| ( SV71
!= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ SY199 ) ) ) )
= $false )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(629,plain,
! [SV21: $i,SV82: $i] :
( ( ( ilf_type @ SV82 @ set_type )
= $false )
| ( ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ( ilf_type @ SY198 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SY198 ) ) ) )
= $true )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(630,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i] :
( ( ( ! [SY192: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY192 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY192 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY192 @ SV72 ) @ SV38 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(631,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i] :
( ( ( ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( ilf_type @ SY193 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SY193 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SY193 @ SV72 ) @ SV38 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(632,plain,
! [SV3: $i,SV62: $i,SV39: $i] :
( ( ( SV39 = SV62 )
= $false )
| ( ( member @ SV39 @ SV3 )
= $false )
| ( ( member @ ( ordered_pair @ SV39 @ SV62 ) @ ( identity_relation_of @ SV3 ) )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(633,plain,
! [SV41: $i,SV5: $i,SV83: $i,SV77: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 ) )
| ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 ) ) )
= $false )
| ( ( ilf_type @ SV83 @ set_type )
= $false )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(634,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(635,plain,
! [SV71: $i,SV21: $i] :
( ( ( ~ ( ilf_type @ ( sK14_SY188 @ SV21 @ SV71 ) @ set_type ) )
= $false )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(636,plain,
! [SV21: $i,SV71: $i] :
( ( ( ~ ~ ! [SY199: $i] :
~ ~ ( ~ ( ilf_type @ SY199 @ set_type )
| ( SV71
!= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ SY199 ) ) ) )
= $false )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(637,plain,
! [SV82: $i,SV21: $i] :
( ( ( ~ ! [SY198: $i] :
~ ~ ( ~ ( ilf_type @ SY198 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SY198 ) ) ) )
= $false )
| ( ( ilf_type @ SV82 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(638,plain,
! [SV61: $i,SV2: $i,SV72: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ilf_type @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ SV72 ) @ SV38 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[630]) ).
thf(639,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i,SV84: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ilf_type @ SV84 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SV84 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SV84 @ SV72 ) @ SV38 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(640,plain,
! [SV41: $i,SV5: $i,SV83: $i,SV77: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 ) ) )
= $false )
| ( ( ilf_type @ SV83 @ set_type )
= $false )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(641,plain,
! [SV5: $i,SV41: $i,SV83: $i,SV77: $i] :
( ( ( ~ ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 ) ) )
= $false )
| ( ( ilf_type @ SV83 @ set_type )
= $false )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(642,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(643,plain,
! [SV5: $i,SV41: $i] :
( ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
= $false )
| ( ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(644,plain,
! [SV71: $i,SV21: $i] :
( ( ( ilf_type @ ( sK14_SY188 @ SV21 @ SV71 ) @ set_type )
= $true )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(645,plain,
! [SV21: $i,SV71: $i] :
( ( ( ~ ! [SY199: $i] :
~ ~ ( ~ ( ilf_type @ SY199 @ set_type )
| ( SV71
!= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ SY199 ) ) ) )
= $true )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[636]) ).
thf(646,plain,
! [SV82: $i,SV21: $i] :
( ( ( ! [SY198: $i] :
~ ~ ( ~ ( ilf_type @ SY198 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SY198 ) ) ) )
= $true )
| ( ( ilf_type @ SV82 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(647,plain,
! [SV61: $i,SV2: $i,SV72: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ilf_type @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ SV72 ) @ SV38 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[638]) ).
thf(648,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i,SV84: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ilf_type @ SV84 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SV84 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SV84 @ SV72 ) @ SV38 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(649,plain,
! [SV41: $i,SV5: $i,SV83: $i,SV77: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 ) )
= $true )
| ( ( ilf_type @ SV83 @ set_type )
= $false )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[640]) ).
thf(650,plain,
! [SV5: $i,SV41: $i,SV83: $i,SV77: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 )
| ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 ) )
= $true )
| ( ( ilf_type @ SV83 @ set_type )
= $false )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(651,plain,
! [SV5: $i,SV41: $i] :
( ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
= $true )
| ( ( ~ ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(652,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(653,plain,
! [SV21: $i,SV71: $i] :
( ( ( ! [SY199: $i] :
~ ~ ( ~ ( ilf_type @ SY199 @ set_type )
| ( SV71
!= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ SY199 ) ) ) )
= $false )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(654,plain,
! [SV82: $i,SV21: $i,SV85: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ SV85 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SV85 ) ) ) )
= $true )
| ( ( ilf_type @ SV82 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(655,plain,
! [SV61: $i,SV2: $i,SV72: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ SV72 ) @ SV38 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(656,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i,SV84: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ SV84 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SV84 ) @ SV2 ) )
| ~ ( member @ ( ordered_pair @ SV84 @ SV72 ) @ SV38 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(657,plain,
! [SV41: $i,SV5: $i,SV83: $i,SV77: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 )
= $true )
| ( ( ilf_type @ SV83 @ set_type )
= $false )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(658,plain,
! [SV5: $i,SV41: $i,SV83: $i,SV77: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 )
= $true )
| ( ( ilf_type @ SV83 @ set_type )
= $false )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(659,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
| ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(660,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(661,plain,
! [SV5: $i,SV41: $i] :
( ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
= $false )
| ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(662,plain,
! [SV71: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ ( sK16_SY199 @ SV21 @ SV71 ) @ set_type )
| ( SV71
!= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ ( sK16_SY199 @ SV21 @ SV71 ) ) ) ) )
= $false )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[653]) ).
thf(663,plain,
! [SV82: $i,SV21: $i,SV85: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV85 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SV85 ) ) ) )
= $false )
| ( ( ilf_type @ SV82 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(664,plain,
! [SV61: $i,SV2: $i,SV72: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) ) @ SV2 ) ) )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[655]) ).
thf(665,plain,
! [SV61: $i,SV2: $i,SV72: $i,SV38: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ SV72 ) @ SV38 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[655]) ).
thf(666,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i,SV84: $i] :
( ( ( ~ ~ ( ~ ( ilf_type @ SV84 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SV84 ) @ SV2 ) ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV84 @ SV72 ) @ SV38 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(667,plain,
! [SV41: $i,SV5: $i,SV83: $i,SV77: $i] :
( ( ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 )
= $false )
| ( ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 )
= $true )
| ( ( ilf_type @ SV83 @ set_type )
= $false )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(668,plain,
! [SV5: $i,SV41: $i,SV83: $i,SV77: $i] :
( ( ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV41 )
= $false )
| ( ( member @ ( ordered_pair @ SV77 @ SV83 ) @ SV5 )
= $true )
| ( ( ilf_type @ SV83 @ set_type )
= $false )
| ( ( ilf_type @ SV77 @ set_type )
= $false )
| ( ( SV5 = SV41 )
= $false )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(669,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 ) )
= $false )
| ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[659]) ).
thf(670,plain,
! [SV5: $i,SV41: $i] :
( ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
= $false )
| ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[659]) ).
thf(671,plain,
! [SV5: $i,SV41: $i] :
( ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
= $true )
| ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
= $false )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(672,plain,
! [SV71: $i,SV21: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK16_SY199 @ SV21 @ SV71 ) @ set_type )
| ( SV71
!= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ ( sK16_SY199 @ SV21 @ SV71 ) ) ) ) )
= $true )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(673,plain,
! [SV82: $i,SV21: $i,SV85: $i] :
( ( ( ~ ( ilf_type @ SV85 @ set_type )
| ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SV85 ) ) )
= $true )
| ( ( ilf_type @ SV82 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(674,plain,
! [SV61: $i,SV2: $i,SV72: $i,SV38: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) ) @ SV2 ) ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[664]) ).
thf(675,plain,
! [SV61: $i,SV2: $i,SV72: $i,SV38: $i] :
( ( ( member @ ( ordered_pair @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ SV72 ) @ SV38 )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[665]) ).
thf(676,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i,SV84: $i] :
( ( ( ~ ( ~ ( ilf_type @ SV84 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SV84 ) @ SV2 ) ) )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV84 @ SV72 ) @ SV38 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(677,plain,
! [SV5: $i,SV41: $i] :
( ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV41 )
= $true )
| ( ( member @ ( ordered_pair @ ( sK10_SY162 @ SV41 @ SV5 ) @ ( sK13_SY197 @ SV5 @ SV41 ) ) @ SV5 )
= $true )
| ( ( SV5 = SV41 )
= $true )
| ( ( ilf_type @ SV41 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV5 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(678,plain,
! [SV71: $i,SV21: $i] :
( ( ( ~ ( ilf_type @ ( sK16_SY199 @ SV21 @ SV71 ) @ set_type )
| ( SV71
!= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ ( sK16_SY199 @ SV21 @ SV71 ) ) ) )
= $false )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(679,plain,
! [SV82: $i,SV21: $i,SV85: $i] :
( ( ( ~ ( ilf_type @ SV85 @ set_type ) )
= $true )
| ( ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SV85 ) )
= $true )
| ( ( ilf_type @ SV82 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(680,plain,
! [SV61: $i,SV2: $i,SV72: $i,SV38: $i] :
( ( ( ~ ( ilf_type @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) ) @ SV2 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(681,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i,SV84: $i] :
( ( ( ~ ( ilf_type @ SV84 @ set_type )
| ~ ( member @ ( ordered_pair @ SV61 @ SV84 ) @ SV2 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV84 @ SV72 ) @ SV38 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[676]) ).
thf(682,plain,
! [SV71: $i,SV21: $i] :
( ( ( ~ ( ilf_type @ ( sK16_SY199 @ SV21 @ SV71 ) @ set_type ) )
= $false )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(683,plain,
! [SV21: $i,SV71: $i] :
( ( ( SV71
!= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ ( sK16_SY199 @ SV21 @ SV71 ) ) )
= $false )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(684,plain,
! [SV82: $i,SV21: $i,SV85: $i] :
( ( ( ilf_type @ SV85 @ set_type )
= $false )
| ( ( ( sK8_SY132 @ SV21 )
!= ( ordered_pair @ SV82 @ SV85 ) )
= $true )
| ( ( ilf_type @ SV82 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(685,plain,
! [SV61: $i,SV2: $i,SV72: $i,SV38: $i] :
( ( ( ~ ( ilf_type @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ set_type ) )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(686,plain,
! [SV2: $i,SV72: $i,SV38: $i,SV61: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV61 @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) ) @ SV2 ) )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(687,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i,SV84: $i] :
( ( ( ~ ( ilf_type @ SV84 @ set_type ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV61 @ SV84 ) @ SV2 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV84 @ SV72 ) @ SV38 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(688,plain,
! [SV71: $i,SV21: $i] :
( ( ( ilf_type @ ( sK16_SY199 @ SV21 @ SV71 ) @ set_type )
= $true )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(689,plain,
! [SV21: $i,SV71: $i] :
( ( ( SV71
= ( ordered_pair @ ( sK14_SY188 @ SV21 @ SV71 ) @ ( sK16_SY199 @ SV21 @ SV71 ) ) )
= $true )
| ( ( member @ SV71 @ SV21 )
= $false )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[683]) ).
thf(690,plain,
! [SV85: $i,SV82: $i,SV21: $i] :
( ( ( ( sK8_SY132 @ SV21 )
= ( ordered_pair @ SV82 @ SV85 ) )
= $false )
| ( ( ilf_type @ SV85 @ set_type )
= $false )
| ( ( ilf_type @ SV82 @ set_type )
= $false )
| ( ( relation_like @ SV21 )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(691,plain,
! [SV61: $i,SV2: $i,SV72: $i,SV38: $i] :
( ( ( ilf_type @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) @ set_type )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(692,plain,
! [SV2: $i,SV72: $i,SV38: $i,SV61: $i] :
( ( ( member @ ( ordered_pair @ SV61 @ ( sK15_SY192 @ SV38 @ SV72 @ SV2 @ SV61 ) ) @ SV2 )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(693,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV61: $i,SV84: $i] :
( ( ( ilf_type @ SV84 @ set_type )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV61 @ SV84 ) @ SV2 ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV84 @ SV72 ) @ SV38 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(694,plain,
! [SV38: $i,SV72: $i,SV2: $i,SV84: $i,SV61: $i] :
( ( ( member @ ( ordered_pair @ SV61 @ SV84 ) @ SV2 )
= $false )
| ( ( ilf_type @ SV84 @ set_type )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV84 @ SV72 ) @ SV38 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(695,plain,
! [SV2: $i,SV61: $i,SV38: $i,SV72: $i,SV84: $i] :
( ( ( member @ ( ordered_pair @ SV84 @ SV72 ) @ SV38 )
= $false )
| ( ( ilf_type @ SV84 @ set_type )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV84 ) @ SV2 )
= $false )
| ( ( member @ ( ordered_pair @ SV61 @ SV72 ) @ ( compose @ SV2 @ SV38 ) )
= $true )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV38 @ binary_relation_type )
= $false )
| ( ( ilf_type @ SV2 @ binary_relation_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(696,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[122,695,692,691,690,689,688,677,675,671,670,668,667,661,644,632,624,623,620,619,618,617,613,606,602,598,597,589,587,583,581,574,547,544,543,541,539,527,526,521,520,517,515,514,513,512,510,475,469,458,457,452,448,436,435,422,397,391,388,381,379,365,362,356,351,288,275,271,270,267,248,245,162]) ).
thf(697,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET678+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 14:47:36 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.63/1.19
% 5.63/1.19 No.of.Axioms: 38
% 5.63/1.19
% 5.63/1.19 Length.of.Defs: 0
% 5.63/1.19
% 5.63/1.19 Contains.Choice.Funs: false
% 5.63/1.19 .........................
% 5.63/1.19
% 5.63/1.19 ********************************
% 5.63/1.19 * All subproblems solved! *
% 5.63/1.19 ********************************
% 5.63/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:39,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:696,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.63/1.19
% 5.63/1.19 %**** Beginning of derivation protocol ****
% 5.63/1.19 % SZS output start CNFRefutation
% See solution above
% 1.16/1.20
% 1.16/1.20 %**** End of derivation protocol ****
% 1.16/1.20 %**** no. of clauses in derivation: 697 ****
% 1.16/1.20 %**** clause counter: 696 ****
% 1.16/1.20
% 1.16/1.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:39,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:696,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------