%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET646+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 : n005.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 10:40:43 AM UTC 2026
% Result : Theorem 38.66s 6.75s
% Output : CNFRefutation 38.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of formulae : 590 ( 167 unt; 0 typ; 0 def)
% Number of atoms : 6654 (1972 equ; 0 cnn)
% Maximal formula atoms : 7 ( 11 avg)
% Number of connectives : 13654 (2408 ~;2610 |; 90 &;8376 @)
% ( 26 <=>; 144 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 7 con; 0-2 aty)
% Number of variables : 1621 ( 0 ^;1611 !; 10 ?;1621 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cross_product,type,
cross_product: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_ilf_type,type,
ilf_type: $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_member_type,type,
member_type: $i > $i ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_relation_like,type,
relation_like: $i > $o ).
thf(tp_relation_type,type,
relation_type: $i > $i > $i ).
thf(tp_sK10_D,type,
sK10_D: $i > $i > $i ).
thf(tp_sK11_D,type,
sK11_D: $i > $i > $i ).
thf(tp_sK12_D,type,
sK12_D: $i > $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i ).
thf(tp_sK14_E,type,
sK14_E: $i > $i > $i ).
thf(tp_sK15_D,type,
sK15_D: $i > $i > $i ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY65,type,
sK2_SY65: $i ).
thf(tp_sK3_SY68,type,
sK3_SY68: $i ).
thf(tp_sK4_SY70,type,
sK4_SY70: $i ).
thf(tp_sK5_D,type,
sK5_D: $i > $i > $i ).
thf(tp_sK6_SY71,type,
sK6_SY71: $i > $i > $i ).
thf(tp_sK7_C,type,
sK7_C: $i > $i ).
thf(tp_sK8_C,type,
sK8_C: $i > $i ).
thf(tp_sK9_C,type,
sK9_C: $i > $i ).
thf(tp_set_type,type,
set_type: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_type,type,
subset_type: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [B: $i] : ( ilf_type @ B @ set_type ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
thf(2,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',p24) ).
thf(3,axiom,
! [B: $i] :
( ( ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( relation_like @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
thf(4,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',p22) ).
thf(5,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',p21) ).
thf(6,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',p20) ).
thf(7,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',p19) ).
thf(8,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',p18) ).
thf(9,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',p17) ).
thf(10,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).
thf(11,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',p15) ).
thf(12,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( B = C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
thf(13,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
thf(14,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',p12) ).
thf(15,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( unordered_pair @ B @ C )
= ( unordered_pair @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
thf(16,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( unordered_pair @ B @ C ) @ set_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
thf(17,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',p9) ).
thf(18,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',p8) ).
thf(19,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 @ set_type )
=> ! [F: $i] :
( ( ilf_type @ F @ set_type )
=> ( ( F
= ( ordered_pair @ D @ E ) )
<=> ( F
= ( unordered_pair @ ( unordered_pair @ D @ E ) @ ( singleton @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
thf(20,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( singleton @ B ) @ set_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
thf(21,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( D
= ( singleton @ C ) )
<=> ! [E: $i] :
( ( ilf_type @ E @ set_type )
=> ( ( member @ E @ D )
<=> ( E = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
thf(22,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',p4) ).
thf(23,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',p3) ).
thf(24,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 @ set_type )
=> ( ( member @ ( ordered_pair @ B @ C ) @ ( cross_product @ D @ E ) )
<=> ( ( member @ B @ D )
& ( member @ C @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
thf(25,axiom,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ ( singleton @ B ) @ C )
<=> ( member @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
thf(26,conjecture,
! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ set_type )
=> ( ( ( member @ D @ B )
& ( member @ E @ C ) )
=> ( ilf_type @ ( singleton @ ( ordered_pair @ D @ E ) ) @ ( relation_type @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_8) ).
thf(27,negated_conjecture,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ! [E: $i] :
( ( ilf_type @ E @ set_type )
=> ( ( ( member @ D @ B )
& ( member @ E @ C ) )
=> ( ilf_type @ ( singleton @ ( ordered_pair @ D @ E ) ) @ ( relation_type @ B @ C ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[26]) ).
thf(28,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 @ set_type )
=> ( ( ( member @ D @ B )
& ( member @ E @ C ) )
=> ( ilf_type @ ( singleton @ ( ordered_pair @ D @ E ) ) @ ( relation_type @ B @ C ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[27]) ).
thf(29,plain,
( ( ! [B: $i] : ( ilf_type @ B @ set_type ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(30,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)],[2]) ).
thf(31,plain,
( ( ! [B: $i] :
( ( ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( relation_like @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(32,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)],[4]) ).
thf(33,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)],[5]) ).
thf(34,plain,
( ( ! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ? [C: $i] : ( ilf_type @ C @ ( member_type @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(35,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)],[7]) ).
thf(36,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)],[8]) ).
thf(37,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)],[9]) ).
thf(38,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( subset @ B @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(39,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)],[11]) ).
thf(40,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( B = C )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( subset_type @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(42,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)],[14]) ).
thf(43,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( unordered_pair @ B @ C )
= ( unordered_pair @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ilf_type @ ( unordered_pair @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(45,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)],[17]) ).
thf(46,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)],[18]) ).
thf(47,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 @ set_type )
=> ! [F: $i] :
( ( ilf_type @ F @ set_type )
=> ( ( F
= ( ordered_pair @ D @ E ) )
<=> ( F
= ( unordered_pair @ ( unordered_pair @ D @ E ) @ ( singleton @ D ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(48,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( singleton @ B ) @ set_type ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(49,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( D
= ( singleton @ C ) )
<=> ! [E: $i] :
( ( ilf_type @ E @ set_type )
=> ( ( member @ E @ D )
<=> ( E = C ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(50,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)],[22]) ).
thf(51,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)],[23]) ).
thf(52,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 @ set_type )
=> ( ( member @ ( ordered_pair @ B @ C ) @ ( cross_product @ D @ E ) )
<=> ( ( member @ B @ D )
& ( member @ C @ E ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(53,plain,
( ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( subset @ ( singleton @ B ) @ C )
<=> ( member @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(54,plain,
( ( ( ilf_type @ sK1_B @ set_type )
=> ! [SY65: $i] :
( ( ilf_type @ SY65 @ set_type )
=> ! [SY66: $i] :
( ( ilf_type @ SY66 @ set_type )
=> ! [SY67: $i] :
( ( ilf_type @ SY67 @ set_type )
=> ( ( ( member @ SY66 @ sK1_B )
& ( member @ SY67 @ SY65 ) )
=> ( ilf_type @ ( singleton @ ( ordered_pair @ SY66 @ SY67 ) ) @ ( relation_type @ sK1_B @ SY65 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(55,plain,
( ( ilf_type @ sK1_B @ set_type )
= $true ),
inference(standard_cnf,[status(thm)],[54]) ).
thf(56,plain,
( ( ! [SY65: $i] :
( ( ilf_type @ SY65 @ set_type )
=> ! [SY66: $i] :
( ( ilf_type @ SY66 @ set_type )
=> ! [SY67: $i] :
( ( ilf_type @ SY67 @ set_type )
=> ( ( ( member @ SY66 @ sK1_B )
& ( member @ SY67 @ SY65 ) )
=> ( ilf_type @ ( singleton @ ( ordered_pair @ SY66 @ SY67 ) ) @ ( relation_type @ sK1_B @ SY65 ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[54]) ).
thf(57,plain,
( ( ~ ! [SY65: $i] :
( ( ilf_type @ SY65 @ set_type )
=> ! [SY66: $i] :
( ( ilf_type @ SY66 @ set_type )
=> ! [SY67: $i] :
( ( ilf_type @ SY67 @ set_type )
=> ( ( ( member @ SY66 @ sK1_B )
& ( member @ SY67 @ SY65 ) )
=> ( ilf_type @ ( singleton @ ( ordered_pair @ SY66 @ SY67 ) ) @ ( relation_type @ sK1_B @ SY65 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[56]) ).
thf(58,plain,
( ( ( ilf_type @ sK2_SY65 @ set_type )
& ( ilf_type @ sK3_SY68 @ set_type )
& ( ilf_type @ sK4_SY70 @ set_type )
& ( member @ sK3_SY68 @ sK1_B )
& ( member @ sK4_SY70 @ sK2_SY65 )
& ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(59,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(extcnf_combined,[status(esa)],[30]) ).
thf(60,plain,
( ( ! [B: $i] :
( ~ ( empty @ B )
| ~ ( ilf_type @ B @ set_type )
| ( relation_like @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(61,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ( ilf_type @ ( sK7_C @ B ) @ set_type )
& ( member @ ( sK7_C @ B ) @ B )
& ! [SY72: $i] :
( ! [SY73: $i] :
( ( ( sK7_C @ B )
!= ( ordered_pair @ SY72 @ SY73 ) )
| ~ ( ilf_type @ SY73 @ set_type ) )
| ~ ( ilf_type @ SY72 @ set_type ) ) )
| ( relation_like @ B ) )
& ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ~ ( relation_like @ B )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ~ ( member @ C @ B )
| ( ( C
= ( ordered_pair @ ( sK5_D @ C @ B ) @ ( sK6_SY71 @ C @ B ) ) )
& ( ilf_type @ ( sK6_SY71 @ C @ B ) @ set_type )
& ( ilf_type @ ( sK5_D @ C @ B ) @ set_type ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(62,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ( ilf_type @ ( sK8_C @ B ) @ set_type )
& ( member @ ( sK8_C @ B ) @ B ) )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ~ ( empty @ B )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ~ ( member @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(63,plain,
( ( ! [B: $i] :
( ( empty @ B )
| ~ ( ilf_type @ B @ set_type )
| ( ilf_type @ ( sK9_C @ B ) @ ( member_type @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(64,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 ) )
& ! [C: $i] :
( ( empty @ C )
| ~ ( ilf_type @ C @ set_type )
| ~ ( member @ B @ C )
| ( ilf_type @ B @ ( member_type @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(65,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ~ ( empty @ ( power_set @ B ) ) )
& ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ilf_type @ ( power_set @ B ) @ set_type ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(66,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ( ilf_type @ ( sK10_D @ C @ B ) @ set_type )
& ( member @ ( sK10_D @ C @ B ) @ B )
& ~ ( member @ ( sK10_D @ C @ B ) @ C ) )
| ( member @ B @ ( power_set @ C ) ) )
& ! [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(extcnf_combined,[status(esa)],[37]) ).
thf(67,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( subset @ B @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(68,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ( ilf_type @ ( sK11_D @ C @ B ) @ set_type )
& ( member @ ( sK11_D @ C @ B ) @ B )
& ~ ( member @ ( sK11_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [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(extcnf_combined,[status(esa)],[39]) ).
thf(69,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ( ilf_type @ ( sK12_D @ C @ B ) @ set_type )
& ( ~ ( member @ ( sK12_D @ C @ B ) @ B )
| ~ ( member @ ( sK12_D @ C @ B ) @ C ) )
& ( ( member @ ( sK12_D @ C @ B ) @ B )
| ( member @ ( sK12_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( B != C )
| ( ! [D: $i] :
( ~ ( ilf_type @ D @ set_type )
| ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( ilf_type @ D @ set_type )
| ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(70,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ilf_type @ ( sK13_C @ B ) @ ( subset_type @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(71,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 ) ) ) )
& ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ~ ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) )
| ( ilf_type @ C @ ( subset_type @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(72,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ( unordered_pair @ B @ C )
= ( unordered_pair @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(73,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ilf_type @ ( unordered_pair @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(74,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(extcnf_combined,[status(esa)],[45]) ).
thf(75,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(extcnf_combined,[status(esa)],[46]) ).
thf(76,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 @ set_type )
| ( ! [F: $i] :
( ~ ( ilf_type @ F @ set_type )
| ( F
!= ( ordered_pair @ D @ E ) )
| ( F
= ( unordered_pair @ ( unordered_pair @ D @ E ) @ ( singleton @ D ) ) ) )
& ! [F: $i] :
( ~ ( ilf_type @ F @ set_type )
| ( F
!= ( unordered_pair @ ( unordered_pair @ D @ E ) @ ( singleton @ D ) ) )
| ( F
= ( ordered_pair @ D @ E ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(77,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ilf_type @ ( singleton @ B ) @ set_type ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(78,plain,
( ( ! [B: $i] :
~ ( ilf_type @ B @ set_type )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ! [D: $i] :
( ~ ( ilf_type @ D @ set_type )
| ( ( ilf_type @ ( sK14_E @ D @ C ) @ set_type )
& ( ( ( sK14_E @ D @ C )
!= C )
| ~ ( member @ ( sK14_E @ D @ C ) @ D ) )
& ( ( ( sK14_E @ D @ C )
= C )
| ( member @ ( sK14_E @ D @ C ) @ D ) ) )
| ( D
= ( singleton @ C ) ) )
& ! [D: $i] :
( ~ ( ilf_type @ D @ set_type )
| ( D
!= ( singleton @ C ) )
| ( ! [E: $i] :
( ~ ( ilf_type @ E @ set_type )
| ( E != C )
| ( member @ E @ D ) )
& ! [E: $i] :
( ~ ( ilf_type @ E @ set_type )
| ~ ( member @ E @ D )
| ( E = C ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(79,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ilf_type @ ( sK15_D @ C @ B ) @ ( relation_type @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(80,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 ) ) ) )
& ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ! [E: $i] :
( ~ ( ilf_type @ E @ ( relation_type @ B @ C ) )
| ( ilf_type @ E @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(81,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 @ set_type )
| ~ ( member @ B @ D )
| ~ ( member @ C @ E )
| ( member @ ( ordered_pair @ B @ C ) @ ( cross_product @ D @ E ) ) )
& ! [E: $i] :
( ~ ( ilf_type @ E @ set_type )
| ~ ( member @ ( ordered_pair @ B @ C ) @ ( cross_product @ D @ E ) )
| ( member @ B @ D ) )
& ! [E: $i] :
( ~ ( ilf_type @ E @ set_type )
| ~ ( member @ ( ordered_pair @ B @ C ) @ ( cross_product @ D @ E ) )
| ( member @ C @ E ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(82,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ~ ( member @ B @ C )
| ( subset @ ( singleton @ B ) @ C ) )
& ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ~ ( subset @ ( singleton @ B ) @ C )
| ( member @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(83,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ~ ( member @ B @ C )
| ( subset @ ( singleton @ B ) @ C ) )
& ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ~ ( subset @ ( singleton @ B ) @ C )
| ( member @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(84,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 @ set_type )
| ~ ( member @ B @ D )
| ~ ( member @ C @ E )
| ( member @ ( ordered_pair @ B @ C ) @ ( cross_product @ D @ E ) ) )
& ! [E: $i] :
( ~ ( ilf_type @ E @ set_type )
| ~ ( member @ ( ordered_pair @ B @ C ) @ ( cross_product @ D @ E ) )
| ( member @ B @ D ) )
& ! [E: $i] :
( ~ ( ilf_type @ E @ set_type )
| ~ ( member @ ( ordered_pair @ B @ C ) @ ( cross_product @ D @ E ) )
| ( member @ C @ E ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(85,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 ) ) ) )
& ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ! [E: $i] :
( ~ ( ilf_type @ E @ ( relation_type @ B @ C ) )
| ( ilf_type @ E @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(86,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ilf_type @ ( sK15_D @ C @ B ) @ ( relation_type @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(87,plain,
( ( ! [B: $i] :
~ ( ilf_type @ B @ set_type )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ! [D: $i] :
( ~ ( ilf_type @ D @ set_type )
| ( ( ilf_type @ ( sK14_E @ D @ C ) @ set_type )
& ( ( ( sK14_E @ D @ C )
!= C )
| ~ ( member @ ( sK14_E @ D @ C ) @ D ) )
& ( ( ( sK14_E @ D @ C )
= C )
| ( member @ ( sK14_E @ D @ C ) @ D ) ) )
| ( D
= ( singleton @ C ) ) )
& ! [D: $i] :
( ~ ( ilf_type @ D @ set_type )
| ( D
!= ( singleton @ C ) )
| ( ! [E: $i] :
( ~ ( ilf_type @ E @ set_type )
| ( E != C )
| ( member @ E @ D ) )
& ! [E: $i] :
( ~ ( ilf_type @ E @ set_type )
| ~ ( member @ E @ D )
| ( E = C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(88,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ilf_type @ ( singleton @ B ) @ set_type ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(89,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 @ set_type )
| ( ! [F: $i] :
( ~ ( ilf_type @ F @ set_type )
| ( F
!= ( ordered_pair @ D @ E ) )
| ( F
= ( unordered_pair @ ( unordered_pair @ D @ E ) @ ( singleton @ D ) ) ) )
& ! [F: $i] :
( ~ ( ilf_type @ F @ set_type )
| ( F
!= ( unordered_pair @ ( unordered_pair @ D @ E ) @ ( singleton @ D ) ) )
| ( F
= ( ordered_pair @ D @ E ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(90,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)],[75]) ).
thf(91,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)],[74]) ).
thf(92,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ilf_type @ ( unordered_pair @ B @ C ) @ set_type ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(93,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ( unordered_pair @ B @ C )
= ( unordered_pair @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(94,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 ) ) ) )
& ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ~ ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) )
| ( ilf_type @ C @ ( subset_type @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(95,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ilf_type @ ( sK13_C @ B ) @ ( subset_type @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(96,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ( ilf_type @ ( sK12_D @ C @ B ) @ set_type )
& ( ~ ( member @ ( sK12_D @ C @ B ) @ B )
| ~ ( member @ ( sK12_D @ C @ B ) @ C ) )
& ( ( member @ ( sK12_D @ C @ B ) @ B )
| ( member @ ( sK12_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( B != C )
| ( ! [D: $i] :
( ~ ( ilf_type @ D @ set_type )
| ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( ilf_type @ D @ set_type )
| ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(97,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ( ilf_type @ ( sK11_D @ C @ B ) @ set_type )
& ( member @ ( sK11_D @ C @ B ) @ B )
& ~ ( member @ ( sK11_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [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)],[68]) ).
thf(98,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( subset @ B @ B ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(99,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ( ( ilf_type @ ( sK10_D @ C @ B ) @ set_type )
& ( member @ ( sK10_D @ C @ B ) @ B )
& ~ ( member @ ( sK10_D @ C @ B ) @ C ) )
| ( member @ B @ ( power_set @ C ) ) )
& ! [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)],[66]) ).
thf(100,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ~ ( empty @ ( power_set @ B ) ) )
& ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ilf_type @ ( power_set @ B ) @ set_type ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(101,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 ) )
& ! [C: $i] :
( ( empty @ C )
| ~ ( ilf_type @ C @ set_type )
| ~ ( member @ B @ C )
| ( ilf_type @ B @ ( member_type @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(102,plain,
( ( ! [B: $i] :
( ( empty @ B )
| ~ ( ilf_type @ B @ set_type )
| ( ilf_type @ ( sK9_C @ B ) @ ( member_type @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(103,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ( ilf_type @ ( sK8_C @ B ) @ set_type )
& ( member @ ( sK8_C @ B ) @ B ) )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ~ ( empty @ B )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ~ ( member @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(104,plain,
( ( ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ( ( ilf_type @ ( sK7_C @ B ) @ set_type )
& ( member @ ( sK7_C @ B ) @ B )
& ! [SY72: $i] :
( ! [SY73: $i] :
( ( ( sK7_C @ B )
!= ( ordered_pair @ SY72 @ SY73 ) )
| ~ ( ilf_type @ SY73 @ set_type ) )
| ~ ( ilf_type @ SY72 @ set_type ) ) )
| ( relation_like @ B ) )
& ! [B: $i] :
( ~ ( ilf_type @ B @ set_type )
| ~ ( relation_like @ B )
| ! [C: $i] :
( ~ ( ilf_type @ C @ set_type )
| ~ ( member @ C @ B )
| ( ( C
= ( ordered_pair @ ( sK5_D @ C @ B ) @ ( sK6_SY71 @ C @ B ) ) )
& ( ilf_type @ ( sK6_SY71 @ C @ B ) @ set_type )
& ( ilf_type @ ( sK5_D @ C @ B ) @ set_type ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(105,plain,
( ( ! [B: $i] :
( ~ ( empty @ B )
| ~ ( ilf_type @ B @ set_type )
| ( relation_like @ B ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(106,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)],[59]) ).
thf(107,plain,
( ( ! [B: $i] : ( ilf_type @ B @ set_type ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(108,plain,
( ( ilf_type @ sK1_B @ set_type )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(109,plain,
( ( ( ilf_type @ sK2_SY65 @ set_type )
& ( ilf_type @ sK3_SY68 @ set_type )
& ( ilf_type @ sK4_SY70 @ set_type )
& ( member @ sK3_SY68 @ sK1_B )
& ( member @ sK4_SY70 @ sK2_SY65 )
& ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(110,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( member @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(111,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK10_D @ SX1 @ SX0 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK10_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( member @ SX0 @ ( power_set @ SX1 ) ) )
| ~ ! [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 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(112,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK11_D @ SX1 @ SX0 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK11_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(113,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 @ set_type )
| ~ ( member @ SX0 @ SX2 )
| ~ ( member @ SX1 @ SX3 )
| ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( ilf_type @ SX3 @ set_type )
| ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) )
| ( member @ SX0 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( ilf_type @ SX3 @ set_type )
| ~ ( member @ ( ordered_pair @ SX0 @ SX1 ) @ ( cross_product @ SX2 @ SX3 ) )
| ( member @ SX1 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(114,plain,
( ( ! [SX0: $i] :
~ ( ilf_type @ SX0 @ set_type )
| ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SX1 @ SX0 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SX1 @ SX0 )
!= SX0 )
| ~ ( member @ ( sK14_E @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK14_E @ SX1 @ SX0 )
= SX0 )
| ( member @ ( sK14_E @ SX1 @ SX0 ) @ SX1 ) ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2 != SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(115,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( empty @ ( power_set @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ( ilf_type @ ( power_set @ SX0 ) @ set_type ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(116,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 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ ( relation_type @ SX0 @ SX1 ) )
| ( ilf_type @ SX2 @ ( subset_type @ ( cross_product @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(117,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 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ilf_type @ SX1 @ ( member_type @ ( power_set @ SX0 ) ) )
| ( ilf_type @ SX1 @ ( subset_type @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(118,plain,
( ( ~ ( ~ ( ilf_type @ sK2_SY65 @ set_type )
| ~ ~ ( ~ ( ilf_type @ sK3_SY68 @ set_type )
| ~ ~ ( ~ ( ilf_type @ sK4_SY70 @ set_type )
| ~ ~ ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(119,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK12_D @ SX1 @ SX0 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK12_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK12_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK12_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(120,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 ) )
| ~ ! [SX1: $i] :
( ( empty @ SX1 )
| ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX0 @ SX1 )
| ( ilf_type @ SX0 @ ( member_type @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(121,plain,
( ( ! [SX0: $i] :
~ ( ilf_type @ SX0 @ set_type )
| ! [SX0: $i] :
~ ( ilf_type @ SX0 @ set_type )
| ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( ordered_pair @ SX0 @ SX1 ) )
| ( SX2
= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) )
| ( SX2
= ( ordered_pair @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(122,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK8_C @ SX0 ) @ set_type )
| ~ ( member @ ( sK8_C @ SX0 ) @ SX0 ) )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(123,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK7_C @ SX0 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK7_C @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( ( sK7_C @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( ilf_type @ SX2 @ set_type ) )
| ~ ( ilf_type @ SX1 @ set_type ) ) ) )
| ( relation_like @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( relation_like @ SX0 )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 )
| ~ ( ~ ~ ( ( SX1
!= ( ordered_pair @ ( sK5_D @ SX1 @ SX0 ) @ ( sK6_SY71 @ SX1 @ SX0 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SX1 @ SX0 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SX1 @ SX0 ) @ set_type ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(124,plain,
! [SV1: $i] :
( ( ~ ( ilf_type @ SV1 @ set_type )
| ! [SY74: $i] :
( ~ ( ilf_type @ SY74 @ set_type )
| ( ilf_type @ ( sK15_D @ SY74 @ SV1 ) @ ( relation_type @ SY74 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(125,plain,
! [SV2: $i] :
( ( ~ ( ilf_type @ SV2 @ set_type )
| ( ilf_type @ ( singleton @ SV2 ) @ set_type ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(126,plain,
! [SV3: $i] :
( ( ~ ( ilf_type @ SV3 @ set_type )
| ! [SY75: $i] :
( ~ ( ilf_type @ SY75 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV3 @ SY75 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(127,plain,
! [SV4: $i] :
( ( ~ ( ilf_type @ SV4 @ set_type )
| ! [SY76: $i] :
( ~ ( ilf_type @ SY76 @ set_type )
| ( ilf_type @ ( cross_product @ SV4 @ SY76 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(128,plain,
! [SV5: $i] :
( ( ~ ( ilf_type @ SV5 @ set_type )
| ! [SY77: $i] :
( ~ ( ilf_type @ SY77 @ set_type )
| ( ilf_type @ ( unordered_pair @ SV5 @ SY77 ) @ set_type ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(129,plain,
! [SV6: $i] :
( ( ~ ( ilf_type @ SV6 @ set_type )
| ! [SY78: $i] :
( ~ ( ilf_type @ SY78 @ set_type )
| ( ( unordered_pair @ SV6 @ SY78 )
= ( unordered_pair @ SY78 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(130,plain,
! [SV7: $i] :
( ( ~ ( ilf_type @ SV7 @ set_type )
| ( ilf_type @ ( sK13_C @ SV7 ) @ ( subset_type @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(131,plain,
! [SV8: $i] :
( ( ~ ( ilf_type @ SV8 @ set_type )
| ( subset @ SV8 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(132,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
| ~ ( ilf_type @ SV9 @ set_type )
| ( ilf_type @ ( sK9_C @ SV9 ) @ ( member_type @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(133,plain,
! [SV10: $i] :
( ( ~ ( empty @ SV10 )
| ~ ( ilf_type @ SV10 @ set_type )
| ( relation_like @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(134,plain,
! [SV11: $i] :
( ( ~ ( ilf_type @ SV11 @ set_type )
| ! [SY79: $i] :
( ~ ( ilf_type @ SY79 @ set_type )
| ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ ( subset_type @ ( cross_product @ SV11 @ SY79 ) ) )
| ( relation_like @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(135,plain,
! [SV12: $i] :
( ( ilf_type @ SV12 @ set_type )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(136,plain,
! [SV13: $i] :
( ( ~ ( ilf_type @ SV13 @ set_type )
| ~ ( ~ ! [SY81: $i] :
( ~ ( ilf_type @ SY81 @ set_type )
| ~ ( member @ SV13 @ SY81 )
| ( subset @ ( singleton @ SV13 ) @ SY81 ) )
| ~ ! [SY82: $i] :
( ~ ( ilf_type @ SY82 @ set_type )
| ~ ( subset @ ( singleton @ SV13 ) @ SY82 )
| ( member @ SV13 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(137,plain,
! [SV14: $i] :
( ( ~ ( ilf_type @ SV14 @ set_type )
| ~ ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK10_D @ SY83 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SY83 ) ) )
| ( member @ SV14 @ ( power_set @ SY83 ) ) )
| ~ ! [SY84: $i] :
( ~ ( ilf_type @ SY84 @ set_type )
| ~ ( member @ SV14 @ ( power_set @ SY84 ) )
| ! [SY85: $i] :
( ~ ( ilf_type @ SY85 @ set_type )
| ~ ( member @ SY85 @ SV14 )
| ( member @ SY85 @ SY84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(138,plain,
! [SV15: $i] :
( ( ~ ( ilf_type @ SV15 @ set_type )
| ~ ( ~ ! [SY86: $i] :
( ~ ( ilf_type @ SY86 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK11_D @ SY86 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SY86 ) ) )
| ( subset @ SV15 @ SY86 ) )
| ~ ! [SY87: $i] :
( ~ ( ilf_type @ SY87 @ set_type )
| ~ ( subset @ SV15 @ SY87 )
| ! [SY88: $i] :
( ~ ( ilf_type @ SY88 @ set_type )
| ~ ( member @ SY88 @ SV15 )
| ( member @ SY88 @ SY87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(139,plain,
! [SV16: $i] :
( ( ~ ( ilf_type @ SV16 @ set_type )
| ! [SY89: $i] :
( ~ ( ilf_type @ SY89 @ set_type )
| ! [SY90: $i] :
( ~ ( ilf_type @ SY90 @ set_type )
| ~ ( ~ ! [SY91: $i] :
( ~ ( ilf_type @ SY91 @ set_type )
| ~ ( member @ SV16 @ SY90 )
| ~ ( member @ SY89 @ SY91 )
| ( member @ ( ordered_pair @ SV16 @ SY89 ) @ ( cross_product @ SY90 @ SY91 ) ) )
| ~ ~ ( ~ ! [SY92: $i] :
( ~ ( ilf_type @ SY92 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SY89 ) @ ( cross_product @ SY90 @ SY92 ) )
| ( member @ SV16 @ SY90 ) )
| ~ ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SY89 ) @ ( cross_product @ SY90 @ SY93 ) )
| ( member @ SY89 @ SY93 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(140,plain,
( ( ( ! [SX0: $i] :
~ ( ilf_type @ SX0 @ set_type ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SX1 @ SX0 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SX1 @ SX0 )
!= SX0 )
| ~ ( member @ ( sK14_E @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK14_E @ SX1 @ SX0 )
= SX0 )
| ( member @ ( sK14_E @ SX1 @ SX0 ) @ SX1 ) ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2 != SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(141,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( empty @ ( power_set @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ( ilf_type @ ( power_set @ SX0 ) @ set_type ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(142,plain,
! [SV17: $i] :
( ( ~ ( ilf_type @ SV17 @ set_type )
| ~ ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ ( subset_type @ ( cross_product @ SV17 @ SY94 ) ) )
| ( ilf_type @ SY95 @ ( relation_type @ SV17 @ SY94 ) ) ) )
| ~ ! [SY96: $i] :
( ~ ( ilf_type @ SY96 @ set_type )
| ! [SY97: $i] :
( ~ ( ilf_type @ SY97 @ ( relation_type @ SV17 @ SY96 ) )
| ( ilf_type @ SY97 @ ( subset_type @ ( cross_product @ SV17 @ SY96 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(143,plain,
! [SV18: $i] :
( ( ~ ( ilf_type @ SV18 @ set_type )
| ~ ( ~ ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ set_type )
| ~ ( ilf_type @ SY98 @ ( subset_type @ SV18 ) )
| ( ilf_type @ SY98 @ ( member_type @ ( power_set @ SV18 ) ) ) )
| ~ ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ set_type )
| ~ ( ilf_type @ SY99 @ ( member_type @ ( power_set @ SV18 ) ) )
| ( ilf_type @ SY99 @ ( subset_type @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(144,plain,
( ( ~ ( ilf_type @ sK2_SY65 @ set_type )
| ~ ~ ( ~ ( ilf_type @ sK3_SY68 @ set_type )
| ~ ~ ( ~ ( ilf_type @ sK4_SY70 @ set_type )
| ~ ~ ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(145,plain,
! [SV19: $i] :
( ( ~ ( ilf_type @ SV19 @ set_type )
| ~ ( ~ ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK12_D @ SY100 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) )
| ~ ( ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) ) ) )
| ( SV19 = SY100 ) )
| ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ( SV19 != SY101 )
| ~ ( ~ ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ set_type )
| ~ ( member @ SY102 @ SV19 )
| ( member @ SY102 @ SY101 ) )
| ~ ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ set_type )
| ~ ( member @ SY103 @ SY101 )
| ( member @ SY103 @ SV19 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(146,plain,
! [SV20: $i] :
( ( ~ ( ilf_type @ SV20 @ set_type )
| ~ ( ~ ! [SY104: $i] :
( ( empty @ SY104 )
| ~ ( ilf_type @ SY104 @ set_type )
| ~ ( ilf_type @ SV20 @ ( member_type @ SY104 ) )
| ( member @ SV20 @ SY104 ) )
| ~ ! [SY105: $i] :
( ( empty @ SY105 )
| ~ ( ilf_type @ SY105 @ set_type )
| ~ ( member @ SV20 @ SY105 )
| ( ilf_type @ SV20 @ ( member_type @ SY105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(147,plain,
( ( ( ! [SX0: $i] :
~ ( ilf_type @ SX0 @ set_type ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( ilf_type @ SX0 @ set_type )
| ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( ordered_pair @ SX0 @ SX1 ) )
| ( SX2
= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) )
| ( SX2
= ( ordered_pair @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(148,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK8_C @ SX0 ) @ set_type )
| ~ ( member @ ( sK8_C @ SX0 ) @ SX0 ) )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(149,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK7_C @ SX0 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK7_C @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( ( sK7_C @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( ilf_type @ SX2 @ set_type ) )
| ~ ( ilf_type @ SX1 @ set_type ) ) ) )
| ( relation_like @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( relation_like @ SX0 )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 )
| ~ ( ~ ~ ( ( SX1
!= ( ordered_pair @ ( sK5_D @ SX1 @ SX0 ) @ ( sK6_SY71 @ SX1 @ SX0 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SX1 @ SX0 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SX1 @ SX0 ) @ set_type ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(150,plain,
! [SV1: $i] :
( ( ( ~ ( ilf_type @ SV1 @ set_type ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( ilf_type @ SY74 @ set_type )
| ( ilf_type @ ( sK15_D @ SY74 @ SV1 ) @ ( relation_type @ SY74 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(151,plain,
! [SV2: $i] :
( ( ( ~ ( ilf_type @ SV2 @ set_type ) )
= $true )
| ( ( ilf_type @ ( singleton @ SV2 ) @ set_type )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(152,plain,
! [SV3: $i] :
( ( ( ~ ( ilf_type @ SV3 @ set_type ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( ilf_type @ SY75 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV3 @ SY75 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(153,plain,
! [SV4: $i] :
( ( ( ~ ( ilf_type @ SV4 @ set_type ) )
= $true )
| ( ( ! [SY76: $i] :
( ~ ( ilf_type @ SY76 @ set_type )
| ( ilf_type @ ( cross_product @ SV4 @ SY76 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(154,plain,
! [SV5: $i] :
( ( ( ~ ( ilf_type @ SV5 @ set_type ) )
= $true )
| ( ( ! [SY77: $i] :
( ~ ( ilf_type @ SY77 @ set_type )
| ( ilf_type @ ( unordered_pair @ SV5 @ SY77 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(155,plain,
! [SV6: $i] :
( ( ( ~ ( ilf_type @ SV6 @ set_type ) )
= $true )
| ( ( ! [SY78: $i] :
( ~ ( ilf_type @ SY78 @ set_type )
| ( ( unordered_pair @ SV6 @ SY78 )
= ( unordered_pair @ SY78 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(156,plain,
! [SV7: $i] :
( ( ( ~ ( ilf_type @ SV7 @ set_type ) )
= $true )
| ( ( ilf_type @ ( sK13_C @ SV7 ) @ ( subset_type @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(157,plain,
! [SV8: $i] :
( ( ( ~ ( ilf_type @ SV8 @ set_type ) )
= $true )
| ( ( subset @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(158,plain,
! [SV9: $i] :
( ( ( ( empty @ SV9 )
| ~ ( ilf_type @ SV9 @ set_type ) )
= $true )
| ( ( ilf_type @ ( sK9_C @ SV9 ) @ ( member_type @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(159,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ SV10 )
| ~ ( ilf_type @ SV10 @ set_type ) )
= $true )
| ( ( relation_like @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(160,plain,
! [SV11: $i] :
( ( ( ~ ( ilf_type @ SV11 @ set_type ) )
= $true )
| ( ( ! [SY79: $i] :
( ~ ( ilf_type @ SY79 @ set_type )
| ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ ( subset_type @ ( cross_product @ SV11 @ SY79 ) ) )
| ( relation_like @ SY80 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(161,plain,
! [SV13: $i] :
( ( ( ~ ( ilf_type @ SV13 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY81: $i] :
( ~ ( ilf_type @ SY81 @ set_type )
| ~ ( member @ SV13 @ SY81 )
| ( subset @ ( singleton @ SV13 ) @ SY81 ) )
| ~ ! [SY82: $i] :
( ~ ( ilf_type @ SY82 @ set_type )
| ~ ( subset @ ( singleton @ SV13 ) @ SY82 )
| ( member @ SV13 @ SY82 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(162,plain,
! [SV14: $i] :
( ( ( ~ ( ilf_type @ SV14 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK10_D @ SY83 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SY83 ) ) )
| ( member @ SV14 @ ( power_set @ SY83 ) ) )
| ~ ! [SY84: $i] :
( ~ ( ilf_type @ SY84 @ set_type )
| ~ ( member @ SV14 @ ( power_set @ SY84 ) )
| ! [SY85: $i] :
( ~ ( ilf_type @ SY85 @ set_type )
| ~ ( member @ SY85 @ SV14 )
| ( member @ SY85 @ SY84 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(163,plain,
! [SV15: $i] :
( ( ( ~ ( ilf_type @ SV15 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY86: $i] :
( ~ ( ilf_type @ SY86 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK11_D @ SY86 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SY86 ) ) )
| ( subset @ SV15 @ SY86 ) )
| ~ ! [SY87: $i] :
( ~ ( ilf_type @ SY87 @ set_type )
| ~ ( subset @ SV15 @ SY87 )
| ! [SY88: $i] :
( ~ ( ilf_type @ SY88 @ set_type )
| ~ ( member @ SY88 @ SV15 )
| ( member @ SY88 @ SY87 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(164,plain,
! [SV16: $i] :
( ( ( ~ ( ilf_type @ SV16 @ set_type ) )
= $true )
| ( ( ! [SY89: $i] :
( ~ ( ilf_type @ SY89 @ set_type )
| ! [SY90: $i] :
( ~ ( ilf_type @ SY90 @ set_type )
| ~ ( ~ ! [SY91: $i] :
( ~ ( ilf_type @ SY91 @ set_type )
| ~ ( member @ SV16 @ SY90 )
| ~ ( member @ SY89 @ SY91 )
| ( member @ ( ordered_pair @ SV16 @ SY89 ) @ ( cross_product @ SY90 @ SY91 ) ) )
| ~ ~ ( ~ ! [SY92: $i] :
( ~ ( ilf_type @ SY92 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SY89 ) @ ( cross_product @ SY90 @ SY92 ) )
| ( member @ SV16 @ SY90 ) )
| ~ ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SY89 ) @ ( cross_product @ SY90 @ SY93 ) )
| ( member @ SY89 @ SY93 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(165,plain,
! [SV21: $i] :
( ( ( ~ ( ilf_type @ SV21 @ set_type ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SX1 @ SX0 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SX1 @ SX0 )
!= SX0 )
| ~ ( member @ ( sK14_E @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK14_E @ SX1 @ SX0 )
= SX0 )
| ( member @ ( sK14_E @ SX1 @ SX0 ) @ SX1 ) ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2 != SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(166,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( empty @ ( power_set @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(167,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ( ilf_type @ ( power_set @ SX0 ) @ set_type ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(168,plain,
! [SV17: $i] :
( ( ( ~ ( ilf_type @ SV17 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ ( subset_type @ ( cross_product @ SV17 @ SY94 ) ) )
| ( ilf_type @ SY95 @ ( relation_type @ SV17 @ SY94 ) ) ) )
| ~ ! [SY96: $i] :
( ~ ( ilf_type @ SY96 @ set_type )
| ! [SY97: $i] :
( ~ ( ilf_type @ SY97 @ ( relation_type @ SV17 @ SY96 ) )
| ( ilf_type @ SY97 @ ( subset_type @ ( cross_product @ SV17 @ SY96 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(169,plain,
! [SV18: $i] :
( ( ( ~ ( ilf_type @ SV18 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ set_type )
| ~ ( ilf_type @ SY98 @ ( subset_type @ SV18 ) )
| ( ilf_type @ SY98 @ ( member_type @ ( power_set @ SV18 ) ) ) )
| ~ ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ set_type )
| ~ ( ilf_type @ SY99 @ ( member_type @ ( power_set @ SV18 ) ) )
| ( ilf_type @ SY99 @ ( subset_type @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(170,plain,
( ( ~ ( ilf_type @ sK2_SY65 @ set_type ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(171,plain,
( ( ~ ~ ( ~ ( ilf_type @ sK3_SY68 @ set_type )
| ~ ~ ( ~ ( ilf_type @ sK4_SY70 @ set_type )
| ~ ~ ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(172,plain,
! [SV19: $i] :
( ( ( ~ ( ilf_type @ SV19 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK12_D @ SY100 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) )
| ~ ( ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) ) ) )
| ( SV19 = SY100 ) )
| ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ( SV19 != SY101 )
| ~ ( ~ ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ set_type )
| ~ ( member @ SY102 @ SV19 )
| ( member @ SY102 @ SY101 ) )
| ~ ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ set_type )
| ~ ( member @ SY103 @ SY101 )
| ( member @ SY103 @ SV19 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(173,plain,
! [SV20: $i] :
( ( ( ~ ( ilf_type @ SV20 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY104: $i] :
( ( empty @ SY104 )
| ~ ( ilf_type @ SY104 @ set_type )
| ~ ( ilf_type @ SV20 @ ( member_type @ SY104 ) )
| ( member @ SV20 @ SY104 ) )
| ~ ! [SY105: $i] :
( ( empty @ SY105 )
| ~ ( ilf_type @ SY105 @ set_type )
| ~ ( member @ SV20 @ SY105 )
| ( ilf_type @ SV20 @ ( member_type @ SY105 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(174,plain,
! [SV22: $i] :
( ( ( ~ ( ilf_type @ SV22 @ set_type ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( ilf_type @ SX0 @ set_type )
| ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( ordered_pair @ SX0 @ SX1 ) )
| ( SX2
= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) )
| ( SX2
= ( ordered_pair @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(175,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK8_C @ SX0 ) @ set_type )
| ~ ( member @ ( sK8_C @ SX0 ) @ SX0 ) )
| ( empty @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(176,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(177,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK7_C @ SX0 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK7_C @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( ( sK7_C @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( ilf_type @ SX2 @ set_type ) )
| ~ ( ilf_type @ SX1 @ set_type ) ) ) )
| ( relation_like @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(178,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( relation_like @ SX0 )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 )
| ~ ( ~ ~ ( ( SX1
!= ( ordered_pair @ ( sK5_D @ SX1 @ SX0 ) @ ( sK6_SY71 @ SX1 @ SX0 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SX1 @ SX0 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SX1 @ SX0 ) @ set_type ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(179,plain,
! [SV1: $i] :
( ( ( ilf_type @ SV1 @ set_type )
= $false )
| ( ( ! [SY74: $i] :
( ~ ( ilf_type @ SY74 @ set_type )
| ( ilf_type @ ( sK15_D @ SY74 @ SV1 ) @ ( relation_type @ SY74 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(180,plain,
! [SV2: $i] :
( ( ( ilf_type @ SV2 @ set_type )
= $false )
| ( ( ilf_type @ ( singleton @ SV2 ) @ set_type )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(181,plain,
! [SV3: $i] :
( ( ( ilf_type @ SV3 @ set_type )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( ilf_type @ SY75 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV3 @ SY75 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(182,plain,
! [SV4: $i] :
( ( ( ilf_type @ SV4 @ set_type )
= $false )
| ( ( ! [SY76: $i] :
( ~ ( ilf_type @ SY76 @ set_type )
| ( ilf_type @ ( cross_product @ SV4 @ SY76 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(183,plain,
! [SV5: $i] :
( ( ( ilf_type @ SV5 @ set_type )
= $false )
| ( ( ! [SY77: $i] :
( ~ ( ilf_type @ SY77 @ set_type )
| ( ilf_type @ ( unordered_pair @ SV5 @ SY77 ) @ set_type ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(184,plain,
! [SV6: $i] :
( ( ( ilf_type @ SV6 @ set_type )
= $false )
| ( ( ! [SY78: $i] :
( ~ ( ilf_type @ SY78 @ set_type )
| ( ( unordered_pair @ SV6 @ SY78 )
= ( unordered_pair @ SY78 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(185,plain,
! [SV7: $i] :
( ( ( ilf_type @ SV7 @ set_type )
= $false )
| ( ( ilf_type @ ( sK13_C @ SV7 ) @ ( subset_type @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(186,plain,
! [SV8: $i] :
( ( ( ilf_type @ SV8 @ set_type )
= $false )
| ( ( subset @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(187,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $true )
| ( ( ~ ( ilf_type @ SV9 @ set_type ) )
= $true )
| ( ( ilf_type @ ( sK9_C @ SV9 ) @ ( member_type @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(188,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ SV10 ) )
= $true )
| ( ( ~ ( ilf_type @ SV10 @ set_type ) )
= $true )
| ( ( relation_like @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(189,plain,
! [SV11: $i] :
( ( ( ilf_type @ SV11 @ set_type )
= $false )
| ( ( ! [SY79: $i] :
( ~ ( ilf_type @ SY79 @ set_type )
| ! [SY80: $i] :
( ~ ( ilf_type @ SY80 @ ( subset_type @ ( cross_product @ SV11 @ SY79 ) ) )
| ( relation_like @ SY80 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(190,plain,
! [SV13: $i] :
( ( ( ilf_type @ SV13 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY81: $i] :
( ~ ( ilf_type @ SY81 @ set_type )
| ~ ( member @ SV13 @ SY81 )
| ( subset @ ( singleton @ SV13 ) @ SY81 ) )
| ~ ! [SY82: $i] :
( ~ ( ilf_type @ SY82 @ set_type )
| ~ ( subset @ ( singleton @ SV13 ) @ SY82 )
| ( member @ SV13 @ SY82 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(191,plain,
! [SV14: $i] :
( ( ( ilf_type @ SV14 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK10_D @ SY83 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SY83 ) ) )
| ( member @ SV14 @ ( power_set @ SY83 ) ) )
| ~ ! [SY84: $i] :
( ~ ( ilf_type @ SY84 @ set_type )
| ~ ( member @ SV14 @ ( power_set @ SY84 ) )
| ! [SY85: $i] :
( ~ ( ilf_type @ SY85 @ set_type )
| ~ ( member @ SY85 @ SV14 )
| ( member @ SY85 @ SY84 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(192,plain,
! [SV15: $i] :
( ( ( ilf_type @ SV15 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY86: $i] :
( ~ ( ilf_type @ SY86 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK11_D @ SY86 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SY86 ) ) )
| ( subset @ SV15 @ SY86 ) )
| ~ ! [SY87: $i] :
( ~ ( ilf_type @ SY87 @ set_type )
| ~ ( subset @ SV15 @ SY87 )
| ! [SY88: $i] :
( ~ ( ilf_type @ SY88 @ set_type )
| ~ ( member @ SY88 @ SV15 )
| ( member @ SY88 @ SY87 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(193,plain,
! [SV16: $i] :
( ( ( ilf_type @ SV16 @ set_type )
= $false )
| ( ( ! [SY89: $i] :
( ~ ( ilf_type @ SY89 @ set_type )
| ! [SY90: $i] :
( ~ ( ilf_type @ SY90 @ set_type )
| ~ ( ~ ! [SY91: $i] :
( ~ ( ilf_type @ SY91 @ set_type )
| ~ ( member @ SV16 @ SY90 )
| ~ ( member @ SY89 @ SY91 )
| ( member @ ( ordered_pair @ SV16 @ SY89 ) @ ( cross_product @ SY90 @ SY91 ) ) )
| ~ ~ ( ~ ! [SY92: $i] :
( ~ ( ilf_type @ SY92 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SY89 ) @ ( cross_product @ SY90 @ SY92 ) )
| ( member @ SV16 @ SY90 ) )
| ~ ! [SY93: $i] :
( ~ ( ilf_type @ SY93 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SY89 ) @ ( cross_product @ SY90 @ SY93 ) )
| ( member @ SY89 @ SY93 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(194,plain,
! [SV21: $i] :
( ( ( ilf_type @ SV21 @ set_type )
= $false )
| ( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SX1 @ SX0 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SX1 @ SX0 )
!= SX0 )
| ~ ( member @ ( sK14_E @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK14_E @ SX1 @ SX0 )
= SX0 )
| ( member @ ( sK14_E @ SX1 @ SX0 ) @ SX1 ) ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2 != SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ~ ( member @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(195,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( empty @ ( power_set @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(196,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ( ilf_type @ ( power_set @ SX0 ) @ set_type ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(197,plain,
! [SV17: $i] :
( ( ( ilf_type @ SV17 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ ( subset_type @ ( cross_product @ SV17 @ SY94 ) ) )
| ( ilf_type @ SY95 @ ( relation_type @ SV17 @ SY94 ) ) ) )
| ~ ! [SY96: $i] :
( ~ ( ilf_type @ SY96 @ set_type )
| ! [SY97: $i] :
( ~ ( ilf_type @ SY97 @ ( relation_type @ SV17 @ SY96 ) )
| ( ilf_type @ SY97 @ ( subset_type @ ( cross_product @ SV17 @ SY96 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(198,plain,
! [SV18: $i] :
( ( ( ilf_type @ SV18 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ set_type )
| ~ ( ilf_type @ SY98 @ ( subset_type @ SV18 ) )
| ( ilf_type @ SY98 @ ( member_type @ ( power_set @ SV18 ) ) ) )
| ~ ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ set_type )
| ~ ( ilf_type @ SY99 @ ( member_type @ ( power_set @ SV18 ) ) )
| ( ilf_type @ SY99 @ ( subset_type @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(199,plain,
( ( ilf_type @ sK2_SY65 @ set_type )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(200,plain,
( ( ~ ( ~ ( ilf_type @ sK3_SY68 @ set_type )
| ~ ~ ( ~ ( ilf_type @ sK4_SY70 @ set_type )
| ~ ~ ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(201,plain,
! [SV19: $i] :
( ( ( ilf_type @ SV19 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK12_D @ SY100 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) )
| ~ ( ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) ) ) )
| ( SV19 = SY100 ) )
| ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ( SV19 != SY101 )
| ~ ( ~ ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ set_type )
| ~ ( member @ SY102 @ SV19 )
| ( member @ SY102 @ SY101 ) )
| ~ ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ set_type )
| ~ ( member @ SY103 @ SY101 )
| ( member @ SY103 @ SV19 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(202,plain,
! [SV20: $i] :
( ( ( ilf_type @ SV20 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY104: $i] :
( ( empty @ SY104 )
| ~ ( ilf_type @ SY104 @ set_type )
| ~ ( ilf_type @ SV20 @ ( member_type @ SY104 ) )
| ( member @ SV20 @ SY104 ) )
| ~ ! [SY105: $i] :
( ( empty @ SY105 )
| ~ ( ilf_type @ SY105 @ set_type )
| ~ ( member @ SV20 @ SY105 )
| ( ilf_type @ SV20 @ ( member_type @ SY105 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(203,plain,
! [SV22: $i] :
( ( ( ilf_type @ SV22 @ set_type )
= $false )
| ( ( ! [SX0: $i] :
~ ( ilf_type @ SX0 @ set_type )
| ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( ordered_pair @ SX0 @ SX1 ) )
| ( SX2
= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) )
| ( SX2
= ( ordered_pair @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(204,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK8_C @ SX0 ) @ set_type )
| ~ ( member @ ( sK8_C @ SX0 ) @ SX0 ) )
| ( empty @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(205,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(206,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK7_C @ SX0 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK7_C @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( ( sK7_C @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( ilf_type @ SX2 @ set_type ) )
| ~ ( ilf_type @ SX1 @ set_type ) ) ) )
| ( relation_like @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(207,plain,
( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ~ ( relation_like @ SX0 )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( member @ SX1 @ SX0 )
| ~ ( ~ ~ ( ( SX1
!= ( ordered_pair @ ( sK5_D @ SX1 @ SX0 ) @ ( sK6_SY71 @ SX1 @ SX0 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SX1 @ SX0 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SX1 @ SX0 ) @ set_type ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(208,plain,
! [SV1: $i,SV23: $i] :
( ( ( ~ ( ilf_type @ SV23 @ set_type )
| ( ilf_type @ ( sK15_D @ SV23 @ SV1 ) @ ( relation_type @ SV23 @ SV1 ) ) )
= $true )
| ( ( ilf_type @ SV1 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(209,plain,
! [SV3: $i,SV24: $i] :
( ( ( ~ ( ilf_type @ SV24 @ set_type )
| ( ilf_type @ ( ordered_pair @ SV3 @ SV24 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(210,plain,
! [SV4: $i,SV25: $i] :
( ( ( ~ ( ilf_type @ SV25 @ set_type )
| ( ilf_type @ ( cross_product @ SV4 @ SV25 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(211,plain,
! [SV5: $i,SV26: $i] :
( ( ( ~ ( ilf_type @ SV26 @ set_type )
| ( ilf_type @ ( unordered_pair @ SV5 @ SV26 ) @ set_type ) )
= $true )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(212,plain,
! [SV6: $i,SV27: $i] :
( ( ( ~ ( ilf_type @ SV27 @ set_type )
| ( ( unordered_pair @ SV6 @ SV27 )
= ( unordered_pair @ SV27 @ SV6 ) ) )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(213,plain,
! [SV9: $i] :
( ( ( ilf_type @ SV9 @ set_type )
= $false )
| ( ( empty @ SV9 )
= $true )
| ( ( ilf_type @ ( sK9_C @ SV9 ) @ ( member_type @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(214,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $false )
| ( ( ~ ( ilf_type @ SV10 @ set_type ) )
= $true )
| ( ( relation_like @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(215,plain,
! [SV11: $i,SV28: $i] :
( ( ( ~ ( ilf_type @ SV28 @ set_type )
| ! [SY106: $i] :
( ~ ( ilf_type @ SY106 @ ( subset_type @ ( cross_product @ SV11 @ SV28 ) ) )
| ( relation_like @ SY106 ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(216,plain,
! [SV13: $i] :
( ( ( ~ ! [SY81: $i] :
( ~ ( ilf_type @ SY81 @ set_type )
| ~ ( member @ SV13 @ SY81 )
| ( subset @ ( singleton @ SV13 ) @ SY81 ) )
| ~ ! [SY82: $i] :
( ~ ( ilf_type @ SY82 @ set_type )
| ~ ( subset @ ( singleton @ SV13 ) @ SY82 )
| ( member @ SV13 @ SY82 ) ) )
= $false )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(217,plain,
! [SV14: $i] :
( ( ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK10_D @ SY83 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SY83 ) ) )
| ( member @ SV14 @ ( power_set @ SY83 ) ) )
| ~ ! [SY84: $i] :
( ~ ( ilf_type @ SY84 @ set_type )
| ~ ( member @ SV14 @ ( power_set @ SY84 ) )
| ! [SY85: $i] :
( ~ ( ilf_type @ SY85 @ set_type )
| ~ ( member @ SY85 @ SV14 )
| ( member @ SY85 @ SY84 ) ) ) )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(218,plain,
! [SV15: $i] :
( ( ( ~ ! [SY86: $i] :
( ~ ( ilf_type @ SY86 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK11_D @ SY86 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SY86 ) ) )
| ( subset @ SV15 @ SY86 ) )
| ~ ! [SY87: $i] :
( ~ ( ilf_type @ SY87 @ set_type )
| ~ ( subset @ SV15 @ SY87 )
| ! [SY88: $i] :
( ~ ( ilf_type @ SY88 @ set_type )
| ~ ( member @ SY88 @ SV15 )
| ( member @ SY88 @ SY87 ) ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(219,plain,
! [SV16: $i,SV29: $i] :
( ( ( ~ ( ilf_type @ SV29 @ set_type )
| ! [SY107: $i] :
( ~ ( ilf_type @ SY107 @ set_type )
| ~ ( ~ ! [SY108: $i] :
( ~ ( ilf_type @ SY108 @ set_type )
| ~ ( member @ SV16 @ SY107 )
| ~ ( member @ SV29 @ SY108 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SY107 @ SY108 ) ) )
| ~ ~ ( ~ ! [SY109: $i] :
( ~ ( ilf_type @ SY109 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SY107 @ SY109 ) )
| ( member @ SV16 @ SY107 ) )
| ~ ! [SY110: $i] :
( ~ ( ilf_type @ SY110 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SY107 @ SY110 ) )
| ( member @ SV29 @ SY110 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(220,plain,
! [SV21: $i,SV30: $i] :
( ( ( ~ ( ilf_type @ SV30 @ set_type )
| ~ ( ~ ! [SY111: $i] :
( ~ ( ilf_type @ SY111 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SY111 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SY111 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) )
| ~ ( ( ( sK14_E @ SY111 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) ) ) )
| ( SY111
= ( singleton @ SV30 ) ) )
| ~ ! [SY112: $i] :
( ~ ( ilf_type @ SY112 @ set_type )
| ( SY112
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY113: $i] :
( ~ ( ilf_type @ SY113 @ set_type )
| ( SY113 != SV30 )
| ( member @ SY113 @ SY112 ) )
| ~ ! [SY114: $i] :
( ~ ( ilf_type @ SY114 @ set_type )
| ~ ( member @ SY114 @ SY112 )
| ( SY114 = SV30 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(221,plain,
! [SV31: $i] :
( ( ~ ( ilf_type @ SV31 @ set_type )
| ~ ( empty @ ( power_set @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(222,plain,
! [SV32: $i] :
( ( ~ ( ilf_type @ SV32 @ set_type )
| ( ilf_type @ ( power_set @ SV32 ) @ set_type ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(223,plain,
! [SV17: $i] :
( ( ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ ( subset_type @ ( cross_product @ SV17 @ SY94 ) ) )
| ( ilf_type @ SY95 @ ( relation_type @ SV17 @ SY94 ) ) ) )
| ~ ! [SY96: $i] :
( ~ ( ilf_type @ SY96 @ set_type )
| ! [SY97: $i] :
( ~ ( ilf_type @ SY97 @ ( relation_type @ SV17 @ SY96 ) )
| ( ilf_type @ SY97 @ ( subset_type @ ( cross_product @ SV17 @ SY96 ) ) ) ) ) )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(224,plain,
! [SV18: $i] :
( ( ( ~ ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ set_type )
| ~ ( ilf_type @ SY98 @ ( subset_type @ SV18 ) )
| ( ilf_type @ SY98 @ ( member_type @ ( power_set @ SV18 ) ) ) )
| ~ ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ set_type )
| ~ ( ilf_type @ SY99 @ ( member_type @ ( power_set @ SV18 ) ) )
| ( ilf_type @ SY99 @ ( subset_type @ SV18 ) ) ) )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(225,plain,
( ( ~ ( ilf_type @ sK3_SY68 @ set_type )
| ~ ~ ( ~ ( ilf_type @ sK4_SY70 @ set_type )
| ~ ~ ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(226,plain,
! [SV19: $i] :
( ( ( ~ ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK12_D @ SY100 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) )
| ~ ( ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) ) ) )
| ( SV19 = SY100 ) )
| ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ( SV19 != SY101 )
| ~ ( ~ ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ set_type )
| ~ ( member @ SY102 @ SV19 )
| ( member @ SY102 @ SY101 ) )
| ~ ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ set_type )
| ~ ( member @ SY103 @ SY101 )
| ( member @ SY103 @ SV19 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(227,plain,
! [SV20: $i] :
( ( ( ~ ! [SY104: $i] :
( ( empty @ SY104 )
| ~ ( ilf_type @ SY104 @ set_type )
| ~ ( ilf_type @ SV20 @ ( member_type @ SY104 ) )
| ( member @ SV20 @ SY104 ) )
| ~ ! [SY105: $i] :
( ( empty @ SY105 )
| ~ ( ilf_type @ SY105 @ set_type )
| ~ ( member @ SV20 @ SY105 )
| ( ilf_type @ SV20 @ ( member_type @ SY105 ) ) ) )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(228,plain,
! [SV22: $i] :
( ( ( ! [SX0: $i] :
~ ( ilf_type @ SX0 @ set_type ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( ordered_pair @ SX0 @ SX1 ) )
| ( SX2
= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) )
| ( SX2
= ( ordered_pair @ SX0 @ SX1 ) ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(229,plain,
! [SV33: $i] :
( ( ~ ( ilf_type @ SV33 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK8_C @ SV33 ) @ set_type )
| ~ ( member @ ( sK8_C @ SV33 ) @ SV33 ) )
| ( empty @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(230,plain,
! [SV34: $i] :
( ( ~ ( ilf_type @ SV34 @ set_type )
| ~ ( empty @ SV34 )
| ! [SY115: $i] :
( ~ ( ilf_type @ SY115 @ set_type )
| ~ ( member @ SY115 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(231,plain,
! [SV35: $i] :
( ( ~ ( ilf_type @ SV35 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK7_C @ SV35 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK7_C @ SV35 ) @ SV35 )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SY116 @ SY117 ) )
| ~ ( ilf_type @ SY117 @ set_type ) )
| ~ ( ilf_type @ SY116 @ set_type ) ) ) )
| ( relation_like @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(232,plain,
! [SV36: $i] :
( ( ~ ( ilf_type @ SV36 @ set_type )
| ~ ( relation_like @ SV36 )
| ! [SY118: $i] :
( ~ ( ilf_type @ SY118 @ set_type )
| ~ ( member @ SY118 @ SV36 )
| ~ ( ~ ~ ( ( SY118
!= ( ordered_pair @ ( sK5_D @ SY118 @ SV36 ) @ ( sK6_SY71 @ SY118 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SY118 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SY118 @ SV36 ) @ set_type ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(233,plain,
! [SV1: $i,SV23: $i] :
( ( ( ~ ( ilf_type @ SV23 @ set_type ) )
= $true )
| ( ( ilf_type @ ( sK15_D @ SV23 @ SV1 ) @ ( relation_type @ SV23 @ SV1 ) )
= $true )
| ( ( ilf_type @ SV1 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(234,plain,
! [SV3: $i,SV24: $i] :
( ( ( ~ ( ilf_type @ SV24 @ set_type ) )
= $true )
| ( ( ilf_type @ ( ordered_pair @ SV3 @ SV24 ) @ set_type )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(235,plain,
! [SV4: $i,SV25: $i] :
( ( ( ~ ( ilf_type @ SV25 @ set_type ) )
= $true )
| ( ( ilf_type @ ( cross_product @ SV4 @ SV25 ) @ set_type )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(236,plain,
! [SV5: $i,SV26: $i] :
( ( ( ~ ( ilf_type @ SV26 @ set_type ) )
= $true )
| ( ( ilf_type @ ( unordered_pair @ SV5 @ SV26 ) @ set_type )
= $true )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(237,plain,
! [SV6: $i,SV27: $i] :
( ( ( ~ ( ilf_type @ SV27 @ set_type ) )
= $true )
| ( ( ( unordered_pair @ SV6 @ SV27 )
= ( unordered_pair @ SV27 @ SV6 ) )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(238,plain,
! [SV10: $i] :
( ( ( ilf_type @ SV10 @ set_type )
= $false )
| ( ( empty @ SV10 )
= $false )
| ( ( relation_like @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(239,plain,
! [SV11: $i,SV28: $i] :
( ( ( ~ ( ilf_type @ SV28 @ set_type ) )
= $true )
| ( ( ! [SY106: $i] :
( ~ ( ilf_type @ SY106 @ ( subset_type @ ( cross_product @ SV11 @ SV28 ) ) )
| ( relation_like @ SY106 ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(240,plain,
! [SV13: $i] :
( ( ( ~ ! [SY81: $i] :
( ~ ( ilf_type @ SY81 @ set_type )
| ~ ( member @ SV13 @ SY81 )
| ( subset @ ( singleton @ SV13 ) @ SY81 ) ) )
= $false )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(241,plain,
! [SV13: $i] :
( ( ( ~ ! [SY82: $i] :
( ~ ( ilf_type @ SY82 @ set_type )
| ~ ( subset @ ( singleton @ SV13 ) @ SY82 )
| ( member @ SV13 @ SY82 ) ) )
= $false )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(242,plain,
! [SV14: $i] :
( ( ( ~ ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK10_D @ SY83 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SY83 ) ) )
| ( member @ SV14 @ ( power_set @ SY83 ) ) ) )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(243,plain,
! [SV14: $i] :
( ( ( ~ ! [SY84: $i] :
( ~ ( ilf_type @ SY84 @ set_type )
| ~ ( member @ SV14 @ ( power_set @ SY84 ) )
| ! [SY85: $i] :
( ~ ( ilf_type @ SY85 @ set_type )
| ~ ( member @ SY85 @ SV14 )
| ( member @ SY85 @ SY84 ) ) ) )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(244,plain,
! [SV15: $i] :
( ( ( ~ ! [SY86: $i] :
( ~ ( ilf_type @ SY86 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK11_D @ SY86 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SY86 ) ) )
| ( subset @ SV15 @ SY86 ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(245,plain,
! [SV15: $i] :
( ( ( ~ ! [SY87: $i] :
( ~ ( ilf_type @ SY87 @ set_type )
| ~ ( subset @ SV15 @ SY87 )
| ! [SY88: $i] :
( ~ ( ilf_type @ SY88 @ set_type )
| ~ ( member @ SY88 @ SV15 )
| ( member @ SY88 @ SY87 ) ) ) )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(246,plain,
! [SV16: $i,SV29: $i] :
( ( ( ~ ( ilf_type @ SV29 @ set_type ) )
= $true )
| ( ( ! [SY107: $i] :
( ~ ( ilf_type @ SY107 @ set_type )
| ~ ( ~ ! [SY108: $i] :
( ~ ( ilf_type @ SY108 @ set_type )
| ~ ( member @ SV16 @ SY107 )
| ~ ( member @ SV29 @ SY108 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SY107 @ SY108 ) ) )
| ~ ~ ( ~ ! [SY109: $i] :
( ~ ( ilf_type @ SY109 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SY107 @ SY109 ) )
| ( member @ SV16 @ SY107 ) )
| ~ ! [SY110: $i] :
( ~ ( ilf_type @ SY110 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SY107 @ SY110 ) )
| ( member @ SV29 @ SY110 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(247,plain,
! [SV21: $i,SV30: $i] :
( ( ( ~ ( ilf_type @ SV30 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY111: $i] :
( ~ ( ilf_type @ SY111 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SY111 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SY111 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) )
| ~ ( ( ( sK14_E @ SY111 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) ) ) )
| ( SY111
= ( singleton @ SV30 ) ) )
| ~ ! [SY112: $i] :
( ~ ( ilf_type @ SY112 @ set_type )
| ( SY112
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY113: $i] :
( ~ ( ilf_type @ SY113 @ set_type )
| ( SY113 != SV30 )
| ( member @ SY113 @ SY112 ) )
| ~ ! [SY114: $i] :
( ~ ( ilf_type @ SY114 @ set_type )
| ~ ( member @ SY114 @ SY112 )
| ( SY114 = SV30 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(248,plain,
! [SV31: $i] :
( ( ( ~ ( ilf_type @ SV31 @ set_type ) )
= $true )
| ( ( ~ ( empty @ ( power_set @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(249,plain,
! [SV32: $i] :
( ( ( ~ ( ilf_type @ SV32 @ set_type ) )
= $true )
| ( ( ilf_type @ ( power_set @ SV32 ) @ set_type )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(250,plain,
! [SV17: $i] :
( ( ( ~ ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ ( subset_type @ ( cross_product @ SV17 @ SY94 ) ) )
| ( ilf_type @ SY95 @ ( relation_type @ SV17 @ SY94 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(251,plain,
! [SV17: $i] :
( ( ( ~ ! [SY96: $i] :
( ~ ( ilf_type @ SY96 @ set_type )
| ! [SY97: $i] :
( ~ ( ilf_type @ SY97 @ ( relation_type @ SV17 @ SY96 ) )
| ( ilf_type @ SY97 @ ( subset_type @ ( cross_product @ SV17 @ SY96 ) ) ) ) ) )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(252,plain,
! [SV18: $i] :
( ( ( ~ ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ set_type )
| ~ ( ilf_type @ SY98 @ ( subset_type @ SV18 ) )
| ( ilf_type @ SY98 @ ( member_type @ ( power_set @ SV18 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(253,plain,
! [SV18: $i] :
( ( ( ~ ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ set_type )
| ~ ( ilf_type @ SY99 @ ( member_type @ ( power_set @ SV18 ) ) )
| ( ilf_type @ SY99 @ ( subset_type @ SV18 ) ) ) )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(254,plain,
( ( ~ ( ilf_type @ sK3_SY68 @ set_type ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(255,plain,
( ( ~ ~ ( ~ ( ilf_type @ sK4_SY70 @ set_type )
| ~ ~ ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(256,plain,
! [SV19: $i] :
( ( ( ~ ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK12_D @ SY100 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) )
| ~ ( ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) ) ) )
| ( SV19 = SY100 ) ) )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(257,plain,
! [SV19: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ( SV19 != SY101 )
| ~ ( ~ ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ set_type )
| ~ ( member @ SY102 @ SV19 )
| ( member @ SY102 @ SY101 ) )
| ~ ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ set_type )
| ~ ( member @ SY103 @ SY101 )
| ( member @ SY103 @ SV19 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(258,plain,
! [SV20: $i] :
( ( ( ~ ! [SY104: $i] :
( ( empty @ SY104 )
| ~ ( ilf_type @ SY104 @ set_type )
| ~ ( ilf_type @ SV20 @ ( member_type @ SY104 ) )
| ( member @ SV20 @ SY104 ) ) )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(259,plain,
! [SV20: $i] :
( ( ( ~ ! [SY105: $i] :
( ( empty @ SY105 )
| ~ ( ilf_type @ SY105 @ set_type )
| ~ ( member @ SV20 @ SY105 )
| ( ilf_type @ SV20 @ ( member_type @ SY105 ) ) ) )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(260,plain,
! [SV22: $i,SV37: $i] :
( ( ( ~ ( ilf_type @ SV37 @ set_type ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( ordered_pair @ SX0 @ SX1 ) )
| ( SX2
= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) )
| ( SX2
= ( ordered_pair @ SX0 @ SX1 ) ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(261,plain,
! [SV33: $i] :
( ( ( ~ ( ilf_type @ SV33 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ilf_type @ ( sK8_C @ SV33 ) @ set_type )
| ~ ( member @ ( sK8_C @ SV33 ) @ SV33 ) )
| ( empty @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(262,plain,
! [SV34: $i] :
( ( ( ~ ( ilf_type @ SV34 @ set_type ) )
= $true )
| ( ( ~ ( empty @ SV34 )
| ! [SY115: $i] :
( ~ ( ilf_type @ SY115 @ set_type )
| ~ ( member @ SY115 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(263,plain,
! [SV35: $i] :
( ( ( ~ ( ilf_type @ SV35 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ilf_type @ ( sK7_C @ SV35 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK7_C @ SV35 ) @ SV35 )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SY116 @ SY117 ) )
| ~ ( ilf_type @ SY117 @ set_type ) )
| ~ ( ilf_type @ SY116 @ set_type ) ) ) )
| ( relation_like @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(264,plain,
! [SV36: $i] :
( ( ( ~ ( ilf_type @ SV36 @ set_type ) )
= $true )
| ( ( ~ ( relation_like @ SV36 )
| ! [SY118: $i] :
( ~ ( ilf_type @ SY118 @ set_type )
| ~ ( member @ SY118 @ SV36 )
| ~ ( ~ ~ ( ( SY118
!= ( ordered_pair @ ( sK5_D @ SY118 @ SV36 ) @ ( sK6_SY71 @ SY118 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SY118 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SY118 @ SV36 ) @ set_type ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(265,plain,
! [SV1: $i,SV23: $i] :
( ( ( ilf_type @ SV23 @ set_type )
= $false )
| ( ( ilf_type @ ( sK15_D @ SV23 @ SV1 ) @ ( relation_type @ SV23 @ SV1 ) )
= $true )
| ( ( ilf_type @ SV1 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(266,plain,
! [SV3: $i,SV24: $i] :
( ( ( ilf_type @ SV24 @ set_type )
= $false )
| ( ( ilf_type @ ( ordered_pair @ SV3 @ SV24 ) @ set_type )
= $true )
| ( ( ilf_type @ SV3 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(267,plain,
! [SV4: $i,SV25: $i] :
( ( ( ilf_type @ SV25 @ set_type )
= $false )
| ( ( ilf_type @ ( cross_product @ SV4 @ SV25 ) @ set_type )
= $true )
| ( ( ilf_type @ SV4 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(268,plain,
! [SV5: $i,SV26: $i] :
( ( ( ilf_type @ SV26 @ set_type )
= $false )
| ( ( ilf_type @ ( unordered_pair @ SV5 @ SV26 ) @ set_type )
= $true )
| ( ( ilf_type @ SV5 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(269,plain,
! [SV6: $i,SV27: $i] :
( ( ( ilf_type @ SV27 @ set_type )
= $false )
| ( ( ( unordered_pair @ SV6 @ SV27 )
= ( unordered_pair @ SV27 @ SV6 ) )
= $true )
| ( ( ilf_type @ SV6 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(270,plain,
! [SV11: $i,SV28: $i] :
( ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ! [SY106: $i] :
( ~ ( ilf_type @ SY106 @ ( subset_type @ ( cross_product @ SV11 @ SV28 ) ) )
| ( relation_like @ SY106 ) ) )
= $true )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(271,plain,
! [SV13: $i] :
( ( ( ! [SY81: $i] :
( ~ ( ilf_type @ SY81 @ set_type )
| ~ ( member @ SV13 @ SY81 )
| ( subset @ ( singleton @ SV13 ) @ SY81 ) ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(272,plain,
! [SV13: $i] :
( ( ( ! [SY82: $i] :
( ~ ( ilf_type @ SY82 @ set_type )
| ~ ( subset @ ( singleton @ SV13 ) @ SY82 )
| ( member @ SV13 @ SY82 ) ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(273,plain,
! [SV14: $i] :
( ( ( ! [SY83: $i] :
( ~ ( ilf_type @ SY83 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK10_D @ SY83 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SY83 @ SV14 ) @ SY83 ) ) )
| ( member @ SV14 @ ( power_set @ SY83 ) ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(274,plain,
! [SV14: $i] :
( ( ( ! [SY84: $i] :
( ~ ( ilf_type @ SY84 @ set_type )
| ~ ( member @ SV14 @ ( power_set @ SY84 ) )
| ! [SY85: $i] :
( ~ ( ilf_type @ SY85 @ set_type )
| ~ ( member @ SY85 @ SV14 )
| ( member @ SY85 @ SY84 ) ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(275,plain,
! [SV15: $i] :
( ( ( ! [SY86: $i] :
( ~ ( ilf_type @ SY86 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK11_D @ SY86 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SY86 @ SV15 ) @ SY86 ) ) )
| ( subset @ SV15 @ SY86 ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(276,plain,
! [SV15: $i] :
( ( ( ! [SY87: $i] :
( ~ ( ilf_type @ SY87 @ set_type )
| ~ ( subset @ SV15 @ SY87 )
| ! [SY88: $i] :
( ~ ( ilf_type @ SY88 @ set_type )
| ~ ( member @ SY88 @ SV15 )
| ( member @ SY88 @ SY87 ) ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(277,plain,
! [SV16: $i,SV29: $i] :
( ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ! [SY107: $i] :
( ~ ( ilf_type @ SY107 @ set_type )
| ~ ( ~ ! [SY108: $i] :
( ~ ( ilf_type @ SY108 @ set_type )
| ~ ( member @ SV16 @ SY107 )
| ~ ( member @ SV29 @ SY108 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SY107 @ SY108 ) ) )
| ~ ~ ( ~ ! [SY109: $i] :
( ~ ( ilf_type @ SY109 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SY107 @ SY109 ) )
| ( member @ SV16 @ SY107 ) )
| ~ ! [SY110: $i] :
( ~ ( ilf_type @ SY110 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SY107 @ SY110 ) )
| ( member @ SV29 @ SY110 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(278,plain,
! [SV21: $i,SV30: $i] :
( ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY111: $i] :
( ~ ( ilf_type @ SY111 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SY111 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SY111 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) )
| ~ ( ( ( sK14_E @ SY111 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) ) ) )
| ( SY111
= ( singleton @ SV30 ) ) )
| ~ ! [SY112: $i] :
( ~ ( ilf_type @ SY112 @ set_type )
| ( SY112
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY113: $i] :
( ~ ( ilf_type @ SY113 @ set_type )
| ( SY113 != SV30 )
| ( member @ SY113 @ SY112 ) )
| ~ ! [SY114: $i] :
( ~ ( ilf_type @ SY114 @ set_type )
| ~ ( member @ SY114 @ SY112 )
| ( SY114 = SV30 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(279,plain,
! [SV31: $i] :
( ( ( ilf_type @ SV31 @ set_type )
= $false )
| ( ( ~ ( empty @ ( power_set @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(280,plain,
! [SV32: $i] :
( ( ( ilf_type @ SV32 @ set_type )
= $false )
| ( ( ilf_type @ ( power_set @ SV32 ) @ set_type )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(281,plain,
! [SV17: $i] :
( ( ( ! [SY94: $i] :
( ~ ( ilf_type @ SY94 @ set_type )
| ! [SY95: $i] :
( ~ ( ilf_type @ SY95 @ ( subset_type @ ( cross_product @ SV17 @ SY94 ) ) )
| ( ilf_type @ SY95 @ ( relation_type @ SV17 @ SY94 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(282,plain,
! [SV17: $i] :
( ( ( ! [SY96: $i] :
( ~ ( ilf_type @ SY96 @ set_type )
| ! [SY97: $i] :
( ~ ( ilf_type @ SY97 @ ( relation_type @ SV17 @ SY96 ) )
| ( ilf_type @ SY97 @ ( subset_type @ ( cross_product @ SV17 @ SY96 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(283,plain,
! [SV18: $i] :
( ( ( ! [SY98: $i] :
( ~ ( ilf_type @ SY98 @ set_type )
| ~ ( ilf_type @ SY98 @ ( subset_type @ SV18 ) )
| ( ilf_type @ SY98 @ ( member_type @ ( power_set @ SV18 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(284,plain,
! [SV18: $i] :
( ( ( ! [SY99: $i] :
( ~ ( ilf_type @ SY99 @ set_type )
| ~ ( ilf_type @ SY99 @ ( member_type @ ( power_set @ SV18 ) ) )
| ( ilf_type @ SY99 @ ( subset_type @ SV18 ) ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(285,plain,
( ( ilf_type @ sK3_SY68 @ set_type )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(286,plain,
( ( ~ ( ~ ( ilf_type @ sK4_SY70 @ set_type )
| ~ ~ ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(287,plain,
! [SV19: $i] :
( ( ( ! [SY100: $i] :
( ~ ( ilf_type @ SY100 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK12_D @ SY100 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) )
| ~ ( ( member @ ( sK12_D @ SY100 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SY100 @ SV19 ) @ SY100 ) ) ) )
| ( SV19 = SY100 ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(288,plain,
! [SV19: $i] :
( ( ( ! [SY101: $i] :
( ~ ( ilf_type @ SY101 @ set_type )
| ( SV19 != SY101 )
| ~ ( ~ ! [SY102: $i] :
( ~ ( ilf_type @ SY102 @ set_type )
| ~ ( member @ SY102 @ SV19 )
| ( member @ SY102 @ SY101 ) )
| ~ ! [SY103: $i] :
( ~ ( ilf_type @ SY103 @ set_type )
| ~ ( member @ SY103 @ SY101 )
| ( member @ SY103 @ SV19 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(289,plain,
! [SV20: $i] :
( ( ( ! [SY104: $i] :
( ( empty @ SY104 )
| ~ ( ilf_type @ SY104 @ set_type )
| ~ ( ilf_type @ SV20 @ ( member_type @ SY104 ) )
| ( member @ SV20 @ SY104 ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(290,plain,
! [SV20: $i] :
( ( ( ! [SY105: $i] :
( ( empty @ SY105 )
| ~ ( ilf_type @ SY105 @ set_type )
| ~ ( member @ SV20 @ SY105 )
| ( ilf_type @ SV20 @ ( member_type @ SY105 ) ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(291,plain,
! [SV22: $i,SV37: $i] :
( ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ! [SX0: $i] :
( ~ ( ilf_type @ SX0 @ set_type )
| ! [SX1: $i] :
( ~ ( ilf_type @ SX1 @ set_type )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( ordered_pair @ SX0 @ SX1 ) )
| ( SX2
= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( ilf_type @ SX2 @ set_type )
| ( SX2
!= ( unordered_pair @ ( unordered_pair @ SX0 @ SX1 ) @ ( singleton @ SX0 ) ) )
| ( SX2
= ( ordered_pair @ SX0 @ SX1 ) ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(292,plain,
! [SV33: $i] :
( ( ( ilf_type @ SV33 @ set_type )
= $false )
| ( ( ~ ( ~ ( ilf_type @ ( sK8_C @ SV33 ) @ set_type )
| ~ ( member @ ( sK8_C @ SV33 ) @ SV33 ) )
| ( empty @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(293,plain,
! [SV34: $i] :
( ( ( ilf_type @ SV34 @ set_type )
= $false )
| ( ( ~ ( empty @ SV34 )
| ! [SY115: $i] :
( ~ ( ilf_type @ SY115 @ set_type )
| ~ ( member @ SY115 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(294,plain,
! [SV35: $i] :
( ( ( ilf_type @ SV35 @ set_type )
= $false )
| ( ( ~ ( ~ ( ilf_type @ ( sK7_C @ SV35 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK7_C @ SV35 ) @ SV35 )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SY116 @ SY117 ) )
| ~ ( ilf_type @ SY117 @ set_type ) )
| ~ ( ilf_type @ SY116 @ set_type ) ) ) )
| ( relation_like @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(295,plain,
! [SV36: $i] :
( ( ( ilf_type @ SV36 @ set_type )
= $false )
| ( ( ~ ( relation_like @ SV36 )
| ! [SY118: $i] :
( ~ ( ilf_type @ SY118 @ set_type )
| ~ ( member @ SY118 @ SV36 )
| ~ ( ~ ~ ( ( SY118
!= ( ordered_pair @ ( sK5_D @ SY118 @ SV36 ) @ ( sK6_SY71 @ SY118 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SY118 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SY118 @ SV36 ) @ set_type ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(296,plain,
! [SV28: $i,SV11: $i,SV38: $i] :
( ( ( ~ ( ilf_type @ SV38 @ ( subset_type @ ( cross_product @ SV11 @ SV28 ) ) )
| ( relation_like @ SV38 ) )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(297,plain,
! [SV13: $i,SV39: $i] :
( ( ( ~ ( ilf_type @ SV39 @ set_type )
| ~ ( member @ SV13 @ SV39 )
| ( subset @ ( singleton @ SV13 ) @ SV39 ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(298,plain,
! [SV13: $i,SV40: $i] :
( ( ( ~ ( ilf_type @ SV40 @ set_type )
| ~ ( subset @ ( singleton @ SV13 ) @ SV40 )
| ( member @ SV13 @ SV40 ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(299,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( ilf_type @ SV41 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK10_D @ SV41 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 ) ) )
| ( member @ SV14 @ ( power_set @ SV41 ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(300,plain,
! [SV14: $i,SV42: $i] :
( ( ( ~ ( ilf_type @ SV42 @ set_type )
| ~ ( member @ SV14 @ ( power_set @ SV42 ) )
| ! [SY119: $i] :
( ~ ( ilf_type @ SY119 @ set_type )
| ~ ( member @ SY119 @ SV14 )
| ( member @ SY119 @ SV42 ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(301,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( ilf_type @ SV43 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK11_D @ SV43 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 ) ) )
| ( subset @ SV15 @ SV43 ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(302,plain,
! [SV15: $i,SV44: $i] :
( ( ( ~ ( ilf_type @ SV44 @ set_type )
| ~ ( subset @ SV15 @ SV44 )
| ! [SY120: $i] :
( ~ ( ilf_type @ SY120 @ set_type )
| ~ ( member @ SY120 @ SV15 )
| ( member @ SY120 @ SV44 ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(303,plain,
! [SV29: $i,SV16: $i,SV45: $i] :
( ( ( ~ ( ilf_type @ SV45 @ set_type )
| ~ ( ~ ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SV16 @ SV45 )
| ~ ( member @ SV29 @ SY121 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY121 ) ) )
| ~ ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY122 ) )
| ( member @ SV16 @ SV45 ) )
| ~ ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY123 ) )
| ( member @ SV29 @ SY123 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(304,plain,
! [SV21: $i,SV30: $i] :
( ( ( ~ ! [SY111: $i] :
( ~ ( ilf_type @ SY111 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SY111 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SY111 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) )
| ~ ( ( ( sK14_E @ SY111 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) ) ) )
| ( SY111
= ( singleton @ SV30 ) ) )
| ~ ! [SY112: $i] :
( ~ ( ilf_type @ SY112 @ set_type )
| ( SY112
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY113: $i] :
( ~ ( ilf_type @ SY113 @ set_type )
| ( SY113 != SV30 )
| ( member @ SY113 @ SY112 ) )
| ~ ! [SY114: $i] :
( ~ ( ilf_type @ SY114 @ set_type )
| ~ ( member @ SY114 @ SY112 )
| ( SY114 = SV30 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(305,plain,
! [SV31: $i] :
( ( ( empty @ ( power_set @ SV31 ) )
= $false )
| ( ( ilf_type @ SV31 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(306,plain,
! [SV17: $i,SV46: $i] :
( ( ( ~ ( ilf_type @ SV46 @ set_type )
| ! [SY124: $i] :
( ~ ( ilf_type @ SY124 @ ( subset_type @ ( cross_product @ SV17 @ SV46 ) ) )
| ( ilf_type @ SY124 @ ( relation_type @ SV17 @ SV46 ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(307,plain,
! [SV17: $i,SV47: $i] :
( ( ( ~ ( ilf_type @ SV47 @ set_type )
| ! [SY125: $i] :
( ~ ( ilf_type @ SY125 @ ( relation_type @ SV17 @ SV47 ) )
| ( ilf_type @ SY125 @ ( subset_type @ ( cross_product @ SV17 @ SV47 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(308,plain,
! [SV18: $i,SV48: $i] :
( ( ( ~ ( ilf_type @ SV48 @ set_type )
| ~ ( ilf_type @ SV48 @ ( subset_type @ SV18 ) )
| ( ilf_type @ SV48 @ ( member_type @ ( power_set @ SV18 ) ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(309,plain,
! [SV18: $i,SV49: $i] :
( ( ( ~ ( ilf_type @ SV49 @ set_type )
| ~ ( ilf_type @ SV49 @ ( member_type @ ( power_set @ SV18 ) ) )
| ( ilf_type @ SV49 @ ( subset_type @ SV18 ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(310,plain,
( ( ~ ( ilf_type @ sK4_SY70 @ set_type )
| ~ ~ ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(311,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( ilf_type @ SV50 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK12_D @ SV50 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
| ~ ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) ) ) )
| ( SV19 = SV50 ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(312,plain,
! [SV19: $i,SV51: $i] :
( ( ( ~ ( ilf_type @ SV51 @ set_type )
| ( SV19 != SV51 )
| ~ ( ~ ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ~ ( member @ SY126 @ SV19 )
| ( member @ SY126 @ SV51 ) )
| ~ ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ set_type )
| ~ ( member @ SY127 @ SV51 )
| ( member @ SY127 @ SV19 ) ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(313,plain,
! [SV20: $i,SV52: $i] :
( ( ( ( empty @ SV52 )
| ~ ( ilf_type @ SV52 @ set_type )
| ~ ( ilf_type @ SV20 @ ( member_type @ SV52 ) )
| ( member @ SV20 @ SV52 ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(314,plain,
! [SV20: $i,SV53: $i] :
( ( ( ( empty @ SV53 )
| ~ ( ilf_type @ SV53 @ set_type )
| ~ ( member @ SV20 @ SV53 )
| ( ilf_type @ SV20 @ ( member_type @ SV53 ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(315,plain,
! [SV22: $i,SV37: $i,SV54: $i] :
( ( ( ~ ( ilf_type @ SV54 @ set_type )
| ! [SY128: $i] :
( ~ ( ilf_type @ SY128 @ set_type )
| ~ ( ~ ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ( SY129
!= ( ordered_pair @ SV54 @ SY128 ) )
| ( SY129
= ( unordered_pair @ ( unordered_pair @ SV54 @ SY128 ) @ ( singleton @ SV54 ) ) ) )
| ~ ! [SY130: $i] :
( ~ ( ilf_type @ SY130 @ set_type )
| ( SY130
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SY128 ) @ ( singleton @ SV54 ) ) )
| ( SY130
= ( ordered_pair @ SV54 @ SY128 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(316,plain,
! [SV33: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK8_C @ SV33 ) @ set_type )
| ~ ( member @ ( sK8_C @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( empty @ SV33 )
= $true )
| ( ( ilf_type @ SV33 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(317,plain,
! [SV34: $i] :
( ( ( ~ ( empty @ SV34 ) )
= $true )
| ( ( ! [SY115: $i] :
( ~ ( ilf_type @ SY115 @ set_type )
| ~ ( member @ SY115 @ SV34 ) ) )
= $true )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(318,plain,
! [SV35: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK7_C @ SV35 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK7_C @ SV35 ) @ SV35 )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SY116 @ SY117 ) )
| ~ ( ilf_type @ SY117 @ set_type ) )
| ~ ( ilf_type @ SY116 @ set_type ) ) ) ) )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(319,plain,
! [SV36: $i] :
( ( ( ~ ( relation_like @ SV36 ) )
= $true )
| ( ( ! [SY118: $i] :
( ~ ( ilf_type @ SY118 @ set_type )
| ~ ( member @ SY118 @ SV36 )
| ~ ( ~ ~ ( ( SY118
!= ( ordered_pair @ ( sK5_D @ SY118 @ SV36 ) @ ( sK6_SY71 @ SY118 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SY118 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SY118 @ SV36 ) @ set_type ) ) ) )
= $true )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(320,plain,
! [SV28: $i,SV11: $i,SV38: $i] :
( ( ( ~ ( ilf_type @ SV38 @ ( subset_type @ ( cross_product @ SV11 @ SV28 ) ) ) )
= $true )
| ( ( relation_like @ SV38 )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(321,plain,
! [SV13: $i,SV39: $i] :
( ( ( ~ ( ilf_type @ SV39 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV13 @ SV39 )
| ( subset @ ( singleton @ SV13 ) @ SV39 ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(322,plain,
! [SV13: $i,SV40: $i] :
( ( ( ~ ( ilf_type @ SV40 @ set_type ) )
= $true )
| ( ( ~ ( subset @ ( singleton @ SV13 ) @ SV40 )
| ( member @ SV13 @ SV40 ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(323,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( ilf_type @ SV41 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ilf_type @ ( sK10_D @ SV41 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 ) ) )
| ( member @ SV14 @ ( power_set @ SV41 ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(324,plain,
! [SV14: $i,SV42: $i] :
( ( ( ~ ( ilf_type @ SV42 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV14 @ ( power_set @ SV42 ) )
| ! [SY119: $i] :
( ~ ( ilf_type @ SY119 @ set_type )
| ~ ( member @ SY119 @ SV14 )
| ( member @ SY119 @ SV42 ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(325,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( ilf_type @ SV43 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ilf_type @ ( sK11_D @ SV43 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 ) ) )
| ( subset @ SV15 @ SV43 ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(326,plain,
! [SV15: $i,SV44: $i] :
( ( ( ~ ( ilf_type @ SV44 @ set_type ) )
= $true )
| ( ( ~ ( subset @ SV15 @ SV44 )
| ! [SY120: $i] :
( ~ ( ilf_type @ SY120 @ set_type )
| ~ ( member @ SY120 @ SV15 )
| ( member @ SY120 @ SV44 ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(327,plain,
! [SV29: $i,SV16: $i,SV45: $i] :
( ( ( ~ ( ilf_type @ SV45 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SV16 @ SV45 )
| ~ ( member @ SV29 @ SY121 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY121 ) ) )
| ~ ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY122 ) )
| ( member @ SV16 @ SV45 ) )
| ~ ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY123 ) )
| ( member @ SV29 @ SY123 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(328,plain,
! [SV21: $i,SV30: $i] :
( ( ( ~ ! [SY111: $i] :
( ~ ( ilf_type @ SY111 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SY111 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SY111 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) )
| ~ ( ( ( sK14_E @ SY111 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) ) ) )
| ( SY111
= ( singleton @ SV30 ) ) ) )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(329,plain,
! [SV21: $i,SV30: $i] :
( ( ( ~ ! [SY112: $i] :
( ~ ( ilf_type @ SY112 @ set_type )
| ( SY112
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY113: $i] :
( ~ ( ilf_type @ SY113 @ set_type )
| ( SY113 != SV30 )
| ( member @ SY113 @ SY112 ) )
| ~ ! [SY114: $i] :
( ~ ( ilf_type @ SY114 @ set_type )
| ~ ( member @ SY114 @ SY112 )
| ( SY114 = SV30 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(330,plain,
! [SV17: $i,SV46: $i] :
( ( ( ~ ( ilf_type @ SV46 @ set_type ) )
= $true )
| ( ( ! [SY124: $i] :
( ~ ( ilf_type @ SY124 @ ( subset_type @ ( cross_product @ SV17 @ SV46 ) ) )
| ( ilf_type @ SY124 @ ( relation_type @ SV17 @ SV46 ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(331,plain,
! [SV17: $i,SV47: $i] :
( ( ( ~ ( ilf_type @ SV47 @ set_type ) )
= $true )
| ( ( ! [SY125: $i] :
( ~ ( ilf_type @ SY125 @ ( relation_type @ SV17 @ SV47 ) )
| ( ilf_type @ SY125 @ ( subset_type @ ( cross_product @ SV17 @ SV47 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(332,plain,
! [SV18: $i,SV48: $i] :
( ( ( ~ ( ilf_type @ SV48 @ set_type ) )
= $true )
| ( ( ~ ( ilf_type @ SV48 @ ( subset_type @ SV18 ) )
| ( ilf_type @ SV48 @ ( member_type @ ( power_set @ SV18 ) ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(333,plain,
! [SV18: $i,SV49: $i] :
( ( ( ~ ( ilf_type @ SV49 @ set_type ) )
= $true )
| ( ( ~ ( ilf_type @ SV49 @ ( member_type @ ( power_set @ SV18 ) ) )
| ( ilf_type @ SV49 @ ( subset_type @ SV18 ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(334,plain,
( ( ~ ( ilf_type @ sK4_SY70 @ set_type ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(335,plain,
( ( ~ ~ ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(336,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( ilf_type @ SV50 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ilf_type @ ( sK12_D @ SV50 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
| ~ ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) ) ) )
| ( SV19 = SV50 ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(337,plain,
! [SV19: $i,SV51: $i] :
( ( ( ~ ( ilf_type @ SV51 @ set_type ) )
= $true )
| ( ( ( SV19 != SV51 )
| ~ ( ~ ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ~ ( member @ SY126 @ SV19 )
| ( member @ SY126 @ SV51 ) )
| ~ ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ set_type )
| ~ ( member @ SY127 @ SV51 )
| ( member @ SY127 @ SV19 ) ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(338,plain,
! [SV20: $i,SV52: $i] :
( ( ( ( empty @ SV52 )
| ~ ( ilf_type @ SV52 @ set_type ) )
= $true )
| ( ( ~ ( ilf_type @ SV20 @ ( member_type @ SV52 ) )
| ( member @ SV20 @ SV52 ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(339,plain,
! [SV20: $i,SV53: $i] :
( ( ( ( empty @ SV53 )
| ~ ( ilf_type @ SV53 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV20 @ SV53 )
| ( ilf_type @ SV20 @ ( member_type @ SV53 ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(340,plain,
! [SV22: $i,SV37: $i,SV54: $i] :
( ( ( ~ ( ilf_type @ SV54 @ set_type ) )
= $true )
| ( ( ! [SY128: $i] :
( ~ ( ilf_type @ SY128 @ set_type )
| ~ ( ~ ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ( SY129
!= ( ordered_pair @ SV54 @ SY128 ) )
| ( SY129
= ( unordered_pair @ ( unordered_pair @ SV54 @ SY128 ) @ ( singleton @ SV54 ) ) ) )
| ~ ! [SY130: $i] :
( ~ ( ilf_type @ SY130 @ set_type )
| ( SY130
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SY128 ) @ ( singleton @ SV54 ) ) )
| ( SY130
= ( ordered_pair @ SV54 @ SY128 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(341,plain,
! [SV33: $i] :
( ( ( ~ ( ilf_type @ ( sK8_C @ SV33 ) @ set_type )
| ~ ( member @ ( sK8_C @ SV33 ) @ SV33 ) )
= $false )
| ( ( empty @ SV33 )
= $true )
| ( ( ilf_type @ SV33 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(342,plain,
! [SV34: $i] :
( ( ( empty @ SV34 )
= $false )
| ( ( ! [SY115: $i] :
( ~ ( ilf_type @ SY115 @ set_type )
| ~ ( member @ SY115 @ SV34 ) ) )
= $true )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(343,plain,
! [SV35: $i] :
( ( ( ~ ( ilf_type @ ( sK7_C @ SV35 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK7_C @ SV35 ) @ SV35 )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SY116 @ SY117 ) )
| ~ ( ilf_type @ SY117 @ set_type ) )
| ~ ( ilf_type @ SY116 @ set_type ) ) ) )
= $false )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(344,plain,
! [SV36: $i] :
( ( ( relation_like @ SV36 )
= $false )
| ( ( ! [SY118: $i] :
( ~ ( ilf_type @ SY118 @ set_type )
| ~ ( member @ SY118 @ SV36 )
| ~ ( ~ ~ ( ( SY118
!= ( ordered_pair @ ( sK5_D @ SY118 @ SV36 ) @ ( sK6_SY71 @ SY118 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SY118 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SY118 @ SV36 ) @ set_type ) ) ) )
= $true )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(345,plain,
! [SV28: $i,SV11: $i,SV38: $i] :
( ( ( ilf_type @ SV38 @ ( subset_type @ ( cross_product @ SV11 @ SV28 ) ) )
= $false )
| ( ( relation_like @ SV38 )
= $true )
| ( ( ilf_type @ SV28 @ set_type )
= $false )
| ( ( ilf_type @ SV11 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(346,plain,
! [SV13: $i,SV39: $i] :
( ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ~ ( member @ SV13 @ SV39 )
| ( subset @ ( singleton @ SV13 ) @ SV39 ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(347,plain,
! [SV13: $i,SV40: $i] :
( ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( ~ ( subset @ ( singleton @ SV13 ) @ SV40 )
| ( member @ SV13 @ SV40 ) )
= $true )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(348,plain,
! [SV14: $i,SV41: $i] :
( ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ~ ( ~ ( ilf_type @ ( sK10_D @ SV41 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 ) ) )
| ( member @ SV14 @ ( power_set @ SV41 ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(349,plain,
! [SV14: $i,SV42: $i] :
( ( ( ilf_type @ SV42 @ set_type )
= $false )
| ( ( ~ ( member @ SV14 @ ( power_set @ SV42 ) )
| ! [SY119: $i] :
( ~ ( ilf_type @ SY119 @ set_type )
| ~ ( member @ SY119 @ SV14 )
| ( member @ SY119 @ SV42 ) ) )
= $true )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(350,plain,
! [SV15: $i,SV43: $i] :
( ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ~ ( ~ ( ilf_type @ ( sK11_D @ SV43 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 ) ) )
| ( subset @ SV15 @ SV43 ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(351,plain,
! [SV15: $i,SV44: $i] :
( ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ~ ( subset @ SV15 @ SV44 )
| ! [SY120: $i] :
( ~ ( ilf_type @ SY120 @ set_type )
| ~ ( member @ SY120 @ SV15 )
| ( member @ SY120 @ SV44 ) ) )
= $true )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(352,plain,
! [SV29: $i,SV16: $i,SV45: $i] :
( ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SV16 @ SV45 )
| ~ ( member @ SV29 @ SY121 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY121 ) ) )
| ~ ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY122 ) )
| ( member @ SV16 @ SV45 ) )
| ~ ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY123 ) )
| ( member @ SV29 @ SY123 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(353,plain,
! [SV21: $i,SV30: $i] :
( ( ( ! [SY111: $i] :
( ~ ( ilf_type @ SY111 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SY111 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SY111 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) )
| ~ ( ( ( sK14_E @ SY111 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SY111 @ SV30 ) @ SY111 ) ) ) )
| ( SY111
= ( singleton @ SV30 ) ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(354,plain,
! [SV21: $i,SV30: $i] :
( ( ( ! [SY112: $i] :
( ~ ( ilf_type @ SY112 @ set_type )
| ( SY112
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY113: $i] :
( ~ ( ilf_type @ SY113 @ set_type )
| ( SY113 != SV30 )
| ( member @ SY113 @ SY112 ) )
| ~ ! [SY114: $i] :
( ~ ( ilf_type @ SY114 @ set_type )
| ~ ( member @ SY114 @ SY112 )
| ( SY114 = SV30 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(355,plain,
! [SV17: $i,SV46: $i] :
( ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( ! [SY124: $i] :
( ~ ( ilf_type @ SY124 @ ( subset_type @ ( cross_product @ SV17 @ SV46 ) ) )
| ( ilf_type @ SY124 @ ( relation_type @ SV17 @ SV46 ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(356,plain,
! [SV17: $i,SV47: $i] :
( ( ( ilf_type @ SV47 @ set_type )
= $false )
| ( ( ! [SY125: $i] :
( ~ ( ilf_type @ SY125 @ ( relation_type @ SV17 @ SV47 ) )
| ( ilf_type @ SY125 @ ( subset_type @ ( cross_product @ SV17 @ SV47 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(357,plain,
! [SV18: $i,SV48: $i] :
( ( ( ilf_type @ SV48 @ set_type )
= $false )
| ( ( ~ ( ilf_type @ SV48 @ ( subset_type @ SV18 ) )
| ( ilf_type @ SV48 @ ( member_type @ ( power_set @ SV18 ) ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(358,plain,
! [SV18: $i,SV49: $i] :
( ( ( ilf_type @ SV49 @ set_type )
= $false )
| ( ( ~ ( ilf_type @ SV49 @ ( member_type @ ( power_set @ SV18 ) ) )
| ( ilf_type @ SV49 @ ( subset_type @ SV18 ) ) )
= $true )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(359,plain,
( ( ilf_type @ sK4_SY70 @ set_type )
= $true ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(360,plain,
( ( ~ ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(361,plain,
! [SV19: $i,SV50: $i] :
( ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ~ ( ~ ( ilf_type @ ( sK12_D @ SV50 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
| ~ ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) ) ) )
| ( SV19 = SV50 ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(362,plain,
! [SV19: $i,SV51: $i] :
( ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ( SV19 != SV51 )
| ~ ( ~ ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ~ ( member @ SY126 @ SV19 )
| ( member @ SY126 @ SV51 ) )
| ~ ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ set_type )
| ~ ( member @ SY127 @ SV51 )
| ( member @ SY127 @ SV19 ) ) ) )
= $true )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(363,plain,
! [SV20: $i,SV52: $i] :
( ( ( empty @ SV52 )
= $true )
| ( ( ~ ( ilf_type @ SV52 @ set_type ) )
= $true )
| ( ( ~ ( ilf_type @ SV20 @ ( member_type @ SV52 ) )
| ( member @ SV20 @ SV52 ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(364,plain,
! [SV20: $i,SV53: $i] :
( ( ( empty @ SV53 )
= $true )
| ( ( ~ ( ilf_type @ SV53 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV20 @ SV53 )
| ( ilf_type @ SV20 @ ( member_type @ SV53 ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(365,plain,
! [SV22: $i,SV37: $i,SV54: $i] :
( ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ! [SY128: $i] :
( ~ ( ilf_type @ SY128 @ set_type )
| ~ ( ~ ! [SY129: $i] :
( ~ ( ilf_type @ SY129 @ set_type )
| ( SY129
!= ( ordered_pair @ SV54 @ SY128 ) )
| ( SY129
= ( unordered_pair @ ( unordered_pair @ SV54 @ SY128 ) @ ( singleton @ SV54 ) ) ) )
| ~ ! [SY130: $i] :
( ~ ( ilf_type @ SY130 @ set_type )
| ( SY130
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SY128 ) @ ( singleton @ SV54 ) ) )
| ( SY130
= ( ordered_pair @ SV54 @ SY128 ) ) ) ) ) )
= $true )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(366,plain,
! [SV33: $i] :
( ( ( ~ ( ilf_type @ ( sK8_C @ SV33 ) @ set_type ) )
= $false )
| ( ( empty @ SV33 )
= $true )
| ( ( ilf_type @ SV33 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(367,plain,
! [SV33: $i] :
( ( ( ~ ( member @ ( sK8_C @ SV33 ) @ SV33 ) )
= $false )
| ( ( empty @ SV33 )
= $true )
| ( ( ilf_type @ SV33 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(368,plain,
! [SV34: $i,SV55: $i] :
( ( ( ~ ( ilf_type @ SV55 @ set_type )
| ~ ( member @ SV55 @ SV34 ) )
= $true )
| ( ( empty @ SV34 )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(369,plain,
! [SV35: $i] :
( ( ( ~ ( ilf_type @ ( sK7_C @ SV35 ) @ set_type ) )
= $false )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(370,plain,
! [SV35: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK7_C @ SV35 ) @ SV35 )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SY116 @ SY117 ) )
| ~ ( ilf_type @ SY117 @ set_type ) )
| ~ ( ilf_type @ SY116 @ set_type ) ) ) )
= $false )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(371,plain,
! [SV36: $i,SV56: $i] :
( ( ( ~ ( ilf_type @ SV56 @ set_type )
| ~ ( member @ SV56 @ SV36 )
| ~ ( ~ ~ ( ( SV56
!= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SV56 @ SV36 ) @ set_type ) ) )
= $true )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(372,plain,
! [SV39: $i,SV13: $i] :
( ( ( ~ ( member @ SV13 @ SV39 ) )
= $true )
| ( ( subset @ ( singleton @ SV13 ) @ SV39 )
= $true )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(373,plain,
! [SV40: $i,SV13: $i] :
( ( ( ~ ( subset @ ( singleton @ SV13 ) @ SV40 ) )
= $true )
| ( ( member @ SV13 @ SV40 )
= $true )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(374,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK10_D @ SV41 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 ) ) ) )
= $true )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(375,plain,
! [SV42: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ ( power_set @ SV42 ) ) )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( ilf_type @ SY119 @ set_type )
| ~ ( member @ SY119 @ SV14 )
| ( member @ SY119 @ SV42 ) ) )
= $true )
| ( ( ilf_type @ SV42 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(376,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK11_D @ SV43 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 ) ) ) )
= $true )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(377,plain,
! [SV44: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV44 ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( ilf_type @ SY120 @ set_type )
| ~ ( member @ SY120 @ SV15 )
| ( member @ SY120 @ SV44 ) ) )
= $true )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(378,plain,
! [SV29: $i,SV45: $i,SV16: $i] :
( ( ( ~ ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SV16 @ SV45 )
| ~ ( member @ SV29 @ SY121 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY121 ) ) )
| ~ ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY122 ) )
| ( member @ SV16 @ SV45 ) )
| ~ ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY123 ) )
| ( member @ SV29 @ SY123 ) ) ) )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(379,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ~ ( ilf_type @ SV57 @ set_type )
| ~ ( ~ ( ilf_type @ ( sK14_E @ SV57 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
| ~ ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) ) ) )
| ( SV57
= ( singleton @ SV30 ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(380,plain,
! [SV21: $i,SV30: $i,SV58: $i] :
( ( ( ~ ( ilf_type @ SV58 @ set_type )
| ( SV58
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY131: $i] :
( ~ ( ilf_type @ SY131 @ set_type )
| ( SY131 != SV30 )
| ( member @ SY131 @ SV58 ) )
| ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV58 )
| ( SY132 = SV30 ) ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(381,plain,
! [SV46: $i,SV17: $i,SV59: $i] :
( ( ( ~ ( ilf_type @ SV59 @ ( subset_type @ ( cross_product @ SV17 @ SV46 ) ) )
| ( ilf_type @ SV59 @ ( relation_type @ SV17 @ SV46 ) ) )
= $true )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(382,plain,
! [SV47: $i,SV17: $i,SV60: $i] :
( ( ( ~ ( ilf_type @ SV60 @ ( relation_type @ SV17 @ SV47 ) )
| ( ilf_type @ SV60 @ ( subset_type @ ( cross_product @ SV17 @ SV47 ) ) ) )
= $true )
| ( ( ilf_type @ SV47 @ set_type )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(383,plain,
! [SV18: $i,SV48: $i] :
( ( ( ~ ( ilf_type @ SV48 @ ( subset_type @ SV18 ) ) )
= $true )
| ( ( ilf_type @ SV48 @ ( member_type @ ( power_set @ SV18 ) ) )
= $true )
| ( ( ilf_type @ SV48 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(384,plain,
! [SV18: $i,SV49: $i] :
( ( ( ~ ( ilf_type @ SV49 @ ( member_type @ ( power_set @ SV18 ) ) ) )
= $true )
| ( ( ilf_type @ SV49 @ ( subset_type @ SV18 ) )
= $true )
| ( ( ilf_type @ SV49 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(385,plain,
( ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
| ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(386,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK12_D @ SV50 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
| ~ ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) ) ) ) )
= $true )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(387,plain,
! [SV51: $i,SV19: $i] :
( ( ( SV19 != SV51 )
= $true )
| ( ( ~ ( ~ ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ~ ( member @ SY126 @ SV19 )
| ( member @ SY126 @ SV51 ) )
| ~ ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ set_type )
| ~ ( member @ SY127 @ SV51 )
| ( member @ SY127 @ SV19 ) ) ) )
= $true )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(388,plain,
! [SV20: $i,SV52: $i] :
( ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( empty @ SV52 )
= $true )
| ( ( ~ ( ilf_type @ SV20 @ ( member_type @ SV52 ) )
| ( member @ SV20 @ SV52 ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(389,plain,
! [SV20: $i,SV53: $i] :
( ( ( ilf_type @ SV53 @ set_type )
= $false )
| ( ( empty @ SV53 )
= $true )
| ( ( ~ ( member @ SV20 @ SV53 )
| ( ilf_type @ SV20 @ ( member_type @ SV53 ) ) )
= $true )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(390,plain,
! [SV22: $i,SV37: $i,SV54: $i,SV61: $i] :
( ( ( ~ ( ilf_type @ SV61 @ set_type )
| ~ ( ~ ! [SY133: $i] :
( ~ ( ilf_type @ SY133 @ set_type )
| ( SY133
!= ( ordered_pair @ SV54 @ SV61 ) )
| ( SY133
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) ) )
| ~ ! [SY134: $i] :
( ~ ( ilf_type @ SY134 @ set_type )
| ( SY134
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
| ( SY134
= ( ordered_pair @ SV54 @ SV61 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(391,plain,
! [SV33: $i] :
( ( ( ilf_type @ ( sK8_C @ SV33 ) @ set_type )
= $true )
| ( ( empty @ SV33 )
= $true )
| ( ( ilf_type @ SV33 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(392,plain,
! [SV33: $i] :
( ( ( member @ ( sK8_C @ SV33 ) @ SV33 )
= $true )
| ( ( empty @ SV33 )
= $true )
| ( ( ilf_type @ SV33 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(393,plain,
! [SV34: $i,SV55: $i] :
( ( ( ~ ( ilf_type @ SV55 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV55 @ SV34 ) )
= $true )
| ( ( empty @ SV34 )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(394,plain,
! [SV35: $i] :
( ( ( ilf_type @ ( sK7_C @ SV35 ) @ set_type )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(395,plain,
! [SV35: $i] :
( ( ( ~ ( ~ ( member @ ( sK7_C @ SV35 ) @ SV35 )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SY116 @ SY117 ) )
| ~ ( ilf_type @ SY117 @ set_type ) )
| ~ ( ilf_type @ SY116 @ set_type ) ) ) )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(396,plain,
! [SV36: $i,SV56: $i] :
( ( ( ~ ( ilf_type @ SV56 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV56 @ SV36 )
| ~ ( ~ ~ ( ( SV56
!= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SV56 @ SV36 ) @ set_type ) ) )
= $true )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(397,plain,
! [SV39: $i,SV13: $i] :
( ( ( member @ SV13 @ SV39 )
= $false )
| ( ( subset @ ( singleton @ SV13 ) @ SV39 )
= $true )
| ( ( ilf_type @ SV39 @ set_type )
= $false )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(398,plain,
! [SV40: $i,SV13: $i] :
( ( ( subset @ ( singleton @ SV13 ) @ SV40 )
= $false )
| ( ( member @ SV13 @ SV40 )
= $true )
| ( ( ilf_type @ SV40 @ set_type )
= $false )
| ( ( ilf_type @ SV13 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(399,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( ilf_type @ ( sK10_D @ SV41 @ SV14 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 ) ) )
= $false )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(400,plain,
! [SV42: $i,SV14: $i] :
( ( ( member @ SV14 @ ( power_set @ SV42 ) )
= $false )
| ( ( ! [SY119: $i] :
( ~ ( ilf_type @ SY119 @ set_type )
| ~ ( member @ SY119 @ SV14 )
| ( member @ SY119 @ SV42 ) ) )
= $true )
| ( ( ilf_type @ SV42 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(401,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( ilf_type @ ( sK11_D @ SV43 @ SV15 ) @ set_type )
| ~ ~ ( ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 ) ) )
= $false )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(402,plain,
! [SV44: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV44 )
= $false )
| ( ( ! [SY120: $i] :
( ~ ( ilf_type @ SY120 @ set_type )
| ~ ( member @ SY120 @ SV15 )
| ( member @ SY120 @ SV44 ) ) )
= $true )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(403,plain,
! [SV29: $i,SV45: $i,SV16: $i] :
( ( ( ~ ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SV16 @ SV45 )
| ~ ( member @ SV29 @ SY121 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY121 ) ) ) )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(404,plain,
! [SV45: $i,SV29: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY122 ) )
| ( member @ SV16 @ SV45 ) )
| ~ ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY123 ) )
| ( member @ SV29 @ SY123 ) ) ) )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(405,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ~ ( ilf_type @ SV57 @ set_type ) )
= $true )
| ( ( ~ ( ~ ( ilf_type @ ( sK14_E @ SV57 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
| ~ ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) ) ) )
| ( SV57
= ( singleton @ SV30 ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(406,plain,
! [SV21: $i,SV30: $i,SV58: $i] :
( ( ( ~ ( ilf_type @ SV58 @ set_type ) )
= $true )
| ( ( ( SV58
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY131: $i] :
( ~ ( ilf_type @ SY131 @ set_type )
| ( SY131 != SV30 )
| ( member @ SY131 @ SV58 ) )
| ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV58 )
| ( SY132 = SV30 ) ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(407,plain,
! [SV46: $i,SV17: $i,SV59: $i] :
( ( ( ~ ( ilf_type @ SV59 @ ( subset_type @ ( cross_product @ SV17 @ SV46 ) ) ) )
= $true )
| ( ( ilf_type @ SV59 @ ( relation_type @ SV17 @ SV46 ) )
= $true )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(408,plain,
! [SV47: $i,SV17: $i,SV60: $i] :
( ( ( ~ ( ilf_type @ SV60 @ ( relation_type @ SV17 @ SV47 ) ) )
= $true )
| ( ( ilf_type @ SV60 @ ( subset_type @ ( cross_product @ SV17 @ SV47 ) ) )
= $true )
| ( ( ilf_type @ SV47 @ set_type )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(409,plain,
! [SV18: $i,SV48: $i] :
( ( ( ilf_type @ SV48 @ ( subset_type @ SV18 ) )
= $false )
| ( ( ilf_type @ SV48 @ ( member_type @ ( power_set @ SV18 ) ) )
= $true )
| ( ( ilf_type @ SV48 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(410,plain,
! [SV18: $i,SV49: $i] :
( ( ( ilf_type @ SV49 @ ( member_type @ ( power_set @ SV18 ) ) )
= $false )
| ( ( ilf_type @ SV49 @ ( subset_type @ SV18 ) )
= $true )
| ( ( ilf_type @ SV49 @ set_type )
= $false )
| ( ( ilf_type @ SV18 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(411,plain,
( ( ~ ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(412,plain,
( ( ~ ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(413,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( ilf_type @ ( sK12_D @ SV50 @ SV19 ) @ set_type )
| ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
| ~ ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) ) ) )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(414,plain,
! [SV51: $i,SV19: $i] :
( ( ( SV19 = SV51 )
= $false )
| ( ( ~ ( ~ ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ~ ( member @ SY126 @ SV19 )
| ( member @ SY126 @ SV51 ) )
| ~ ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ set_type )
| ~ ( member @ SY127 @ SV51 )
| ( member @ SY127 @ SV19 ) ) ) )
= $true )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(415,plain,
! [SV52: $i,SV20: $i] :
( ( ( ~ ( ilf_type @ SV20 @ ( member_type @ SV52 ) ) )
= $true )
| ( ( member @ SV20 @ SV52 )
= $true )
| ( ( empty @ SV52 )
= $true )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(416,plain,
! [SV53: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV53 ) )
= $true )
| ( ( ilf_type @ SV20 @ ( member_type @ SV53 ) )
= $true )
| ( ( empty @ SV53 )
= $true )
| ( ( ilf_type @ SV53 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(417,plain,
! [SV22: $i,SV37: $i,SV54: $i,SV61: $i] :
( ( ( ~ ( ilf_type @ SV61 @ set_type ) )
= $true )
| ( ( ~ ( ~ ! [SY133: $i] :
( ~ ( ilf_type @ SY133 @ set_type )
| ( SY133
!= ( ordered_pair @ SV54 @ SV61 ) )
| ( SY133
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) ) )
| ~ ! [SY134: $i] :
( ~ ( ilf_type @ SY134 @ set_type )
| ( SY134
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
| ( SY134
= ( ordered_pair @ SV54 @ SV61 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(418,plain,
! [SV34: $i,SV55: $i] :
( ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( ~ ( member @ SV55 @ SV34 ) )
= $true )
| ( ( empty @ SV34 )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(419,plain,
! [SV35: $i] :
( ( ( ~ ( member @ ( sK7_C @ SV35 ) @ SV35 )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SY116 @ SY117 ) )
| ~ ( ilf_type @ SY117 @ set_type ) )
| ~ ( ilf_type @ SY116 @ set_type ) ) )
= $false )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(420,plain,
! [SV36: $i,SV56: $i] :
( ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( ~ ( member @ SV56 @ SV36 )
| ~ ( ~ ~ ( ( SV56
!= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SV56 @ SV36 ) @ set_type ) ) )
= $true )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(421,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( ilf_type @ ( sK10_D @ SV41 @ SV14 ) @ set_type ) )
= $false )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(422,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 ) ) )
= $false )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(423,plain,
! [SV42: $i,SV14: $i,SV62: $i] :
( ( ( ~ ( ilf_type @ SV62 @ set_type )
| ~ ( member @ SV62 @ SV14 )
| ( member @ SV62 @ SV42 ) )
= $true )
| ( ( member @ SV14 @ ( power_set @ SV42 ) )
= $false )
| ( ( ilf_type @ SV42 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(424,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( ilf_type @ ( sK11_D @ SV43 @ SV15 ) @ set_type ) )
= $false )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(425,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 ) ) )
= $false )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(426,plain,
! [SV44: $i,SV15: $i,SV63: $i] :
( ( ( ~ ( ilf_type @ SV63 @ set_type )
| ~ ( member @ SV63 @ SV15 )
| ( member @ SV63 @ SV44 ) )
= $true )
| ( ( subset @ SV15 @ SV44 )
= $false )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(427,plain,
! [SV29: $i,SV45: $i,SV16: $i] :
( ( ( ! [SY121: $i] :
( ~ ( ilf_type @ SY121 @ set_type )
| ~ ( member @ SV16 @ SV45 )
| ~ ( member @ SV29 @ SY121 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY121 ) ) ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(428,plain,
! [SV45: $i,SV29: $i,SV16: $i] :
( ( ( ~ ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY122 ) )
| ( member @ SV16 @ SV45 ) )
| ~ ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY123 ) )
| ( member @ SV29 @ SY123 ) ) ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(429,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ~ ( ~ ( ilf_type @ ( sK14_E @ SV57 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
| ~ ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) ) ) )
| ( SV57
= ( singleton @ SV30 ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(430,plain,
! [SV21: $i,SV30: $i,SV58: $i] :
( ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ( SV58
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY131: $i] :
( ~ ( ilf_type @ SY131 @ set_type )
| ( SY131 != SV30 )
| ( member @ SY131 @ SV58 ) )
| ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV58 )
| ( SY132 = SV30 ) ) ) )
= $true )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(431,plain,
! [SV46: $i,SV17: $i,SV59: $i] :
( ( ( ilf_type @ SV59 @ ( subset_type @ ( cross_product @ SV17 @ SV46 ) ) )
= $false )
| ( ( ilf_type @ SV59 @ ( relation_type @ SV17 @ SV46 ) )
= $true )
| ( ( ilf_type @ SV46 @ set_type )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(432,plain,
! [SV47: $i,SV17: $i,SV60: $i] :
( ( ( ilf_type @ SV60 @ ( relation_type @ SV17 @ SV47 ) )
= $false )
| ( ( ilf_type @ SV60 @ ( subset_type @ ( cross_product @ SV17 @ SV47 ) ) )
= $true )
| ( ( ilf_type @ SV47 @ set_type )
= $false )
| ( ( ilf_type @ SV17 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(433,plain,
( ( ~ ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(434,plain,
( ( ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(435,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( ilf_type @ ( sK12_D @ SV50 @ SV19 ) @ set_type ) )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(436,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
| ~ ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) ) ) )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(437,plain,
! [SV51: $i,SV19: $i] :
( ( ( ~ ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ~ ( member @ SY126 @ SV19 )
| ( member @ SY126 @ SV51 ) )
| ~ ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ set_type )
| ~ ( member @ SY127 @ SV51 )
| ( member @ SY127 @ SV19 ) ) )
= $false )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(438,plain,
! [SV52: $i,SV20: $i] :
( ( ( ilf_type @ SV20 @ ( member_type @ SV52 ) )
= $false )
| ( ( member @ SV20 @ SV52 )
= $true )
| ( ( empty @ SV52 )
= $true )
| ( ( ilf_type @ SV52 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(439,plain,
! [SV53: $i,SV20: $i] :
( ( ( member @ SV20 @ SV53 )
= $false )
| ( ( ilf_type @ SV20 @ ( member_type @ SV53 ) )
= $true )
| ( ( empty @ SV53 )
= $true )
| ( ( ilf_type @ SV53 @ set_type )
= $false )
| ( ( ilf_type @ SV20 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(440,plain,
! [SV22: $i,SV37: $i,SV54: $i,SV61: $i] :
( ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ~ ( ~ ! [SY133: $i] :
( ~ ( ilf_type @ SY133 @ set_type )
| ( SY133
!= ( ordered_pair @ SV54 @ SV61 ) )
| ( SY133
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) ) )
| ~ ! [SY134: $i] :
( ~ ( ilf_type @ SY134 @ set_type )
| ( SY134
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
| ( SY134
= ( ordered_pair @ SV54 @ SV61 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(441,plain,
! [SV34: $i,SV55: $i] :
( ( ( member @ SV55 @ SV34 )
= $false )
| ( ( ilf_type @ SV55 @ set_type )
= $false )
| ( ( empty @ SV34 )
= $false )
| ( ( ilf_type @ SV34 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(442,plain,
! [SV35: $i] :
( ( ( ~ ( member @ ( sK7_C @ SV35 ) @ SV35 ) )
= $false )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(443,plain,
! [SV35: $i] :
( ( ( ~ ! [SY116: $i] :
( ! [SY117: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SY116 @ SY117 ) )
| ~ ( ilf_type @ SY117 @ set_type ) )
| ~ ( ilf_type @ SY116 @ set_type ) ) )
= $false )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(444,plain,
! [SV36: $i,SV56: $i] :
( ( ( ~ ( member @ SV56 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV56
!= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SV56 @ SV36 ) @ set_type ) ) )
= $true )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(445,plain,
! [SV14: $i,SV41: $i] :
( ( ( ilf_type @ ( sK10_D @ SV41 @ SV14 ) @ set_type )
= $true )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(446,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 ) ) )
= $true )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(447,plain,
! [SV42: $i,SV14: $i,SV62: $i] :
( ( ( ~ ( ilf_type @ SV62 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV62 @ SV14 )
| ( member @ SV62 @ SV42 ) )
= $true )
| ( ( member @ SV14 @ ( power_set @ SV42 ) )
= $false )
| ( ( ilf_type @ SV42 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(448,plain,
! [SV15: $i,SV43: $i] :
( ( ( ilf_type @ ( sK11_D @ SV43 @ SV15 ) @ set_type )
= $true )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(449,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 ) ) )
= $true )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(450,plain,
! [SV44: $i,SV15: $i,SV63: $i] :
( ( ( ~ ( ilf_type @ SV63 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV63 @ SV15 )
| ( member @ SV63 @ SV44 ) )
= $true )
| ( ( subset @ SV15 @ SV44 )
= $false )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(451,plain,
! [SV29: $i,SV45: $i,SV16: $i,SV64: $i] :
( ( ( ~ ( ilf_type @ SV64 @ set_type )
| ~ ( member @ SV16 @ SV45 )
| ~ ( member @ SV29 @ SV64 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV64 ) ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(452,plain,
! [SV45: $i,SV29: $i,SV16: $i] :
( ( ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY122 ) )
| ( member @ SV16 @ SV45 ) )
| ~ ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY123 ) )
| ( member @ SV29 @ SY123 ) ) )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(453,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ~ ( ~ ( ilf_type @ ( sK14_E @ SV57 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
| ~ ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) ) ) ) )
= $true )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(454,plain,
! [SV21: $i,SV30: $i,SV58: $i] :
( ( ( SV58
!= ( singleton @ SV30 ) )
= $true )
| ( ( ~ ( ~ ! [SY131: $i] :
( ~ ( ilf_type @ SY131 @ set_type )
| ( SY131 != SV30 )
| ( member @ SY131 @ SV58 ) )
| ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV58 )
| ( SY132 = SV30 ) ) ) )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(455,plain,
( ( ~ ( member @ sK3_SY68 @ sK1_B )
| ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(456,plain,
( ( ilf_type @ ( singleton @ ( ordered_pair @ sK3_SY68 @ sK4_SY70 ) ) @ ( relation_type @ sK1_B @ sK2_SY65 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(457,plain,
! [SV19: $i,SV50: $i] :
( ( ( ilf_type @ ( sK12_D @ SV50 @ SV19 ) @ set_type )
= $true )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(458,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
| ~ ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) ) ) )
= $true )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(459,plain,
! [SV51: $i,SV19: $i] :
( ( ( ~ ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ~ ( member @ SY126 @ SV19 )
| ( member @ SY126 @ SV51 ) ) )
= $false )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(460,plain,
! [SV19: $i,SV51: $i] :
( ( ( ~ ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ set_type )
| ~ ( member @ SY127 @ SV51 )
| ( member @ SY127 @ SV19 ) ) )
= $false )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(461,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i] :
( ( ( ~ ! [SY133: $i] :
( ~ ( ilf_type @ SY133 @ set_type )
| ( SY133
!= ( ordered_pair @ SV54 @ SV61 ) )
| ( SY133
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) ) )
| ~ ! [SY134: $i] :
( ~ ( ilf_type @ SY134 @ set_type )
| ( SY134
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
| ( SY134
= ( ordered_pair @ SV54 @ SV61 ) ) ) )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(462,plain,
! [SV35: $i] :
( ( ( member @ ( sK7_C @ SV35 ) @ SV35 )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(463,plain,
! [SV35: $i] :
( ( ( ! [SY116: $i] :
( ! [SY117: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SY116 @ SY117 ) )
| ~ ( ilf_type @ SY117 @ set_type ) )
| ~ ( ilf_type @ SY116 @ set_type ) ) )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(464,plain,
! [SV36: $i,SV56: $i] :
( ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV56
!= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SV56 @ SV36 ) @ set_type ) ) )
= $true )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(465,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV14 )
| ~ ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 ) )
= $false )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(466,plain,
! [SV42: $i,SV14: $i,SV62: $i] :
( ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( ~ ( member @ SV62 @ SV14 )
| ( member @ SV62 @ SV42 ) )
= $true )
| ( ( member @ SV14 @ ( power_set @ SV42 ) )
= $false )
| ( ( ilf_type @ SV42 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(467,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV15 )
| ~ ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 ) )
= $false )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(468,plain,
! [SV44: $i,SV15: $i,SV63: $i] :
( ( ( ilf_type @ SV63 @ set_type )
= $false )
| ( ( ~ ( member @ SV63 @ SV15 )
| ( member @ SV63 @ SV44 ) )
= $true )
| ( ( subset @ SV15 @ SV44 )
= $false )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(469,plain,
! [SV29: $i,SV45: $i,SV16: $i,SV64: $i] :
( ( ( ~ ( ilf_type @ SV64 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV16 @ SV45 )
| ~ ( member @ SV29 @ SV64 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV64 ) ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(470,plain,
! [SV45: $i,SV29: $i,SV16: $i] :
( ( ( ~ ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY122 ) )
| ( member @ SV16 @ SV45 ) ) )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(471,plain,
! [SV45: $i,SV29: $i,SV16: $i] :
( ( ( ~ ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY123 ) )
| ( member @ SV29 @ SY123 ) ) )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(472,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ~ ( ilf_type @ ( sK14_E @ SV57 @ SV30 ) @ set_type )
| ~ ~ ( ~ ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
| ~ ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) ) ) )
= $false )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(473,plain,
! [SV21: $i,SV30: $i,SV58: $i] :
( ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ~ ( ~ ! [SY131: $i] :
( ~ ( ilf_type @ SY131 @ set_type )
| ( SY131 != SV30 )
| ( member @ SY131 @ SV58 ) )
| ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV58 )
| ( SY132 = SV30 ) ) ) )
= $true )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(474,plain,
( ( ~ ( member @ sK3_SY68 @ sK1_B ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(475,plain,
( ( ~ ( member @ sK4_SY70 @ sK2_SY65 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(476,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
| ~ ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) ) )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(477,plain,
! [SV51: $i,SV19: $i] :
( ( ( ! [SY126: $i] :
( ~ ( ilf_type @ SY126 @ set_type )
| ~ ( member @ SY126 @ SV19 )
| ( member @ SY126 @ SV51 ) ) )
= $true )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(478,plain,
! [SV19: $i,SV51: $i] :
( ( ( ! [SY127: $i] :
( ~ ( ilf_type @ SY127 @ set_type )
| ~ ( member @ SY127 @ SV51 )
| ( member @ SY127 @ SV19 ) ) )
= $true )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(479,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i] :
( ( ( ~ ! [SY133: $i] :
( ~ ( ilf_type @ SY133 @ set_type )
| ( SY133
!= ( ordered_pair @ SV54 @ SV61 ) )
| ( SY133
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) ) ) )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(480,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i] :
( ( ( ~ ! [SY134: $i] :
( ~ ( ilf_type @ SY134 @ set_type )
| ( SY134
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
| ( SY134
= ( ordered_pair @ SV54 @ SV61 ) ) ) )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(481,plain,
! [SV65: $i,SV35: $i] :
( ( ( ! [SY135: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SV65 @ SY135 ) )
| ~ ( ilf_type @ SY135 @ set_type ) )
| ~ ( ilf_type @ SV65 @ set_type ) )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(482,plain,
! [SV36: $i,SV56: $i] :
( ( ( ~ ~ ( ( SV56
!= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type ) )
| ~ ( ilf_type @ ( sK5_D @ SV56 @ SV36 ) @ set_type ) )
= $false )
| ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(483,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV14 ) )
= $false )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(484,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 ) )
= $false )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(485,plain,
! [SV42: $i,SV14: $i,SV62: $i] :
( ( ( ~ ( member @ SV62 @ SV14 ) )
= $true )
| ( ( member @ SV62 @ SV42 )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( member @ SV14 @ ( power_set @ SV42 ) )
= $false )
| ( ( ilf_type @ SV42 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(486,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV15 ) )
= $false )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(487,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 ) )
= $false )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(488,plain,
! [SV44: $i,SV15: $i,SV63: $i] :
( ( ( ~ ( member @ SV63 @ SV15 ) )
= $true )
| ( ( member @ SV63 @ SV44 )
= $true )
| ( ( ilf_type @ SV63 @ set_type )
= $false )
| ( ( subset @ SV15 @ SV44 )
= $false )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(489,plain,
! [SV29: $i,SV45: $i,SV16: $i,SV64: $i] :
( ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ~ ( member @ SV16 @ SV45 )
| ~ ( member @ SV29 @ SV64 )
| ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV64 ) ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(490,plain,
! [SV45: $i,SV29: $i,SV16: $i] :
( ( ( ! [SY122: $i] :
( ~ ( ilf_type @ SY122 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY122 ) )
| ( member @ SV16 @ SV45 ) ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(491,plain,
! [SV45: $i,SV29: $i,SV16: $i] :
( ( ( ! [SY123: $i] :
( ~ ( ilf_type @ SY123 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SY123 ) )
| ( member @ SV29 @ SY123 ) ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(492,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ~ ( ilf_type @ ( sK14_E @ SV57 @ SV30 ) @ set_type ) )
= $false )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(493,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
| ~ ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) ) ) )
= $false )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(494,plain,
! [SV21: $i,SV58: $i,SV30: $i] :
( ( ( ~ ! [SY131: $i] :
( ~ ( ilf_type @ SY131 @ set_type )
| ( SY131 != SV30 )
| ( member @ SY131 @ SV58 ) )
| ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV58 )
| ( SY132 = SV30 ) ) )
= $false )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(495,plain,
( ( member @ sK3_SY68 @ sK1_B )
= $true ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(496,plain,
( ( member @ sK4_SY70 @ sK2_SY65 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(497,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) ) )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(498,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) ) )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(499,plain,
! [SV51: $i,SV19: $i,SV66: $i] :
( ( ( ~ ( ilf_type @ SV66 @ set_type )
| ~ ( member @ SV66 @ SV19 )
| ( member @ SV66 @ SV51 ) )
= $true )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(500,plain,
! [SV19: $i,SV51: $i,SV67: $i] :
( ( ( ~ ( ilf_type @ SV67 @ set_type )
| ~ ( member @ SV67 @ SV51 )
| ( member @ SV67 @ SV19 ) )
= $true )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(501,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i] :
( ( ( ! [SY133: $i] :
( ~ ( ilf_type @ SY133 @ set_type )
| ( SY133
!= ( ordered_pair @ SV54 @ SV61 ) )
| ( SY133
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(502,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i] :
( ( ( ! [SY134: $i] :
( ~ ( ilf_type @ SY134 @ set_type )
| ( SY134
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
| ( SY134
= ( ordered_pair @ SV54 @ SV61 ) ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(503,plain,
! [SV65: $i,SV35: $i] :
( ( ( ! [SY135: $i] :
( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SV65 @ SY135 ) )
| ~ ( ilf_type @ SY135 @ set_type ) ) )
= $true )
| ( ( ~ ( ilf_type @ SV65 @ set_type ) )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(504,plain,
! [SV36: $i,SV56: $i] :
( ( ( ~ ~ ( ( SV56
!= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type ) ) )
= $false )
| ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[482]) ).
thf(505,plain,
! [SV36: $i,SV56: $i] :
( ( ( ~ ( ilf_type @ ( sK5_D @ SV56 @ SV36 ) @ set_type ) )
= $false )
| ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[482]) ).
thf(506,plain,
! [SV14: $i,SV41: $i] :
( ( ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV14 )
= $true )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(507,plain,
! [SV14: $i,SV41: $i] :
( ( ( ~ ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 ) )
= $true )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(508,plain,
! [SV42: $i,SV14: $i,SV62: $i] :
( ( ( member @ SV62 @ SV14 )
= $false )
| ( ( member @ SV62 @ SV42 )
= $true )
| ( ( ilf_type @ SV62 @ set_type )
= $false )
| ( ( member @ SV14 @ ( power_set @ SV42 ) )
= $false )
| ( ( ilf_type @ SV42 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(509,plain,
! [SV15: $i,SV43: $i] :
( ( ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV15 )
= $true )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(510,plain,
! [SV15: $i,SV43: $i] :
( ( ( ~ ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 ) )
= $true )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(511,plain,
! [SV44: $i,SV15: $i,SV63: $i] :
( ( ( member @ SV63 @ SV15 )
= $false )
| ( ( member @ SV63 @ SV44 )
= $true )
| ( ( ilf_type @ SV63 @ set_type )
= $false )
| ( ( subset @ SV15 @ SV44 )
= $false )
| ( ( ilf_type @ SV44 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(512,plain,
! [SV64: $i,SV29: $i,SV45: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV45 )
| ~ ( member @ SV29 @ SV64 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV64 ) )
= $true )
| ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(513,plain,
! [SV45: $i,SV29: $i,SV16: $i,SV68: $i] :
( ( ( ~ ( ilf_type @ SV68 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV68 ) )
| ( member @ SV16 @ SV45 ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(514,plain,
! [SV45: $i,SV29: $i,SV16: $i,SV69: $i] :
( ( ( ~ ( ilf_type @ SV69 @ set_type )
| ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV69 ) )
| ( member @ SV29 @ SV69 ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(515,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ilf_type @ ( sK14_E @ SV57 @ SV30 ) @ set_type )
= $true )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(516,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ~ ( ~ ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
| ~ ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) ) ) )
= $true )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(517,plain,
! [SV21: $i,SV58: $i,SV30: $i] :
( ( ( ~ ! [SY131: $i] :
( ~ ( ilf_type @ SY131 @ set_type )
| ( SY131 != SV30 )
| ( member @ SY131 @ SV58 ) ) )
= $false )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(518,plain,
! [SV21: $i,SV30: $i,SV58: $i] :
( ( ( ~ ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV58 )
| ( SY132 = SV30 ) ) )
= $false )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(519,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
= $true )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(520,plain,
! [SV19: $i,SV50: $i] :
( ( ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
| ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
= $true )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(521,plain,
! [SV51: $i,SV19: $i,SV66: $i] :
( ( ( ~ ( ilf_type @ SV66 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV66 @ SV19 )
| ( member @ SV66 @ SV51 ) )
= $true )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(522,plain,
! [SV19: $i,SV51: $i,SV67: $i] :
( ( ( ~ ( ilf_type @ SV67 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV67 @ SV51 )
| ( member @ SV67 @ SV19 ) )
= $true )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(523,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i,SV70: $i] :
( ( ( ~ ( ilf_type @ SV70 @ set_type )
| ( SV70
!= ( ordered_pair @ SV54 @ SV61 ) )
| ( SV70
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(524,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i,SV71: $i] :
( ( ( ~ ( ilf_type @ SV71 @ set_type )
| ( SV71
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
| ( SV71
= ( ordered_pair @ SV54 @ SV61 ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(525,plain,
! [SV72: $i,SV65: $i,SV35: $i] :
( ( ( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SV65 @ SV72 ) )
| ~ ( ilf_type @ SV72 @ set_type ) )
= $true )
| ( ( ~ ( ilf_type @ SV65 @ set_type ) )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(526,plain,
! [SV36: $i,SV56: $i] :
( ( ( ~ ( ( SV56
!= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type ) ) )
= $true )
| ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(527,plain,
! [SV36: $i,SV56: $i] :
( ( ( ilf_type @ ( sK5_D @ SV56 @ SV36 ) @ set_type )
= $true )
| ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(528,plain,
! [SV14: $i,SV41: $i] :
( ( ( member @ ( sK10_D @ SV41 @ SV14 ) @ SV41 )
= $false )
| ( ( member @ SV14 @ ( power_set @ SV41 ) )
= $true )
| ( ( ilf_type @ SV41 @ set_type )
= $false )
| ( ( ilf_type @ SV14 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(529,plain,
! [SV15: $i,SV43: $i] :
( ( ( member @ ( sK11_D @ SV43 @ SV15 ) @ SV43 )
= $false )
| ( ( subset @ SV15 @ SV43 )
= $true )
| ( ( ilf_type @ SV43 @ set_type )
= $false )
| ( ( ilf_type @ SV15 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(530,plain,
! [SV64: $i,SV29: $i,SV45: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV45 ) )
= $true )
| ( ( ~ ( member @ SV29 @ SV64 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV64 ) )
= $true )
| ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(531,plain,
! [SV45: $i,SV29: $i,SV16: $i,SV68: $i] :
( ( ( ~ ( ilf_type @ SV68 @ set_type ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV68 ) )
| ( member @ SV16 @ SV45 ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(532,plain,
! [SV45: $i,SV29: $i,SV16: $i,SV69: $i] :
( ( ( ~ ( ilf_type @ SV69 @ set_type ) )
= $true )
| ( ( ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV69 ) )
| ( member @ SV29 @ SV69 ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(533,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ~ ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
| ~ ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) ) )
= $false )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(534,plain,
! [SV21: $i,SV58: $i,SV30: $i] :
( ( ( ! [SY131: $i] :
( ~ ( ilf_type @ SY131 @ set_type )
| ( SY131 != SV30 )
| ( member @ SY131 @ SV58 ) ) )
= $true )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(535,plain,
! [SV21: $i,SV30: $i,SV58: $i] :
( ( ( ! [SY132: $i] :
( ~ ( ilf_type @ SY132 @ set_type )
| ~ ( member @ SY132 @ SV58 )
| ( SY132 = SV30 ) ) )
= $true )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(536,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 ) )
= $true )
| ( ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
= $true )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(537,plain,
! [SV19: $i,SV50: $i] :
( ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
= $true )
| ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 )
= $true )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(538,plain,
! [SV51: $i,SV19: $i,SV66: $i] :
( ( ( ilf_type @ SV66 @ set_type )
= $false )
| ( ( ~ ( member @ SV66 @ SV19 )
| ( member @ SV66 @ SV51 ) )
= $true )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(539,plain,
! [SV19: $i,SV51: $i,SV67: $i] :
( ( ( ilf_type @ SV67 @ set_type )
= $false )
| ( ( ~ ( member @ SV67 @ SV51 )
| ( member @ SV67 @ SV19 ) )
= $true )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(540,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i,SV70: $i] :
( ( ( ~ ( ilf_type @ SV70 @ set_type ) )
= $true )
| ( ( ( SV70
!= ( ordered_pair @ SV54 @ SV61 ) )
| ( SV70
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(541,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i,SV71: $i] :
( ( ( ~ ( ilf_type @ SV71 @ set_type ) )
= $true )
| ( ( ( SV71
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
| ( SV71
= ( ordered_pair @ SV54 @ SV61 ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(542,plain,
! [SV72: $i,SV65: $i,SV35: $i] :
( ( ( ( sK7_C @ SV35 )
!= ( ordered_pair @ SV65 @ SV72 ) )
= $true )
| ( ( ~ ( ilf_type @ SV72 @ set_type ) )
= $true )
| ( ( ~ ( ilf_type @ SV65 @ set_type ) )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(543,plain,
! [SV36: $i,SV56: $i] :
( ( ( ( SV56
!= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
| ~ ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type ) )
= $false )
| ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(544,plain,
! [SV64: $i,SV29: $i,SV45: $i,SV16: $i] :
( ( ( member @ SV16 @ SV45 )
= $false )
| ( ( ~ ( member @ SV29 @ SV64 ) )
= $true )
| ( ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV64 ) )
= $true )
| ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(545,plain,
! [SV45: $i,SV29: $i,SV16: $i,SV68: $i] :
( ( ( ilf_type @ SV68 @ set_type )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV68 ) )
| ( member @ SV16 @ SV45 ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(546,plain,
! [SV45: $i,SV29: $i,SV16: $i,SV69: $i] :
( ( ( ilf_type @ SV69 @ set_type )
= $false )
| ( ( ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV69 ) )
| ( member @ SV29 @ SV69 ) )
= $true )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(547,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ~ ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) ) )
= $false )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(548,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ~ ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) ) )
= $false )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(549,plain,
! [SV21: $i,SV58: $i,SV30: $i,SV73: $i] :
( ( ( ~ ( ilf_type @ SV73 @ set_type )
| ( SV73 != SV30 )
| ( member @ SV73 @ SV58 ) )
= $true )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(550,plain,
! [SV21: $i,SV30: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( ilf_type @ SV74 @ set_type )
| ~ ( member @ SV74 @ SV58 )
| ( SV74 = SV30 ) )
= $true )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(551,plain,
! [SV19: $i,SV50: $i] :
( ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
= $false )
| ( ( ~ ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 ) )
= $true )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(552,plain,
! [SV51: $i,SV19: $i,SV66: $i] :
( ( ( ~ ( member @ SV66 @ SV19 ) )
= $true )
| ( ( member @ SV66 @ SV51 )
= $true )
| ( ( ilf_type @ SV66 @ set_type )
= $false )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(553,plain,
! [SV19: $i,SV51: $i,SV67: $i] :
( ( ( ~ ( member @ SV67 @ SV51 ) )
= $true )
| ( ( member @ SV67 @ SV19 )
= $true )
| ( ( ilf_type @ SV67 @ set_type )
= $false )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(554,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i,SV70: $i] :
( ( ( ilf_type @ SV70 @ set_type )
= $false )
| ( ( ( SV70
!= ( ordered_pair @ SV54 @ SV61 ) )
| ( SV70
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(555,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i,SV71: $i] :
( ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( ( SV71
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
| ( SV71
= ( ordered_pair @ SV54 @ SV61 ) ) )
= $true )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(556,plain,
! [SV72: $i,SV65: $i,SV35: $i] :
( ( ( ( sK7_C @ SV35 )
= ( ordered_pair @ SV65 @ SV72 ) )
= $false )
| ( ( ~ ( ilf_type @ SV72 @ set_type ) )
= $true )
| ( ( ~ ( ilf_type @ SV65 @ set_type ) )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(557,plain,
! [SV36: $i,SV56: $i] :
( ( ( SV56
!= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
= $false )
| ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(558,plain,
! [SV36: $i,SV56: $i] :
( ( ( ~ ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type ) )
= $false )
| ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(559,plain,
! [SV45: $i,SV16: $i,SV64: $i,SV29: $i] :
( ( ( member @ SV29 @ SV64 )
= $false )
| ( ( member @ SV16 @ SV45 )
= $false )
| ( ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV64 ) )
= $true )
| ( ( ilf_type @ SV64 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(560,plain,
! [SV68: $i,SV45: $i,SV29: $i,SV16: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV68 ) ) )
= $true )
| ( ( member @ SV16 @ SV45 )
= $true )
| ( ( ilf_type @ SV68 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(561,plain,
! [SV69: $i,SV45: $i,SV29: $i,SV16: $i] :
( ( ( ~ ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV69 ) ) )
= $true )
| ( ( member @ SV29 @ SV69 )
= $true )
| ( ( ilf_type @ SV69 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(562,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
| ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
= $true )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(563,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
| ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
= $true )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(564,plain,
! [SV21: $i,SV58: $i,SV30: $i,SV73: $i] :
( ( ( ~ ( ilf_type @ SV73 @ set_type ) )
= $true )
| ( ( ( SV73 != SV30 )
| ( member @ SV73 @ SV58 ) )
= $true )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(565,plain,
! [SV21: $i,SV30: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( ilf_type @ SV74 @ set_type ) )
= $true )
| ( ( ~ ( member @ SV74 @ SV58 )
| ( SV74 = SV30 ) )
= $true )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(566,plain,
! [SV19: $i,SV50: $i] :
( ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV50 )
= $false )
| ( ( member @ ( sK12_D @ SV50 @ SV19 ) @ SV19 )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ilf_type @ SV50 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(567,plain,
! [SV51: $i,SV19: $i,SV66: $i] :
( ( ( member @ SV66 @ SV19 )
= $false )
| ( ( member @ SV66 @ SV51 )
= $true )
| ( ( ilf_type @ SV66 @ set_type )
= $false )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(568,plain,
! [SV19: $i,SV51: $i,SV67: $i] :
( ( ( member @ SV67 @ SV51 )
= $false )
| ( ( member @ SV67 @ SV19 )
= $true )
| ( ( ilf_type @ SV67 @ set_type )
= $false )
| ( ( SV19 = SV51 )
= $false )
| ( ( ilf_type @ SV51 @ set_type )
= $false )
| ( ( ilf_type @ SV19 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(569,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i,SV70: $i] :
( ( ( SV70
!= ( ordered_pair @ SV54 @ SV61 ) )
= $true )
| ( ( SV70
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
= $true )
| ( ( ilf_type @ SV70 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(570,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i,SV71: $i] :
( ( ( SV71
!= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
= $true )
| ( ( SV71
= ( ordered_pair @ SV54 @ SV61 ) )
= $true )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(571,plain,
! [SV65: $i,SV35: $i,SV72: $i] :
( ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( ( sK7_C @ SV35 )
= ( ordered_pair @ SV65 @ SV72 ) )
= $false )
| ( ( ~ ( ilf_type @ SV65 @ set_type ) )
= $true )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(572,plain,
! [SV36: $i,SV56: $i] :
( ( ( SV56
= ( ordered_pair @ ( sK5_D @ SV56 @ SV36 ) @ ( sK6_SY71 @ SV56 @ SV36 ) ) )
= $true )
| ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(573,plain,
! [SV36: $i,SV56: $i] :
( ( ( ilf_type @ ( sK6_SY71 @ SV56 @ SV36 ) @ set_type )
= $true )
| ( ( member @ SV56 @ SV36 )
= $false )
| ( ( ilf_type @ SV56 @ set_type )
= $false )
| ( ( relation_like @ SV36 )
= $false )
| ( ( ilf_type @ SV36 @ set_type )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(574,plain,
! [SV68: $i,SV45: $i,SV29: $i,SV16: $i] :
( ( ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV68 ) )
= $false )
| ( ( member @ SV16 @ SV45 )
= $true )
| ( ( ilf_type @ SV68 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(575,plain,
! [SV69: $i,SV45: $i,SV29: $i,SV16: $i] :
( ( ( member @ ( ordered_pair @ SV16 @ SV29 ) @ ( cross_product @ SV45 @ SV69 ) )
= $false )
| ( ( member @ SV29 @ SV69 )
= $true )
| ( ( ilf_type @ SV69 @ set_type )
= $false )
| ( ( ilf_type @ SV45 @ set_type )
= $false )
| ( ( ilf_type @ SV29 @ set_type )
= $false )
| ( ( ilf_type @ SV16 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(576,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ( sK14_E @ SV57 @ SV30 )
!= SV30 )
= $true )
| ( ( ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
= $true )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(577,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
= $true )
| ( ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 )
= $true )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(578,plain,
! [SV21: $i,SV58: $i,SV30: $i,SV73: $i] :
( ( ( ilf_type @ SV73 @ set_type )
= $false )
| ( ( ( SV73 != SV30 )
| ( member @ SV73 @ SV58 ) )
= $true )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(579,plain,
! [SV21: $i,SV30: $i,SV58: $i,SV74: $i] :
( ( ( ilf_type @ SV74 @ set_type )
= $false )
| ( ( ~ ( member @ SV74 @ SV58 )
| ( SV74 = SV30 ) )
= $true )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(580,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i,SV70: $i] :
( ( ( SV70
= ( ordered_pair @ SV54 @ SV61 ) )
= $false )
| ( ( SV70
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
= $true )
| ( ( ilf_type @ SV70 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(581,plain,
! [SV22: $i,SV37: $i,SV61: $i,SV54: $i,SV71: $i] :
( ( ( SV71
= ( unordered_pair @ ( unordered_pair @ SV54 @ SV61 ) @ ( singleton @ SV54 ) ) )
= $false )
| ( ( SV71
= ( ordered_pair @ SV54 @ SV61 ) )
= $true )
| ( ( ilf_type @ SV71 @ set_type )
= $false )
| ( ( ilf_type @ SV61 @ set_type )
= $false )
| ( ( ilf_type @ SV54 @ set_type )
= $false )
| ( ( ilf_type @ SV37 @ set_type )
= $false )
| ( ( ilf_type @ SV22 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(582,plain,
! [SV72: $i,SV35: $i,SV65: $i] :
( ( ( ilf_type @ SV65 @ set_type )
= $false )
| ( ( ( sK7_C @ SV35 )
= ( ordered_pair @ SV65 @ SV72 ) )
= $false )
| ( ( ilf_type @ SV72 @ set_type )
= $false )
| ( ( relation_like @ SV35 )
= $true )
| ( ( ilf_type @ SV35 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(583,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
= $false )
| ( ( ~ ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 ) )
= $true )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(584,plain,
! [SV21: $i,SV58: $i,SV30: $i,SV73: $i] :
( ( ( SV73 != SV30 )
= $true )
| ( ( member @ SV73 @ SV58 )
= $true )
| ( ( ilf_type @ SV73 @ set_type )
= $false )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(585,plain,
! [SV21: $i,SV30: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( member @ SV74 @ SV58 ) )
= $true )
| ( ( SV74 = SV30 )
= $true )
| ( ( ilf_type @ SV74 @ set_type )
= $false )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(586,plain,
! [SV21: $i,SV30: $i,SV57: $i] :
( ( ( member @ ( sK14_E @ SV57 @ SV30 ) @ SV57 )
= $false )
| ( ( ( sK14_E @ SV57 @ SV30 )
= SV30 )
= $false )
| ( ( SV57
= ( singleton @ SV30 ) )
= $true )
| ( ( ilf_type @ SV57 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(587,plain,
! [SV21: $i,SV58: $i,SV30: $i,SV73: $i] :
( ( ( SV73 = SV30 )
= $false )
| ( ( member @ SV73 @ SV58 )
= $true )
| ( ( ilf_type @ SV73 @ set_type )
= $false )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(588,plain,
! [SV21: $i,SV30: $i,SV58: $i,SV74: $i] :
( ( ( member @ SV74 @ SV58 )
= $false )
| ( ( SV74 = SV30 )
= $true )
| ( ( ilf_type @ SV74 @ set_type )
= $false )
| ( ( SV58
= ( singleton @ SV30 ) )
= $false )
| ( ( ilf_type @ SV58 @ set_type )
= $false )
| ( ( ilf_type @ SV30 @ set_type )
= $false )
| ( ( ilf_type @ SV21 @ set_type )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(589,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[108,588,587,586,582,581,580,577,575,574,573,572,568,567,566,559,537,529,528,527,515,511,509,508,506,496,495,462,457,456,448,445,441,439,438,432,431,410,409,398,397,394,392,391,359,345,305,285,280,269,268,267,266,265,238,213,199,186,185,180,135]) ).
thf(590,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET646+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
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 14:47:44 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.66/6.75
% 38.66/6.75 No.of.Axioms: 25
% 38.66/6.75
% 38.66/6.75 Length.of.Defs: 0
% 38.66/6.75
% 38.66/6.75 Contains.Choice.Funs: false
% 38.66/6.75 ........................
% 38.66/6.75
% 38.66/6.75 ********************************
% 38.66/6.75 * All subproblems solved! *
% 38.66/6.75 ********************************
% 38.66/6.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:26,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:589,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 38.66/6.75
% 38.66/6.75 %**** Beginning of derivation protocol ****
% 38.66/6.75 % SZS output start CNFRefutation
% See solution above
% 38.66/6.76
% 38.66/6.76 %**** End of derivation protocol ****
% 38.66/6.76 %**** no. of clauses in derivation: 590 ****
% 38.66/6.76 %**** clause counter: 589 ****
% 38.66/6.76
% 38.66/6.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:26,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:589,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------